,,einstein                        ,,the 
,,searcher                   ,,his      
,,work ,,explained ,,from               
,,dialogues ,,with ,,einstein           
,,by                      ,,alexander   
,,moszkowski                            
,,translated ,,by                       
,,henry ,l4 ,,brose                     
,,methuen  ,,co4 ,,ltd4                 
#cf ,,essex ,,street ,w4,c4             
,,london          ,,extract ,,from ,,the
 ,,author',s  ,,preface      ,,the book 
which is herewith presented to the      
public has few  contemporaries of a like
 nature2 it deserves special attention  
inasmuch  as it is illuminated by the   
name ,albert ,einstein1 and deals with a
  personality whose achievements mark a 
turning-point in the development  of    
science4    ,every investigator1 who    
enlarges our vision by some permanent   
discovery1  becomes a milestone on the  
road to knowledge1 and great would be   
the  array of those who have defined the
 stages of the long avenue of  research4

 ,one might endeavour1 then1 to decide  
to whom mankind owes the  greater debt1 
to ,euclid or to ,archimedes1 to ,plato 
or to ,aristotle1 to  ,descartes or to  
,pascal1 to ,lagrange or to ,gauss1 to  
,kepler or to  ,copernicus4 ,one would  
have to investigate--as far as this is  
possible--in how far each outstanding   
personality was in advance of his  time1
 whether some contemporary might not    
have had the equal good  fortune to     
stumble on the same discovery1 and      
whether1 indeed1 the time  had not come 
when it must inevitably have been       
revealed4 ,if we then  further selected 
only those who saw far beyond their own 
age into the  inimitable future of      
knowledge1 this great number of         
celebrities would  be considerably      
diminished4 ,we should glance away from 
the milestones1  and fix our gaze on the
 larger signs that denote the lines of  
demarcation of the sciences1 and among  
them we should find the name of  ,albert
 ,einstein4 ,we may find it necessary to

 proceed to a still more  rigorous      
classification2 ,science1 herself1 may  
rearrange her  chronological table      
later1 and reckon the time at which     
,einstein's  doctrine first appeared as 
the beginning of an important era4      
,this would in itself justify--nay1     
render imperative--the writing of  a    
book about ,einstein4 ,but this need has
 already been satisfied on  several     
occasions1 and there is even now a      
considerable amount of  literature about
 him4 ,at the end of this generation we 
shall possess a  voluminous library     
composed entirely of books about        
,einstein4 ,the  present book will      
differ from most of these1 in that      
,einstein here  occurs not only         
objectively but also subjectively4 ,we  
shall1 of course1  speak of him here    
too1 but we shall also hear him speak   
himself1 and  there can be no doubt that
 all who are devoted to the world       
thought can  but gain by listening to   
him4    ,the title agrees with the      

circumstance to which this book owes its
  birth4 ,and in undertaking to address 
itself to the circle of readers as  to  
an audience1 it promises much eloquence 
that came from ,einstein's own  lips1   
during hours of social intercourse1 far 
removed from academic  purposes and not 
based on any definite scheme intended   
for instruction4  ,it will1 therefore1  
be neither a course of lectures nor     
anything similar  aiming at a systematic
 order and development4 ,nor is it a    
mere  phonographic record1 for this is  
made impossible if for no other reason  
than that whoever has the good fortune  
to converse with this man1 finds  every 
minute far too precious to waste it in  
snatching moments to take  shorthand    
notes4 ,what he has heard and discussed 
crystallizes itself in  subsequent      
notes1 and to some extent he relies on  
his memory1 which  would have to be     
extraordinarily lax if it managed to    
forget the  essentials of such          
conversations4    ,but these essentials 

could not be attained by clinging       
closely to the  exact terms of          
utterance4 ,this would be a gain neither
 for the scheme of  the book nor for the
 reader who wishes to follow a great    
thinker in all  the ramifications of his
 ideas4 ,it must be reiterated that this
 book is  intended neither as a textbook
 nor as a guide leading to a complete   
system of thought2 nor1 above all1 is it
 in any way due to ,einstein1 nor       
desired by him4 ,any value and          
attraction of the book is rather to be  
sought in its kaleidoscopic nature1 its 
loose connexion1 which expresses  a     
general meaning without being narrowed  
to pedantic limits by a  restriction to 
literal repetition4 ,it is just this    
absence of the method  that is rightly  
demanded of a textbook1 which may enable
 these  conversations to pass on to the 
world a little of the pleasure which    
they originally gave me4 ,perhaps they  
will even be sufficient to furnish  the 
reader with a picture of the eminent    

scientist1 sufficient to give  him a    
glimpse of his personality1 without     
demanding a detailed study to  secure   
this end4 ,even here ,i should like to  
state that the range of  ,einstein's    
genius extends much further than is     
generally surmised by  those who have   
busied themselves only with the actual  
physical theory4  ,it sends out rays in 
all directions1 and brings into view    
wonderful  cosmic features under his    
stimulus--features which are1 of course1
  embedded in the very refractory       
mathematical shell of his physics which 
embraces the whole world4 ,but only     
minds of the distant future1 perhaps1   
will be in a position to realize that   
all our mental knowledge is  illuminated
 by the light of his doctrine4          
,einstein's mission is that of a king   
who is pursuing building operations  on 
a large scale2 carters and workmen1 each
 in their own line1 receive  employment 
for decades ahead4 ,but apart from the  
technical work1 there  may still be room

 for non-technical account1 which1      
without following a  definite programme1
 yet pursues a definite object1 to offer
 ,einsteiniana  in an easily            
intelligible and ever-changing form1 to 
represent him1 as  it were1 wandering   
over fields and meadows1 and every now  
and then  stooping to pluck some problem
 in the guise of a flower4 ,seeing that 
he  granted me the pleasure of          
accompanying him on these excursions1 it
 was  not within my sphere to expect in 
addition that he would direct his  steps
 according to a preconceived plan4      
,often enough the goal vanished1  and   
there remained nothing but the pleasure 
of the rambles themselves  with the     
consciousness of their purpose4 ,as     
,schopenhauer remarks1 one  who walks   
for leisure can never be said to be     
making detours2 and this  holds true    
independently of the nature of the      
country that happens to be  traversed at
 the moment4 ,if ,i just now mentioned  
walks on meadowy  slopes1 this is not to

 be understood literally4 ,in           
,einstein's company  one encounters from
 moment to moment quite suddenly some   
adventure which  destroys our comparison
 with idyllic rambles4 ,abysmal depths  
appear1 and  one has to pass along      
dangerous pathways4 ,it is at these     
moments that  unexpected views present  
themselves1 and many strips of landscape
 that1  according to our previous       
estimate1 appeared to be situated on    
higher  slopes1 are now discovered      
reposing far below4 ,we are familiar    
with the  ,wanderer ,fantasie of        
,schubert2 its tonal disposition is     
realistic1  conforming to ,nature1 yet  
its general expression is               
transcendental3 so  is a ramble with    
,einstein2 he remains firmly implanted  
in reality1 but  the distant views that 
he points out stretch into              
transcendental  regions4 ,he seems to me
 to be essentially as much an artist as 
a  discoverer1 and if some sense of this
 heaven-sent combination of gifts       

should be inspired by this book1 it     
alone would justify the publication  of 
these talks4          ,,translator',s   
,,note      ,,it is scarcely necessary  
to enlarge on the scope and design of   
the  present book1 which manifest       
themselves at a glance4    ,the author  
merits our thanks for making accessible 
to us material about  ,einstein which1  
in the ordinary course of events1 would 
ever remain  unknown4 ,an account of    
,einstein's work would be incomplete    
without a  sketch of his personality4   
,mr4 ,moszkowski invites us to ramble   
with  ,einstein into realms not confined
 to pure physics4 ,many subjects that   
have a peculiar interest at the present 
critical stage of the world's  history  
receive illuminating attention4 ,it is  
hoped that the appearance  of the book  
in ,english will stimulate further      
interest in the  thought-world of a     
great scientist4    ,warm thanks are due
 to ,mr4 ,raymond ,kershaw1 ,b4,a41 and 
to my sister1 ,miss  ,hilda ,brose1 for 

help in reading the manuscript and the  
proofs4                                 
,,henry ,l4 ,,brose    ,,oxford1 #aiba  
,,contents    ,,chapter    ,i4          
,phenomena in the ,heavens    ,,ii4     
,beyond our ,power    ,,iii4 ,valhalla  
,,iv4 ,education    ,v4 ,the ,discoverer
    ,,vi4 ,of ,different ,worlds        
,,vii4 ,problems    ,,viii4 ,highways   
and ,by-ways    ,,ix4 ,an ,experimental 
,analogy    ,x4 ,disconnected           
,suggestions    ,,xi4 ,einstein's ,life 
and ,personality    ,,index             
,,einstein ,,the ,,searcher             
,,chapter ,i    ,,phenomena ,,in ,,the  
,,heavens      ,proclamation of the ,new
 ,mechanics4--,verification of          
,theoretical  ,results4--,parallels with
 ,leverrier4--,neptune and              
,mercury4--,testing the  ,theory of     
,relativity4--,the ,solar ,eclipse of   
#aiai4--,the ,programme of an           
,expedition4--,the ,curved ,ray of      
,light4--,refinement of ,calculation and
  ,measurement4--,stellar               

,photography4--,the ,principle of       
,equivalence4--,the  ,sun ,myth4        
,,on the #acth ,october #aiaj a         
memorable event took place in the       
,berlin  ,scientific ,association3      
,henri ,poincar1 the eminent physicist  
and  mathematician1 had been announced  
to give a lecture in the rooms of the   
institute ,urania2 an audience of rather
 meagre dimensions assembled4 ,i  still 
see him before me in my mind's eye1 a   
scholar who was snatched  away in the   
prime of his creative period1 a man     
whose external  appearance did not      
suggest the light of genius1 and whose  
carefully  trimmed beard reminded one   
rather of the type of a practising      
barrister4  ,he walked up and down the  
platform1 accompanying his speech with  
gestures marked by an easy elegance4    
,there was no sign of an attempt to     
force a doctrine4 ,he developed his     
thesis1 in spite of the foreign         
language1 in fluent and readily         
intelligible terms4    ,it was at this  

lecture that we heard the name ,albert  
,einstein pronounced  for the first     
time4    ,poincar's address was on the  
,new ,mechanics1 and was intended to    
make  us acquainted with the beginning  
of a tendency which1 he himself         
confessed1 had violently disturbed the  
equilibrium of his former  fundamental  
views4 ,he repeatedly broke the usually 
even flow of his  voice to indicate1    
with an emphatic gesture1 that we had   
perhaps arrived  at a critical1 nay     
epochal1 point marking the commencement 
of a new era  of thought4    ,perhaps   
was a word he never failed to emphasize4
 ,he persistently laid  stress on his   
doubts1 differentiated between hardened 
facts and  hypotheses1 still clinging to
 the hope that the new doctrine he was  
expounding would yet admit of an avenue 
leading back to the older views4  ,this 
revolution1 so he said1 seemed to       
threaten things in science which  a     
short while ago were looked upon as     
absolutely certain1 namely1  fundamental

 theorems of classical mechanics1 for   
which we are indebted  to the genius of 
,newton4 ,for the present this          
revolution is of course  only a         
threatening spectre1 for it is quite    
possible that1 sooner or  later1 the old
 established dynamical principles of    
,newton will emerge  victoriously4      
,later in the course of his lecture he  
declared repeatedly  that he felt a     
diffidence akin to fear at the sight of 
the accumulating  number of hypotheses1 
and that it seemed to border on the     
impossible to  attempt to arrange them  
into a system4    ,it is a matter of    
complete indifference how the           
revelations of ,poincar  affected us    
individually2 if ,i may infer from my   
own case1 there is only  one word to    
express it--staggering6 ,oblivious of   
the doubts of the  lecturer1 ,i was     
swept along under the impetus of this   
new and mighty  current of thought4     
,this awakened two wishes in me3 to     
become acquainted  with ,einstein's     

researches as far as lay within my      
power1 and1 if  possible1 to see him    
once in person4 ,in me the abstract had 
become  inseparable from the concrete   
personal element4 ,the presentiment of  
the  happy moment in the future hovered 
before my vision1 whispering that ,i    
should hear his doctrine from his own   
lips4    ,several years later ,einstein 
was appointed professor of the ,academy 
of  ,sciences with the right of         
lecturing at the ,university of ,berlin4
 ,this  brought my personal wish within 
reach4 ,trusting to good fortune1 ,i set
  about materializing it4 ,in           
conjunction with a colleague ,i wrote   
him a  letter asking him to honour with 
his presence one of the informal        
evenings instituted by our ,literary    
,society at the ,htel ,bristol4 ,here   
he was my neighbour at table1 and       
chatted with me for some hours4         
,nowadays his appearance is known to    
every one through the innumerable       
photos which have appeared in the       

papers4 ,at that time ,i had never seen 
his countenance before1 and ,i became   
absorbed in studying his features1      
which struck me as being those of a     
kindly1 artistically inclined1  being1  
in nowise suggesting a professor4 ,he   
seemed vivacious and  unrestrained in   
conversation1 and1 in response to our   
request1 willingly  touched upon his own
 subject as far as the place and        
occasion allowed1  exemplifying         
,horace's saying1 ,omne tulit punctum1  
qui miscuit utile  dulci1 tironem       
delectando pariterque monendo4 ,it was  
certainly most  delightful4 ,yet at     
moments ,i was reminded of a male       
sphinx1 suggested by  his highly        
expressive enigmatic forehead4 ,even    
now1 after a warm  acquaintanceship     
stretching over years1 ,i cannot shake  
off this  impression4 ,it often         
overcomes me in the midst of a pleasant 
conversation interspersed with jests    
whilst enjoying a cigar after tea2  ,i  
suddenly feel the mysterious sway of a  

subtle intellect which  captivates and  
yet baffles the mind4    ,at that time1 
early in #aiaf1 only a few members of   
the ,literary ,society  divined who it  
was that was enjoying their hospitality4
 ,in the eyes of  ,berlin1 ,einstein's  
star was beginning its upward course1   
but was still  too near the horizon to  
be visible generally4 ,my own vision1   
sharpened  by the ,french lecture and by
 a friend who was a physicist1          
anticipated  events1 and already saw    
,einstein's star at its zenith1 although
 ,i was  not even aware at that time    
that ,poincar had in the meantime       
overcome  his doubts and had fully      
recognized the lasting importance of    
,einstein's  researches4 ,i had the     
instinctive feeling that ,i was sitting 
next to a  ,galilei4 ,the fanfares      
sounded in the following years as a sign
 of  appreciation by his contemporaries 
were only a fuller instrumentation of   
the music of destiny which had vibrated 
in my ears ever since that time4    ,i  

recollect one little incident3 one of   
these lovers of literature1 who  was1   
however1 totally ignorant of natural    
science1 had accidentally seen  several 
learned articles dealing with           
,einstein's ,reports for the  ,academy1 
and had preserved the cuttings in his   
pocket-book4 ,he  considered this a     
fitting opportunity for enlightenment4  
,surely a brief  question would suffice 
to guide one through these intricate    
channels4  ,professor1 will you kindly  
tell me the meaning of potential1       
invariant1  contravariant1              
energy-tensor1 scalar1                  
relativity-postulate1  hyper-,euclidean1
 and inertial system8 ,can you explain  
them to me in a  few words8--,certainly1
 said ,einstein1 those are merely       
technical  expressions6 ,that was the   
end of the little lesson4    ,far into  
the night three of us sat in a caf while
 ,einstein gently  lifted the veil from 
his newest discovery for the benefit of 
my  journalist friend and myself4 ,we   

gathered from his remarks that a        
,special ,theory of ,relativity formed a
 prelude to a general theory which      
embraced the problem of gravitation in  
its widest sense1 and hence also  the   
physical constitution of the world4     
,what interested me apart from  this    
theme1 which was1 of course1 only       
touched upon lightly1 was the  personal 
question in its psychological aspect4   
,professor1 said ,i1 such investigations
 must involve enormous mental           
excitement4 ,i imagine that there lurks 
behind every solved problem ever  and   
again some new problem with a           
threatening or a fascinating aspect1  as
 the case may be1 each one calling up a 
tumult of emotion in its  author4 ,how  
do you succeed in mastering this        
difficulty8 ,are you not  continually   
tormented by restless thoughts that     
noisily invade your  dreams8 ,do you    
ever succeed at all in enjoying         
undisturbed slumber8    ,the very tone  
in which the answer was given showed    

clearly how free he  felt himself of    
such nervous troubles which usually     
oppress even the  mediocre thinker4 ,it 
is fortunate that such affections do not
 penetrate  to his high level4 ,i break 
off whenever ,i wish1 he said1 and      
banish  all difficulties when the hour  
for sleep arrives4 ,thinking during     
dreams1 as in the case of artists1 such 
as poets and composers1 by which  they  
weave the thread of day on into the     
night1 is quite foreign to me4          
,nevertheless1 ,i must confess that at  
the very beginning1 when the  special   
theory of relativity began to germinate 
in me1 ,i was visited by  all sorts of  
nervous conflicts4 ,when young ,i used  
to go away for weeks  in a state of     
confusion1 as one who at that time had  
yet to overcome the  stage of           
stupefaction in his first encounter with
 such questions4 ,things  have changed  
since then1 and ,i can assure you that  
there is no need to  worry about my     
rest4    ,notwithstanding1 ,i answered1 

cases may arise in which a certain      
result is to be verified by observation 
and experiment4 ,this might  easily give
 rise to nerve-racking experiences4 ,if1
 for instance1 a  theory leads to a     
calculation which does not agree with   
reality1 the  propounder must surely    
feel considerably oppressed by this mere
  possibility4 ,let us take a particular
 event4 ,i have heard that you have     
made a new calculation of the path of   
the planet ,mercury on the basis of     
your doctrine4 ,this must certainly have
 been a laborious and involved  piece of
 work4 ,you were firmly convinced of the
 theory1 perhaps you  alone4 ,it had not
 yet been verified by an actual fact4   
,in such cases  conditions of great     
psychological tension must surely assert
 themselves4  ,what in ,heaven's name   
will happen if the expected result does 
not  appear8 ,what if it contradicts the
 theory8 ,the effect on the founder of  
the theory cannot even be imagined6     
,such questions1 said ,einstein1 did not

 lie in my path4 ,that result  could not
 be otherwise than right4 ,i was only   
concerned in putting the  result into a 
lucid form4 ,i did not for one second   
doubt that it would  agree with         
observation4 ,there was no sense in     
getting excited about what  was         
self-evident4    ,let us now consider   
several facts of natural science1 apart 
from this  chat1 but suggested by it1   
which caused ,einstein little           
excitement1 but  the whole world        
generally1 so much the more4 ,by way of 
illustration we  shall link them up with
 the result of a forerunner who1 like   
,einstein1  fixed on paper what should  
happen in the heavens4    ,formerly1    
whenever one wished to play a           
particularly effective trump  card in   
favour of research work it was customary
 to quote the  achievement of the       
,french astronomer ,leverrier who1 pen  
in hand1  established the material      
existence of a planet at that time quite
  unknown and unnoticed4 ,certain       

disturbances in the orbit of the planet 
,uranus1 which was regarded as being the
 most distant of the wandering  stars1  
at that time had caused him to believe  
in the certainty of the  existence of a 
still more distant planet1 and by using 
merely the  theoretical methods of      
celestial mechanics in connexion with   
the problem  of three bodies he         
succeeded in revealing what was hidden  
behind the  visible constellations4 ,he 
reported the result of his calculations 
to  the ,berlin ,observatory about      
seventy-five years ago1 as it was at    
that  time in possession of the best    
instruments4 ,it was then that the      
amazing  event happened3 on the very    
same evening an observer in ,berlin1    
,gottfried ,galle1 discovered the       
predicted new star almost exactly at the
  point of the heavens for which it was 
prophesied1 only half the moon's        
diameter from it4 ,the new planet       
,neptune1 the farthest outpost of our   
solar system1 reposed as a prisoner in  

his telescope2 the seemingly            
undiscoverable star had capitulated in  
the face of mental efforts of a         
mathematical scholar1 who1 in reasoning 
meditation1 had sketched his  curves in 
the quiet atmosphere of his study4      
,this was certainly bewildering enough1 
but nevertheless this incredible  result
 which stirred the imagination so       
strongly was directly rooted in         
reality1 lay on the path of research1   
followed of necessity from the  laws of 
motion known at that time1 and disclosed
 itself as a new proof  of the doctrines
 of astronomy which had long been       
recognized as supreme  and              
incontestable4 ,leverrier had not       
created these1 but had found them       
ready2 he applied them with the mind of 
genius4 ,anyone who nowadays is         
sufficiently trained to work through the
 highly complicated calculation  of     
,leverrier has every reason to marvel at
 a work which is entirely  mathematical 
throughout4    ,our own times have been 

marked by an event of still greater     
significance4    ,irregularities had    
shown themselves in observation of the  
heavens that  could not be explained or 
grasped by the accepted methods of      
classical  mechanics4 ,to interpret     
them1 ideas of a revolutionary nature   
were  necessary4 ,man's view of the plan
 according to which the universe is     
mapped out had to be radically reformed 
to bring within comprehension  the      
problems that presented themselves in   
macroscopic as well as in  microscopic  
regions1 in the courses of the stars as 
well as in the  motions of the ultimate 
constituents of the atom of material    
bodies1  incapable of being directly    
observed4 ,the goal consisted in        
bringing  those doctrines in which truth
 had been proclaimed in its essential   
features1 but not exhaustively1 by the  
genius of ,copernicus1 ,galilei1        
,kepler1 and ,newton1 to their          
conclusion by penetrating as far as     
possible into the mysteries of the      

structure of the universe4 ,this is     
where ,einstein comes forward4          
,whereas the outermost planet ,neptune  
had bowed to the accepted laws1 by      
merely disclosing his presence1         
,mercury1 the innermost planet1         
preserved  an obstinate attitude even in
 the face of the most refined           
calculations4  ,these always led to an  
unaccountable remainder1 a disagreement1
 which  seemed very small when expressed
 in numbers and words1 and yet enclosed 
a deep secret4 ,wherein did this        
disagreement consist8 ,in a difference  
of  arc which had likewise been         
discovered by ,leverrier and which      
defied  explanation4 ,it was only a     
matter of about forty-five insignificant
  quantities1 seconds of arc1 which     
seemed vanishingly small since this     
deviation did not occur within a month  
or a year1 but was spread over a  whole 
century4 ,by just so much1 or rather so 
little1 the rotation of  ,mercury's     
orbit differed from what might be termed

 the allowable  astronomical value4     
,observation was exact1 calculation was 
exact2 why1  then1 the discrepancy8     
,it was thus inferred that there was    
still some hidden unexplored factor     
which had to be taken into account in   
the fundamental principles of  celestial
 mechanics4 ,the formerly invisible     
,neptune confirmed the old  rule by     
appearing4 ,mercury1 which was visible1 
opposed the rule4    ,in #aiaj ,poincar 
had touched upon this embarrassing      
question1  mentioning that here was a   
possibility of testing the new          
mechanics4    ,he declined the          
suggestion of some astronomers that this
 was again a  ,leverrier problem and    
that there must exist another           
undiscovered planet  still nearer the   
sun and disturbing ,mercury's orbit4 ,he
 also refused to  accept the assumption 
that the disturbance might be caused by 
a ring of  cosmic matter distributed    
round the sun4 ,poincar divined that the
 new  mechanics could supply the key to 

the enigma1 but1 obviously to be quite  
conscientious1 he expressed his         
presentiment in very cautious terms4 ,on
  that occasion he said that some       
special cause had yet to be found to    
explain the anomaly of ,mercury's       
behaviour2 till that was discovered one 
could only say that the new doctrine    
could not be regarded as in             
contradiction to astronomical facts4    
,but the true explanation was  gradually
 drawing near4 ,five years later1 on    
#ahth ,november #aiae1 ,albert          
,einstein presented to the ,prussian    
,academy of ,sciences a paper which     
solved this riddle which1 expressed in  
seconds1 seemed so insignificant  and   
yet was of such enormous importance in  
its bearing on fundamental  questions4  
,he proved the problem was solved quite 
accurately if the  general ,theory of   
,relativity he had founded was accepted 
as the only  valid basis for the        
phenomena of cosmic motions4    ,many   
would at this point express a wish to   

have the essence of the  doctrine of    
relativity explained in an easily       
intelligible manner4  ,indeed1 some     
would go even further in their desire1  
and would ask for a  simple description 
in a few succinct sentences4 ,this1     
measured in terms  of difficulty and    
possibility1 would be about equivalent  
to wishing to  learn the history of the 
world by reading several quarto pages of
  manuscript or a novelette4 ,but even  
if we start at long range and use       
elaborate materials for our description1
 we should have to give up the  idea    
that this knowledge may be gained with  
playful ease4 ,for this  doctrine1      
inasmuch as it discloses the            
relationship between mathematical  and  
physical events1 emerges out of         
mathematics1 which thus limits the  mode
 of its representation4 ,whoever        
undertakes to present it in a form  in  
which it is easily intelligible1 that is
 quite unmathematical and yet  complete1
 is engaged in an impossible venture2 he

 is like one who would  whistle         
,kepler's ,laws on the flute or would   
elucidate ,kant's ,critique of  ,pure   
,reason by means of coloured            
illustrations4 ,in all frankness we must
  confess once and for all that whenever
 popular accounts are attempted  they   
can be only in the nature of vague      
suggestions removed from the  domain of 
mathematics4 ,but even such indications 
have a fruitful result  if they succeed 
in focusing the attention of the reader 
or the hearer so  that the connexions1  
the ,leitmotivs1 so to speak1 of the    
doctrine1 are  at least suggested4      
,it must therefore suffice if we place  
the conception of approximation in  the 
foreground here as in other parts of    
this book4 ,till quite recently         
,newton's ,equations of ,motion were    
used as a foundation for verifying      
astronomical occurrences4 ,these are    
symbolical representations expressed  as
 formul that contain in an exceedingly  
simple form the law of mass  attraction4

 ,they express the comprehensive        
principle that the attraction  is       
directly proportional to the mass and   
inversely proportional to the  square of
 the distance2 so that the moving force 
is doubled when the  mass is doubled1   
whereas if the distance is double1 the  
force is only a  quarter as great1 if   
the distance is trebled1 the force      
becomes  one-ninth as great4            
,according to the ,theory of ,relativity
 this fundamental law is not wrong  or  
invalid1 but no longer holds fully if   
pursued to its last inferences4  ,in    
applying corrections to it1 new factors 
occur1 such as the ratio of  given      
velocities to the velocity of light1 and
 the new geometry which  operates with  
world-lines in space which1 amalgamated 
with the  dimension of time1 is regarded
 as a quadruply extended continuum4     
,einstein has actually supplemented     
these fundamental equations for the     
motion of masses so that the original   
form states the true condition of       

affairs only approximately1 whereas     
,einstein's equations give the motion   
with very great accuracy4    ,the       
above-mentioned essay of ,einstein is   
carried out as if the structure         
bequeathed to us by ,newton required the
 addition of a final1 very  delicate    
pinnacle4 ,for the mathematician this   
pinnacle is given as a  combination of  
signs1 representing a so-called         
,elliptic ,interval4 ,such  an interval 
is a very weird construction1 and the   
man who will make it  apprehended by the
 general reader is yet to be born4 ,when
 ,lord ,byron  said3         ,and       
,coleridge1 too1 has lately taken wing4 
,but like a hawk encumbered with his    
hood1--      ,explaining ,metaphysics to
 the nation--     ,i wish he would      
explain his ,explanation4               
7,dedication to ,don ,juan47      he had
 still a sure footing in                
intelligibility1 compared with the      
non-mathematician1 who demands an       
explanation for such a construction4    

,and what a complex of mathematical     
dangers must be overcome even before    
the question of the meaning of this     
integral is crystallized out6    ,but   
now the explanation had arrived and     
could be evaluated1 if only             
approximately4 ,before we give the      
result1 let us just describe at least   
one technical term1 namely1 ,perihelion4
 ,it is that point of a  planetary orbit
 which lies nearest the sun4 ,this orbit
 is an ellipse1  that is1 an elongated  
curved fine in the interior of which one
  distinguishes a major axis in the     
direction of elongation1 and a minor    
axis perpendicular to the former at its 
middle point4 ,the perihelion of  a     
planetary orbit is at one of the end    
points of the major axis4    ,in time   
the perihelion alters its position in   
space1 advancing in the  same sense as  
the orbit is traversed4 ,it would       
naturally be assumed that  the amount of
 this advance as measured astronomically
 would agree with  the calculation      

resulting from ,newton's theory4 ,but   
this was not the  case4 ,an             
unaccountable remainder was left over1  
which astronomers  ascertained to be #de
 seconds 7of arc7 per #ajj years1 with a
 possible  fluctuation of plus or minus 
#e seconds4 ,thus1 if the new result    
were  found to be between #dj and #ej   
seconds1 the new theory would henceforth
  have to be regarded as the only valid 
one4    ,it happened just as ,einstein  
predicted3 calculation according to his 
theory shows that for the planet        
,mercury the perihelion should advance  
#dc seconds per #ajj years4 ,this       
signifies full agreement with           
observation  and fully removes the      
former apparent difficulty4 ,whereas    
,leverrier in  his time had pointed out 
a new planet1 ,einstein brought to view 
something far more important3 a new     
truth4    ,it was a test of accuracy so 
dazzling that it alone would have       
sufficed  to prove the correctness of   
,einstein's ,principles4 ,yet1 a second 

test1  fraught with graver and more     
far-reaching consequences1 presented    
itself--a test which could be applied   
only several years later1 and  which    
developed into a scientific event of the
 highest importance4    ,for at the same
 time that ,einstein solved the problem 
of ,mercury1 he had  investigated the   
path of light-rays according to his     
revolutionary  method1 and had arrived  
at the conclusion that every ray under  
the  influence of a gravitational field1
 as1 for example1 in the  neighbourhood 
of the sun1 must become curved4 ,this   
daring announcement  gave a new         
possibility of putting the theory to a  
practical test during  the total eclipse
 of the sun on #bith ,may #aiai4 ,for1  
when the disc of the  sun is obscured1  
the stars that are closest to it become 
visible 7even  to the naked eye74 ,they 
may be photographed1 and the distances  
of the  points of light on the negative 
allow us to detect whether the rays from
  the stars in passing the massive body 

of the sun have actually been  deflected
 by the amount prophesied by ,einstein4 
,once again current thought encountered 
a sharp corner1 and common  sense1 which
 furnishes its own certificate of merit1
 threatened to  become rebellious4 ,how 
now8 ,a ray from a star could be curved8
 ,does not  this contradict the         
elementary conception of the straight   
lines1 that  is1 the shortest lines1 for
 which we have no better picture than   
just  these rays8 ,did not ,leonardo da 
,vinci define the straight line by means
  of the term linea radiosa4    ,but    
such supposedly self-evident facts have 
no longer a place in the  space-time    
world4 ,the point was to test whether a 
physical anomaly which  had been        
predicted actually existed4 ,if the     
deflection of the rays  really happened1
 it should manifest itself in the       
distances between the  stars on the     
photographic plate being greater than   
one would expect from  their actual     
position4    ,for the curvature has its 

concave side towards the sun1 as is easy
 to  see1 once the phenomenon is        
regarded as possible4 ,it is as if the  
ray  were directly subject to           
gravitation4 ,let us take two stars1 one
 on each  side of the sun4 ,on account  
of the concavities the eye receives rays
  from them under a greater visual angle
 than if the rays were straight1  and   
interprets this angle as denoting a     
greater distance between the  sources of
 light1 that is1 it sees the two stars  
farther apart than in  the case of      
rectilinear propagation4    ,by how much
 farther apart8 ,the preceding          
calculation and the subsequent  direct  
observation demanded incredible delicacy
 of measurement4 ,if we  suppose the    
whole arc of the heavens divided into   
easily picturable  units such as        
degrees1 then the apparent width of the 
moon is about half  a degree4 ,we may   
still easily imagine the thirtieth part 
of this1  namely1 a minute of arc4 ,but 
the sixtieth part of the latter1 the    

second  of arc1 vanishes almost out of  
the range of sense-perception4 ,and it  
was  just this minute measure that came 
into question1 for the theory which  had
 been developed from pure thought       
predicted a deflection of seconds  of   
arc4 ,this corresponds to about a       
hairbreadth when seen at a distance  of 
#ag yards1 or to the thickness of a     
match at a distance of over half a      
mile4    ,one of the greatest problems  
of the most comprehensive science       
depended  on this unthinkably small     
measure4    ,in no sense did ,einstein  
himself entertain a possibility of      
doubt4    ,on repeated occasions before 
,may #aiai ,i had opportunities of      
questioning  him on this point4 ,there  
was no shadow of a scruple1 no ominous  
fears  clouded his anticipations4 ,yet  
great things were at stake4             
,observation was to show the correctness
 of ,einstein's world system by  a fact 
clearly intelligible to the whole world1
 one depending on a very  sensitive test

 of less than two seconds of arc4       
,but1 ,professor1 said ,i1 on various   
occasions1 what if it turns out to  be  
more or less8 ,these things are         
dependent on apparatus that may be      
faulty1 or on unforeseen imperfections  
of observation4 ,a smile was            
,einstein's only answer1 and this smile 
expressed his unshakeable faith  in the 
instruments and the observers to whom   
this duty was to be  entrusted4         
,moreover1 it is to be remarked that no 
great lengths of time were  available   
for comfortable experimentation in      
taking this photographic  record4 ,for  
the greatest possible duration of a     
total eclipse of the sun  viewed at a   
definite place amounts to less than     
eight minutes1 so that  there was no    
room for mishaps in this short space of 
time1 nor must any  intervening cloud   
appear4 ,the kindly co-operation of the 
heavens was  indispensable--and was not 
refused4 ,the sun1 in this case the     
darkened  sun1 brought this fact to     

light4    ,two ,english expeditions had 
been equipped for the special occasion  
of  the eclipse--one to proceed to      
,sobral and the other to the ,island of 
,principe1 off ,portuguese ,africa2 they
 were sent officially with  equipment   
provided in the main by the             
time-honoured ,royal ,society4          
,considering the times1 it was regarded 
as the first symptom of the  revival of 
international science1 a praiseworthy   
undertaking4 ,a huge  apparatus was set 
into motion for a purely scientific     
object with not  the slightest relation 
to any purpose useful in practical life4
 ,it was a  highly technical            
investigation whose real significance   
could be grasped  by only very few      
minds4 ,yet interest was excited in     
circles reaching far  beyond that of the
 professional scientist4 ,as the solar  
eclipse  approached1 the consciousness  
of amateurs became stirred with         
indefinite  ideas of cosmic phenomena4  
,and just as the navigator gazes at the 

,polar  ,star1 so men directed their    
attention to the constellation of       
,einstein1  which was not yet depicted  
in stellar maps1 but1 from which        
something  uncomprehended1 but          
undoubtedly very important1 was to blaze
 forth4    ,in ,june it was announced   
that the star photographs had been      
successful  in most cases1 yet for      
weeks1 nay for months1 we had to        
exercise  patience4 ,for the            
photographs1 although they required     
little time to be  taken1 took much     
longer to develop and1 above all1 to be 
measured2 in  view of the order of      
smallness of the distances to be        
compared1 this was  a difficult and     
troublesome task1 for the points of     
light on the plate  did not answer      
immediately with ,yes or ,no1 but only  
after mechanical  devices of extreme    
delicacy had been carefully applied4    
,at the end of ,september they          
proclaimed their message4 ,it was in the
  affirmative1 and this ,yes out of     

far-distant transcendental regions      
called forth a resounding echo in the   
world of everyday life4 ,genuinely  and 
truly the seconds of arc had come out1  
correct to the decimal point4  ,these   
points representing ciphers1 as it were1
 had chanted of the  harmony of the     
spheres in their ,pythagorean tongue4   
,the transmission of  this message      
seemed to be accompanied by the echoing 
words of ,goethe's  ,ariel3             
,with a crash the ,light draws near6    
,pealing rays and trumpet-blazes1--     
,eye is blinded1 ear amazes4      ,never
 before had anything like this happened4
 ,a wave of amazement swept  over the   
continents4 ,thousands of people who had
 never in their lives  troubled about   
vibrations of light and gravitation were
 seized by this  wave and carried on    
high1 immersed in the wish for knowledge
 although  incapable of grasping it4    
,this much all understood1 that from the
 quiet  study of a scholar an           
illuminating gospel for exploring the   

universe had  been irradiated4          
,during that time no name was quoted so 
often as that of this man4  ,everything 
sank away in face of this universal     
theme which had taken  possession of    
humanity4 ,the converse of educated     
people circled about  this pole1 could  
not escape from it1 continually reverted
 to the same  theme when pressed aside  
by necessity or accident4 ,newspapers   
entered on  a chase for contributors who
 could furnish them with short or long1 
technical or non-technical1 notices     
about ,einstein's theory4 ,in all  nooks
 and corners social evenings of         
instruction sprang up1 and  wandering   
universities appeared with errant       
professors that led people  out the     
three-dimensional misery of daily life  
into the more hospitable  ,elysian      
fields of four-dimensionality4 ,women   
lost sight of domestic  worries and     
discussed co-ordinate systems1 the      
principle of  simultaneity1 and         
negatively-charged electrons4 ,all      

contemporary  questions had gained a    
fixed centre from which threads could be
 spun to  each4 ,relativity had become  
the sovereign password4 ,in spite of    
some  grotesque results that followed on
 this state of affairs it could not     
fail to be recognized that we were      
watching symptoms of mental hunger  not 
less imperative in its demands than     
bodily hunger1 and it was no  longer to 
be appeased by the former books by      
writers on popular science  and by      
misguided idealists4    ,and whilst     
leaders of the people1 statesmen1 and   
ministers made vain  efforts to steer in
 the fog1 to arrive at results          
serviceable to the  nation1 the         
multitude found what was expedient for  
it1 what was  uplifting1 what sounded   
like the distant hammering of           
reconstruction4  ,here was a man who had
 stretched his hands towards the stars2 
to forget  earthly pains one had but to 
immerse oneself in his doctrine4 ,it was
 the  first time for ages that a chord  

vibrated through the world invoking all 
eyes towards something which1 like music
 or religion1 lay outside  political or 
material interests4    ,the mere thought
 that a living ,copernicus was moving in
 our midst  elevated our feelings4      
,whoever paid him homage had a sensation
 of  soaring above ,space and ,time1 and
 this homage was a happy augury in an   
epoch so bare of brightness as the      
present4         99     99     99     99
     99     99     99     99    ,as     
already remarked1 there was no lack of  
rare fruits among the  newspaper        
articles1 and a chronicler would        
doubtless have been able to  make an    
attractive album of them4 ,i brought    
,einstein several foreign  papers with  
large illustrations which must certainly
 have cost the  authors and publishers  
much effort and money4 ,among others    
there were  full-page beautifully       
coloured pictures intended to give the  
reader an  idea of the paths pursued by 
the rays from the stars during the total

  eclipse of the sun4 ,these afforded   
,einstein much amusement1 namely1 e     
contrario1 for from the physical point  
of view these pages contained  utter    
nonsense4 ,they showed the exact        
opposite of the actual course of  the   
rays inasmuch as the author of the      
diagrams had turned the convex  side of 
the deflected ray towards the sun4 ,he  
had not even a vague idea  of the       
character of the deflection1 for his    
rays proceeded in a straight  line      
through the universe until they reached 
the sun1 where they  underwent a sudden 
change of direction reminiscent of a    
stork's legs4  ,the din of journalistic 
homage was not unmixed with scattered   
voices of  dissent1 even of hostility4  
,einstein combated these not only       
without  anger but with a certain       
satisfaction4 ,for indeed the series of 
unbroken  ovations became discomfiting1 
and his feelings took up arms against   
what  seemed to be developing into a    
star-artist cult4 ,it was like a breath 

of  fresh air when some column of a     
chance newspaper was devoted to a       
polemic against his theory1 no matter   
how unfounded or unreasoned it may  have
 been1 merely because a dissonant tone  
broke the unceasing chorus of  praise4  
,on one occasion he even said of a      
shrill disputant1 ,the man is  quite    
right6 ,and these words were uttered in 
the most natural manner  possible4 ,one 
must know him personally if one is to   
understand these  excesses of           
toleration4 ,so did ,socrates defend his
 opponents4    ,in our conversation we  
returned to the original question1 and  
,i asked  whether there was no means of 
making the deflection of the ray        
intelligible to an average person4      
,einstein replied3 ,in a very           
superficial manner this is certainly    
possible4 ,and with a few strokes on the
 paper1 which ,i shall here try  to     
describe in words1 he gave his          
explanation in terms something like  the
 following3    ,this square is to denote

 the cross-section of a closed box which
 we  imagine to be situated somewhere in
 the universe4 ,inside it there lives  a
 physicist who makes observations and   
draws inferences from them4 ,in  the    
course of time he perceives1 what is    
familiar to all of us1 that  every body 
not supported and left to itself1 for   
example1 a stone that  is released1     
drops to the floor with uniform         
acceleration1 that is1 with  a steady   
increase of velocity in going downwards4
 ,there are two ways  open to him to    
explain this phenomenon4    ,firstly1 he
 might suspect--and this suspicion would
 be most likely to  occur to him--that  
his box was resting on some body in the 
heavens4 ,for  if indeed the box were a 
cave in some part of the world1 the     
falling of  the stone would suggest     
nothing unusual2 it would be quite      
self-evident  to every occupant1 and    
quite explicable to the physicist       
according to  ,galilei's 7or ,newton's7 
,laws for ,falling ,bodies4 ,he need not

 necessarily  restrict himself to the   
,earth1 for if the box happened to be on
 some  other star1 this phenomenon of   
falling would likewise occur1 with      
greater or less speed1 and the body     
would certainly fall with uniform       
acceleration4 ,thus the physicist could 
say3 this is an effect of  gravitation1 
exhibiting the property of weight which 
,i explain to myself  as usual1 as due  
to the attraction of a heavenly body4   
,secondly1 another idea might strike    
him4 ,for we stipulated nothing  about  
the position of the box1 and assumed    
only that it was to exist  somewhere in 
the universe4 ,the physicist in the box 
might reason as  follows3    ,supposing 
,i am separated by incalculable         
distances from every attracting         
heavenly body1 and supposing gravitation
 existed neither for me nor for  the    
stone which ,i release from my hand1    
then it would still be possible  for me 
to give a complete explanation of the   
phenomena ,i observe4 ,i  should only   

have to assume that the body is moving  
with uniform  acceleration upwards4 ,the
 motion previously interpreted by me as 
a  falling downwards need not take place
 at all4 ,the stone1 as an inert  body1 
could persist in its position 7relative 
to the box or the  observer71 and would1
 in spite of this1 show exactly the same
 behaviour  when the box moves with     
acceleration upwards as if it were      
falling with  increasing velocity       
downwards4    ,now since our physicist  
has no system which might serve for     
reference  and orientation1 and since in
 his box which is shut off from the     
universe he has no means at his disposal
 of determining whether he is in  the   
sphere of influence of an attracting    
heavenly body or not1 both the  above   
explanations are feasible for him and   
both are equally valid1 and  it is      
impossible for him to come to a decision
 in his choice4 ,he can  interpret the  
acceleration in either way1 as being    
upwards or downwards1  connected to one 

another by relativity2 a fundamental    
reason for  preferring one              
interpretation to the other cannot be   
furnished1 since  the phenomenon of     
falling is represented unchanged whether
 he assumes  the stone to be falling and
 the box to be at rest1 or vice versa4  
,this  may be generalized in these      
words3    ,at every point of the world  
the observed acceleration of a body left
 to  itself may be interpreted either as
 a gravitational or as an inertial      
effect--that is1 from the point of view 
of physics we may assert with  equal    
right that the system 7the box1 the     
complex defining the  orientation7 from 
which ,i observe the event is           
accelerated1 or that the  event takes   
place in a gravitational field4 ,the    
equal right to these two  views is      
called the ,principle of ,equivalence by
 ,einstein4 ,it asserts  the equivalence
 or the identity of inertial and        
gravitational mass4 ,if  we familiarize 
ourselves with this identity1 an        

exceedingly important  road to knowledge
 is opened up to our consciousness4 ,we 
arrive at the  inevitable conclusion    
that every inertial effect that we      
perceive in  bodies1 the most essential 
quality of it1 itself so to speak in its
  persistent nature1 is to be traced    
back to the influence to which it is    
subjected by other bodies4 ,when this   
has become clear to us1 we feel         
impelled to inquire how a ray of light  
would behave under the influence  of    
gravitation4 ,hence we return to our    
physicist in the box1 and we now  know  
that as a consequence of the ,principle 
of ,equivalence we are free  to assume  
either that an attracting heavenly body1
 such as the sun1 is  situated somewhere
 below the box1 or to refer the         
phenomena to the box  regarded as being 
accelerated upwards4 ,in the box we     
distinguish the  floor1 the ceiling1    
four walls1 and among these again1      
according to the  position we take up1  
the wall on the left and its opposite   

one on the  right4    ,we now imagine a 
marksman to be outside the box and      
having no connexion  with us1 being     
poised freely in space1 and suppose him 
to fire out of a  horizontal gun at the 
box so that the bullet pierces both the 
wall on  the left and the wall on the   
right4 ,now1 if everything else were to 
remain at rest1 the holes in both walls 
would be equally distant from  the      
floor1 and the bullet would move in a   
straight line parallel to the  floor and
 to the ceiling4 ,but1 as we have seen1 
all events happen as if  the box itself 
moved with constant acceleration4 ,the  
bullet that  requires time to pass from 
one wall to the other thus finds that   
when it  reaches the wall on the right  
the latter has advanced a little1 so    
that  the resulting hole is a little    
lower than that on the left wall4 ,this 
means that the flight of the bullet1    
according to our observation in the     
interior of the box1 is no longer       
rectilinear4 ,in fact1 if we trace the  

bullet from point to point1 we should   
find that for us1 situated in the  box1 
it would describe a line bent downwards1
 with its concave side to  the floor4   
,exactly the same thing happens with a  
ray of light which is emitted by a      
source outside in a horizontal direction
 and which traverses the space  between 
the walls 7supposed transparent74 ,only 
the velocity would be  different4 ,in   
the course of its flight the ray would  
move like a  projectile that is whizzing
 along at the rate of #ahj1jjj miles per
  second4 ,but provided sufficiently    
delicate means of measurement are       
applied1 it should still be possible to 
prove the existence of an  infinitesimal
 deflection from the rectilinear        
horizontal path1 an  insignificant      
concavity towards the floor4            
,consequently this curvature of the     
light-ray 7say1 from a star7 must  also 
be perceptible in places where it is    
subject to the influence of a           
gravitational field4 ,if we drop our    

imaginary picture of the box1 the       
argument is in nowise altered4 ,a ray   
from a star which passes close by  the  
sun seems to our perception to be bent  
in towards the sun1 and the  order of   
this deflection can be determined if    
sufficiently delicate  instruments be   
used4 ,as above remarked1 it is a       
question of detecting a  difference of  
#a4g seconds of arc1 which is to be     
manifested as a  distance on the        
photographic plate1 and is actually     
found to be present4    ,the fact that  
scientists are able to detect this      
appears in itself a  marvel of technical
 precision far in advance of splitting  
hairs1 for  in comparison a single hair 
is1 in this case1 to be removed to a    
considerable distance if we are to use  
it to give an idea of the size of  angle
 under consideration4 ,fortunately      
stellar photography has been  developed 
so wonderfully that in every single case
 extraordinarily  accurate results are  
got even from preliminary measurements4 

,in ordinary astronomical practice it is
 usually found that a millimetre  in    
linear measure on the plate corresponds 
to a minute of arc4 ,this  means that   
the sun's disc itself has a diameter of 
#c centimetres on the  photograph4 ,the 
stars appear as tiny dots1 which may be 
sharply  differentiated in an           
enlargement4 ,stars of the fourteenth   
order of  magnitude and beyond it become
 visible1 whereas the naked eye cannot  
see  those of order higher than the     
sixth4 ,a grating whose lines are       
millimetre wide is copied on to the     
plate to make the  measurement more     
accurate1 so that the positions of      
objects can be  ascertained with        
certainty to within a few tenths of a   
second of arc4  ,thus the problem which 
was to be solved by the solar eclipse of
 #aiai lay  within the realm of         
possibility as regards our means of     
measurement4    ,a copy of this         
photograph had been sent to ,einstein   
from ,england1 and he  told me of it    

with evident pleasure4 ,he continually  
reverted to the  delightful little      
picture of the heavens1 quite fascinated
 by the thing  itself1 without the      
slightest manifestation of a personal   
interest in  his own success4 ,indeed1  
,i may go further and am certainly not  
mistaken  in saying his new mechanics   
did not even enter his head1 nor the    
verification of it by the plate2 on the 
contrary1 he displayed that  disposition
 of the mind which in the case of genius
 as well as in that  of children shows  
itself as navet4 ,the prettiness of the 
photograph charmed him1 and the thought 
that the heavens had been drawn  up as  
for parade to be a model for it4    ,all
 things are repeated in the history of  
life4 ,in these happenings1  which mark 
the #bith ,may #aiai as a red-letter day
 in the history of  science1 we         
recognize a revival of the ,sun ,myth1  
unperceived by the  individual1 but as  
an expression of the universal          
consciousness1 just as  when ,copernicus

 converted the geocentric picture of the
 universe into a  heliocentric one1 the 
,sun ,myth again sprang into life2 the  
symbolization  of faith in the          
light-giving and heat-giving star4 ,this
 time it has  arisen1 purified of all   
dross1 scarcely perceptible to our      
senses1 like  an aureole spun about the 
sun by far-distant sources of light1 in 
honour  of a principle1 and even if most
 of us do not yet know what a system of 
reference means1 yet for many such a    
system has unconsciously evolved1  a    
thought-system serving as a reference   
for the development of their  knowledge 
when they thought or spoke of ,einstein4
          ,,chapter ,,ii    ,,beyond    
,,our ,,power    ,useful and ,latent    
,forces4--,connexion between ,mass1     
,energy1 and ,velocity  of              
,light4--,deriving ,power by            
,combustion4--,one ,gramme of           
,coal4--,unobtainable                   
,calories4--,economics of ,coal4--,hopes
 and ,fears4--,dissociated ,atoms4      

#bith ,march #aibj    ,,we spoke of the 
forces that are available for man and   
which he derives  from ,nature as being 
necessary for his existence and for the 
development  of life4 ,what forces are  
at our disposal8 ,what hopes have we of 
elaborating our supply of these forces8 
,einstein first explained the conception
 of energy1 which is intimately         
connected with the conception of mass   
itself4 ,every amount of substance  7,i 
am paraphrasing his words71 the greatest
 as well as the smallest1 may  be       
regarded as a store of power1 indeed1 it
 is essentially identical  with energy4 
,all that appears to our senses and our 
ordinary  understanding as the visible1 
tangible mass1 as the objective body    
corresponding to which we1 in virtue of 
our individual bodies1 abstract  the    
conceptual outlines1 and become aware of
 the existence of a definite  copy is1  
from the physical point of view1 a      
complex of energies4 ,these  in part act
 directly1 in part exist in a latent    

form as strains which1  for us1 begin to
 act only when we release them from     
their state of  strain by some          
mechanical or chemical process1 that is1
 when we succeed  in converting the     
potential energy into kinetic energy4   
,it may be said1  indeed1 that we have  
here a physical picture of what ,kant   
called the  thing in itself4 ,things as 
they appear in ordinary experience are  
composed of the sum of our direct       
sensations2 each thing acts on us       
through its outline1 colour1 tone1      
pressure1 impact1 temperature1  motion1 
chemical behaviour1 whereas the thing in
 itself is the sum-total  of its energy1
 in which there is an enormous          
predominance of those  energies which   
remain latent and are quite inaccessible
 in practice4    ,but this thing in     
itself1 to which we shall have occasion 
to refer  often with a certain regard to
 its metaphysical significance1 may be  
calculated4 ,the fact that it is        
possible to calculate it takes its      

origin1 like many other things which had
 in no wise been suspected1 in          
,einstein's ,theory of ,relativity4     
,quite objectively and without betraying
 in the slightest degree that an        
astonishing world-problem was being     
discussed1 ,einstein expressed  himself 
thus3    ,according to the ,theory of   
,relativity there is a calculable       
relation  between mass1 energy1 and the 
velocity of light4 ,the velocity of     
light  7denoted by c1 as usual7 is equal
 to #c4ajaj cm4 per second4             
,accordingly the square of c is equal to
 #i times #ajbj cm4 per second1  or1 in 
round numbers1 #ajba cm4 per second4    
,this c#b plays an  essential part if we
 introduce into the calculation the     
mechanical  equivalent of heat1 that is1
 the ratio of a certain amount of energy
 to  the heat theoretically derivable   
from it2 we get for each gramme         
#bj4ajab1 that is1 #bj billion calories4
    ,we shall have to explain the       
meaning of this brief physical statement

 in  its bearing on our practical lifes4
 ,it operates with only a small array   
of symbols1 and yet encloses a whole    
universe1 widening our perspective  to a
 world-wide range6    ,to simplify the  
reasoning and make it more evident we   
shall not think of  the conception of   
substance as an illimitable whole1 but  
shall fix our  ideas on a definite      
substance1 say coal4    ,there seems    
little that may strike us when we set   
down the words3                         
,one ,gramme of ,coal4    ,we shall soon
 see what this one gramme of coal       
conveys when we translate  the          
above-mentioned numbers into a language 
to which a meaning may be  attached in  
ordinary life4 ,i endeavoured to do this
 during the above  conversation1 and was
 grateful to ,einstein for agreeing to  
simplify his  argument by confining his 
attention to the most valuable fuel in  
our  economic life4    ,once whilst ,i  
was attending a students' meeting1      
paying homage to  ,wilhelm ,dove1 the   

celebrated discoverer took us aback with
 the following  remark3 ,when a man     
succeeds in climbing the highest        
mountain of ,europe  he performs a task 
which1 judged from his personal point of
 view1  represents something stupendous4
 ,the physicist smiles and says quite   
simply1 ,two pounds of coal4 ,he means  
to say that by burning #b lb4 of  coal  
we gain sufficient energy to lift a man 
from the sea-level to the  summit of    
,mont ,blanc4    ,it is assumed1 of     
course1 that an ideal machine is used1  
which converts  the heat of combustion  
without loss into work4 ,such a machine 
does not  exist1 but may easily be      
imagined by supposing the imperfections 
of  machines made by human hands to be  
eliminated4    ,such effective heat is  
usually expressed in calories4 ,a       
calorie is the  amount of heat that is  
necessary to raise the temperature of a 
gramme of  water by one degree          
centigrade4 ,now the theorem of the     
,mechanical  ,equivalent1 which is      

founded on the investigations of        
,carnot1 ,robert  ,mayer1 and ,clausius1
 states that from one calorie we may    
obtain  sufficient energy to lift a     
pound weight about #c feet4 ,since #b   
lb4 of  coal may be made to yield #h    
million calories1 they will enable us to
  lift a pound weight through #bd       
million feet1 theoretically1 or1 what   
comes to the same approximately1 to lift
 a #ag-stone man through #ajj1jjj  feet1
 that is1 nearly #ai miles3 this is     
nearly seven times the height of  ,mont 
,blanc4    ,at the time when ,dove was  
lecturing1 ,einstein had not yet been   
born1 and  when ,einstein was working   
out his ,theory of ,relativity1 ,dove   
had long  passed away1 and with him     
there vanished the idea of the small    
value of  the energy stored in substance
 to give way to a very much greater     
value  of which we can scarce form an   
estimate4 ,we should feel dumbfounded if
  the new calculation were to be a      
matter of millions1 but actually we are 

to imagine a magnification to the extent
 of billions4 ,this sounds almost  like 
a fable when expressed in words4 ,but a 
million is related to a  billion in     
about the same way as a fairly wide city
 street to the width  of the ,atlantic  
,ocean4 ,our ,mont ,blanc sinks to      
insignificance4 ,in the  above          
calculation it would have to be replaced
 by a mountain #ej million  miles high4 
,since this would lead far out into     
space1 we may say that  the energy      
contained in a kilogramme of coal is    
sufficient to project a  man so far that
 he will never return1 converting him   
into a human comet4  ,but for the       
present this is only a theoretical store
 of energy which  cannot yet be utilized
 in practice4    ,nevertheless1 we      
cannot avoid it in our calculations just
 as we cannot  avoid that remarkable    
quantity c1 the velocity of light that  
plays its  part in the tiny portion of  
substance as it does in everything1     
asserting itself as a regulative factor 

in all world phenomena4 ,it is a        
natural constant that preserves itself  
unchanged as #ahj1jjj miles per  second 
under all conditions1 and which truly   
represents what appeared to  ,goethe as 
the immovable rock in the surging sea of
 phenomena1 as a  phantasm beyond the   
reach of investigators4    ,it is       
difficult for one who has not been      
soaked in all the elements of  physical 
thought to get an idea of what a natural
 constant means2 so  much the more when 
he feels himself impelled to picture the
 constant1 so  to speak1 as the rigid   
axis of a world constructed on          
relativity4  ,everything1 without       
exception1 is to be subjected not only  
to continual  change 7and this was what 
,heraclitus assumed as a fundamental    
truth in  his assertion panta rhei1     
everything flows71 but every            
length-measurement and time-measurement1
 every motion1 every form and  figure   
are dependent on and change with the    
position of the observer1 so  that the  

last vestige of the absolute vanishes   
from whatever comes into  the realm of  
observation4 ,nevertheless1 there is an 
absolute despot1 who  preserves his     
identity inflexibly among all           
phenomena--the velocity of  light1 c1 of
 incalculable influence in practice and 
yet capable of  measurement4 ,its nature
 has been characterized in one of the   
main  propositions of ,einstein stated  
in #aije3 ,every ray of light is        
propagated in a system at rest with a   
definite1 constant velocity  independent
 of whether the ray is emitted by a body
 at rest or in  motion4 ,but this       
constancy of the omnipotent c is not    
only in  accordance with world          
relativity3 it is actually the main     
pillar which  supports the whole        
doctrine2 the further one penetrates    
into the theory1  the more clearly does 
one feel that it is just this c which is
  responsible for the unity1            
connectivity1 and invincibility of      
,einstein's  world system4    ,in our   

example of the coal1 from which we      
started1 c occurs as a  square1 and it  
is as a result of multiplying #cjj1jjj  
by itself 7that is1  forming c#b7 that  
we arrive at the thousands of milliards 
of energy  units which we associated    
above with such a comparatively         
insignificant  mass4 ,let us picture    
this astounding circumstance in another 
way1  although we shall soon see that   
,einstein clips the wings of our soaring
  imagination4 ,the huge ocean liner    
,imperator1 which can develop a  greater
 horsepower than could the whole of the 
,prussian cavalry before  the war1 used 
to require for one day's travel the     
contents of two very  long series of    
coal-trucks 7each series being as long  
as it takes the  strongest locomotive to
 pull74 ,we now know that there is      
enough energy  in two pounds of coal to 
enable this boat to do the whole trip   
from  ,hamburg to ,new ,york at its     
maximum speed4    ,i quoted this fact1  
which1 although it sounds so incredibly 

fantastic1  is quite true1 to ,einstein 
with the intention of justifying the    
opinion  that it contained the key to a 
development which would initiate a new  
epoch in history and would be the       
panacea of all human woe4 ,i drew an    
enthusiastic picture of a dazzling      
,utopia1 an orgy of hopeful dreams1  but
 immediately noticed that ,i received no
 support from ,einstein for  these      
visionary aspirations4 ,to my           
disappointment1 indeed1 ,i perceived    
that ,einstein did not even show a      
special interest in this circumstance   
which sprang from his own theory1 and   
which promised such bountiful  gifts4   
,and to state the conclusion of the     
story straight away ,i must  confess    
that his objections were strong enough  
not only to weaken my  rising hopes1 but
 to annihilate them completely4         
,einstein commenced by saying3 ,at      
present there is not the slightest      
indication of when this energy will be  
obtainable1 or whether it will be       

obtainable at all4 ,for it would        
presuppose a disintegration of the atom 
effected at will--a shattering of the   
atom4 ,and up to the present there  is  
scarcely a sign that this will be       
possible4 ,we observe atomic            
disintegration only where ,nature       
herself presents it1 as in the case of  
radium1 the activity of which depends   
upon the continual explosive            
decomposition of its atom4              
,nevertheless1 we can only establish the
  presence of this process1 but cannot  
produce it2 ,science in its present     
state makes it appear almost impossible 
that we shall ever succeed in so  doing4
    ,the fact that we are able to       
abstract a certain number of calories   
from  coal and put them to practical use
 comes about owing to the circumstance  
that combustion is only a molecular     
process1 a change of configuration1     
which leaves fully intact the atoms of  
which the molecules are composed4  ,when
 carbon and oxygen combine1 the         

elementary constituent1 the atom1       
remains quite unimpaired4 ,the above    
calculation1 mass multiplied by the     
square of the velocity of light2 would  
have a technical significance  only if  
we were able to attack the interior of  
the atom2 and of this  there seems1 as  
remarked1 not the remotest hope4    ,out
 of the history of technical science it 
might seem possible to draw  on examples
 contradictory to this first argument   
which is soon to be  followed by others 
equally important4 ,as a matter of fact1
 rigorous  science has often declared to
 be impossible what was later discovered
 to  be within the reach of technical   
attainment--things that seem to us      
nowadays to be ordinary and             
self-evident4 ,werner ,siemens          
considered it  impossible to fly by     
means of machines heavier than air1 and 
,helmholtz  proved mathematically that  
it was impossible4 ,antecedent to the   
discovery of the locomotive the         
impossible of the academicians played   

an important part2 ,stephenson as well  
as ,riggenbach 7the inventors of  the   
locomotive7 had no easy task to         
establish their inventions in the  face 
of the general reproach of craziness    
hurled at them4 ,the eminent  physicist 
,babinet applied his mathematical       
artillery to demolish the  ideas of the 
advocates of a telegraphic cable between
 ,europe and  ,america4 ,philipp ,reis1 
the forerunner of the telephone1 failed 
only as a  result of the impossible of  
the learned physicist ,poggendorff2 and 
even when the practical telephone of    
,graham ,bell 7#ahgf7 had been found  to
 work in ,boston1 on this side of the   
,atlantic there was still a hubbub  of  
impossible owing to scientific reasons4 
,to these illustrations is  to be added 
,robert ,mayer's mechanical equivalent  
of heat1 a determining  factor in our   
above calculations of billions2 it      
likewise had to  overcome very strong   
opposition on the part of leading       
scientists4    ,let us imagine the state

 of mankind before the advent of        
machines and  before coal had been made 
available as a source of power4 ,even at
 that  time a far-seeing investigator   
would have been able to discover from   
theoretical grounds the #hjjj calories  
mentioned earlier and also their        
transformation into useful forces4 ,he  
would have expressed it in another  way 
and would have got different figures1   
but he would have arrived at  the       
conclusion3 ,here is a virtual          
possibility which must unfortunately    
remain virtual1 as we have no machine in
 which it can be used4 ,and  however    
far-sighted he may have been1 the idea  
of1 say1 a modern dynamo  or a          
turbine-steamer would have been utterly 
inconceivable to him4 ,he  would not    
have dreamed such a thing4 ,nay1 we may 
even imagine a human  being of the misty
 dawn of prehistoric ages1 of the       
diluvial period1 who  had suddenly had a
 presentiment of the connexion between a
 log of wood  and the sun's heat1 but   

who was yet unaware of the uses of fire2
 he  would argue from his primordial    
logic that it was not possible and never
  would be possible to derive from the  
piece of wood something which sends  out
 warmth like the sun4    ,i believe now1
 indeed1 that we have grounds for       
considering ourselves  able to mark off 
the limits of possibility more clearly  
than the present  position of science   
would seem to warrant4 ,there is the    
same relation  between such             
possibilities and absolute              
impossibilities as there is  between    
,leibniz's vrits de fait and the vrits  
ternelles4  ,the fact that we shall     
never succeed in constructing a plane   
isosceles  triangle with unequal base   
angles is a vrit ternelle4 ,on the      
other hand1 it is only a vrit de fait   
that science is precluded  from giving  
mortal man eternal life4 ,this is only  
improbable in the  highest degree1 for  
the fact that1 up to the present1 all   
our ancestors  have died is only a      

finite proof4 ,the well-known ,cajus of 
our logic  books need not die2 the      
chances of his dying are only nn#a1     
where  we denote the total of all       
persons that have passed away up to this
  moment by n4 ,if ,i ask a present-day 
authority in biology or medicine  what  
evidence there is that it will be       
possible to preserve an  individual     
person permanently from death1 he would 
confess3 not the  slightest4            
,nevertheless1 ,helmholtz declared3 ,to 
a person who tells me  that by using    
certain means the life of a person may  
be prolonged  indefinitely ,i can oppose
 my extreme disbelief1 but ,i cannot    
contradict  him absolutely4    ,einstein
 himself once pointed out to me such    
very remote possibilities2  it was in   
connexion with the following            
circumstance4 ,it is quite  impossible  
for a moving body ever to attain a      
velocity greater than that  of light1   
because it is scientifically            
inconceivable4 ,on the other hand1  it  

is conceivable1 and therefore within the
 range of possibility1 that  man may yet
 fly to the most distant constellations4
    ,there is1 therefore1 no absolute   
contradiction to the notion of making   
available for technical purposes the    
billions of calories that occurred  in  
our problem4 ,as soon as we admit it as 
possible for discussion1 we  find       
ourselves inquiring what the solution of
 the problem could signify4  ,in our    
intercourse we actually arrived at this 
question1 and discovered  the most      
radical answer in a dissertation which  
,friedrich ,siemens has  written about  
coal in general without touching in the 
slightest on these  possibilities of the
 future4 ,i imagine that this           
dissertation was a big  trump in my     
hand1 but had soon to learn from the    
reasoned contradiction  of ,einstein    
that the point at issue was not to be   
decided in this way4    ,nevertheless1  
it will repay us to consider these      
arguments for a moment4    ,friedrich   

,siemens starts from two premises which 
he seemingly bases on  scientific       
reasoning1 thus claiming their validity 
generally4 ,they are3  ,coal is the     
measure of all things4 ,the price of    
every product  represents1 directly or  
indirectly1 the value of the coal       
contained in  it4    ,as all economic   
values in over-populated countries are  
the result of  work1 and as work        
presupposes coal1 capital is synonymous 
with coal4 ,the  economic value of each 
object is the sum-total of the coal that
 had to  be used to manufacture the     
object in question4 ,in over-populated  
states  each wage is the value of the   
coal that is necessary to make this     
extra  life possible4 ,if there is a    
scarcity of coal1 the wages go down in  
value2 if there is no coal1 the wages   
are of no value at all1 no matter  how  
much paper money be issued4    ,as soon 
as agriculture requires coal 7this      
occurs when it is practised  intensively
 and necessitates the use of railways1  

machines1 artificial  manures71 coal    
becomes involved with food-stuffs4      
,thanks to  industrialism1 coal is      
involved in clothing and housing1 too4  
,since money is equivalent to coal1     
proper administration of finance is     
equivalent to a proper administration of
 coal resources1 and our  standard of   
currency is in the last instance a      
coal-currency4 ,gold as  money is now   
concentrated coal4    ,the most advanced
 people is that which derives from one  
kilogramme of  coal the greatest        
possibilities conducive to life4 ,wise  
statesmanship  must resolve itself into 
wise administration of coal4 ,or1 as it 
has been  expressed in other words      
elsewhere3 ,we must think in terms of   
coal4    ,these fundamental ideas were  
discussed1 and the result was that      
,einstein  admitted the premises in the 
main1 but failed to see the             
conclusiveness  of the inferences4 ,he  
proved to me1 step by step1 that        
,siemens' line of  thought followed a   

vicious circle1 and1 by begging the     
question1 arrived  at a false           
conclusion4 ,the essential factor1 he   
said1 is man-power1 and  so it will     
remain2 it is this that we have to      
regard as the primary  factor4 ,just so 
much can be saved to advantage as there 
is man-power  available for purposes    
other than for the production of coal   
from which  they are now released4 ,if  
we succeed in getting greater use out of
 a  kilogramme of coal by better        
management1 then this is measurable in  
man-power1 with which one may dispense  
for the mining of coal1 and which  may  
be applied to other purposes4    ,if the
 assertion3 ,coal is the measure of all 
things1 were generally  valid1 it should
 stand every test4 ,we need only try it 
in a few  instances to see that the     
thesis does not apply4 ,for example1    
said  ,einstein3 ,however much coal we  
may use1 and however cleverly we may    
dispose of it1 it will not produce      
cotton4 ,certainly the freightage of    

cotton-wool could be reduced in price1  
but the value-factor represented  by    
man-power can never disappear from the  
price of the cotton4    ,the most that  
can be admitted is that an increase of  
the amount of power  obtained from coal 
would make it possible for more people  
to exist than  is possible at present1  
that is1 that the margin of             
over-population  would become extended4 
,but we must not conclude that this     
would be a  boon to mankind4 ,a maximum 
is not an optimum4    ,he who proclaims 
the maximum without qualification as the
 greatest  measure of good is like one  
who studies the various gases in the    
atmosphere to ascertain their good or   
bad effect on our breathing1 and        
arrives at the conclusion3 the nitrogen 
in the air is harmful1 so we  must      
double the proportion of oxygen to      
counteract it2 this will confer  a great
 benefit on humanity6    #a99;,armed    
with this striking analogy1 we can now  
subject the foundation  of ,siemens'    

theory to a new scrutiny1 and we shall  
then discover that  even the premises   
contain a trace of the petitio principii
 that  finally receives expression in   
the radical and one-sided expression3   
,coal is everything4    ,footnote #a3   
,the parts included between 9944499 are 
to be regarded as  supplementary        
portions intended to elucidate the      
arguments involved in  the dialogue4 ,in
 many points they are founded on        
utterances of ,einstein1  but also      
contain reflections drawn from other    
sources1 as well as  opinions and       
inferences which fall to the account of 
the author1 as  already remarked in the 
preface4 ,one will not get far by       
judging these  statements as right or   
wrong1 for even the debatable view may  
prove  itself to be expeditious and     
suggestive in the perspective of these  
conversations4 ,wherever it was         
possible1 without the connexion being   
broken1 ,i have called attention to the 
parts which ,einstein corrected or      

disapproved of4 ,in other places ,i     
refrained from this1 particularly when  
the subject under discussion demanded an
 even flow of argument4 ,it would  have 
disturbed the exposition if ,i had made 
mention of every  counter-argument of   
the opposing side in all such cases     
while the  explanation was proceeding   
along broad lines4    ,as if built on   
solid foundations this first statement  
looms before us3  ,coal is solar energy4
 ,this is so far indisputable4 ,for all 
the coal  deposits that are still       
slumbering in the earth were once       
stately  plants1 dense woods of fern1   
which1 bearing the burden of millions of
  years1 have saved up for us what they 
had once extracted as nutrition  from   
the sun's rays4 ,we may let the parallel
 idea pass without  contention3 ,in the 
beginning was not the ,word1 nor the    
,deed1 but1 in the  beginning was the   
,sun4 ,the energy sent out by the sun to
 the earth for  mankind is the only     
necessary and inevitable condition for  

deeds4 ,deeds  mean work1 and work      
necessitates life4 ,but we immediately  
become  involved in an unjustifiable    
subdivision of the idea1 for the        
propounder  of the theory says next3 444
 ,coal is solar energy1 therefore coal  
is  necessary if we are to work 444 and 
this has already thrust us from the     
paths of logic2 the prematurely         
victorious ergo breaks down4 ,for1 apart
  from the solar energy converted into  
coal1 the warmth of our mother  planet  
radiates on us1 and furnishes us with   
the possibility of work4  ,siemens'     
conclusion1 from the point of view of   
logic1 is tantamount to2  ,graphite is  
solar energy2 hence graphite is         
necessary1 if we are to be  able to     
work4 ,the true expression of the state 
of affairs is3 ,coal is1  for our       
present conditions of life1 the most    
important1 if not the  exclusive1       
preliminary for human work4    ,and when
 we learn from political economy that in
 a social state only  the necessary     

human labour and the demand for         
power-installations which  require coal1
 and hence again labour for their       
production1 come into  question1 this in
 no way implies the assertion1 as       
,siemens appears to  assume1 that coal  
can be made out of labour4 ,but it does 
signify that  work founded on the sun's 
energy need not necessarily be reducible
 to  coal4 ,and this probably coincides 
with ,einstein's opinion1 which is so   
much the more significant1 as his own   
doctrine points to the highest  measure 
of effect in forces1 even if only       
theoretically499    ,nevertheless1 it is
 a fact that every increase in the      
quantity of power  derived1 when        
expressed per kilo1 denotes a mitigation
 of life's  burdens2 it is only a       
question of the limits involved4        
,firstly1 is technical science with its 
possibilities1 as far as they can  be   
judged at present1 still able to        
guarantee the future for us8 ,can it    
spread out the effective work so far    

that we may rely peacefully on the      
treasures of coal slumbering in the     
interior of the earth8    ,evidently    
not4 ,for in this case we are dealing   
with quantities that may  be            
approximately estimated4 ,and even if we
 get three times1 nay ten  times1 as    
many useful calories as before1 there is
 a parallel  calculation of evil omen   
that informs us3 there will be an end to
 this  feast of energy4    ,in spite of 
all the embarrassments due to the       
present shortage of coal  we have still 
always been able to console ourselves   
with the thought  that there is really a
 sufficiency1 and that it is only a     
question of  overcoming stoppages4 ,it  
is a matter of fact that from the time  
of the  foundation of the ,german       
,empire to the beginning of the ,world  
,war coal  production had been rising   
steadily1 and it was possible to        
calculate  that in spite of the         
stupendous quantities that were being   
removed from  the black caves of        

,germany1 there remained at least #bjjj 
milliards of  marks in value 7taken at  
the nominal rate1 that is1              
#ajj1jjj1jjj1jjj74  ,nevertheless1      
geologists and mining experts tell us   
that our whole  supply will not last    
longer than #bjjj years1 in the case of 
,england #ejj  years1 and in that of    
,france #bjj years4 ,even if we allow   
amply for the  opening up of new        
coal-fields in other continents1 we     
cannot get over  the fact that in the   
prehistoric fern forests the sun has    
stored up only  a finite1 exhaustible   
amount of energy1 and that within a few 
hundred  years humanity will be faced   
with a coal famine4    ,now1 if coal    
were really the measure of all things1  
and if the  possibility of life depended
 only on the coal supply1 then our      
distant  descendants would not only     
relapse into barbarity1 but they would  
have  to expect the absolute zero of    
existence4 ,we should not need to worry 
at  all about the entropy death of the  

universe1 as our own extinction on  this
 earthly planet beckons to us from an   
incomparably nearer point of  time4     
,at this stage of the discussion        
,einstein revealed prospects which were 
entirely in accordance with his         
conviction that the whole argument based
  on the coal assumption was untenable4 
,he stated that it was by no means  a   
,utopian idea that technical science    
will yet discover totally new ways  of  
setting free forces1 such as using the  
sun's radiation1 or water  power1 or the
 movement of the tides1 or power        
reservoirs of ,nature1  among which the 
present coal supply denotes only one    
branch4 ,since the  beginning of coal   
extraction we have lived only on the    
remains of a  prehistoric capital that  
has lain in the treasure-chests of the  
earth4  ,it is to be conjectured that   
the interest on the actual capital of   
force  will be very much in excess of   
what we can fetch out of the            
depositories  of former ages4    ,to    

form an estimate of this actual capital1
 entirely independent of  coal1 we may  
present some figures4 ,let us consider a
 tiny water canal1 a  mere nothing in   
the watery network of the earth1 the    
,rhine-falls at  ,schaffhausen1 that may
 appear mighty to the beholder1 but only
 because  he applies his tourist's      
measure instead of a planetary one4 ,but
 even  this bagatelle in the household  
of ,nature represents very considerable 
effectual values for us3 #bjj cubic     
metres spread over a terrace #bj  metres
 high yield #fg1jjj horse-power1        
equivalent to #ej1jjj kilowatts4  ,this 
cascade alone would suffice to keep     
illuminated to their full  intensity    
#a1jjj1jjj glowlamps1 each of #ej       
candle-power1 and according to  our     
present tariff we should have to pay at 
least #gj1jjj marks 7#cejj  nominally7  
per hour4 ,the coal-worshipper will be  
more impressed by a  different          
calculation4 ,the ,rhine-falls at       
,schaffhausen is equivalent in  value to

 a mine that yields every day #ade tons 
of the finest brown coal4  ,if we took  
the ,niagara ,falls as an illustration1 
these figures would  have to be         
multiplied by about #hj4    ,and by what
 factor would we have to multiply them1 
if we wished to get  only an approximate
 estimate of the energy that the        
breathing earth  rolls about in the form
 of the tides8 ,the astronomer ,bessel  
and the  philosopher-physicist ,fechner 
once endeavoured to get at some         
comparative picture of these events4 ,it
 required #cfj1jjj men twenty  years to 
build the greatest ,egyptian pyramid1   
and yet its cubical  contents are only  
about the millionth of a cubic mile1 and
 perhaps if we  sum up everything that  
men and machinery have moved since the  
time of  the ,flood till now1 a cubic   
mile would not yet have been completed4 
,in  contrast with this1 the earth in   
its tidal motion moves #bjj cubic miles 
of water from one quadrant of the       
earth's circumference to another in     

every quarter of a day4 ,from this we   
see at once that all the  coal-mines in 
the world would mean nothing to us if we
 could once  succeed in making even a   
fraction of the pulse-beat of the earth 
available for purposes of industry4     
,if1 however1 we should be compelled to 
depend on coal1 our imaginations  cling 
so much more closely to that enormous   
quantity given by the  expression mc#b1 
which was derived from the theory of    
relativity4    ,the #bj billion calories
 that are contained in each gramme of   
coal  exercise a fascination on our     
minds4 ,and although ,einstein states   
that  there is not the slightest        
indication that we shall get at this    
supply1  we get carried along by an     
irresistible impulse to picture what it 
would  mean if we should actually       
succeed in tapping it4 ,the transition  
from  the golden to the iron age1 as    
pictured in ,hesiod1 ,aratus1 and ,ovid1
  takes shape before our eyes1 and      
following our bent of continuing this   

cyclically1 we take pleasure in fancying
 ourselves being rescued from  the      
serfdom of the iron and of the coal age 
to a new golden age4 ,a  supply1 such as
 is piled up in an average city         
storing-place1 would be  sufficient to  
supply the whole world with energy for  
an immeasurable  time4 ,all the troubles
 and miseries arising from the running  
of  machines1 the mechanical production 
of wares1 house-fires would vanish1  and
 all the human labour at present        
occupied in mining coal would become    
free to cultivate the land1 all railways
 and boats would run almost  without    
expense1 an inconceivable wave of       
happiness would sweep over  mankind4 ,it
 would mean an end of coal-1 freight-1  
and food-shortage6 ,we  should at last  
be able to escape out of the hardships  
of the day1 which  is broken up by      
strenuous work1 and soar upwards to     
brighter spheres  where we would be     
welcomed by the true values of life4    
,how alluring is  the song of ,sirens   

chanted by our physics with its high ,c1
 the  velocity of light to the second   
power1 which we have got to know as a   
factor in this secret store of energy4  
,but these dreams are futile4 ,for      
,einstein1 to whom we owe this formula  
so promising of wonders1 not only denies
 that it can be applied  practically1   
but also brings forward another argument
 that casts us down  to earth again4    
,supposing1 he explained1 it were       
possible to set free  this enormous     
store of energy1 then we should only    
arrive at an age1  compared with which  
the present coal age would have to be   
called golden4    ,and1 unfortunately1  
we find ourselves obliged to fall in    
with this view1  which is based in the  
wise old saw  1 ne quid  nimis1 nothing 
in excess4 ,applied to our case1 this   
means that when  such a measure of power
 is set free1 it does not serve a useful
 purpose1  but leads to destruction4    
,the process of burning1 which we used  
as an  illustration1 calls up the       

picture of an oven in which we can      
imagine  this wholesale production of   
energy1 and experience tells us that we 
should not heat an oven with dynamite4  
,if technical developments of this kind 
were to come about1 the energy  supply  
would probably not be capable of        
regulation at all4 ,it makes no         
difference if we say that we only want a
 part of those #bj billion  calories1   
and that we should be glad to be able to
 multiply the #hjjj  calories required  
to-day by #ajj4 ,that is not possible1  
for if we should  succeed in            
disintegrating the atom1 it seems that  
we should have the  billions of calories
 rushing unchecked on us1 and we should 
find  ourselves unable to cope with     
them1 nay1 perhaps even the solid       
ground1  on which we move1 could not    
withstand them4    ,no discovery remains
 a monopoly of only a few people4 ,if a 
very careful  scientist should really   
succeed in producing a practical heating
 or  driving effect from the atom1 then 

any untrained person would be able to   
blow up a whole town by means of only a 
minute quantity of substance4  ,and any 
suicidal maniac who hated his fellows   
and wished to pulverize  all habitations
 within a wide range would only have to 
conceive the plan  to carry it out at a 
moment's notice4 ,all the bombardments  
that have  taken place ever since       
fire-arms were invented would be mere   
child's  play compared with the         
destruction that could be caused by two 
buckets  of coal4    ,at intervals we   
see stars light up in the heavens1 and  
then become  extinguished again2 from   
these we infer that world catastrophes  
have  occurred4 ,we do not know whether 
it is due to the explosion of hydrogen  
with other gases1 or to collisions      
between two stellar bodies4 ,there is   
still room for the assumption that1     
immeasurably far away in yonder  regions
 of celestial space1 something is       
happening which a malevolent  inhabitant
 of our earth1 who has discovered the   

secret of smashing the  atom1 might here
 repeat4 ,and even if our imaginations  
can be stretched  to paint the blessings
 of this release of energy1 they        
certainly fail to  conjure up visions of
 the disastrous effects which would     
result4    ,einstein turned to a page in
 a learned work of the mathematical     
physicist ,weyl of ,zrich1 and pointed  
out a part that dealt with such  an     
appalling liberation of energy4 ,it     
seemed to me to be of the nature  of a  
fervent prayer that ,heaven preserve us 
from such explosive forces  ever being  
let loose on mankind6    ,subject to    
present impossibility1 it is possible to
 weave many parallel  instances4 ,it is 
conceivable that by some yet            
undiscovered process  alcohol may be    
prepared as plentifully and as cheaply  
as ordinary water4  ,this would end the 
shortage of alcohol1 and would assure   
delirium  tremens for hundreds of       
thousands4 ,the evil would far outweigh 
the good1  although it might be         

avoidable1 for one can1 even if with    
great  difficulty1 imagine precautionary
 measures4    ,war technique might lead 
to the use of weapons of great range1   
which  would enable a small number of   
adventurers to conquer a ,great ,power4 
,it  will be objected3 this will hold   
vice versa1 too4 ,nevertheless1 this    
would not alter the fact that such      
long-range weapons would probably  lead 
to the destruction of civilization4 ,our
 last hope of an escape  would be in a  
superior moral outlook of future        
generations1 which the  optimist may    
imagine to himself as the force majeure4
    ,there are apparently only two      
inventions1 in themselves triumphs of   
intellect1 against which one would have 
no defence4 ,the first would be         
thought-reading made applicable to all1 
and with which ,kant has dealt  under   
the term thinking aloud4 ,what is       
nowadays a rare and very  imperfect     
telepathic turn may yet be generalized  
and perfected in a  manner which ,kant  

supposed not impossible on some distant 
planet4 ,the  association and converse  
of man with his fellows would not stand 
the  test of this invention1 and we     
should have to be angels to survive it  
even for a day4    ,the second invention
 would be the solution of this          
mc#b-problem1 which  ,i call a problem  
only because ,i fail to discover a      
proper term1 whereas  so far was it from
 being a problem for ,einstein that it  
was only in my  presence he began to    
reckon it out in figures from the       
symbolic formula4  ,to us average beings
 a ,utopia may disclose itself1 a short 
frenzy of joy  followed by a cold       
douche3 ,einstein stands above it as the
 pure  searcher1 who is interested only 
in the scientific fact1 and who1 even   
at the first knowledge of it1 preserves 
its essentially theoretical  importance 
from attempts to apply it practically4  
,if1 then1 another  wishes to hammer out
 into a fantastic gold-leaf what he has 
produced as  a little particle of gold  

in his physical investigations1 he      
offers no  opposition to such           
thought-experiments1 for one of the     
deepest traits of  his nature is        
tolerance4    ,a4 ,pflger1 one of the   
best qualified heralds of the new       
doctrine1 has  touched on the above     
matter in his essay1 ,the ,principle of 
,relativity4  ,einstein praised this    
pamphlet2 ,i mentioned that the author  
took a view  different from that of     
,einstein1 of the possibility of making 
accessible  the mc#b4 ,in discussing the
 practical significance of this         
eventuality1 ,pflger says3 ,it will be  
time to talk of this point again  a     
hundred years hence4 ,this seems a short
 time-limit1 even if none of  us will   
live to be present at the discussion4   
,einstein smiled at this  pause of a    
hundred years1 and merely repeated1 ,a  
very good essay6 ,it  is not for me to  
offer contradictions2 and1 as far as the
 implied  prognostication is concerned1 
it will be best for mankind if it should

  prove to be false4 ,if the optimum is 
unattainable1 at least we shall be      
spared the worst1 which is what the     
realization of this prophecy would      
inflict on us4    ,some months after the
 above discussion had first been put to 
paper1 the  world was confronted by a   
new scientific event4 ,the ,english     
physicist  ,rutherford had1 with        
deliberate intention1 actually succeeded
 in  splitting up the atom4 ,when ,i    
questioned ,einstein on the possible    
consequences of this experimental       
achievement1 he declared with his  usual
 frankness1 one of the treasures of his 
character1 that he had now  occasion to 
modify somewhat the opinion he had      
shortly before expressed4  ,this is not 
to mean that he now considered the      
practical goal of getting  unlimited    
supply of energy as having been brought 
within the realm of  possibility4 ,he   
gave it as his view that we are now     
entering on a new  stage of development1
 which may perhaps disclose fresh       

openings for  technical science4 ,the   
scientific importance of these new      
experiments  with the atom was certainly
 to be considered very great4    ,in    
,rutherford's operations the atom is    
treated as if he were dealing  with a   
fortress3 he subjects it to a           
bombardment and then seeks to fire  into
 the breach4 ,the fortress is still     
certainly far from capitulating1  but   
signs of disruption have become         
observable4 ,a hail of bullets caused   
holes1 tears1 and splinterings4    ,the 
projectiles hurled by ,rutherford are   
alpha-particles shot out by  radium1 and
 their velocity approaches two-thirds   
that of light4 ,owing to  the extreme   
violence of the impact1 they succeeded  
in doing damage to  certain atoms       
enclosed in evacuated glass tubes4 ,it  
was shown that atoms  of nitrogen had   
been disrupted4 ,it is still unknown    
what quantities of  energy are released 
in this process4 ,this splitting up of  
the atom  carried out with intention    

can1 indeed1 be detected only by the    
most  careful investigations4    ,as far
 as practical applications are          
concerned1 then1 we have got no         
further1 although we have renewed       
grounds for hope4 ,the unit of measure1 
as it were1 is still out of proportion  
to the material to be cut4 ,for  the    
forces which ,rutherford had to use to  
attain this result are  relatively very 
considerable4 ,he derived them from a   
gramme of radium1  which is able to     
liberate several milliard calories1     
whereas the net  practical result in    
,rutherford's experiment is still       
immeasurably small4  ,nevertheless1 it  
is scientifically established that it is
 possible to  split up atoms of one's   
own free will1 and thus the fundamental 
objection raised above falls to the     
ground4    ,there is also another reason
 for increased hope4 ,it seems feasible 
that1  under certain conditions4 ,nature
 would automatically continue the       
disruption of the atom1 after a human   

being had intentionally started  it1 as 
in the analogous case of a conflagration
 which extends1 although  it may have   
started from a mere spark4    ,a        
by-product of future research might lead
 to the transmutation of lead  into     
gold4 ,the possibility of this          
transformation of elements is subject   
to the same arguments as those above    
about the splitting up of the atom  and 
the release of great quantities of      
energy4 ,the path of decay from  radium 
to lead lies clearly exposed even now1  
but it is very  questionable whether    
mankind will finally have cause to offer
 up hymns  of thanksgiving if this line 
from lead on to the precious metals     
should  be continued1 for it would cause
 our conception of the latter to be     
shattered4 ,gold made from lead would   
not give rise to an increase in the     
value of the meaner metal1 but to the   
utter depreciation of gold1 and  hence  
the loss of the standard of value that  
has been valid since the  beginning of  

our civilization4 ,no economist would be
 possessed of a  sufficiently           
far-sighted vision to be able to measure
 the consequences  on the world's market
 of such a revolution in values4    ,the
 chief product would1 of course1 be the 
gain in energy1 and we must  bear this  
in mind when we give ourselves up to our
 speculations1 however  optimistic or   
catastrophic they may be4 ,the          
impenetrable barrier  impossible no     
longer exists4 ,einstein's wonderful    
,open ,sesame1 mass  times the square of
 the velocity of light1 is thundering at
 the portals4    ,and mankind finds a   
new meaning in the old saw3 ,one should 
never say  never6          ,,chapter    
,,iii    ,,valhalla    ,order of        
,distinction and ,characteristics of    
,great ,discoverers4--,galilei  and     
,newton4--,forerunners and              
,priority4--,science and                
,religion4--,inheritance  of            
,talent4--,a ,dynasty of                
,scholars4--,alexander von ,humboldt and

  ,goethe4--,leonardo da                
,vinci4--,helmholtz4--,robert ,mayer and
 ,dhring4--,gauss  and ,riemann4--,max  
,planck4--,maxwell and ,faraday4      ,i
 ,,had made up my mind to question      
,einstein about a number of famous men1 
not concerning mere facts of their lives
 and works1 for these details  were also
 procurable elsewhere1 and1 moreover1 ,i
 was not ignorant of  them1 but what    
attracted me particularly was to try to 
discover how the  greatness of one might
 be compared with that of another4 ,this
 sometimes  helps us to see a           
personality in a different light and    
from a new  perspective1 which leads us 
to assign to him a new position in the  
series of orders of merit4    ,i had    
really sketched out a list for this     
purpose1 including a great  number of   
glorious names from the annals of       
physics and regions just  beyond3 a     
table1 as it were1 from which one might 
set up a directory for  ,valhalla6 ,it  
seemed to me a pleasing thought to roam 

through this hall  of celebrities in    
company with ,einstein1 and to pause at 
the pedestal of  the busts of the great1
 who1 in spite of their number1 are     
still too  few1 far too few1 in         
comparison with the far too many who    
populate the  earth like so many        
factory-produced articles4 ,if we set to
 work to draw  up a list of this sort1  
we soon find that there is no end to    
these  heroes of ,valhalla1 and we are  
reminded of the hall of fame of the     
,northern ,saga1 of the mythological    
,valhalla1 whose ceiling was so high    
that the gable was invisible1 and whose 
extent was so great that anyone  wishing
 to enter could choose from five hundred
 and forty entrances4    ,in reality our
 little excursion was far from taking   
these dimensions1  the chief reason     
being probably that we had begun at     
,newton4 ,however  attractive it may be 
to hear ,einstein talk of ,newton1 a    
disadvantage  arises in that we find it 
hard to take leave of his bust situated 

at the  main portal1 and that we        
continually revert to it even when we   
call to  mind the remaining paths free  
for our choice and stretching out of    
sight4    ,reality1 even figuratively1  
offered a picture which differed        
considerably from the measures of       
greatness apportioned by legendary      
accounts4 ,in ,einstein's workroom1     
certainly1 a visitor encounters         
portraits1 not busts1 and it would be   
rash to speak of this little  collection
 of portraits as of a miniature museum4 
,no1 it is certainly  not that1 for its 
catalogue numbers only to three4 ,but   
here they act as  a trinity with a      
special significance under the gaze of  
,einstein1 who  looks up to them with   
reverence4 ,to him their contribution of
 thought is  immeasurable2 ,faraday1    
,maxwell with his rich coils of hair1   
and between  them1 ,newton with his     
flowing wig1 represented in an excellent
 ,english  engraving1 whose border      
consists of symbolic insignias          

encircling his  distinguished-looking   
countenance4         99     99     99   
99     99     99     99     99          
,according to ,schopenhauer1 the measure
 of reverence that one can feel is  a   
measure of one's own intrinsic value4   
,tell me how much respect you can  feel1
 and ,i shall tell you what is your     
worth4 ,it is certainly not  necessary  
to emphasize this quality specially in  
the case of ,einstein1  for there are   
other points of vantage from which we   
may form an estimate  of his excellence4
 ,nevertheless1 ,i make special mention 
of the  circumstance to give an         
indication of the difference between a  
revolutionary discoverer and            
revolutionary pioneers in other fields4 
,it  is particularly noticeable that    
inborn respect is seldom found in       
modernists of ,art4 ,the only means of  
propaganda known to them consists  in a 
passionate denunciation of what has been
 developed historically by  gradual and 
patient effort2 their retrospect        

consists of unmitigated  contempt2 they 
profess to be disciples only of what is 
most recent1  remaining confined within 
the narrow circle surrounding their own 
ego4  ,the horizon of the discoverer has
 a different radius4 ,he takes over     
responsibility for the future by never  
ceasing his offerings at the  altar of  
the ,past4 ,there is probably no        
discoverer who is devoid of this        
characteristic1 but ,i should like to   
emphasize that1 among all the           
scientists with whom ,i am acquainted1  
no one recognizes the merit of  others  
so warmly as ,einstein4 ,he becomes     
carried away with enthusiasm  when he   
talks of great men1 or of such as appear
 great to him4 ,his  ,valhalla is not1  
of course1 the same as that favoured by 
,encyclopdias1  and many a one whom we  
rank as a ,sirius among men is to be    
found lower  than the sixth order of    
magnitude in ,einstein's list4          
,nevertheless1 the  number of selection 
of constellations is no mean one1 and   

the reverence  that was originally      
inspired by reasoned thought has become 
infused in  his temperament and become a
 part of his emotional self4    ,one    
need only mention the name of           
,newton--and even this is scarcely      
necessary1 for ,newton seems always near
 at hand2 if ,i happen to start  with   
,descartes or ,pascal1 it does not take 
long before we arrive at  ,newton1   6  
,once we began with ,laplace2 and it    
seemed almost as if the ,trait de  la   
mchanique cleste was to become the      
subject of discussion4 ,but  ,einstein  
left his seat1 and1 taking up a position
 in front of his series  of portraits on
 the wall1 he meditatively passed his   
hand through his  hair1 and declared3   
,in my opinion the greatest creative    
geniuses are ,galilei and ,newton1  whom
 ,i regard in a certain sense as forming
 a unity4 ,and in this unity  ,newton is
 he who has achieved the most imposing  
feat in the realm of  science4 ,these   
two were the first to create a system of

 mechanics  founded on a few laws and   
giving a general theory of motions1 the 
totality of which represents the events 
of our world4    ,interrupting his      
remarks1 ,i asked3 ,can ,galilei's      
fundamental law of  inertia 7,newton's  
,first ,law of ,motion7 be said to be a 
law deduced from  experience8 ,my reason
 for asking is that the whole of natural
 science is  a science of experience1   
and not merely something based on       
speculation4  ,it might easily suggest  
itself to one that an elementary law    
like that  of ,galilei or ,newton could 
be derived from our everyday experience4
 ,but1  if this is the case1 how is it  
that science had to wait so long before 
this simple fact was discovered8        
,experience is as old as the hills2 why 
did the law of inertia not make its     
appearance at the very beginning1  when 
,nature was first subjected to inquiry8 
,by no means6 replied ,einstein4 ,the   
discovery of the law of  rectilinear    
motion of a body under no external      

influences is not at all  a result of   
experience4 ,on the contrary6 ,a circle1
 too1 is a simple line  of motion1 and  
has often been proclaimed as such by    
predecessors of  ,newton1 for example1  
by ,aristoteles4 ,it required the       
enormous power of  abstraction possessed
 only by a giant of reason to stabilize 
rectilinear  motion as the fundamental  
form4    ,to this may be added that     
before and even after the time of       
,galilei1 not  only the circle but also 
other non-rectilinear lines have been   
regarded  even by serious thinkers as   
the primary lines given by ,nature2     
these  thinkers even dared to apply     
their curvilinear views to explaining   
world  phenomena that could be made     
clear only after ,galilei's abstraction 
had  been accepted4    ,i asked whether 
the theory of gravitation was already   
implicitly  contained in ,galilei's     
,laws of ,falling ,bodies4 ,einstein's  
answer was in  the negative3 the        
gravitational theory falls entirely to  

the credit of  ,newton1 and the         
greatness of this intellectual          
achievement remains  unimpaired even if 
the efforts of certain forerunners are  
recognized4 ,he  mentioned ,robert      
,hooke1 whom1 among others1             
,schopenhauer sets up against  ,newton1 
with absolute injustice and from petty  
feelings of antipathy1  which takes its 
origin from ,schopenhauer's             
unmathematical type of mind4  ,the vast 
difference between ,hooke's preliminary 
attempts at explaining  gravitation1 and
 ,newton's monumental structure1 was    
beyond his power of  discernment4       
99,schopenhauer 7vol4 ,,ii4 of the      
,parerga7 uses two arguments to         
discredit ,newton4 ,firstly1 he refers  
to two original works1 both of  which he
 misinterprets2 secondly1 he undertakes 
a psychological analysis  of ,newton4   
,he uses psychological means1 which     
would be about equally  reasonable as   
applying the ,integral ,calculus to     
proving facts of ,ethical  ,psychology1 

and he arrives at the conclusion that   
priority in  discovering the law of     
gravitation is due to some one else2    
,hooke is  pictured as having been      
treated like ,columbus3 we now hear of  
,america1  and likewise ,newton's       
,gravitational ,system6    ,schopenhauer
 has1 however1 quite forgotten that he  
himself1 some pages  earlier1 trumpeted 
forth ,newton's imperishable fame with  
the words3 ,to  form an estimate of the 
great value of the gravitational system 
which  was at least completed and firmly
 established by ,newton1 we must remind 
ourselves how entirely nonplussed about 
the origin of the motion of  celestial  
bodies thinkers had previously been for 
thousands of years4  ,that bears the    
ring of truth4 ,newton's greatness can  
be grasped only if  thousands of years  
are used as a measure4    ,whereas      
,schopenhauer argued from grounds drawn 
from psychology and the  principle of   
universal knowledge1 his antagonist     
,hegel1 who was still  more vague in    

these fields1 sought to dispense with   
both ,newton and  ,kepler by calling to 
his aid the so-called pure intuition of 
the curved  line4 ,in an exposition of  
truly comical prolixity1 such as would  
have  delighted the hearts of           
scholiasts1 he proves that the ellipse  
must  represent the fundamental type of 
planetary motion1 this being quite      
independent of ,newton's laws1 ,kepler's
 observations1 and resulting            
mathematical relationships4 ,and ,hegel 
actually succeeds1 with a nebulous      
verbosity almost stultifying in its     
unmeaningness1 in paraphrasing          
,kepler's second law in his own fashion4
 ,it reads like an extract from  some   
carnival publication issued by          
scientists in a bibulous mood to  make  
fun of themselves4    ,but these        
extravagances1 too1 serve to add lustre 
to ,newton1 for his  genius shines out  
most brilliantly when it is a question  
of expressing  clearly1 and without     
assumptions1 a phenomenon of cosmic     

motion4 ,here  there are no forerunners1
 not even with regard to his own law of 
gravitation4 ,newton showed with truly  
triumphant logic that ,kepler's  second 
law belongs to those things that are    
really self-evident4    ,this law1 taken
 alone1 offers considerable difficulties
 to anyone who  learns of it for the    
first time4 ,every planet describes an  
ellipse2 that  is accepted without      
demur4 ,but the uninitiated will        
possibly or even  probably deduce from  
this that the planet will pass over     
equal lengths  of arc in equal times4   
,by no means1 says ,kepler2 the arcs    
traversed in  equal times are unequal4  
,but if we connect every point of the   
elliptic  path with a definite point    
within the curve 7the focus of the      
ellipse7  by means of straight lines1   
each of which is called a radius vector1
 we  get that the areas swept out by the
 radius vector in equal times 7and  not 
the arcs7 are equally great4    ,why is 
this so8 ,this cannot be understood a   

priori4 ,but one might  argue that since
 the attraction of the sun is the       
governing force1 this  will probably    
have something to do with ,newton's law 
of gravitation1 in  particular with the 
inverse square of the distance4 ,and one
 might  further infer that1 if a        
different principle of gravitation      
existed1  ,kepler's law would assume a  
new form4    ,a fact amazing in its     
simplicity here comes to light4 ,newton 
states the  proposition3 ,according to  
whatever law an accelerating force acts 
from  a centre on a body moving freely1 
the radius vector will always sweep  out
 equal areas in equal lengths of time4  
,nothing is assumed except the law of   
inertia and a little elementary         
mathematics1 namely1 the theorem that   
triangles on the same base and of  the  
same altitude are equal in area4 ,the   
form in which this theorem  occurs in   
,newton's simple drawing is certainly   
astonishing4 ,one feels  that there in a
 few strokes a cosmic problem is solved2

 the impression  is ineffaceable4       
,this theorem together with its proof is
 contained in ,newton's chief  work1    
,philosophi naturalis principia         
mathematica4 ,the interfusion of        
philosophy and mathematics furnished him
 with the natural principles of         
knowledge499    ,einstein made some     
illuminating remarks about ,newton's    
famous phrase3  ,hypotheses non fingo4  
,i had said that ,newton must have been 
aware that  it is impossible to build up
 a science entirely free from           
hypotheses4  ,even geometry itself has  
arrived at that critical stage at which 
,gauss  and ,riemann discovered its     
hypothetical foundations4    ,einstein  
replied3 ,accentuate the words correctly
 and the true sense  will reveal itself6
 ,it is the last word that is to be     
stressed and not  the first4 ,newton did
 not want to feel himself free from     
hypotheses1 but  rather from the        
assumption that he invented them1 except
 when this was  absolutely necessary4   

,newton1 then1 wished to express that he
 did not go  further back in his        
analysis of causes than was absolutely  
inevitable4    ,perhaps1 ,i allowed     
myself to interject1 a more violent     
suspicion against  the word hypotheses  
was prevalent with scholars in ,newton's
 time than  now4 ,newton's emphatic     
defence would then appear a shade more  
intelligible4 ,or did he cherish the    
belief that his world-law was the  only 
possible one in ,nature8    ,einstein   
again referred to the universality of   
,newton's genius1 saying  that ,newton  
was doubtless aware of the range within 
which his law was  valid3 this law      
applies to the realm of observation and 
experience1 but  is not given a priori1 
no more than ,galilei's ,law of         
,inertia4 ,it is  certainly conceivable 
that beyond the domain of human         
experience there  may be an             
undiscoverable universe in which a      
different fundamental law  holds1 and   
one which1 nevertheless1 does not       

contradict the principle of  sufficient 
reason4    ,the antithesis3             
,simplicity--,complexity1 led the       
conversation into a  short bypath2 it   
arose out of an example which ,i quoted 
and that ,i shall  repeat here even if  
it may seem irrelevant4    ,one might   
well expect that just as for attraction 
there must be a  general law for        
resistance or repulsion4 ,and if        
attraction occurs  according to the     
inverse square of the distance1 then it 
would be an  extremely interesting      
parallel if a similar law were to hold  
for  repulsion except that the          
proportionality were direct instead of  
inverse4 ,there have actually been      
physicists who have proclaimed a  direct
 square law of repulsion2 ,i have heard 
it in lectures myself4 ,the  action of a
 resisting medium1 as1 for example1 the 
resistance of the air  to the flight of 
a cannon-ball1 is stated to be          
proportional to the  square of the      
velocity of the projectile4    ,this    

theorem is wrong4 ,if it were correct1  
and verified by experiment1  we should  
have to regard it as being presumably   
the only possible and  directly evident 
form of the law of repulsion or         
resistance4 ,there  would1 at least1 be 
no logical reason for contradicting it4 
,but here we have a mixed relationship1 
as ,einstein calls it--that is1 we  are 
unable to express an exact connexion    
between the velocity of a body  in      
flight and the air resistance4    ,this 
fallacious assumption by no means       
proceeded from illogical  reasoning1 and
 it seemed to rest on a sound physical  
basis4 ,for1 so it  was argued1 if the  
velocity is doubled1 there is twice as  
much air to be  displaced1 so that the  
resistance will be four times as great4 
,but this  was contradicted outright by 
experimental evidence4 ,one cannot even 
call  it an approximate law1 except for 
very low speeds4 ,for greater speeds we 
find1 instead of a quadratic relation1 a
 cubical one1 or one of a more  complex 

nature4 ,photographs have demonstrated  
that the resistance  experienced by a   
projectile in flight is due to the      
excitation of a  powerful central wave1 
to the friction between the air and the 
surface  of the projectile1 and to      
eddies produced behind the              
projectile--that  is1 to various        
conjoined factors1 each of which follows
 a different law1  and such that the    
combined effect cannot be expressed by a
 simple  formula at all4 ,this          
phenomenon is thus very complicated and 
offers  almost insuperable difficulties 
to analysis4 ,a beautiful remark was    
once  made1 which characterizes such    
events in ,nature4    ,during a         
conversation with ,laplace1 ,fresnel    
said that ,nature does not  worry about 
analytical difficulties4 ,there is      
nothing simpler than  ,newton's ,law in 
spite of the complicated nature of      
planetary motions4  ,nature here        
despises our analytical difficulties1   
said ,fresnel2 she  applies simple      

means1 and then by combining them       
produces an almost  inextricable net of 
confusion4 ,simplicity lies concealed in
 this chaos1  and it is only for us to  
discover it6 ,but this simplicity when  
it is  discovered is not always found to
 be expressible in simple formulae1 not 
must it be forgotten that even the      
ultimate discoverable simplicity  points
 to certain hypothetical assumptions4   
,hypotheses non fingo6 ,this phrase of  
,newton's remains true1 if we  maintain 
,einstein's interpretation3 ,he did not 
wish to go further back  in his analysis
 of causes than was absolutely          
inevitable4 ,it interested  me to pursue
 this line of thought suggested by      
,einstein still further1  and ,i        
discovered that these words of ,newton  
had actually been falsely  accentuated  
and hence misinterpreted by many        
authorities on science4  ,even ,mill and
 the great scholar1 ,william ,whewell1  
succumbed to this  misunderstanding4    
,credit must be given to a more modern  

scholar1  ,professor ,vaihinger of      
,halle1 for being sufficiently keen of  
hearing to  detect the true             
accentuation2 and now that ,einstein has
 corroborated  fully this explanation1  
doubts as to the true sense of the words
 are no  longer to be feared4    ,the   
trend of our talk brought us to a       
discussion of the conception1 law  of   
nature4 ,einstein recalled ,mach's      
remarks1 and indicated that the  point  
was to determine how much we read out of
 ,nature2 and these  observations made  
at least one thing clear1 namely1 that  
every law  signifies some limitation2 in
 the case of human laws1 expressed in   
the  civil and penal code1 the          
limitation affects the will1 and        
possible  actions1 whereas natural laws 
signify the limitations which we1 taught
  by experience1 prescribe to our       
expectations4 ,nevertheless1 the        
conception remains elastic1 for the     
question will always intrude itself3    
,what does prescription mean8 ,who      

prescribes8 ,kant has assigned to ,man  
the foremost position inasmuch as it is 
he who is regarded by ,kant as          
prescribing laws to ,nature4 ,bacon of  
,verulam emphasizes the ambiguous  point
 of view by asserting3 ,natura non      
vincitur nisi parendo1 ,man  conquers   
,nature only by obeying her1 that is1 by
 conforming to her  immanent norms4     
,thus the laws exist without us1 and we 
have only to  discover them4 ,when they 
have been found1 ,man can react by      
applying them  to subdue ,nature4 ,man  
becomes the dictator and dictates to    
,nature the  laws according to which she
 for her part has to subjugate mankind4 
,whether we adopt the one view or the   
other1 there is a vicious circle1  from 
which there is no escape4 ,a law is a   
creation of intellect1 and  ,mephisto's 
words remain true3 ,in the end we depend
 on the creatures of  our own making6   
,in ,newton's soul obedience and the    
wish to obey must have been  pre-eminent
 traits4 ,is he not reputed to have been

 pious and strong of  faith8            
,einstein confirmed this1 and1 raising  
his voice1 he generalized from it1      
saying3 ,in every true searcher of      
,nature there is a kind of religious    
reverence2 for he finds it impossible to
 imagine that he is the first to  have  
thought out the exceedingly delicate    
threads that connect his  perceptions4  
,the aspect of knowledge which has not  
yet been laid bare  gives the           
investigator a feeling akin to that     
experienced by a child who  seeks to    
grasp the masterly way in which elders  
manipulate things4    ,this explanation 
implied a personal confession4 ,for he  
had spoken of the  childlike longing    
felt by all1 and had interpreted the    
subtle  intricacies of the scientist's  
ideas in particular as springing from a 
religious source4 ,not all have         
confessed this2 we know1 indeed1 that   
the  convictions of many a one were not 
so4 ,let us cling to the fact that the  
greatest in the realm of                

science--,newton1 ,descartes1 ,gauss1   
and  ,helmholtz--were pious1 although   
their faith varied in degree4 ,and let  
us  not forget that the most bitter     
opponent of this attitude of mind1 the  
originator of ,ecrasez l'infame1 finally
 had a temple built bearing the         
inscription3 ,deo erexit ,voltaire4     
,in ,newton positivism found its most   
faithful disciple1 and his research  was
 directly affected by his religious     
attitude4 ,he1 himself1 was the  author 
of that beautiful thought3 ,a limited   
measure of knowledge takes  us away from
 ,god2 an increased measure of knowledge
 takes us back to  ,him4 ,it was he who 
considered that the world-machine that  
he had  disclosed was not sufficiently  
stabilized by his mathematical law1 and 
so he enlisted the intermittent help of 
an assistant for the ,creator1          
,concursus ,dei1 to attend to the       
functioning of the machine4 ,finally1 he
  slipped from the path of nave faith on
 to theological bypaths and  wrote      

devout essays on apocalyptic matters4   
,on the other hand1  ,descartes' piety1 
which was genuine at root1 exhibited    
suspicious  offshoots1 and one cannot   
shake off the feeling that he was       
smiling up  his sleeve when he was      
making some of his solemn declarations4 
,he was a  master of compromise1 and    
gave due expression to its spirit1 which
 ,f4 ,a4  ,lange bluntly stated was     
merely a veil for ,cowardice towards the
  ,church4 ,voltaire1 an apostle of     
,newton's system of natural philosophy1 
went so far in his condemnation of      
,descartes' confession of faith that  he
 affirmed3 ,the ,cartesian doctrine has 
been mainly instrumental in  persuading 
many not to recognize a ,god4    ,as    
,einstein had called special attention  
to the childlike nature of the          
scientist's root-impulse1 ,i quoted a   
remark of ,newton that seemed to me  at 
the moment to be a confirmation of      
,einstein's attitude3    ,i do not know 
what ,i may appear to the world1 but to 

myself ,i seem to  have been only like a
 boy playing on the seashore1 and       
diverting myself  in now and then       
finding a smoother pebble or a prettier 
shell than  ordinary1 whilst the great  
ocean of truth lay all undiscovered     
before  me4    ,are we not to regard    
this analogy of ,newton's as being      
intended to  convey a religious meaning8
    ,there is no objection to this1 said
 ,einstein1 although it seems to me     
more probable that1 in saying this1     
,newton set down the view only of the   
pure investigator4 ,the essential       
purpose of his remarks was to express   
how small is the range of the attainable
 compared with the infinite  expanse    
offered for research4    ,through some  
unexpected phrase that was dropped1 the 
conversation took a  new turn at this   
point1 which ,i should not like to      
withhold1 inasmuch as  it gave rise to a
 noteworthy observation of ,einstein    
about the nature of  genius4 ,we were   
talking about the possibility of genius 

for science  being inherited and about  
the comparative rareness with which it  
occurs4 ,there seems to have been only  
one case of a real dynasty of  great    
minds1 that of the ten ,bernoullis who  
were descended of a line of             
mathematicians1 and all of them achieved
 important results1 some of them  making
 extraordinary discoveries4 ,why is this
 exception unique8 ,in other  examples  
we do not get beyond three or four names
 in the same family1  even if we take   
,science and ,art conjointly4 ,there    
were two ,plinys1 two  ,galileis1 two   
,herschels1 two ,humboldts1 two ,lippis1
 two ,dumas1 several  ,bachs1 ,pisanos1 
,robbias1 and ,holbeins--the net result 
is very poor1 even  if we count similar 
names1 disregarding the fact of         
relationship2 there  is no recognizable 
dynasty except in the case of the ten   
,bernoullis4#b  ,and so1 ,i continued1  
the conclusion seems justified that     
,nature has  nothing to do with a       
genealogy of talents1 and that1 if we   

happen to  notice manifestations of     
talent in one and the same family1 this 
is a  mere play of chance4    ,footnote 
#b3 ,the ,roman family ,cosmati 7of the 
thirteenth century71 which  gave us     
seven splendid representatives of       
architecture and mosaic work1  hardly   
comes into consideration1 since not one 
of them is regarded in  the history of  
art as a real genius4    ,einstein1     
however1 contradicted this emphatically3
 ,inherited talent  certainly occurs in 
many cases1 where we do not observe it1 
for genius  in itself and the           
possibility of genius being apprehended 
are certainly  far from always appearing
 in conjunction4 ,there are only        
insignificant  differences between the  
genius that expresses itself in         
remarkable  achievements and the genius 
that is latent4 ,at a certain instant1  
perhaps1 only some impulse was wanting  
for the latent genius to burst  forth   
with all clearness and brilliance2 or1  
perhaps1 it required only  an unusual   

situation in the development of science 
to call into action  his special        
talents1 and thus it remained dormant1  
whereas a very slight  change of        
circumstances would have caused them to 
assert themselves in  definite results4 
,in passing ,i should like to remark    
that you just now mentioned the two     
,humboldts2 it seems to me that         
,alexander von ,humboldt1 at least1 is  
not  to be counted as a genius4 ,it has 
struck me repeatedly that you           
pronounced his name with particular     
reverence----    ,and ,i have observed  
equally often1 ,professor1 that you made
 a sign of  disapproval4 ,for this      
reason slight doubts have gradually been
 rising in  me4 ,but it is difficult to 
get free from the orders of greatness   
that  one has recognized for decades4   
,in my youth people spoke of 'a         
,humboldt'  just as we speak of 'a      
,csar' or 'a ,michelangelo1' to denote  
some  pinnacle of unrivalled height4 ,to
 me at that time ,humboldt's ,kosmos was

  the ,bible of ,natural ,science1 and  
probably such memories have a certain   
after-effect4    ,that is easy to       
understand1 said ,einstein4 ,but we must
 make it clear  to ourselves that for us
 of the present day ,humboldt scarcely  
comes into  consideration when we direct
 our gaze on to the great seers4 ,or1   
let us  say more clearly1 he does not   
belong to this category4 ,i certainly   
grant  him his immense knowledge and his
 admirable faculty of getting into      
touch with the unity of ,nature1 which  
reminds us of ,goethe4    ,yes2 this    
feeling for the uniformity of the cosmos
 had probably  persuaded me in his      
favour1 ,i answered1 and ,i am glad that
 you draw a  parallel with ,goethe in   
this respect4 ,it reminds me of ,heine's
 story3 ,if  ,god had created the whole 
world1 except the trees and the birds1  
and had  said to ,goethe3 ',my dear     
,goethe1 ,i leave it to you to complete 
this  work1' ,goethe would have solved  
the problem correctly and in a god-like 

manner--that is1 he would have painted  
the trees green and given the  birds    
feathers4    ,humboldt could equally    
well have been entrusted with this task4
 ,but  various objections may be raised 
against such reflections of a playful   
poetic character 444 one objection being
 that ,goethe's own knowledge of        
ornithology was exceedingly limited4    
,even when nearly eighty he could  not  
distinguish a lark from a yellow-hammer 
or a sparrow6 ,is that a  fact8         
,fully confirmed3 ,eckermann gives a    
detailed report of it in a  conversation
 which took place in #ahbg4 ,as ,i      
happened to come across the  passage    
only yesterday1 ,i can quote the exact  
words if you will allow  me3 ',great and
 good man1' thought ,eckermann1 'who    
hast explored ,nature  as few have ever 
done1 in ornithology thou seemest still 
a child6'    ,for a speculative         
philosopher1 it may here be interposed1 
this might  well serve as the           
starting-point of an attractive         

investigation4 ,goethe1  on the one     
hand1 cannot recognize a lark1 but would
 have been able to  grasp the ,platonic 
idea of the feathered species1 even if  
there had been  no such things as birds3
 ,humboldt1 on the other hand1 would    
perhaps have  been able to create the   
revolving planets1 if ,heaven had       
commanded it2  but he would never have  
succeeded in becoming the author of what
 we call  an astronomical achievement1  
such as that of ,copernicus or of       
,kepler4    ,and with reference to      
certain other men ,i elicited from      
,einstein  utterances that reduced      
somewhat my estimate of their           
importance4    ,we were speaking of     
,leonardo da ,vinci1 omitting all       
reference to his  significance in the   
world of ,art--that is1 only of         
,leonardo the ,scholar  and the         
,searcher4 ,einstein is far from        
disputing his place in the  ,valhalla of
 great minds1 but it was clear that he  
wished to recommend a  re-numbering of  

my list1 so that the ,italian master    
would not occupy a  position in just the
 first rank4    ,the problem of         
,leonardo excited great interest in me1 
and it deserves  the consideration of   
every one4 ,the further the examination 
of his  writings advances1 the more does
 this problem resolve itself into the   
question3 ,how much altogether does     
modern science owe to ,leonardo8        
,nowadays it is declared in all         
earnestness that he was a painter and a 
sculptor only by the way1 that his chief
 profession was that of an  engineer1   
and that he was the greatest engineer of
 all times4 ,this has  in turn given    
rise to the opinion that1 as a          
scientist1 he is the light  of all ages1
 and in the abundance of his discoveries
 he has never been  surpassed before or 
after his own time4    ,as this question
 had arisen once before1 ,i had come    
equipped with a  little table of facts1 
hastily drawn from special works to     
which ,i had  access4 ,according to my  

scheme1 ,leonardo was the true          
discoverer and  author of the following 
things3        ,law of ,conservation of 
,momentum4        ,law of ,virtual      
,velocities 7before ,ubaldi and         
,galilei74        ,wave ,theory 7before 
,newton74        ,discovery of the      
,circulation of the ,blood 7before      
,harvey74        ,laws of ,friction     
7before ,coulomb74        ,law of       
,pressure for connected ,tubes          
containing          ,fluid 7before      
,pascal74        ,action of ,pressure on
 ,fluids 7before ,stevin and ,galilei74 
,laws of ,falling ,bodies 7before       
,galilei74        ,true interpretation  
of the twinkling of stars 7before       
,kepler1 who1 moreover1 did not succeed 
in finding          the real            
explanation74        ,explanation of the
 reflected light of the moon 7before    
,kepler74        ,principle of ,least   
,action 7before ,galilei74              
,introduction of the plus and the minus 
signs into          calculations4       

,definition of kinetic energy from mass 
and velocity4        ,theory of         
,combustion 7before ,bacon74            
,explanation of the motion of the sea   
7before ,maury74        ,explanation of 
the ascent of fluids in plants 7before  
,hales74        ,theory of              
,fossilization 7before ,palissy74       
,added to these there are a great number
 of inventions1 in particular  those    
connected with problems of aviation1    
such as the parachute 7before           
,lenormand71 and so forth4    ,this fist
 aroused great distrust in ,einstein3 he
 regarded it as the  outcome of an      
inquisitive search for sources1         
excusable historically1  but leading to 
misrepresentation4 ,we are falsely led  
to regard slightly  related beginnings1 
vague tracks1 hazy indications1 which   
are found1 as  evidences of a real      
insight1 which disposes us to elevate   
one above all  others4 ,hence a         
mythological process results1 comparable
 to that which1  in former times1 thrust

 all conceivable feats of strength on to
 one  ,hercules4    ,i learned that     
recently a strong reaction has asserted 
itself in  scientific circles against   
this one-sided hero-worship2 its purpose
 is  to reduce ,leonardo's merits to    
their proper measure4 ,einstein made it 
quite clear that he was certainly not to
 be found on the side of the            
ultra-,leonardists4    ,it cannot be    
denied that the latter have valuable    
arguments to support  their case1 and   
that these arguments become multiplied  
in proportion as  the publication of    
,leonardo's writings 7in the ,codex     
,atlanticus1  etc471 which are so       
difficult to decipher1 proceeds4 ,the   
partisans of  ,leonardo derive          
considerable support in many points from
 recognized  authorities1 as in the case
 of ,cantor1 the author of the          
monumental  history of mathematics4 ,we 
there read3 ,the greatest ,italian      
painter of  the fifteenth century was   
not less great as a scientist4 ,in the  

history  of science his name is famous  
and his achievements are extolled1      
particularly those which give him a     
claim to be regarded as one of the      
founders of ,optics4 ,he is placed on a 
level with ,regiomantus as one of  the  
chief builders of mathematics of that   
time4 ,nevertheless1 ,cantor  raises    
certain doubts by remarking that the    
results of investigations  made up to   
the present do not prove ,leonardo to be
 a great  mathematician4 ,on another    
page he is proclaimed simultaneously    
with  ,archimedes and ,pappus as a      
pioneer of the doctrines of the centre  
of  gravity4    ,with regard to the main
 points1 ,leonardo's priority in the    
case of the  ,laws of ,falling ,bodies1 
the ,theory of ,wave-motion1 and the    
other  fundamental principles of        
physics1 ,einstein has the conviction   
that the  partisans of ,leonardo are    
either mistaken in the facts or that    
they  overlook forerunners4 ,in the case
 of these principles1 above all1 there  

is always some predecessor1 and it is   
almost impossible to trace the  line of 
discoveries back to the first source4   
,just as writers have  wished to deprive
 ,galilei1 ,kepler1 and ,newton of their
 laurels in favour  of ,leonardo1 so the
 same might be done with ,copernicus4   
,this has actually been attempted4 ,the 
real ,copernicus1 so one reads1 was     
,hipparchus of ,nica1 and if we go back 
still further1 a hundred years  earlier1
 two thousand years ago1 we find that   
,aristarchus of ,samos  taught that the 
world rotated about its own axis and    
revolved round the  sun4    ,and we need
 not even stop there1 in ,einstein's    
opinion4 ,for it is open  to conjecture 
that ,aristarchus in his turn has drawn 
on ,egyptian  sources4 ,this            
retrogressive investigation may excite  
the interest of  archologists1 and in   
particular cases perhaps lead to the    
discovery of  a primary claim to        
authorship1 but it cannot fail to excite
 suspicion  against the conscious       

intention of conferring all the honours 
of science  on an individual discoverer4
 ,leonardo's superlative constructive   
genius  is not attacked in these        
remarks1 and there seems no reason for  
objecting if anyone wishes to call him  
the most ingenious engineer of  all     
times4    ,all the pressures and        
tensions occurring in ,nature seemed to 
be repeated  in him as inner virtues1 an
 expression borrowed from ,helmholtz1   
who  used it with reference to himself4 
,this analogy might be extended by      
saying that1 in the works of both1 ,man 
himself with his organic  functions and 
requirements plays an important rle4    
,for them the  abstract was a means of  
arriving at what was perceptual1        
physiologically  useful1 and stimulating
 in its effect on life4 ,leonardo       
started out from  ,art1 and throughout  
the realm of mechanics and machines he  
remained an  artist in method4          
,helmholtz set out from the medical side
 of physiology  and transferred the     

valuations of beauty derived from the   
senses to his  pictures of mechanical   
relationships4 ,the life-work of each   
has an  sthetic colouring1 ,leonardo's  
being of a gloomy hue1 that of          
,helmholtz  exhibiting brighter and     
happier tints4 ,common to both is an    
almost  inconceivable versatility and an
 inexhaustible productivity4            
,whenever ,einstein talks of ,helmholtz 
he begins in warm terms of              
appreciation1 which tend to become      
cooler in the course of the             
conversation4 ,i cannot quote his exact 
words1 and as ,i cannot thus give  a    
complete account for which full         
responsibility may be taken1 it may be  
allowable to offer a few important      
fragments that ,i have gathered4        
,judged by the average of his           
accomplishments1 ,helmholtz is regarded 
by  ,einstein as an imposing figure     
whose fame in later times is assured2   
,helmholtz himself tasted of this       
immortality while still alive4 ,but when

  efforts are made to rank him with     
great thinkers of the calibre of        
,newton1 ,einstein considers that this  
estimate cannot be fully borne out4  ,in
 spite of all the excellence1 subtlety1 
and effectiveness of  ,helmholtz's      
astoundingly varied inspirations1       
,einstein seems to fail to  discover in 
him the source of a really great        
intellectual achievement4    ,at a      
,science ,congress held in ,paris in    
#ahfg1 at which ,helmholtz was  present1
 a colleague of his was greeted with    
unanimous applause when he  toasted him 
with the words3 ,l'ophthalmologie tait  
dans les  tnbres1--,dieu parla1 que     
,helmholtz naqut--,et la lumire tait    
faite6 ,it was an almost exact          
paraphrase of the homage which ,pope    
once  addressed to ,newton4 ,at that    
time the words of the toast were        
re-echoed  throughout the world2        
ophthalmology was enlarged to science   
generally1  and the apotheosis was      
applied universally4 ,du ,bois-,reymond 

declared  that no other nation had in   
its scientific literature a book that   
could  be compared with ,helmholtz's    
works on ,physiological ,optics and on  
,sensations of ,tone4 ,helmholtz was    
regarded as a god1 and there are not a  
few to whom he still appears crowned    
with this divine halo4    ,a shrill     
voice pierced the serene atmosphere1    
attacking one of his main  achievements4
 ,the dissentient was ,eugen ,dhring1 to
 whose essay on the  ,principles of     
,mechanics a coveted prize was awarded1 
a fact which seemed  to stamp him as    
being specially authorized to be a judge
 of pre-eminent  achievements in this   
sphere4 ,dhring's aim was to dislodge   
one of the  fundamental supports of     
,helmholtz's reputation by attacking his
 ,law of  the ,conservation of ,energy4 
,if this assault proved successful1 the 
god  would lie shattered at his own     
pedestal4    ,dhring1 indeed1 used every
 means to bespatter his fair name in    
science2 and it is hardly necessary to  

remark that ,einstein abhors this  kind 
of polemic4 ,what is more1 he regards it
 as a pathological symptom1  and has    
only a smile of disdain for many of     
,dhring's pithy sayings4 ,he  regards   
them as documents of unconscious humour 
to be preserved in the  archives of     
science as warnings against future      
repetitions of such  methods4    ,dhring
 belonged also to those who wished to   
exalt one above all  others4 ,he raised 
an altar to ,robert ,mayer1 and offered 
up sanguinary  sacrifices4 ,accustomed  
to doing his work thoroughly1 he did not
 stop at  ,helmholtz in choosing his    
victims4 ,no hecatomb seemed to him too 
great  to do honour to the discoverer of
 the ,mechanical ,equivalent of ,heat1  
and  so his next prey was ,gauss and    
,riemann4    ,gauss and ,riemann6 ,each 
was a giant in ,einstein's opinion4 ,he 
knew well  that this raging ,ajax had   
also made an assault against them1 but  
he had  no longer a clear recollection  
of the detailed circumstances2 as the   

references were near at hand1 he allowed
 me to repeat a few lines of  this      
tragi-comedy4    ,helmholtz1 according  
to ,dhring 7who also calls him          
,helmklotz71 has  done no more than     
distort ,mayer's fundamental mechanical 
idea1 and  interpret it falsely4 ,by    
philosophizing over it1 he has          
completely  spoilt it1 and rendered it  
absurd4 ,it was the greatest of all     
humiliations practised on ,mayer that   
his name had been coupled with that  of 
one whom he had easily out-distanced1   
and whose clumsy attempts at  being a   
physicist were even worse than those by 
which he sought to  establish himself as
 a philosopher4    ,the offences of     
,gauss and ,riemann against ,mayer are  
shrouded in  darkness4 ,but there was   
another would-be scientist1 ,justus von 
,liebig1  who1 being opposed to ,mayer1 
aroused the suspicions of ,dhring1      
particularly as he had used his         
brazen-tongue to defend the two         
renowned mathematicians4 ,after he1 and 

,clausius too1 had been brought to      
earth1 ,dhring launched out against the 
giants of ,gttingen4 ,in the  chapter on
 ,gauss and ,gauss-worship1 we read3    
,his megalomania rendered  it impossible
 for him to take exception to any tricks
 that the deficient  parts of his own   
brain played on him1 particularly in the
 realm of  geometry4 ,thus he arrived at
 a pretentiously mystical denial of     
,euclid's  axioms and theorems1 and     
proceeded to set up the foundations of  
an  apocalyptic geometry not only of    
nonsense but of absolute stupidity4444  
,they are abortive products of the      
deranged mind of a mathematical         
professor1 whose mania for greatness    
proclaims them as new and  superhuman   
truths6444 ,the mathematical delusions  
and deranged ideas in  question are the 
fruits of a veritable paranoia          
geometrica4    ,after ,herostratus had  
burnt to ashes the consecrated temple1  
the ,ionian  cities issued a            
proclamation that his name was to be    

condemned to  perpetual oblivion6 ,the  
iconoclast ,dhring is immortalized1 for1
 apart  from the charge of arson1 he is 
notable in himself4 ,in his case we     
found  ourselves confronted with        
unfathomable problems of a scholar's    
complex  nature1 problems which even a  
searcher like ,einstein failed to solve4
  ,the simplest solution would be to    
turn the tables and to apply the term   
paranoia as a criticism to the book on  
,robert ,mayer1 and thus demolish  it4  
,but this will not do1 for if we merely 
pass over the pages of  distorted       
thought1 we are still left with a       
considerable quantity of  valuable      
material4    ,does ,dhring1 after all1  
himself deserve a place in our          
,valhalla8 ,the  question seems         
monstrous1 and yet cannot be directly   
answered in the  negative4 ,the         
individual is to be judged according to 
his greatest  achievement1 and not      
according to his aberrations4 ,the works
 of  ,aristotle teem with nonsensical   

utterances1 and ,leonardo's ,bestiarius 
is an orgy of abstruse concoctions4 ,if 
,dhring had written nothing  beyond his 
studies of personalities ranging from   
,archimedes to ,lagrange1  the portals  
would yet have been open to him4 ,even  
in his eulogy of  ,robert ,mayer1 which 
is besmirched with unseemly remarks1 he 
displays at  least the courage of his   
convictions4    ,the attempt at a       
comparison between ,robert ,mayer and   
,helmholtz is doomed  to failure even   
when considered dispassionately1        
inasmuch as the  disturbing factor of   
priority here intrudes itself4 ,the     
definite fixing  of the ,law of ,energy 
is certainly to the credit of           
,helmholtz1 but  perhaps he would have  
gained by laying more stress on the     
discovery of  it five years earlier by  
the doctor in ,heilbronn4 ,and again1   
this would  not have been final1 for the
 invariance of the sum of energy during 
mechanical actions was known even by    
,huyghens4 ,the ,heilbronn doctor       

performed one act of genius in his life1
 whereas ,helmholtz during his  whole   
life moved asymptotically to the fine of
 genius without ever  reaching it4 ,if  
my interpretation of ,einstein's opinion
 is correct1  ,helmholtz is to be       
credited with having the splendour of an
 overpowering  gift for research        
predominant in his nature1 but is not   
necessarily to  be given a seat among   
the most illustrious of his branch of   
science4  ,einstein wishes to preserve a
 certain line of demarcation between    
this  type and not only the ,titans of  
the past1 but also those of the present4
  ,when he speaks of the latter1 his    
tone becomes warmer4 ,he does not need  
circuitous expressions1 each syllable   
rings with praise4 ,he has in mind1     
above all1 ,hendrik ,antoon ,lorentz in 
,leyden1 ,max ,planck1 and ,niels ,bohr2
  we then see that he feels ,valhalla   
about him4         99     99     99     
99     99     99     99     99    ,the  
reason that ,i have tried to maintain   

the metaphor of a ,temple of  ,fame is  
due to an echo of ,einstein's own words 
at a celebration held in  honour of the 
sixtieth birthday of the physicist      
,planck in the ,may of  #aiah4 ,this    
speech created the impression of a happy
 harmony resulting  from a fusion of two
 melodies1 one springing from the       
intellect1 the  other rising from the   
heart4 ,we were standing as at the      
,propylons with a  new ,heraclitus      
uttering the cry3 ,introite1 nam et hic 
dii sunt6    ,i should like to give the 
gist of this beautiful address in an    
extract  uninterrupted by commentaries4 
,the ,temple of ,science--so ,einstein  
began--is a complex structure of  many  
parts4 ,not only are the inmates diverse
 in nature1 but so also are  the inner  
forces that they have introduced into   
the temple4 ,many a one  among them is  
engaged in ,science with a happy feeling
 of a superior  mind1 and finds ,science
 the sport which is congenial to him1   
and which  is to give him an outlet for 

his strong life-forces1 and to bring him
  the realization of his ambitions4     
,there are1 indeed1 many1 too1 who      
offer up their sacrifice of brain-matter
 only in the cause of useful            
achievements4 ,if now an angel of heaven
 were to come and expel all from  the   
temple who belonged to these two        
categories1 a considerable  reduction   
would result1 but there would still     
remain within the temple  men of present
 and former times3 among these we count 
our ,planck1 and  that is why he has our
 warm affection4    ,i know full well   
that1 in doing this1 we have            
light-heartedly caused  many to be      
driven out who contributed much to the  
building of the  temple2 in many cases  
our angel would find a decision         
difficult4444 ,but  let us fix our gaze 
on those who find full favour with him6 
,most of them  are peculiar1 reserved1  
and lonely men1 who1 in spite of what   
they have  in common1 are really less   
alike than those who have been expelled4

 ,what  led them into the temple8444 ,in
 the first place1 ,i agree with         
,schopenhauer that one of the most      
powerful motives that attract people  to
 ,science and ,art is the longing to    
escape from everyday life with its      
painful coarseness and unconsoling      
barrenness1 and to break the fetters  of
 their own ever-changing desires4 ,it   
drives those of keener  sensibility out 
of their personal existence into the    
world of objective  perception and      
understanding4 ,this motive force is    
similar to the  longing which makes the 
city-dweller leave his noisy1 confused  
surroundings and draws him with         
irresistible force to restful ,alpine   
heights1 where his gaze covers the wide 
expanse lying peacefully before  him on 
all sides1 and softly passes over the   
motionless outlines that  seem created  
for all eternity4 ,associated with this 
negative motive is a  positive one1 by  
virtue of which ,man seeks to form a    
simplified  synoptical view of the world

 in a manner conformable to his own     
nature1  in order to overcome the world 
of experience by replacing it1 to a     
certain degree1 by this picture4 ,this  
is what the painter does1 as also  the  
poet1 the speculative philosopher1 and  
the research scientist1 each  in his own
 way4 ,he transfers the centre of his   
emotional existence into  this picture1 
in order to find a sure haven of peace1 
one such as is not  offered in the      
narrow limits of turbulent personal     
experience4    ,what position does the  
world-picture of the theoretical        
physicist  occupy among all those that  
are possible8 ,he demands the greatest  
rigour  and accuracy in his             
representation1 such as can be gained   
only by using  the language of          
mathematics4 ,but for this very reason  
the physicist has  to be more modest    
than others in his choice of material1  
and must  confine himself to the        
simplest events of the empirical world1 
since all  the more complex events      

cannot be traced by the human mind with 
that  refined exactness and logical     
sequence which the physicist demands4444
  ,is the result of such a restricted   
effort worthy of the proud name         
'world-picture'8    ,i believe this     
distinction is well deserved1 for the   
most general laws  on which the system  
of ideas set up by theoretical physics  
is founded  claim to be valid for every 
kind of natural phenomenon4 ,from them  
it  should be possible by means of pure 
deduction to find the picture1 that  is1
 the theory1 of every natural process1  
including those of living  organism1    
provided that this process of deduction 
does not exceed the  powers of human    
thought4 ,thus there is no fundamental  
reason why the  physical picture of the 
world should fall short of              
perfection4444    ,evolution has shown  
that among all conceivable theoretical  
constructions there is at each period   
one which shows itself to be  superior  
to all others1 and that the world of    

perception determines in  practice the  
theoretical system1 although there is no
 logical road from  perception to the   
axioms of the theory1 but rather that we
 are led  towards the latter by our     
intuition1 which establishes contact    
with  experience4444    ,the longing to 
discover the pre-established harmony    
recognized by  ,leibniz is the source of
 the inexhaustible patience with which  
we see  ,planck devoting himself to the 
general problems of our science1        
refusing  to allow himself to be        
distracted by more grateful and more    
easily  attainable objects4444 ,the     
emotional condition which fits him for  
his  task is akin to that of a devotee  
or a lover2 his daily striving is not   
the result of a definite purpose or a   
programme of action1 but of a  direct   
need4444 ,may his love for ,science     
grace his future course of  life1 and   
lead him to a solution of that          
all-important problem of the  day which 
he himself propounded1 and to an        

understanding of which he has           
contributed so much6 ,may he succeed in 
combining the ,quantum ,theory with     
,electrodynamics and ,mechanics in a    
logically complete system6         99   
99     99     99     99     99     99   
99    ,what grips me most in your       
address1 ,i said1 is that it            
simultaneously  surveys the whole       
horizon of science in every direction1  
and traces back  the longing for        
knowledge to its root in emotion4 ,when 
your speech was  concluded1 ,i regretted
 only one thing--that it had ended so   
soon4  ,fortunate is he who may study   
the text4    ,do you attach any         
importance to it8 asked ,einstein2 then 
accept this  manuscript4 ,it is due to  
this act of generosity that ,i have been
 able  to adorn the foregoing           
description of the excursion into       
,valhalla with  such a valuable         
supplement4         99     99     99    
99     99     99     99     99    ,the  
conversation had begun with the         

brilliant constellation                 
,galilei-,newton1 and near the end      
inclined again towards the              
consideration of a double-star3 the     
names of ,faraday and ,maxwell          
presented themselves4    ,both pairs1   
,einstein declared1 are of the same     
magnitude4 ,i regard  them as           
fundamentally equal in their services in
 the onward march of  knowledge4        
,should we not have to add ,heinrich    
,hertz as a third in this bond8 ,this   
assistant of ,helmholtz is surely       
regarded as one of the founders of the  
,electromagnetic ,theory of ,light1 and 
we often hear their names coupled1  as  
in the case of the ,maxwell-,hertz      
equations4    ,doubtless1 replied       
,einstein1 ,hertz1 who is often         
mentioned together  with ,maxwell1 has  
an important rank and must be placed    
very high in the  world of experimental 
physics1 yet1 as regards the influence  
of his  scientific personality1 he      
cannot be classed with the others we    

have  named4 ,let us1 then1 confine     
ourselves to the twin geniuses ,faraday 
and  ,maxwell1 whose intellectual       
achievement may be summarized in a few  
words4 ,classical mechanics referred all
 phenomena1 electrical as well as       
mechanical1 to the direct action of     
particles on one another1  irrespective 
of their distances from one another4    
,the simplest law of  this kind is      
,newton's expression3 ',attraction      
equals ,mass times ,mass  divided by the
 square of the distance4' ,in           
contradistinction to this1  ,faraday and
 ,maxwell have introduced an entirely   
new kind of physical  realities1 namely1
 fields of force4 ,the introduction of  
these new  realities gives us the       
enormous advantage that1 in the first   
place1 the  conception of action at a   
distance1 which is contrary to our      
everyday  experience1 is made           
unnecessary1 inasmuch as the fields are 
superimposed  in space from point to    
point without a break2 in the second    

place1 the  laws for the field1         
especially in the case of electricity1  
assume a much  simpler form than if no  
field be assumed1 and only masses and   
motions be  regarded as realities4      
,he enlarged still further on the       
subject of fields1 and while he was     
describing the technical details1 ,i saw
 him metaphorically enveloped in  a     
magnetic field of force4 ,here1 too1 an 
influence1 transmitted through  space   
from point to point1 made itself felt1  
and there could be no  question of      
action at a distance inasmuch as the    
effective source was  so near at hand4  
,his gaze1 as if drawn magnetically1    
passed along the  wall of the room and  
fixed affectionately on ,maxwell and    
,faraday4          ,,chapter ,,iv       
,,education    ,school ,curricula and   
,reform of ,teaching4--,value of        
,language ,study4--,economy  of         
,time4--,practice in ,manual            
,work4--,picturesque                    
,illustrations4--,art  of               

,lecturing4--,selection of ,talents by  
,means of ,examinations4--,women        
,students4--,social                     
,difficulties4--,necessity as           
,instructress4      ,,our conversation  
turned towards a series of pdagogic     
questions1 in  which ,einstein is deeply
 interested4 ,for he himself is actively
 engaged  in teaching1 and never        
disguises the pleasure which he derives 
from  imparting instruction4 ,without   
doubt he has a gift of making his spoken
  words react on wide circles anxious to
 be instructed1 composed not only  of   
,university students1 but of many others
 quite outside this category4  ,when1   
recently1 popular lectures on a large   
scale were instituted1 he  was one of   
the first to offer his services in this 
sound undertaking4 ,he  lectured to     
people of the working class1 who could  
not be assumed to  have any preliminary 
information on the subject1 and he      
succeeded in  presenting his lectures so
 that even the less trained minds could 

easily  follow his argument4    ,his    
attitude towards general questions of   
school education is1 of  course1        
conditioned by his own personality and  
his own work in the past4  ,his first   
care is that a young person should get  
an insight into the  relationship       
underlying natural phenomena1 that is1  
that the curricula  should be mapped out
 so that a knowledge of facts is the    
predominating  aim4    ,my wish1        
,einstein declared to me1 is far removed
 from the desire to  eliminate          
altogether the fundamental features of  
the old grammar  schools1 with their    
preference for ,latin1 by making        
over-hasty reforms1  but ,i am just as  
little inclined to wax enthusiastic     
about the so-called  humanistic schools4
 ,certain recollections of my own school
 life suffice  to prevent this1 and     
still more1 a certain presentiment of   
the  educational problems of the        
future4--,to speak quite candidly1 he   
said1 in my opinion the educative value 

of languages is1 in general1  much      
over-estimated4    ,i took the liberty  
of quoting a saying that is still       
regarded as  irrefutable by certain     
scholars4 ,it was ,charles ,v who said3 
,each  additional acquired language     
represents an additional personality2   
and  to suggest the root of language    
formation he said it in ,latin3 ,quot   
linguas quis callet1 tot homines valet4 
,this saying has been handed  down      
through the ages in ,german in the form3
 ,soviel ,sprachen1 soviel  ,sinnen 7,an
 added language means an added sense74  
,einstein replied3 ,i doubt whether this
 aphorism is generally valid1 for  ,i   
believe that it would at no time have   
stood a real test4 ,all  experience     
contradicts it4 ,otherwise we should be 
compelled to assign  the highest        
positions among intellectual beings to  
linguistic athletes  like ,mithridates1 
,mezzofanti1 and similar persons4 ,the  
exact opposite1  indeed1 may be proved1 
namely1 that in the case of the         

strongest  personalities1 and of those  
who have contributed most to progress1  
the  multiplicity of their senses in no 
wise depended on a comprehensive        
knowledge of languages1 but rather that 
they avoided burdening their  minds with
 things that made excessive claims on   
their memories4    ,certainly1 said ,i1 
it may be admitted that this gives rise 
to  exaggeration in some cases1 and that
 the linguistic sort of sport  practised
 by many a scholar degenerates to a mere
 display of knowledge4  ,an intellectual
 achievement of lasting merit has very  
rarely or never  been the result of a   
superabundance of acquired linguistic   
knowledge4 ,an  instance occurs to me at
 this moment4 ,nietzsche became a       
philosopher of  far-reaching influence  
only after he had passed the stage of   
the  philologist4 ,as far as our present
 discussion is concerned1 the question  
is narrowed down considerably3 it       
reduces itself to inquiring whether we  
do sufficient1 too little1 or too much  

,greek and ,latin4 ,i must remark at    
the very outset that1 formerly1 school  
requirements went much further in  this 
respect than nowadays1 when we scarcely 
meet with a scholar even in  the upper  
classes who knows ,latin and ,greek     
perfectly4    ,it is just this fact that
 ,einstein regards as a sign of         
improvement and  a result of examining  
the true aims of a school4 ,he          
continued3 ,man must  be educated to    
'react delicately'2 he is to acquire and
 develop  'intellectual muscles'6 ,and  
the methods of language drill are much  
less  suited to this purpose than those 
of a more general training that gives   
greatest weight to a sharpening of one's
 own powers of reflection4  ,naturally1 
the inclination of the pupil for a      
particular profession must  not be      
neglected1 especially in view of the    
circumstance that such  inclination     
usually asserts itself at an early age1 
being occasioned by  personal gifts1 by 
examples of other members of the family1

 and by  various circumstances that     
affect the choice of his future         
life-work4  ,that is why ,i support the 
introduction into schools1 particularly 
schools devoted to classics1 of a       
division into two branches at1 say1  the
 fourth form1 so that at this stage the 
young pupil has to decide in  favour of 
one or other of the courses4 ,the       
elementary foundation to the  fourth    
form may be made uniform for all1 as    
they are concerned with  factors on     
education that are scarcely open to the 
danger of being  exaggerated in any one 
direction4 ,if the pupil finds that he  
has a  special interest in what are     
called humaniora by the educationist1   
let  him by all means continue along the
 road of ,latin and ,greek1 and1        
indeed1 without being burdened by tasks 
that1 owing to his disposition1  oppress
 or alarm him4    ,you are referring1 ,i
 interposed1 to the distress which      
pupils feel in  the time allotted to    
mathematics4 ,there are actually people 

of  considerable intelligence who seem  
to be smitten with absolute stupidity   
when confronted with mathematics1 and   
whose school-life becomes poisoned      
owing to the torment caused by this     
subject4 ,there are many cases of       
living surgeons1 lawyers1 historians1   
and litterateurs1 who1 till late  in    
life1 are visited by dreams of their    
earlier mathematical ordeals4  ,their   
horror has a very real foundation1 for1 
whereas the pupil who is  bad at ,latin 
yet manages to get an idea of the       
language1 and he who is  weak in history
 has at least a notion of what is being 
discussed1 the  one who is              
unmathematical by nature has to worry   
his way through  numberless lessons in a
 subject which is entirely              
incomprehensible to  him1 as if         
belonging to another world and being    
presented to him in a  totally strange  
tongue4 ,he is expected to answer       
questions1 the sense of  which he cannot
 even guess1 and to solve problems1     

every word and every  figure of which   
glares at him like a sphinx of evil     
omen4 ,sitting on  each side of him are 
pupils to whom this is merely play1 and 
some of  whom could complete the whole  
of school mathematics within a few      
months  at express rate4 ,this leads to 
a contrast between the pupils1 which may
  press with tragical force on the      
unfortunate member throughout his whole 
school existence4 ,that is why a reform 
is to be welcomed that sifts out  in    
time those who should be separated from 
the rest1 and which adapts  the school  
curriculum as closely as possible to    
individual talents4    ,einstein called 
my attention to the fact that this      
division had already  been made in many 
schools in foreign countries1 as in     
,france and in  ,denmark1 although not  
so exclusively as suggested by him4     
,moreover1 he  added1 ,i am by no means 
decided whether the torments that you   
mentioned  are founded primarily on     
absence of talent in the pupil4 ,i feel 

much  more inclined to throw the        
responsibility in most cases on the     
absence  of talent in the teacher4 ,most
 teachers waste their time by asking    
questions which are intended to discover
 what a pupil does not know1  whereas   
the true art of questioning has for its 
purpose to discover what  the pupil     
knows or is capable of knowing4         
,whenever sins of this sort are         
committed--and they occur in all        
branches of knowledge--the personality  
of the teacher is mostly at fault4 ,the 
results of the class furnish an  index  
for the quality of the preceptor4 ,all  
things being taken into  consideration1 
the average of ability in the class     
moves1 with only  slight fluctuations1  
about mean values1 with which tolerably 
satisfactory results may be obtained4   
,if the progress of the class is  not up
 to this standard1 we must not speak of 
a bad year but rather of  an inefficient
 instructor4 ,it may be assumed that1 as
 a rule1 the  teacher understands the   

subject with which he is entrusted1 and 
has  mastered its content1 but not that 
he knows how to impart his  information 
in an interesting manner4 ,this is      
almost always the source  of the        
trouble4 ,if the teacher generates an   
atmosphere of boredom1 the  progress is 
stunted in the suffocating surroundings4
 ,to know how to  teach is to be able to
 make the subject of instruction        
interesting1 to  present it1 even if it 
happens to be abstract1 so that the soul
 of the  pupil resonates in sympathy    
with that of his instructor1 and so that
 the  curiosity of the pupil is never   
allowed to wane4    ,that is in itself  
an ideal postulate4 ,if we assume it to 
be fulfilled1  how do you wish to see   
the subjects distributed in the         
curriculum8    ,we must leave the       
detailed discussion of this question for
 another  occasion4 ,one of the main    
points would be the economy of time2 all
 that  is superfluous1 vexatious1 and   
only intended as a drill must be        

dropped4 ,at present the aim of the     
whole course is the leaving             
certificate4 ,this test must be given   
up6    ,is that serious4 ,professor8 ,do
 you wish to do away with the           
examination  for matriculation8         
,exactly4 ,for it is like some fearful  
monster guarding our exit from  school1 
throwing its shadow far ahead1 and      
compelling teacher and pupil  to work   
incessantly towards an artificial show  
of knowledge4 ,this  examination has    
been elevated by forcible means to a    
level which the  violently drilled      
candidates can keep only for a few      
hours1 and is then  lost to sight for   
ever4 ,if it is eliminated1 it will     
carry away with it  this painful        
drilling of the memory2 it will no      
longer be necessary to  hammer in for   
years what will be entirely forgotten   
within a few months1  and what deserves 
to be forgotten4 ,let us return to      
,nature1 which  upholds the principle of
 getting the maximum amount of effect   

from the  minimum of effort1 whereas the
 matriculation test does exactly the    
opposite4    ,yes1 but who is then to be
 allowed to enter the university8       
,every one who has shown himself to be  
capable not only in a crucial  test of  
an accidental kind1 but in his whole    
behaviour4 ,the teacher will  be the    
judge of this1 and if he does not know  
who is qualified1 he again  is to be    
blamed4 ,he will find it so much the    
easier to decide who is  sufficiently   
advanced to obtain a leaving            
certificate1 in proportion as  the      
curriculum has weighed less on the minds
 of the young people4 ,six  hours a day 
should be ample--four at school and two 
for home-work2 that  should be the      
maximum4 ,if this should appear too     
little to you1 ,i must  ask you to bear 
in mind that a young mind is being      
subjected to strain  even in leisure    
hours1 as it has to receive a whole     
world of  perceptions4 ,and if you ask  
how the steadily increasing curriculum  

is to  be covered in this very moderate 
number of hours1 my answer is3 ,throw   
all that is unnecessary overboard6 ,i   
count as unnecessary the major part  of 
the subject that is called ',universal  
,history1' and which is1 as a  rule1    
nothing more than a blurred mass of     
history compressed into dry  tables of  
names and dates4 ,this subject should be
 brought within the  narrowest possible 
limits1 and should be presented only in 
broad  outline1 without dates having to 
be crammed4 ,leave as many gaps as you  
like1 especially in ancient history2    
they will not make themselves felt  in  
our ordinary existences4 ,in nowise can 
,i regard it as a misfortune if  the    
pupil learns nothing of ,alexander the  
,great1 and of the dozens of  other     
conquerors whose documentary remains    
burden his memory like so  much useless 
ballast4 ,if he is to get a glimpse of  
the grey dawn of  time1 let him be      
spared from ,cyrus1 ,artaxerxes1 and    
,vercingetorix1 but  rather tell him    

something of the pioneers of            
civilization1 ,archimedes1  ,ptolemy1   
,hero1 ,appolonius1 and of inventors and
 discoverers1 so that the  course does  
not resolve into a series of adventures 
and massacres4    ,would it not be      
expedient1 ,i interrupted1 to take some 
of the history  time to branch off into 
an elementary treatment of the real     
evolution of  the state1 including      
sociology and the legal code8           
,einstein does not consider this        
desirable1 although he himself is deeply
  interested in all manifestations of   
public life4 ,he does not favour an     
elementary political training received  
at school1 presumably above all  owing  
to the fact that in this branch the     
instruction cannot be removed  from     
official influences1 and because        
political questions require the         
attention of a mature mind4 ,his picture
 of how a youth is to meet the          
requirements of modern life is something
 quite different1 far removed  from all 

theories4 ,his whole efforts are        
directed at finding a means of          
counteracting the tendency to overburden
 one side of the youthful mind4  ,i     
should demand the introduction of       
compulsory practical work4 ,every  pupil
 must learn some handicraft4 ,he should 
be able to choose for  himself which it 
is to be1 but ,i should allow no one to 
grow up without  having gained some     
technique1 either as a joiner1          
bookbinder1 locksmith1  or member of any
 other trade1 and without having        
delivered some useful  product of his   
trade4    ,do you attach greater        
importance to the technique itself or to
 the  feeling of social relationship    
with the broad masses of the people     
which  it engenders8    ,both factors   
are equally important to me1 said       
,einstein1 and others  become added to  
these which help to justify my wish in  
this respect4 ,the  handiwork need not  
be used as a means of earning money by  
the pupil of  the secondary school1 but 

it will enlarge and make more solid the 
foundation on which he will rest as an  
ethical being4 ,in the first  place1 the
 school is not to produce future        
officials1 scholars1  lecturers1        
barristers1 and authors1 but human      
beings1 not merely mental  machines4    
,prometheus did not begin his education 
of mankind with  astronomy1 but by      
teaching the properties of fire and its 
practical  uses4444    ,this brings to  
my mind another analogy1 ,i continued1  
namely1 that of  the old ,meistersinger1
 who were1 all of them1 expert smiths1  
tinkers1  or shoemakers1 and yet        
succeeded in building a bridge to the   
arts4 ,and  at bottom1 the sciences1    
too1 belong to the category of free     
arts4 ,yet1  a difficulty seems to me to
 arise4 ,in demanding a compulsory      
handicraft1  you lay stress on practical
 use1 whereas in your other remarks you 
declared science in itself as being     
utterly independent of practice4    ,i  
do this1 replied ,einstein1 only when ,i

 speak of the ultimate aims  of pure    
research1 that is1 of aims that are     
visible to only a vanishing  minority4  
,it would be a complete misconception of
 life to uphold this  point of view and 
to expect its regulative effectiveness  
in cases in  which we are dealing only  
with the preliminaries of science4 ,on  
the  contrary1 ,i maintain that science 
can be taught much more practically at  
schools than it is at present when      
bookwork has the upper hand4 ,for       
example1 to return to the question of   
mathematical teaching3 it seems to  me  
to be almost universally at fault1 if   
only for the reason that it is  not     
built up on what is practically         
interesting1 what appeals directly  to  
the senses1 and what can be seized      
intuitively4 ,child-minds are fed  with 
definitions instead of being presented  
with what they can grasp1  and they are 
expected to be able to understand purely
 conceptual things1  although they have 
had no opportunity given them of        

arriving at the  abstract by way of     
concrete things4 ,it is very easy to do 
the latter4  ,the first beginnings      
should not be taught in the schoolroom  
at all1 but  in open ,nature4 ,a boy    
should be shown how a meadow is measured
 and  compared with another4 ,his       
attention must be directed to the height
 of a  tower1 to the length of his      
shadow at various times1 to the         
corresponding altitude of the sun2 by   
this means he will grasp the            
mathematical relationships much more    
rapidly1 more surely1 and with  greater 
zeal1 than if words and chalk-marks are 
used to instil into him  the conceptions
 of dimensions1 of angles1 or perchance 
of some  trigonometrical function4 ,what
 is the actual origin of such branches  
of  science8 ,they are derived from     
practice1 as1 for example1 when ,thales 
first measured the height of the        
pyramids with the help of a short rod1  
which he set up at the ultimate point of
 the pyramid's shadow4 ,place a  stick  

in the boy's hand and lead him on to    
make experiments with it by  way of a   
game1 and if he is not quite devoid of  
sense1 he will discover  the thing for  
himself4 ,it will please him to have    
discovered the height  of the tower     
without having climbed it1 and this is  
the first thrill of  the pleasure which 
he feels later when he learns the       
geometry of similar  triangles and the  
proportionality of their sides4    ,in  
the matter of physics1 pursued          
,einstein1 the first lessons should     
contain nothing but what is experimental
 and interesting to see4 ,a  pretty     
experiment is in itself often more      
valuable than twenty formul  extracted  
from our minds2 it is particularly      
important that a young mind  that has   
yet to find its way about in the world  
of phenomena should be  spared from     
formul altogether4 ,in his physics they 
play exactly the  same weird and fearful
 part as the figures of dates in        
,universal  ,history4 ,if the           

experimenter is ingenious and expert1   
this subject may  be begun as early as  
in the middle forms1 and one may then   
count on a  responsiveness that is      
rarely observable during the hours of   
exercise in  ,latin grammar4    ,this   
leads me1 said ,einstein1 to speak in   
this connexion of a means  of education 
that has so far been used only by way of
 trial in  class-teaching1 but from an  
improved application of which ,i expect 
fruitful results later4 ,i mean the     
school cinema4 ,the triumphal march of  
the cinematograph will be continued into
 pedagogic regions1 and here it  will   
have a chance to make good its wrongs in
 thousands of picture shows  in showing 
absurd1 immoral1 and melodramatic       
subjects4 ,by means of the  school-film1
 supplemented by a simple apparatus for 
projection1 it would  be possible       
firstly to infuse into certain subjects1
 such as geography1  which is at present
 wound off organ-like in the form of    
dead  descriptions1 the pulsating life  

of a metropolis4 ,and the lines on a map
  will gain an entirely new complexion  
in the eyes of the pupil1 if he  learns1
 as if during a voyage1 what they       
actually include1 and what is  to be    
read between them4 ,an abundance of     
information is imparted by the  film1   
too1 if it gives an accelerated or      
retarded view of such things as  a plant
 growing1 an animal's heart beating1 or 
the wing of an insect  moving4 ,the     
cinema seems to me to have a still more 
important function  in giving pupils an 
insight into the most important branches
 of  technical industry1 a knowledge of 
which should become common property4    
,very few hours would suffice to impress
 permanently on the schoolboy's  mind   
how a power-station1 a locomotive1 a    
newspaper1 a book1 or a  coloured       
illustration is produced1 or what takes 
place in an electrical  plant1 a glass  
factory1 or a gasworks4 ,and1 to return 
to natural  science1 many of the rather 
difficult experiments that cannot be    

shown  by means of school apparatus may 
be shown with almost as great clearness 
on a film4 ,taken all in all1 the       
redeeming word in school-teaching is1   
for me3 an increased appeal to the      
senses4 ,wherever it is possible1       
learning must become living1 and this   
principle will predominate in  future   
reforms of school-teaching4         99  
99     99     99     99     99     99   
99    ,university study was only touched
 on lightly during this talk4 ,it has   
become known that ,einstein is a very   
strong supporter of the principle  of   
free learning1 and that he would prefer 
to dispense entirely with the  regular  
documents of admission which qualify    
holders to attend lecture  courses4     
,this is to be interpreted as meaning   
that as soon as anyone  desirous of     
furthering his studies has demonstrated 
his fitness to  follow the lecturer's   
reasoning by showing his ability in     
class  exercises or in the laboratory1  
he should be admitted immediately4      

,einstein would not demand the usual    
certificate of general education1  but  
only of fitness for the special subject1
 particularly as1 in his own            
experience1 he has frequently found the 
cleverest people and those with  the    
most definite aims to be prone to       
one-sidedness4 ,according to this1  even
 the intermediate schools should be     
authorized to bestow a  certificate of  
fitness to enter on a course in a single
 definite subject  as soon as the pupil 
has proved himself to have the necessary
 ability4  ,if he earlier spoke in      
favour of abolishing the matriculation  
examination1 this is only an indication 
of his effort to burst open the  portals
 of higher education for every one4     
,nevertheless1 ,i remarked  that1 in the
 course of university work itself1 he is
 not in favour of  giving up all        
regulation concerning the ability of the
 student--at  least1 not in the case of 
those who intend to devote themselves to
  instruction later4 ,he does not desire

 an intermediate examination 7in  the   
nature of the tentamen physicum of      
doctors71 but he considers it           
profitable for the future schoolmaster  
to have an opportunity early in  his    
course to prove his fitness for         
teaching4 ,in this matter1 too1         
,einstein reveals his affectionate      
interest in the younger generation1     
whose development is threatened by      
nothing so much as by incapable         
teachers3 the sum of these              
considerations is that the pupil is     
examined  as little as possible1 but the
 teacher so much the more closely4 ,a   
candidate for the teaching profession1  
who in the early stages of his  academic
 career fails to show his fitness1 his  
individual facultas  docendi1 should be 
removed from the university4    ,there  
can be no doubt but that ,einstein has a
 claim to be heard as an  authority on  
these questions4 ,there are few in the  
realm of the learned  in whose faces it 
is so clearly manifest that they are    

called to excite  a desire for knowledge
 by means of the living word1 and to    
satisfy this  desire4 ,if great         
audiences assemble around him1 if so    
many foreign  academies open their arms 
to him to make him their own1 these are 
not  only signs of a magnetic influence 
that emanates from the famous           
discoverer1 but they are indications    
that he is far famed as a teacher  with 
a captivating personality4 ,let us      
consider what this signifies in  his    
profession4 ,philosophers1 historians1  
lawyers1 doctors1 and  theologians have 
at their disposal innumerable words     
which they merely  need to pronounce to 
get into immediate contact with their   
audiences4 ,in  ,einstein's profession1 
theoretical physics1 man disappears2 it 
leaves no  scope for the play of        
emotion2 its implement mathematics--and 
what an  instrument it is6--bristles    
with formal difficulties1 which can be  
overcome only by means of symbols and by
 using a language which has no  means of

 displaying eloquence1 being devoid of  
expression1 emotion1 and  regular       
periods4 ,yet here we have a physicist1 
a mathematician1 whose  first word      
throws a charm over a great crowd of    
people1 and who extracts  from their    
minds1 so to speak1 what1 in reality1 he
 alone works out  before them4 ,he does 
not adhere closely to written pages1 nor
 to a  scheme which has been prepared   
beforehand in all its details2 he       
develops his subject freely1 without the
 slightest attempt at rhetoric1  but    
with an effect which comes of itself    
when the audience feels itself  swept   
along by the current4 ,he does not need 
to deliver his words  passionately1 as  
his passion for teaching is so manifest4
 ,even in  regions of thought in which  
usually only formul1 like glaciers1 give
  an indication of the height1 he       
discovers similes and illustrations with
  a human appeal1 by the aid of which he
 helps many a one to conquer the        
mountain sickness of mathematics4 ,his  

lectures betray two factors that  are   
rarely found present in investigators of
 abstract subjects2 they are            
temperament and geniality4 ,he never    
talks as if in a monologue or as if     
addressing empty space4 ,he always      
speaks like one who is weaving threads  
of some idea1 and these become spun out 
in a fascinating way that robs  the     
audience of the sense of time4 ,we all  
know that no iron curtain  marks the    
close of ,einstein's lecture2 anyone who
 is tormented by some  difficulty or    
doubt1 or who desires illumination on   
some point1 or has  missed some part of 
the argument1 is at liberty to question 
him4  ,moreover1 ,einstein stands firm  
through the storm of all questions4 ,on 
the very day on which the above         
conversation took place he had come     
straight from a lecture on              
four-dimensional space1 at the          
conclusion of  which a tempest of       
questions had raged about him4 ,he spoke
 of it not as  of an ordeal that he had 

survived1 but as of a refreshing shower4
 ,and  such delights abound in his      
teaching career4         99     99      
99     99     99     99     99     99   
,it was the last lecture before his     
departure for ,leyden 7in ,may #aibj71  
where the famous faculty of science1    
under the auspices of the great         
physicist ,lorentz1 had invited him to  
accept an honorary professorship4  ,this
 was not the first invitation of this   
kind1 and will not be the  last1 for    
distinctions are being showered on him  
from all parts of the  world4 ,it is    
true that the universities who confer a 
degree on him  honoris causa are        
conferring a distinction on themselves1 
but ,einstein  frankly acknowledges the 
value of these honours1 which he regards
 as  referring only to the question in  
hand1 and not the person4 ,it gives him 
pleasure on account of the principle    
involved being recognized1 and he       
regards himself essentially only as one 
whom fate has ordained as the  personal 

exponent of these principles4    ,what  
this life of hustle and bustle about a  
scientist signifies is  perhaps more    
apparent to me1 who have a modest share 
in these  conversations1 than to        
,einstein himself1 for ,i am an old man 
who--unfortunately--have to think back a
 long way to my student days1  and can  
set up comparisons which are out of     
reach of ,einstein4 ,formerly1  many    
years ago1 but in my own time1 there was
 an auditorium maximum  which only one  
man could manage to fill with an        
audience1 namely1 ,eugen  ,dhring1 the  
noted scholar1 who was doomed to remain 
a lecturer  inasmuch as he went under in
 his quarrels with confrres of a higher 
rank4 ,but before he made his onslaught 
against ,helmholtz1 he was  regarded as 
a man of unrivalled magnetic power1 for 
his philosophical  and economical       
lectures gathered together over three   
hundred hearers1 a  record number in    
those times4 ,nowadays1 in the case of  
,einstein1 four  times this number has  

been surpassed1 a fact which has brought
 into  circulation the playful saying3  
,one can never miss his auditorium2     
whither all are hastening1 that is the  
goal6 ,to make just comparisons1  we    
must take account of the faithfulness of
 the assembled crowd1 as well  as its   
number4 ,many an eminent scholar has in 
earlier times had reason  to declare1   
like ,faust3 ,i had the power to attract
 you1 yet had no  power to hold you4    
,helmholtz began regularly every term   
with a crowded  lecture-hall1 but in a  
short time he found himself deserted1   
and he  himself was well aware that no  
magnetic teaching influence emanated    
from  him4 ,there is yet another case in
 university history of a brilliant      
personality who1 from similar flights of
 ecstasy1 was doomed to  disappointment4
 ,i must mention his name1 which1 in    
this connexion1 will  probably cause    
great surprise1 namely1 ,schiller6 ,he  
had fixed his first  lecture in history 
at ,jena1 to which he was appointed1 and

 had prepared  for an audience of about 
a hundred students4 ,but crowd upon     
crowd  hustled along1 and ,schiller1 who
 saw the oncoming stream from his       
window1 was overcome with the impression
 that there was no end to it4  ,the     
whole street took alarm1 for at first it
 was imagined that a fire  had broken   
out1 and at the palace the watch was    
called out--yet1 a  little later in the 
course1 there was a depressing ebb of   
the tide1  after the first curiosity had
 been appeased2 the audience gradually  
vanished into thin air1 a proof of the  
fact that the nimbus of a name  does not
 suffice to maintain the interest       
between the lecturer's desk  and the    
audience4    ,i mentioned this example  
at the time when ,einstein's gift for   
teaching  had gradually increased the   
number of his hearers to the record     
figure  of #abjj1 yet ,i did not on this
 occasion detect any inordinate joy in  
him  about his success4 ,i gained the   
impression that he had strained his     

voice in the vast hall4 ,his mood       
betrayed in consequence a slight        
undercurrent of irritation4 ,in an      
access of scepticism he murmured the    
words1 ,a mere matter of fashion4 ,i    
cannot imagine that he was entirely  in 
earnest4 ,it goes without saying that ,i
 protested against the  expression4     
,but1 even if there were a particle of  
truth in it1 we might  well be pleased  
to find such a fashion in intellectual  
matters1 one that  persists so long and 
promises to last4 ,the world would      
recover its  normal healthy state if    
fashions of this kind were to come into 
full  swing4 ,it is1 of course1 easy to 
understand on psychological grounds     
that ,einstein himself takes up a sort  
of defensive position against his  own  
renown1 and that he occasionally tries  
to attack it by means of  sarcasm1      
seeing that he cannot find serious      
arguments to oppose it4         99      
99     99     99     99     99     99   
99    ,whether ,einstein's ideas and    

proposals concerning educational reform 
will be capable of realization          
throughout is a question that time alone
  can answer4 ,we must make it clear to 
ourselves that1 if carried out  along   
free-thinking lines1 they will demand   
certain sacrifices1 and it  depends on  
the apportionment of these sacrifices as
 to what the next1 or  the following1   
generation will have to exhibit in the  
way of mental  training4    ,an         
appreciable restriction will have to be 
imposed on the time given to  languages4
 ,it is a matter of deciding how far    
this will affect the  foundations that1 
under the collective term humaniora1    
have supported  the whole system of     
classical schools for centuries4 ,the   
fundamental  ideas of reform1 which1    
owing to the redivision of school-hours 
and the  economy of work1 no longer     
claim precedence for languages1 indicate
 that  not much will be left of the     
original ,latin and ,greek basis4    ,we
 have noticed above that ,einstein1     

although he does not1 in principle1     
oppose the old classicism1 no longer    
expects much good of it4 ,but  nowadays 
the state of affairs is such that it is 
hardly a question of  supporting or     
opposing its retention in fragmentary   
form4 ,whoever does  not support it with
 all his power strengthens indirectly   
the mighty  chorus of those who are     
radically antagonistic to it4 ,and it is
 a  remarkable fact that this chorus    
includes many would-be authorities on   
languages who have influence among us   
because they are champions of the  cause
 of retaining languages4    ,they do not
 wish to rescue languages as such1 but  
only the ,german  tongue2 they point to 
the humaniora of classical schools1 or  
to  ,humanisterei1 as they call it1 as  
the enemy and corrupter of their        
language4 ,in what sense they mean this 
is obvious from their articles of       
faith1 of which ,i should like to cite a
 few in the original words of one  of   
their party-leaders3    ,up to the time 

of the hazardous enterprise of          
,thomasius 7who first  announced        
lectures in the ,german language in     
#afhg7 ,german scholars as a  body were 
the worst enemies of their own          
tongue4--,luther did not take  his      
models for writing ,german from the     
humanistic mimics who aped the  old     
,latins4 ,in the case of many1 including
 ,lessing and ,goethe1 we  observe them 
making a definite attempt to shake      
themselves free from the  chaos of      
humanistic influences in ,germany--,the 
inheritance of  pseudo-learned          
concoctions of words stretches back to  
pretentious  humanism as do most of     
essential vices of learned styles4--,the
  far-reaching and lasting corruption of
 the ,german language by this  poisonous
 ,latin has its beginnings in the       
humanism of the sixteenth  century4     
,and1 quite logically1 these heralds    
extend their attacks along the whole    
academic front4 ,for1 according to their
 point of view1 the whole army of       

professors is deeply immersed in the    
language slime of the traditional       
humanism of the ,greeks and ,latins4    
,the whole language evil of our  times1 
so these leaders say1 is at bottom due  
to scientists1 who1 in  the opinionated 
guise of a language caste1 and without  
enriching our  conceptions in the       
slightest1 seek by tinkling empty words 
to give us  the illusion of a new and   
particularly mysterious occult science1 
an  impression which is unfortunately   
often produced on ignorant minds4444    
,however many muddy outlets official    
institutions and language  associations 
may purge and block up1 ditch-water from
 ever new quagmires  and drains pours   
unceasingly into the stately stream of  
our language4    ,thus the attack on the
 ,latin and ,greek language foundation  
in schools  identifies itself with the  
struggle against the academic world as a
  whole1 and a scholar who does defend  
the classical system of education  with 
all his might finds himself             

unconsciously drifting into the ranks   
of the brotherhood which in the last    
instance is seeking his own             
extermination4    ,this danger must not 
be under-estimated4 ,it is just this    
peril1 so  threatening to our           
civilization1 that moves me to show my  
colours  frankly here4 ,i am not a      
supporter of bookworm drudgery in       
schools1 but  ,i feel myself impelled to
 use every effort in speech and writing 
to  combat the anti-humanists whose     
password1 ,for our language1 at root    
signifies ,enemies of ,science6    ,we  
must put no weapons into their hands1   
and the only means to avoid  this is1 in
 my opinion1 to state our creed         
emphatically and openly after  the      
manner of almost all our classical      
writers4    ,this creed1 both as regards
 language and substance1 is to be       
understood  as being based on the       
efficacy of the old classical languages4
 ,it is the  luminous centre of the life
 and work of the men who caused ,bulwer 

to  proclaim our country the country of 
poets and thinkers4 ,the  superabundance
 of these is so excessive that it is    
scarcely fair to  mention only a few    
names such as ,goethe1 ,lessing1        
,schiller1 ,wieland1  ,kant1 and        
,schopenhauer4 ,our literature would be 
of a provincial standard  and not a     
world possession if this creed had not  
asserted its sway at  all times4    ,if 
the question is raised as to where our  
youth is to find time for  learning     
ancient languages under the present     
conditions of crowded  subjects1 the    
answer is to be furnished by improved   
methods of  instruction4 ,my personal   
point of view is that even the older    
methods  were not so bad4 ,goethe found 
himself in no wise embarrassed through  
lack of time in acquiring all sorts of  
knowledge and mental equipment1         
although even as a boy of eight years he
 could write in ,latin in a way  which1 
compared with the bungling efforts of   
the modern sixth-form boy1  seems       

,ciceronian4 ,montaigne could express   
himself earlier in ,latin than  in      
,french1 and if he had not had this     
,latin poison injected into his  blood  
he would never have become ,montaigne4  
,it seems to me by no means impossible  
that the cultured world will one  day in
 the distant future return to the once  
self-evident view of  classical         
languages1 and indeed just for reasons  
of economy of time1  unless the         
universal language so ardently desired  
by ,hebbel--not to be  confused with the
 artificial patchwork called            
,esperanto--should become a  reality4   
,but even this language1 at present     
,utopian1 but one which will  help to   
link together the nations1 will disclose
 the model of the  ancient languages in 
its structure4 ,scientific language of  
the present  day shows where the route  
lies2 and this route will be made       
passable in  spite of all the efforts of
 ,teutonic language saints and assassins
 of  humanism to block it4    ,the      

working out of ideas by research        
scientists leads to enrichment of       
language4 ,and since1 as is quite       
natural1 they draw copiously on antique 
forms of expression1 they are really the
 trustees of an instruction that  makes 
these expressions intelligible not      
merely as components of an  artificial  
language like ,volapk but as organic    
growths4 ,that is how  they proceed when
 they carry on their research1 or       
describe it and  lecture on their own   
subject4 ,but if they are to decide how 
the school  is to map out its course in 
actual practice1 the problem of time    
again  becomes their chief              
consideration--that is1 they feel in    
duty bound to  give preference to what  
is most important4 ,hence there results 
the wish  to reduce the hours           
apportioned to the language subjects as 
much as  possible4    ,on this matter we
 have a detailed essay by the           
distinguished ,ernst ,mach  mentioned   
earlier1 who exposes the actual dilemma 

with the greatest  clearness4 ,he treats
 this exceedingly important question in 
all its  phases1 and arrives at almost  
the same conclusion as ,einstein4 ,at   
the  outset he certainly chants a ,latin
 psalm almost in the manner of          
,schopenhauer4 ,its lower tones         
represent an elegy lamenting that ,latin
 is  no longer the universal language   
among educated people1 as it was from   
the fifteenth to the eighteenth century4
 ,its fitness for this purpose is  quite
 indisputable1 for it can be adapted to 
express every conception  however modern
 or subtle it may be4    ,what a        
profusion of new conceptions was        
introduced into science by ,sir  ,isaac 
,newton1 to all of which he succeeded in
 giving correct and precise  ,latin     
names6 ,the natural inference suggests  
itself to us that young  people should  
learn the ancient classical tongues--and
 yet a different  result is coming      
about2 the modern child is to be content
 with  understanding words with a       

world-wide currency1 without knowing    
their  philological origin4    ,it is   
not necessary to be a schoolmaster to   
feel the inadequacy of this  proceeding4
 ,it is true that without knowing       
,arabic we can grasp the  sense and     
meaning of the word ,algebra1 and in the
 same way we can  extract the essence of
 a number of ,greek and ,latin          
expressions without  digging at their   
etymological roots4 ,but these          
expressions are to be  counted in       
hundreds and thousands1 and are         
increasing daily1 so that we  are put   
before the question whether1 merely from
 the point of view of  time1 it is      
practicable to learn them as individual 
foreign terms or as  natural products of
 a root language with which we have once
 and for all  become familiar4    ,it is
 scarcely necessary for me to point out 
that ,einstein himself is  not sparing  
in the use of these technical           
expressions1 even when he is  using     
popular language4 ,he assumes or        

introduces terms of which the  following
 are a few examples3 continuum1         
co-ordinate system1  dimensional1       
electrodynamics1 kinetic theory1        
transformation1 covariant1  heuristic1  
parabola1 translation1 principle of     
equivalence1 and he is  quite justified 
in assuming that every one is fully     
acquainted with such  generally accepted
 expressions as3 gravitation1 spectral  
analysis1  ballistic1 phoronomy1        
infinitesimal1 diagonal1 component1     
periphery1  hydrostatics1 centrifugal1  
and numberless others which are diffused
  through educated popular language in  
all directions4 ,taken all together     
these represent a foreign realm in which
 the entrant can always succeed  in     
orientating himself when he receives    
explanations1 examples1 or              
translations1 whereas with a little     
preliminary knowledge of the ancient    
languages he immediately feels himself  
at home with them2 in this we  have not 
even taken into consideration the       

general cultural value of  this training
 in view of the access it gives to the  
old literature and  to ,hellenic        
culture4    ,perhaps ,i am going too far
 in adopting the attitude of a laudator 
temporis acti towards ,einstein's very  
advanced opinion4 ,we are here  dealing 
with a question in which nothing can be 
proved1 and in which  everything depends
 on disposition and personal            
experiences4 ,in my own  case this      
experience includes the fact that at a  
very early age1 in  spite of the very   
discouraging school methods1 ,i enjoyed 
the study of  ,latin and ,greek1 and    
that ,i learned ,horatian odes by heart1
 not because  ,i had to1 but because    
they appealed to me1 and finally that   
,homer opened  up a new world to me4    
,when ,einstein expresses his abhorrence
 of drill1 ,i  agree with him2 but these
 languages need not be taught as if we  
are on  parade4 ,we see thus that it is 
a question of method and not of the     
subject involved4 ,einstein gives the   

subject its due by recommending a       
double series of classes4 ,he allows the
 paths to diverge1 giving his  special  
blessing to the group along the one     
without setting up obstacles  to prevent
 the other pilgrims from attaining      
happiness in their own way4         99  
99     99     99     99     99     99   
99    ,we spoke of higher education for 
women1 and ,einstein expressed his views
  which1 as was to be expected1 were    
tolerant1 and yet did not suggest  those
 of a champion of the cause4 ,it was    
impossible to overlook the fact  that in
 spite of his approval he had certain   
reservations of a  theoretical nature4  
,as in all other directions1 he said1 so
 in that of science the way  should be  
made easy for women4 ,yet it must not be
 taken amiss if ,i  regard the possible 
results with a certain amount of        
scepticism4 ,i am  referring to certain 
obstacles in woman's organization which 
we must  regard as given by ,nature1 and
 which forbid us from applying the same 

standard of expectation to women as to  
men4    ,you believe1 then1 ,professor1 
that high achievements cannot be        
accomplished by women8 ,to keep our     
attention on science1 can one not  quote
 ,madame ,curie as a proof to the       
contrary8    ,surely only as one proof  
of brilliant exceptions1 more of which  
may  occur without refuting the statute 
of sexual organization4    ,perhaps this
 will be possible after all if a        
sufficient time for  development be     
allowed4 ,there may be much fewer       
geniuses among the other  sex1 but there
 has certainly been a concentration of  
talent4 ,or1 in  other words1 totally   
ignorant women have become much rarer4  
,you1  ,professor1 are fortunate in not 
being in a position to compare young    
women of to-day with those of forty or  
more years ago4 ,this ,i can do1  and   
just as once ,i found it natural that   
there should be swarms of  little geese 
and peacocks1 ,i never recover from my  
astonishment nowadays  at the amount of 

knowledge acquired by young womanhood4  
,it requires a  considerable effort on  
my part very often to avoid being       
completely  overshadowed by a partner at
 dinner4 ,the more this stratum of      
talent  increases1 the more we have     
reason to expect a greater number of    
geniuses from them in the future4       
,you are given to prognostication1 said 
,einstein1 and calculate with           
probabilities which sometimes are       
lacking in foundation4 ,increased       
education and even an increase of       
talents are quantitative assumptions    
that make an inference regarding higher 
quality reaching to genius  appear very 
bold4--,a passing look of ominous       
portent flashed over his  face1 and ,i  
noticed that he was preparing to launch 
a sarcastic  aphorism4 ,so it was1 for  
the next words were3 ,it is conceivable 
that  ,nature may have created a sex    
without brains6    ,i grasped the sense 
of this grotesque remark1 which was in  
no way to be  taken literally4 ,it was  

intended as an amusing exaggeration of  
what he  had earlier called the reason  
for his failing expectation3 the organic
  difference which1 being rooted in the 
physical constitution1 had  somewhere to
 express itself on the mental plane1    
too4 ,the soul of woman  strong in      
impulse shows a refinement of feeling of
 which we men are not  susceptible1     
whereas the greatest achievements of    
reason probably depend  on a            
preponderance of brain substance4 ,it is
 this plus beyond the normal  amount    
that gives promise of great discoveries1
 inventions1 and  creations4 ,we can    
just as little imagine a female         
,galilei1 ,kepler1 and  ,descartes1 as a
 female ,michelangelo or ,sebastian     
,bach4 ,but when we think  of these     
extreme cases1 let us also recall the   
balance on the other  side3 although a  
woman could not create the differential 
calculus1 it  was she that created      
,leibniz2 similarly she produced ,kant  
if not the  ,critique of ,pure ,reason4 

,woman1 as the author of all great      
minds1 has at  least a right of access  
to all means of education and to all    
advancement  that is proffered by       
universities4 ,and in this connexion    
,einstein  expressed his wish clearly   
enough4         99     99     99     99 
99     99     99     99    ,one of the  
most discussed themes in matters        
touching school education is  at the    
present time3 the selection of gifted   
pupils4 ,it has developed  into a       
principle that is generally recognized  
by the great majority1 the  only point  
of disagreement being in respect to the 
number that is to be  selected4    ,the 
idea running through it is that derived 
from ,darwin's theory of  selection3 man
 completes the method of selection      
practised by ,nature4 ,he  sifts and    
chooses1 and allows those that are more 
talented to come to  the fore more      
rapidly and more decidedly2 he favours  
their advancement  and makes easy their 
ascent4    ,this principle has really   

always been in existence4 ,it started   
with the  distribution of prizes in     
ancient ,olympia and reaches to the     
present-day  examinations that are      
clearly intended as a means of selecting
 talents4  ,a greater discrimination    
based on a systematic search for talents
 was  reserved for our own day4    ,it  
was scarcely a matter of doubt to me    
what attitude ,einstein would  take up  
towards this matter4 ,i had already     
heard him say hard words  about the     
system of examinations1 and knew his    
leaning towards allowing  each mind to  
develop its power freely and naturally4 
,in effect1 ,einstein declared to me    
that he would hear nothing of a         
breeding of talents in a sort of        
sporting way4 ,the dangers of the       
methods of sport would creep in and lead
 to results that had only the           
appearance of truth4 ,from the results  
so far obtained it was impossible  to   
come to a final decision about it4 ,yet 
it was conceivable that a  selective    

process conducted along reasonable lines
 would in general  prove of advantage in
 education1 particularly in the respect 
that many a  talent that would          
ordinarily become stunted owing to its  
being kept in  darkness would now have  
an opportunity of coming to light4      
,this resolved itself into a talk       
bearing on many questions1 and of which 
,i should like to state the main issue  
here4 ,it was specially intended to     
make clear the gambling method that     
,einstein repudiates1 and the danger  of
 which seems still more threatening to  
me than to him4    ,if certain          
pedagogues1 whose creed is force1 were  
to have their way1 the  most gifted     
pupils would be able1 or would be       
compelled1 to rush  through school at   
hurricane speed1 and1 at an age at which
 their fellows  were still spending     
weary hours at their desks1 they would  
have to  clamber to the topmost branches
 of the academic tree4 ,all things are  
possible1 and history even furnishes    

cases of such forced marches4  ,luther's
 friend ,melanchthon qualified at the   
age of thirteen to enter  the           
,university of ,heidelberg1 and at the  
age of seventeen he became a  professor 
at ,tbingen1 where he gave lectures on  
the most difficult  problems of         
philosophy1 as well on the ,roman and   
,greek writers of  classical antiquity4 
,this single instance need only be      
generalized1 and  we have the new ideal 
rising up before our astonished gaze3 a 
race of  professorial striplings whose  
upper lips are scarcely darkened with   
the  down of youth6 ,it is a mere matter
 of making an early discovery of the    
most gifted1 and then raising the       
scaffolding up which the precocious     
know-alls can climb as easily as        
possible4    ,interposed query3 ,where  
are these discoverers of talent1 and how
 do  they prove their own talent8 ,there
 was a good opportunity for them in a   
case which ,i must here mention4        
,einstein told me in another connexion  

that1 as early as #aijg1 that is1 when  
he was still very young in years1  he   
had not only succeeded in successfully  
representing the ,principle of          
,equivalence1 one of the main supports  
of the ,general ,principle of           
,relativity1 but had even published it2 
yet it made not the slightest           
impression on the learned world4 ,no one
 suspected the far-reaching             
consequences1 and no one pointed out    
this flaming up of a new talent of  the 
highest order4 ,and just as this was    
able to remain concealed from  the      
learned ,areopagus of the world at that 
time1 so a similar lack of              
understanding may easily be possible on 
a smaller scale at school4 ,we  know    
actually that among the recognized great
 men of science1 there were  many who   
did only moderately well at school2 as1 
for example1 ,humphry  ,davy1 ,robert   
,mayer1 ,justus ,liebig1 and many       
others4 ,wilhelm ,ostwald goes  so far  
as to affirm3 ,boys ordained to be      

discoverers later in life  have1 almost 
without exception1 been bad at school6  
,it is just the most  gifted young      
people who have resisted most strongly  
the form of  intellectual development   
prescribed by the school6 ,schools never
 cease  to show themselves to be the    
bitter1 unrelenting enemies of          
genius6--in  spite of all efforts at    
selection which have always been in     
vogue in the  guise of advancement into 
higher forms4    ,but the new mode of   
selection is intended to prevent        
mistakes and  oversights4 ,is this      
possible8 ,do not the traces of previous
 attempts  inspire distrust8 ,there was 
once a very ideal selection that had to 
stand the test of one of the most       
eminent bodies in existence1 the        
,french ,academy4 ,its duty was to      
discover geniuses on an incomparably    
higher plane4 ,it1 however1 repudiated  
or overlooked3 ,molire1  ,descartes1    
,pascal1 ,diderot1 the two ,rousseaus1  
,beaumarchais1 ,balzac1  ,branger1 the  

,goncourts1 ,daudet1 ,emile ,zola1 and  
many other extremely  gifted people1    
whom it should really have been able to 
find4    ,the only true1 and at the same
 time necessary as well as sufficient1  
breeding is carried out by ,nature      
herself in conjunction with social      
conventions1 which promise the more     
success the less they assume the        
character of incubators and breeding    
establishments4 ,if you wish to  apply  
tests to discover pupils of genius in   
any class1 examine as much  as you like1
 excite interest and ambition1          
distribute prizes even1 but  not for the
 purpose of separating at short         
intervals the shrewd and  needle-witted 
heads from the rest2 and do not lose    
sight of the fact  that among those who 
appear as the sheep as a result of these
  systematized tests to discover        
ingenuity there are many who1 ten or    
twenty years later1 will take up their  
positions as men of eminent  talent4    
,there is no essential difference       

between the forced promotion of such    
pupils and the breeding of super-men    
according to ,nietzsche's recipe as     
exemplified by his ,zarathustra4        
,assuming that super-men are justified  
in existing at all1 they will come      
about of themselves1 but cannot simply  
be manufactured4 ,workmen1 taken  as a  
class1 represent super-men more         
definitely than an individual such  as  
,napoleon or ,csar ,borgia4 ,so the     
super-scholar exists perhaps  already   
to-day1 not as an individual phenomenon1
 but as a whole1  representing his      
class4 ,whoever has had experience in   
these things will  know that nowadays   
there are difficult subjects in which it
 is possible  to apply to pupils of     
fifteen years of age tests that are far 
above the  plane of comprehension of    
pupils of the same age in former times1 
provided that the average is considered1
 that no accidental or  artificial      
separation has occurred1 that no        
pretentiously witty  questions have had 

to be answered1 and that there has been 
no systematic  and inquisitive search   
for talent4    ,let us rest satisfied if
 we find that the sum-total of talent is
  continually on the increase4 ,on the  
other hand1 it is by no means proved    
that we are doing civilization a service
 by persisting in the impossible        
project of abolishing from the world the
 struggle for existence  prescribed by  
,nature4 ,it is an elementary fact1 and 
one that is easy to  understand1 that   
many talents perish unnoticed4 ,on the  
other hand1  observe the long list of   
eminent men who fought their way upwards
 out of  the lowest stages of existence 
only to recognize that the difficulties 
that have been overcome are mostly      
necessary accompaniments of talent1     
that is1 that ,nature's way of selection
 is to oppose obstacles and raise       
difficulties in order to test their     
powers4 ,in the case of the poor        
lens-grinder ,spinoza and many others   
ranging to ,branger1 who was a  waiter1 

what a chain of desperate experiences1  
yet what triumphs6  ,herschel1 the      
astronomer1 was too poor to buy a       
refracting telescope1  and it was just  
this dispensation of poverty that made  
him succeed in  constructing a          
reflecting type composed of a mirror4   
,faraday1 the son of  a blacksmith      
without means1 made his way for years as
 a bookbinder's  apprentice4 ,joule1 one
 of the founders of the mechanical      
theory of heat1  started as a           
beer-brewer4 ,kepler1 the discoverer of 
the planetary laws1  was descended from 
a poverty-stricken innkeeper4 ,of the   
members in  ,goethe's circle1           
,jung-,stilling1 of whom ,nietzsche was 
so fond1 was a  tailor's apprentice2    
,eckermann1 ,goethe's intimate          
associate1 was a  swine-herd1 and       
,zelter was a mason4 ,we could add many 
recent names to  this list1 and very    
many more if we continue the line       
backwards to  ,euripides1 whose father  
was a publican and whose mother was a   

vendor of  vegetables4 ,this might serve
 as a basis for many reflections about  
the  upward course of the talented1 and 
about its less favourable reverse  side4
 ,for one might put the apparently      
paradoxical question whether a  soaring 
career for many or all talents is a     
necessity for our  civilization1 or     
whether it would not be better to have a
 substratum  interspersed with talent1  
to cultivate a mossy undergrowth which  
is to  serve as nourishment for the     
blooming plants of the upper layer4     
,maximum is not equivalent to optimum1  
and we learned elsewhere that  ,einstein
 is far removed from identifying them4  
,in the previous case it  was a question
 of the problem of population2 and in   
the course of the  discussion he        
mentioned that we are subject to an old 
error of  calculation when we regard it 
as a desirable aim to have a maximum    
number of human beings on the earth4 ,it
 seems1 indeed1 that this false         
conclusion is already in process of     

being corrected4 ,a beginning is  being 
made with new and very active           
organizations and unions whose          
programme is to reduce the number so    
that an optimum may be attainable  by   
those left4    ,if we extend this line  
of reasoning still further1 we arrive at
 the  depressing question whether too   
much might not be done for talent1 not  
only as regards breeding it1 but also in
 favouring the greatest number4  ,it is 
quite possible that in doing so1 we     
might overlook1 or take  insufficient   
account of the harm that might be done  
to the lower  stratum1 in that we should
 be depriving it of forces which1       
according to  the economy of ,nature1   
should remain and act in concealment4   
,this fear1 as here expressed1 is not   
shared by ,einstein4 ,however  brusquely
 he repudiates breeding1 he speaks in   
favour of smoothing the  way for talent4
 ,i believe1 he said1 that a sensible   
fostering of  gifts is of advantage to  
humanity generally and prevents         

injustice being  done to the individual4
 ,in great cities which give such lavish
  opportunities of education1 this      
injustice manifests itself less often2  
but it occurs so much the more in rural 
districts1 where there are  certainly   
many cases of gifted youths who1 if     
recognized as such at the  right age1   
would attain to an important position1  
but who1 together with  their gifts1    
become stunted1 nay1 go to ruin1 if the 
principle of  selection does not        
penetrate to their circle4    ,this     
brings us to the most difficult and most
 dangerous point4 ,the  spectre of      
responsibility is rapping at the portals
 of society1 and is  reminding us       
insistently that it is our duty to see  
that no injustice be  done to any talent
 that may be among us4 ,and this duty is
 but little  removed from the demand    
that it should be disburdened of the    
worries of  daily life1 for1 so the     
moral argument runs1 talent will ripen  
the more  surely the less it has to     

combat these ceaseless disturbances of  
ordinary life4    ,but this thesis1 so  
evident on moral grounds1 will never be 
proved  empirically4 ,on the contrary1  
we have good reason to suppose that     
necessity1 the mother of invention on   
the broader scale1 will often in  the   
case of the individual talent prove to  
be the mother of its best  results4     
,goethe required for his development an 
unchallenged life of  ease1 whereas     
,schiller1 who never emerged from his   
life of misery1 and  who1 up to the time
 when he wrote ,don ,carlos1 had not    
been able to  earn sufficient with his  
pen to buy a writing-desk1 required     
distress to  make his genius burst into 
flower4 ,jean ,paul recognized this     
blessing of  gloomy circumstances when  
he glorified poverty in his novels4     
,hebbel  followed him along this path by
 saying that it is more fruitful to     
refuse the most talented person the     
necessities of life than to grant  them 
to the least gifted4 ,for among a       

hundred who have been chosen by  the    
method of sifting1 there will be only   
one on the average who will  receive the
 certificate of excellence in the test  
of future generations1  for the latter  
use entirely different methods of       
sifting from that  practised by a       
committee of examiners who expect ready 
answers to  prepared questions4    ,this
 projects us on to the horns of a severe
 dilemma that scarcely  allows of       
escape4 ,the consciousness of duty      
towards the optimum  expresses itself   
only in a maximum of assistance1 and    
overhears the  whispered objection of   
reason that ,nature has also coarser    
means at her  disposal to attain her    
ends2 in her own cruelty of selection   
she often  enough proves the truth of   
,menander's saying1 which1 freely       
translated1  says3 to be tormented is   
also part of man's education4 ,the fact 
that  ,einstein--with certain           
reservations--favours the giving of help
 to the  selected few1 it is for me a   

proof1 among many others1 of his love   
towards his fellow-men1 which fills his 
heart absolutely1 all questions  of     
relativity notwithstanding4             
,,chapter ,v    ,,the ,,discoverer      
,relation of ,discovery and ,philosophy 
in ,history4--,the ,absolute and the    
,relative4--,the ,creative ,act4--,value
 of ,intuition4--,constructive          
,activity4--,invention4--,the ,artist as
 ,discoverer4--,theory and              
,proof4--,classical                     
,experiments4--,physics in ,primitive   
,ages4--,experimentum                   
,crucis4--,spectral ,analysis and       
,periodic ,system4--,the ,rle of        
,chance4--,disappointed                 
,expectations4--,the ,michelson-,morley 
,experiment  and the ,new ,conception of
 ,time4      ,,next time--so one of our 
talks ended--next time1 as you insist on
 it1 we  shall talk of discovery in     
general4 ,this1 was a promise of special
  import for me1 for it meant that ,i   
was to draw near to a fountain-head  of 

instruction1 and to have an opportunity 
of hearing the pronouncements  of one   
whose authority could scarcely be       
transcended4    ,we are precluded from  
questioning ,galilei personally about   
the  foundations of ,mechanics1 or      
,columbus about the inner feelings of a 
navigator who discovers new lands1 or   
,sebastian ,bach about the merits of    
,counterpoint1 but a great discoverer   
lives among our contemporaries who  is  
to give us a clue to the nature of      
discovery4 ,was it not natural that  ,i 
should feel the importance of his       
acceptance of my proposal8    ,before   
meeting him again ,i was overwhelmed    
with ideas that arose in me  at the     
slightest echo of the word discovery in 
my mind4 ,nothing1 it  seemed to me1    
could be higher3 man's position in the  
sphere of creation  and the sum of his  
knowledge can be deduced from the sum of
 his  discoveries which find their      
climax in the conceptions civilization  
and  philosophy1 just as they are partly

 conditioned by the philosophy of the   
time4 ,we might be tempted to ask3 which
 of these two precedes1 and which       
follows8 ,and perhaps the ambiguous     
nature of this question would furnish   
us with the key to the answer4 ,for1    
ultimately1 these two elements  cannot  
at all be resolved into the relationship
 of cause and effect1  antecedent and   
consequent4    ,neither is primary1 and 
neither secondary3 they are intimately  
interwoven with one another1 and are    
only different aspects of one and  the  
same process4 ,at the root of this      
process is our axiomatic belief  that   
the world can be comprehended1 and the  
indomitable will of all  thinking men1  
acting as an elementary instinct1 to    
bring the perceptual  events in the     
universe into harmony with the inner    
processes of thought4  ,this impulse is 
eternal2 it is only the form of these   
attempts to make  the world fully       
intelligible that alters and is subject 
to the change of  time4 ,this form finds

 expression in the current philosophy   
which brings  each discovery to         
fruition1 just as philosophy bears in   
itself  constituents of the ripe        
discovery4    ,it seemed to me that even
 at this stage of my reflections ,i was 
somewhere near interpreting ,einstein's 
intellectual achievement4 ,for his      
principle of relativity is tantamount to
 a regulative world-principle  that has 
left a mighty mark in the thought of our
 times4 ,we have lived  to see the death
 of absolutism2 the relativity of the   
constituents of  political power1 and   
their mutability according to view-point
 and  current tendencies1 become        
manifest to us with a clearness         
unapproached  by any experience of      
earlier historical epochs4 ,the world   
was far enough  advanced in its views   
for a final achievement of thought which
 would  demolish the absolute also from 
the mathematico-physical aspect4 ,this  
is  how ,einstein's discovery appeared  
as inevitable4    ,yet a shadow of doubt

 crossed my mind4 ,einstein's           
discoveries came to  light in the year  
#aije--that is1 at a time when hardly a 
cloud was  visible to forewarn us of the
 storms which were to uproot absolutism 
in  the world4 ,but what if a different 
kind of necessity had imposed itself  on
 world-history1 and hence on the        
world-view8 ,nowadays we know from      
authentic accounts1 which no one doubts1
 that all that we have  experienced     
during the war and the revolution has   
hung upon the  activities of one frail  
human being of quite insignificant      
exterior1 a  bureaucrat of the          
,wilhelm-,strasse1 a choleric eccentric 
who succeeded in  frustrating the       
,anglo-,german alliance which was       
unceasingly being  pressed upon us for  
six long years after the beginning of   
the century4    ,amid the noisy progress
 of universal evolution the secret and  
insignificant nibbling of a mole cannot 
be regarded as of momentous  importance 
for history1 and yet if we eliminate it 

from the complete  picture of events we 
find as a result that all our           
experiences have been  inverted4        
,absolutism would not have been thrown  
overboard1 but would  probably have kept
 the helm with greater mastery than ever
 as the  exponent of an ,anglo-,german  
hegemony of the world1 and a political  
outlook fundamentally different in      
tendency would now have been  prevailing
 on the earth4    ,but ,einstein's      
,theory of ,relativity would not have   
taken the slightest  heed of this4 ,it  
would have arisen independently of the  
current forms of  political conceptions1
 simply because we had reached that     
point in our  intellectual development  
and because ,einstein was living and    
spinning  his webs of thought4 ,and the 
question whether his theory will also   
have  crushed absolutism for the        
non-physicist cannot be answered4    ,it
 may indeed be doubted whether its time 
had already come4 ,in the case  of many 
important events in the history of      

thought their moment of birth  can be   
fixed to within about ten years1 as for 
example the ,theory of  ,evolution1     
which had been conceived in several     
minds at the same time  and had of      
necessity to come to life in one of     
them1 even if it had  failed in the case
 of the others4 ,i venture to say that  
without  ,einstein1 the ,theory of      
,relativity in its widest sense1 that   
is1  including the new doctrine of      
gravitation1 would perhaps have had to  
wait another two hundred years before   
being born4    ,this contradiction is   
cleared up if we use sufficiently great 
time  intervals4 ,history does not adapt
 itself to the time measures of         
politics and of journalism1 and         
philosophies are not to be calculated in
  terms of days4 ,the philosophy of     
,aristotle held sway right through the  
,middle ,ages1 and that of ,epicurus    
will gain its full force only in the    
coming generation4 ,but if we make our  
unit a hundred years the connexion      

between philosophies and great          
discoveries remains true4    ,whoever   
undertakes to explore the necessity of  
this connexion cannot  evade the fact   
that the lines of the result had been   
marked out in the  region of pure       
thought1 as can be proved1 before even  
the great  discovery or invention was   
able to present it in a fully           
intelligible  form4 ,even the           
achievement of ,copernicus would follow 
this general rule  of development3 it   
was the last consequence of the belief  
in the ,sun  ,myth which had never been 
forsaken by man in spite of the violent 
efforts of the ,church and of man       
himself to force the geocentric view4   
,copernicus concentrated what had       
survived of the wisdom of the earliest  
priests--which includes also the germ of
 our modern ideas of energy and         
electricity--of the teachings of        
,anaxagoras and the ,eleatics which had 
remained latent in our consciousness3   
his discovery was the  transformation of

 a myth into science4 ,mankind1 whose   
wandering fancy  first feels            
presentiments1 then thinks and wishes to
 know1 is a large  edition of the       
individual thinker4 ,the latter sees    
further only because  he1 so to speak1  
stands on the shoulders of a sum-total  
of beings with a  world-view4    ,let us
 turn our attention to an example from  
the most recent history of  philosophy  
and discovery4 ,the absolute continuity 
of events was one of  the generally     
accepted canons of thought1 and is even 
nowadays taught by  serious philosophers
 as an incontrovertible element in our  
knowledge4  ,the old quotation ,natura  
non facit saltus1 popularized by ,linn1 
is  one of the formulae of this         
apparently invincible truth4 ,but deep  
down  in the consciousness of man there 
has always been an opposition to it1    
and when the ,french philosopher ,henri 
,bergson set out to break up this  line 
of continuity by metaphysical means in  
ascribing to human knowledge  an        

intermittent1 cinematographic character1
 he was proclaiming in an  audible and  
eloquent form only what had lain latent 
in a new but as yet  incomplete         
philosophy4 ,bergson made no new        
discovery1 he felt his way  intuitively 
into a new field of knowledge and       
recognized that the time  was ripe for  
the real discovery4 ,this was actually  
presented to us in  our day by the      
eminent physicist ,max ,planck1 the     
winner of the ,nobel  ,prize for        
,physics in #aiai1 in the form of his   
,quantum ,theory4 ,this is  not to be   
taken as meaning that a revolutionary   
philosophy and a triumph  of scientific 
research now become coincident1 but only
 that a  discontinuous1 intermittent    
sequence1 an atomistic structure1 was   
proved  by means of the weapons of exact
 science1 to be true of energies which1 
according to current belief1 were       
expected to be radiated regularly and   
connectedly4 ,this was probably not a   
case of the accidental coincidence  of a

 new philosophical view with the results
 of reasoning from physical  grounds1   
but a demand of time1 exacting that the 
claims of a new  principle of thought be
 recognized4    ,as above suggested1 it 
is more difficult to find a link between
  ,einstein's discoveries and antecedent
 presentiments of relativity4 ,for a    
mere reference to the downfall of       
absolutism in the world of human  events
 will not suffice4 ,in the case of      
,einstein1 we see such a  tremendous    
rush of thought in one being that we    
almost feel compelled to  recognize an  
analogy with the ,quantum ,theory and   
believe in a  discontinuity in the      
course of intellectual history4 ,yet    
there are  certainly threads that       
connect ,einstein's achievement with a  
prophetic  insight4 ,in this case1      
however1 we must spread out over        
centuries what  in the case of other    
discoveries extends1 in comparison1 only
 over  decades4 ,that doubt of ,faust1  
which troubles the spirit of every      

thinker3 whether in yonder spheres there
 is also an ,above and a ,below1  and   
which goes back as far as ,pyrrhon and  
,protagoras1 is itself  relativistic2 it
 expresses doubt whether the co-ordinate
 system passing  through our own lifes  
as centres is valid4 ,it is ultimately a
 matter of  point of view1 and the      
mathematico-physical consequences of the
 endless  series of questions1 and the  
relation1 which arises from the couple1 
,above-,below1 probably leads to a new  
mode of comprehending the  constitution 
of the world1 for which ,einstein's     
creative work found the  adequate       
expression in abstract terms4 ,and from 
this point onwards1 in  accordance with 
the principle of reciprocal action1 a   
new stream of  knowledge will pour      
itself into the hazy stretches of       
philosophy4 ,a  fundamental and radical 
reform of our philosophy seems          
inevitable1  particularly with respect  
to our conceptions of ,space and ,time1 
perhaps1  too1 even with respect to     

,infinity and ,causality4 ,much dross   
will have  to be sifted out of our old  
categories of thought and out of our    
world  wisdom1 which once served as     
material for fine structures4 ,what will
 the  finer ones look like that are to  
take their places in obedience to the   
command of physics8 ,who would care to  
take it upon himself to form an         
estimate8    ,much will be uprooted1 and
 it is possible that even the defiant   
ignorabimus1 the antipole of the search 
for truth from ,pyrrhon to  ,dubois1    
will again take up the cudgel4 ,for in  
the face of despairing  uncertainty     
there is the one certainty3 what cannot 
be comprehended is  being encircled more
 and more by the great discoverers6 ,and
 even if the  absolute point of         
convergence can never be reached1 there 
is within our  reach at least another   
point which is a haven of rest in the   
passing  stream of philosophies1 namely1
 a moral centre around which eddies of  
happiness circle4 ,at the heart of this 

world-view there is the uplifting       
belief in an advance of knowledge in    
spite of all1 and a belief in the       
vanishing of age-long problems and      
difficulties under the flood of         
discoveries4 ,and even if afterwards and
 concurrently ever new problems  and    
difficulties arise1 these do not        
suppress our feeling of triumph4  ,every
 achievement in this field gives us a   
sense of enfranchisement from           
prejudices1 not the least of which is   
narrowness of national outlook4  ,not   
only do discoverers construct bridges of
 thought that stretch to  astronomical  
distances1 but1 what is more difficult1 
they build bridges  for our feelings1   
that surmount political obstacles4      
,every thinking  being who plays a part 
in the making of some great discovery   
and who1  with deepened vision1 bows    
before a new achievement of mind1       
gradually  becomes a disciple of the    
religion of universal politics1 the     
creed of  which is faith in the         

brotherhood of thought4 ,the nucleus of 
a  philosophy that belongs to the future
 is the recognition that differing      
national view must be compounded into a 
unity1 and that every great  discovery  
means a step towards attaining this end4
    ,even if we accept ,pascal's        
wonderful dictum that human knowledge is
  represented by a sphere which is      
continually growing and increasing its  
points of contact with the unknown1 we  
must not interpret it as a sign  of     
despair4 ,it is not the enlargement of  
the unknown1 but only that of  knowledge
 that stirs our feelings with ethical   
forces4 ,the positive  calls up in us a 
living force by inspiring in us the     
feeling that the  sphere of knowledge is
 destined to grow1 and that there can be
 no higher  duty for all the energies of
 mind than to obey the call for combined
  action towards this growth which will 
bring the world into harmony4    ,full  
of such reflections ,i entered the home 
of the great discoverer1  whose         

activities unceasingly hovered before my
 vision as ideal examples  of creative  
effort4 ,i discovered him1 as almost    
always1 seated before  loose sheets of  
paper which his hand had covered with   
mathematical  symbols1 with             
hieroglyphics of that universal language
 in which1  according to ,galilei1 the  
great book of ,nature is written4       
,what a very different picture many an  
outsider draws of the manner in  which a
 seeker in the heavens works6 ,he is    
imagined like ,tycho ,brahe to  be      
surrounded by unusual pieces of         
apparatus1 spying through the ocular  of
 a long range refractor into the        
universe1 seeking to unravel its        
ultimate secrets4 ,the true picture does
 not correspond to this fancy in  the   
slightest4 ,nothing in the make-up of   
the room reminds one of  super-earthly  
sublimity1 no abundance of instruments  
or books is to be  seen1 and one soon   
becomes aware that here a thinker reigns
 whose only  requirement for his work1  

which encompasses the world1 is his own 
mind1  plus a sheet of paper and a      
pencil4 ,all that acts on the           
observatories  outside1 that gives rise 
to great scientific expeditions1 that1  
indeed1  ultimately regulates the       
relationship of mankind to the          
constitution of  the universe1 the      
revolution in the knowledge of things   
connecting  heaven and earth1 all this  
is here concentrated in the simple      
figure of  a still youthful scholar1 who
 spins out endless threads from the     
fabric  of his mind3 the words of a poet
 are recalled to our memory1 which1     
addressed to all of us1 have been       
fulfilled to the last degree by one     
living among us3--         ,whereso thou
 roamest in space1 thy ,zenith and      
,nadir unite thee--      ,this to the   
heavenly height1 that to the pole of the
 world1--      ,whatsoever thou do1 let 
thy will mount up into ,heaven--        
,but let the pole of the world still    
o'er thine actions preside4             

7,schiller3 ,translation by ,merivale47 
,and this one helped to fulfil this aim 
and ,i must break off his thread  of    
thought to put the question3 ,what is   
,discovery1 and what does it  signify8  
,it is a purely abstract question that  
may appear to many to be devoid of      
content4 ,such will repeat to           
themselves1 as best they can1 the list  
of  discoveries and think a man makes a 
discovery when he finds out  something  
important1 such as the ,laws of ,falling
 ,bodies1 the formation  of ,rainbows1  
or the ,origin of ,species3 a general   
denomination may be  found for it       
perhaps only by ascribing to ,discovery 
something requiring  a powerful mind1 a 
creative genius4    ,at first it        
staggered me to hear ,einstein say3 ,the
 use of the word  ',discovery' in itself
 is to be deprecated4 ,for discovery is 
equivalent  to becoming aware of a thing
 which is already formed2 this links up 
with  proof1 which no longer bears the  
character of 'discovery' but1 in the    

last instance1 of the means that leads  
to discovery4 ,he then stated at  first 
in blunt terms1 which he afterwards     
elaborated by giving detailed           
illustrations3 ,discovery is really not 
a creative act6    ,arguments for and   
against this view flashed through my    
mind1 and ,i  thought involuntarily of a
 great master of music who1 when he was 
asked3  ,what is ,genius8 answered3 ,a  
genius is one to whom ideas occur4 ,this
  parallel might be carried still       
further1 for ,i have repeatedly heard   
,einstein call ideas what we would      
regard as wonderful thoughts4 ,does  not
 the philosopher ,fritz ,mauthner speak 
of the discovery of gravitation  as     
being an aperu of ,newton2 yes1 in the  
sense of aperus as  applied in ancient  
,greek philosophy1 and which included   
almost  everything that was left by     
,pythagoras1 ,heraclitus1 etc41 as a    
token of  their genius4 ,on the other   
hand1 we are all possessed of the desire
 to  differentiate clearly between an   

idea and a creative act of thought1 as  
occurs in ,grillparzer's aphorism3 ,an  
idea is not a thought2 a thought  knows 
its bounds1 whereas the idea leaps over 
them and succeeds in  accomplishing     
nothing6    ,here1 then1 we must revise 
our view4 ,we know1 for example1 how    
much  ,einstein's ideas1 felt by him to 
be such and named so accordingly1       
accomplished4 ,let us hear how he       
characterizes in a few words his own    
idea which shook the world3    ,the     
underlying thought of relativity1 he    
said1 in connexion with this  question1 
is that there is physically no unique   
7specially favoured7  state of motion4  
,or1 more exactly1 among all states of  
motion there is  none that is favoured  
in the sense that1 in contradistinction 
to the  others1 it may be said to be a  
state of rest4 ,rest and ,motion are not
  only by formal definition but also by 
their intrinsic physical meaning        
relative conceptions4    ,well1 then1 ,i
 interposed1 surely this was a creative 

act6 ,this first  flashed across your   
mind1 ,professor2 it represents your    
discovery1 so  that we may well let the 
word retain the meaning usually         
associated with  it6    ,by no means1   
answered ,einstein1 for it is not true  
that this  fundamental principle        
occurred to me as the primary thought4  
,if this had  been so perhaps it would  
be justifiable to call it a discovery4  
,but  the suddenness with which you     
assume it to have occurred to me must be
  denied4 ,actually1 ,i was lead to it  
by steps arising from the  individual   
laws derived from experience4           
,einstein supplemented this by          
emphasizing the conception invention1   
and ascribed a considerable importance  
to it3 ,invention occurs here as  a     
constructive act4 ,this does not1       
therefore1 constitute what is           
essentially original in the matter1 but 
the creation of a method of  thought to 
arrive at a logically coherent system   
444 the really valuable  factor is      

intuition6    ,i had thought1 long and  
intently1 about these theses to discover
 as  nearly as possible what            
distinguished their content from the    
usual view4  ,the fundamental           
differences suggest an abundance of     
ideas whose  importance grows in value  
as we apply them to various cases as    
illustrations4 ,and ,i feel convinced   
that we shall yet have to occupy        
ourselves with these words of ,einstein1
 which present themselves as a          
confession1 as with the famous          
hypotheses non fingo that ,newton set up
  as the idea underlying his work4      
,the latter as well as the former       
implies something negative3 it denies   
something4 ,in ,einstein's words there  
is apparently a repudiation of the      
really creative act in discovery2 he    
lays stress on the gradual1  methodical 
constructive factors1 not omitting to   
emphasize intuition4  ,there is no other
 course open to us but to seek          
indirectly a synthesis  of these        

conceptions1 and to eliminate what is   
apparently contradictory  in them4    ,i
 consider this possible if we decide to 
subdivide the discovery into a  series  
of individual acts in which succession  
takes the place of  instantaneous       
suddenness ,the creative factor may then
 remain intact2  indeed1 it attains a   
still higher degree of importance if we 
imagine to  ourselves that a series of  
creative ideas must be finked together  
to  make possible a single important    
discovery4    ,the original idea never  
springs fully equipped and armed like   
,minerva  out of the head of its        
creator4 ,and it is wise to bear in mind
 that even  ,jupiter had to suffer in   
his head a period of pregnancy          
accompanied with  great pain4 ,it is    
only in the after-picture that ,pallas  
,athene appears  with the attribute of  
suddenness4 ,it is the nature of our    
myth-building  imagination to leap over 
the actual act of birth so as to give a 
more  brilliant form to the finished    

creation4    ,we feel great satisfaction
 when we learn that ,gauss1 the ,prince 
of  ,mathematicians1 declared in one of 
his valuable flashes of insight3 ,i     
have the result1 only ,i do not yet know
 how to get to it4 ,for in this         
utterance we see above all that he      
emphasizes a lightning-like  intuition4 
,he has possession of a thing1 which is1
 however1 not yet his  own1 and which   
can only become his own when he has     
found the way to it4  ,is this          
contradictory8 ,from the point of view  
of elementary logic1  certainly2 but    
methodologically1 by no means4 ,here it 
is a question of3  ,erwirb es um es zu  
besitzen6 ,this makes necessary a series
 of further  intuitions along the road  
of invention1 and of construction4      
,this is1 then1 where that phase        
commences1 which ,einstein denotes by   
the  word gradual1 or by steps4 ,the    
first intuition must be present2 its    
presence as a rule usually guarantees   
that further intuition will follow  in  

logical sequence4    ,this does not     
always happen4 ,in passing1 we discussed
 several special  cases from which      
particular inferences may be drawn4 ,the
 powerful  mathematician ,pierre ,fermat
 has presented the world with a theorem 
of  extremely simple form which he      
discovered1 a proof of which is being   
sought even nowadays1 two and a half    
centuries after he stated it4 ,in  easy 
language1 it is this3 the sum of two    
squares may again be a square1  for     
example1 #eb  #abb  #acb1 since #be     
#add  #afi2 but the sum of two  cubes   
can never be a cube1 and1 more          
generally1 as soon as the exponent1  the
 power index n1 is greater than #b1 the 
equation xn  yn   zn can never be       
satisfied by whole number values for x1 
y1 and  z2 it is impossible to find     
three whole numbers for x1 y1 and z1    
which1 when substituted in the equation1
 give a correct result4    ,this is     
certainly true2 it is an intuitive      
discovery4 ,but ,fermat's  assertion    

that he possessed a wonderful proof1 is 
for very good  reasons open to          
contradiction4 ,no one doubts the       
absolute truth of the  theorem4 ,but the
 later inspiration1 the next step after 
the intuition1  has occurred neither to 
,fermat nor to anyone else4 ,it cannot  
be  established whether his remark about
 the proof was due to a subjective      
error1 or was baseless4 ,in any case it 
seems probable that ,fermat had  arrived
 at the result per intuitionem without  
knowing the way to it4  ,his creative   
act stopped short2 it was only a first  
flare of a  conflagration1 and did not  
fulfil the condition that ,einstein     
associates  with the conception of a    
logically complete method4    ,we may1  
indeed1 pursue this case of ,fermat     
still further4 ,he had  enunciated      
another theorem1 again per intuitionem1 
namely1 that it was  possible to        
construct prime numbers of any magnitude
 by a formula he  gave4 ,euler later    
showed by a definite example that the   

theorem was  false4 ,it was stated in a 
letter to ,pascal written in #afed in   
the words3  the result of squaring #b   
continuously and then adding #a must in 
each  case be a prime number1 that is1  
#b7bk7  #a must always be a prime no    
matter what value k may have4 ,fermat   
added3 ,this is a property for  the     
truth of which ,i answer4 ,euler chanced
 to try k  #e1 and found  that #bcb  #a 
#d1bid1ifg1big1 which may be represented
 as the product  of #fda and #f1gjj1dag1
 and hence is not a prime4    ,it is    
conceivable that no ,euler might have   
lived1 and that no one else  might have 
discovered this contradiction4 ,what    
would then have been the  position of   
this discovery of ,fermat8    ,we should
 certainly not have disputed its        
creative character1 for we  should have 
said that it corresponds to a fact which
 is fully formed1  but cannot be proved4
 ,but now that we know that the fact    
does not exist  at all1 the tiling      
assumes a different colour4 ,it was not 

a discovery at  all1 but an erroneous   
conjecture4 ,but one would never be able
 to arrive  at an erroneous conclusion  
of this sort without being a            
mathematical  genius1 and having the    
inspiration of the moment4 ,and from    
this again it  follows that to make a   
discovery in the full sense of the word 
the  intuition of the moment does not   
suffice1 but must be supported by a     
series of intuitions1 and this is the   
condition that it become a  permanent   
component of universal truth4    ,the   
fact that ,einstein refers to the action
 of inventing in his  explanation1 gives
 support1 it seems to me1 to the view   
that1 strictly  speaking1 discovering   
and inventing are never to be regarded  
as being  separable4 ,in discovering1   
what has to be constructed persists1 and
 in  inventing1 it is a question of     
finding the path along which there is   
the  promise of success1 be it by a     
method1 a proof1 or by some general     
work4  ,we spoke of works of art1 and ,i

 was delighted to see that ,einstein was
  by no means disinclined to claim      
certain works of pure thought1 which    
are usually placed in the category of   
scientific discovery1 as works of  art4 
,in the latter1 however1 the pure       
process of invention plays the          
prominent part1 for in them something is
 represented that did not exist  at all 
before2 this has repeatedly led to the  
artist's achievement being  given the   
higher rank1 as being properly and      
exclusively creative4 ,the  argument    
runs somewhat along these lines3 the    
infinitesimal calculus  would certainly 
have been discovered even if there had  
been no ,newton  and no ,leibniz1 but   
without ,beethoven we should never have 
had a ,c ,minor  ,symphony1 and never in
 the future would it have appeared1 for 
it was a  subjective1 absolutely        
personal1 and unique product of its     
creator4    ,i believe this may be      
admitted1 and that we may nevertheless  
retain the  view that in the work of    

art1 too1 the act of discovering is to  
be  found4 ,let us consider for a moment
 the elementary substance of the  first 
movement of this fifth symphony1 a      
colossal movement of #ejj bars1  which  
expresses itself quite definitely in    
four notes1 of which one is  repeated   
three times4 ,thus ,destiny thunders at 
the gates is  ,beethoven's motto for    
this section2 it is expressed tonally in
 a  succession of notes which through   
all eternity existed among the  possible
 permutative arrangements of these      
sounds4    ,beethoven1 so it is         
expressed1 invented it4 ,but it is just 
as correct to  say--in ,einstein's      
words--he became aware of what was      
already  formed--that is1 he discovered 
the fundamental theme1 and afterwards   
proved it in terms of musical logic     
unheard-of beauty in a methodical       
elaboration4 ,we may1 indeed1 go further
 still4 ,this motif of four  tones was  
not only extant as an abstractum1 as a  
possible mathematical  arrangement1 but 

also as something natural4 ,czerny1 a   
pupil of  ,beethoven1 to whom the master
 confided many a remark about the origin
 of  his compositions1 reports that a   
bird1 the yellow-hammer1 had sung this  
theme to ,beethoven in the woods4 ,but  
neither the bird nor any other  living  
creature had invented it2 rather what   
could not be created1  because it had   
always been in existence1 became        
objectified in the  medium of sound4    
,beethoven found it2 it was res nullius 
when he found  it and when he discovered
 simultaneously with the succession of  
tones  that they were appropriate for a 
powerful musical representation of      
sombre ,destiny4 ,every theme1 be it of 
,beethoven1 ,bach1 ,wagner1 or anyone   
else1 may be represented graphically by 
a curve 7in the case of ,bach's  fugal  
themes this has1 in fact1 been done for 
special purposes71 and  just as it is   
certain that every elliptic-arc existed 
before all  geometry1 so it may be      
affirmed with equal certainty that      

everything  musical was in existence    
before the advent of composition1 and   
was  merely waiting for a discoverer    
whom we designate the inventor1 the     
creative organ4    ,but may not some of 
this glory be reflected on to scientific
 discovery8  ,when we are in an ecstasy 
of admiration1 we talk of a creative act
 as of  something divine2 may we not    
also grant to the scientist this tribute
  which1 owing to a slight confusion of 
conceptions1 we shower on the  artists8 
,and ,i believe that ,einstein's        
definition does not set up an           
insuperable barrier in this respect to  
our admiration1 which exerts  every     
effort to pass beyond1 refuses to come  
to a standstill before the  rigid fact  
that the discoverer reveals only what is
 preformed2 our  emotions prove to be   
stronger than our minds with their      
objective  valuation4 ,in the last      
instance1 we opine1 the scientific      
discoverer1  too1 creates something new1
 namely1 a piece of knowledge that was  

previously not in existence4 ,and we    
obey the impulse of hero-worship1  when 
we call a definite first discoverer a   
creator4    ,this silences opposition   
certainly only for a time1 without      
vanquishing  it4 ,for this knowledge1   
too1 lay ready before the first         
discoverer  appeared3 he did not create 
it1 but merely drew back the veil that  
enveloped it4 ,so that1 ultimately1 we  
get back to intuition in its  literal   
sense1 a becoming aware of things1 an   
exact consideration of  things1 states1 
and relationships2 and this intensive   
consideration1  full of wonderment1 has 
always been a privilege of a very few   
chosen  men4    ,it might be asked3 ,was
 there any knowledge of ,pythagoras'    
,theorems  before ,pythagoras gave us   
his proof8 ,we should have to answer3   
,it was in  existence at least in the   
still dark field of vision of           
,pythagoras1  which became illumined one
 day when he took such a view of the    
number-ratios #c--d--e that an exact    

intuition could actually come about4    
,it is erroneous to assume that a       
creative act suddenly called up before  
his soul as if by magic the figure with 
the three squares drawn  externally on  
the sides of a triangle4 ,rather1 he    
took his stride 7as  we know from       
,vitruvius7 by considering a triangle   
whose sides were of a  definite length2 
and the well-known proof1 which is      
linked indissolubly  in our minds with  
his work1 is not his at all1 but        
,euclid's4 ,yet our  annals grow musty1 
centuries pass by1 and the credit of    
being the  creator rests with the man   
who first succeeded in getting a clear  
picture of such a triangle4    ,it seems
 natural to test discoveries by         
experiments4 ,the first result of  doing
 this is a very remarkable increase in  
the rate at which the  intuitive process
 has developed4 ,in ancient times1      
intuition1 it seems1  scarcely felt the 
need of proving things by experiment2   
all that was  discovered by ,archimedes 

in mechanics1 by the ,pythagoreans in   
acoustics1  by ,euclid in optics1 may be
 reduced practically to the formula     
heureka1 and it is probably scarcely an 
exaggeration to say that more  and more 
fruitful experiments are performed in   
one week nowadays than in  the whole of 
the classical age taken together4#c     
,footnote #c3 ,recently certain         
precisians in definition have been      
seeking  to establish a fundamental     
difference between physicists of        
reality1  experimental physicists1 and  
blackboard-physicists4 ,the last term is
  given jeeringly to theoretical        
physicists because they1 in the opinion 
of these critics1 wish to found ,nature 
entirely on formul argued out  on the   
blackboard4 ,the history of science does
 recognize this  distinction1 although  
it is1 of course1 quite possible for a  
physicist  to arrive at important       
discoveries without making any          
experiments4    ,one might be more      
justified in asserting that the great   

theorist need  not necessarily be a     
great experimenter and vice versa4 ,but 
,i can quote  no example of a physicist 
who confined himself obstinately to     
blackboard  discussion1 and on principle
 disowned all experimental work4    ,i  
must add that ,einstein himself is fond 
of experimenting1 and has had  much     
success in experimental work4 ,the      
amount of advice and  encouragement that
 he has given1 and still gives1 to many 
workers in  this field is very          
considerable4 ,but he does not practise 
experimental  work regularly1 and       
remarked that he is obliged to appeal to
 outside  help for certain practical    
tests4 ,there are specific experimental 
geniuses1 whose activity assumes the    
happiest and most fruitful form  when it
 supplements that of the theorist and   
fertilizes it4    ,experiments have     
become1 if not the sole1 yet the most   
definite1 test of  intuition4 ,i need   
only recall the observations of the     
solar eclipse of  #aiai1 which were of  

an experimental character inasmuch as   
they used  apparatus to question        
,nature4 ,to the world generally1 they  
gave the  irrefutable confirmation of   
,einstein's ,theory of ,gravitation1 but
 not to  ,einstein himself1 whose       
intuition felt itself so certain that   
the  confirmation was a mere matter of  
course4    ,but this is not the average 
case2 in many cases the intuition of the
  discoverer appeals to experiment as a 
judge of great authority1 who is  to    
confirm1 reject1 or correct4    ,let us 
take some examples of cases in which the
 intensity and the value  of intuition  
were measured by the experimental       
results4 ,benjamin  ,franklin's ,kite   
,experiment may be taken as a classical 
instance4 ,here is  a man in whose head 
the idea takes root that lightning and  
electricity  are one and the same thing4
 ,innumerable persons before and after  
his  time might have hit on the same    
idea1 which is now the common knowledge 
of children4 ,yet1 a single man had to  

appear who became aware of this         
pre-formed fact and who simultaneously  
thought out a method of putting  it to  
proof4 ,in #ageb he constructed a kite1 
sent it up into the clouds  during a    
storm1 and caught up sparks on the      
ground by a metallic  contrivance1 and1 
as d',alembert so aptly described it to 
the ,french  ,academy3          ,eripuit
 coelo fulmen 444      ,he wrested the  
lightning from the heavens4 ,jupiter    
,tonans illuminated a  great discovery1 
a mighty intuition which had entered    
like a lightning  stroke into the brain 
of a discoverer4    ,this case would be 
classical1 were it not that nine-tenths 
of it is  based on legend4 ,franklin was
 by no means the first who had this     
intuition1 and his experimental test was
 so full of faults that it was  within  
an ace of failing4 ,franklin used a dry 
thread of hemp1 which he  thought to be 
a conductor1 but which became a         
conductor only after it  had been made  
wet by rain4 ,till that moment the      

exhibition of sparks on  the ground had 
been poor enough1 and little was wanting
 for ,franklin to  give up his attempt  
and confess that he had been inspired1  
not with an  intuition1 but with a      
hallucination4    ,but to whom then is  
the glory of this discovery due8 ,this  
is a difficult  point to decide4 ,as    
early as #agdf1 that is1 six years      
before ,franklin's  kite made its ascent
 in ,philadelphia1 ,professor ,winkler  
of ,leipzig had  asserted in a          
dissertation that the two phenomena were
 identical1 and  had proved this        
theoretically2 and three years earlier  
still ,abb  ,nollet had declared the    
storm clouds to be the conductors of an 
electrical induction machine4 ,almost   
simultaneously with ,franklin1          
,dalibard1 ,delor1 ,buffon1 ,le         
,monnier1 ,canton1 ,bevis1 and ,wilson  
made  experiments on an elaborate scale1
 which far exceeded that of ,franklin   
in their results4 ,to this must be added
 that the experiment was  conducted with

 evident success only in #agec1 when de 
,romas of ,nerac in  ,south ,france wove
 a real conductor of thin annealed wire 
into the  kite-string1 and succeeded in 
bringing down a regular thunderstorm    
with  flashes of lightning ten feet     
long1 accompanied by a deafening uproar4
  ,it was only then that the track of   
the inspiration was traced back  through
 time to the ,roman ,kings1 ,numa       
,pompilius and ,tullus ,hostilius1 as   
the first experimenters with lightning4 
,and then the physicist  ,lichtenberg   
sought to furnish a proof that the old  
,hebrew ark of the  ,covenant1 together 
with the tabernacle1 were nothing other 
than great  pieces of electrical        
apparatus highly charged with           
electricity derived  from the air2 thus 
the first intuition1 and the priority of
 discovery1  would have to be ascribed  
to ,moses or ,aaron6 ,and connected with
 this was  the fact1 supported by       
substantial proof1 that the ,temple of  
,solomon was  protected by              

lightning-conductors4    ,i must not    
omit to mention that ,einstein regards  
this whole chain of  proofs stretching  
back to early times as by no means      
established1  although besides          
,lichtenberg1 other important scholars1 
such as ,bendavid  in ,berlin and       
,michaelis in ,gttingen1 have vouched   
for their truth4 ,and  as it is a matter
 of electrical relationships1           
,einstein's doubts cannot  be passed    
over4 ,as far as ,i recollect1 they were
 not directed against  the rough facts  
in themselves1 but against the sense    
that is construed  into them--that is to
 say1 in the case of both the ancient   
,roman and the  ,biblical data1 the     
conception of discovery must be         
excluded1 and must be  awarded rather to
 those intellectual efforts which have  
led to the  creation of a method of     
thought4 ,none the less1 we may uphold  
our  statement that in this case1       
presumed to be classical1 neither       
,franklin  nor anyone else is to be     

claimed as the discoverer or as the     
central  figure in a creative act4      
,the experimental case of spectral      
analysis is incomparably simpler and    
less open to dispute4 ,it is without    
doubt a discovery of fundamental        
importance bearing all the              
characteristics of originality1 for no  
predecessors are discernible4 ,i have   
always felt a little dissatisfied  with 
the fact that it required two men to    
think it out1 that a duo of  minds was  
necessary for one act of thought which  
appears quite uniform1  elementary and  
inseparable from the intuition of a     
single mind4 ,but it  seems possible    
that tradition has not handed the facts 
down to us  faithfully1 and that the two
 men1 with a unanimity arising from     
their  partnership in work1 combined    
their results1 which were not1 at the   
beginning1 of a dual character4 ,this   
possibility became clear to me from  a  
remark of ,einstein which made it plain 
to me that the conjunction  ,kirchhoff  

and ,bunsen is to be taken as denoting  
,kirchhoff and then1  after a pause1    
,bunsen in the next breath6 ,but if we  
discard this  question of unity or      
duality1 we are left with the fact that 
the idea of  a spectral analysis        
occurred to some one 7as a result of    
preceding  optical experiments with     
,fraunhofer lines71 and was fully       
confirmed by  later experiments4 ,only  
fully confirmed8 ,no1 the classic rank  
of this  case manifested itself in a    
much more triumphant manner1 for it is  
impossible that the intuition of        
,kirchhoff and ,bunsen could have       
grasped  the whole significance and     
range of their discovery even after they
 had  made it their own4    ,every      
discovery encloses a germ of hope4      
,however great this may have  been in   
the case of ,kirchhoff1 it could not by 
any stretch of  imagination approach the
 degree of its fulfilment4 ,the         
fundamental  theoretical idea that a    
vapour absorbs from the ray-complex of  

white  light only those wave-lengths    
which it can emit gave rise to a        
process1  the ingenuity1 delicacy1 and  
certainty of which is almost            
inconceivable4  ,when rays of light     
emitted by incandescent vapour were     
separated by a  prism1 there were       
discovered fine coloured lines that     
betrayed some  unknown mystery4 ,the    
spectroscopic experiments proved1 in a  
succession  of results1 that the author 
of the above idea had made not only one 
discovery1 but a whole host of them4    
,for example1 it was observed that1  in 
burning minute residues obtained by     
evaporating certain mineral  waters1 a  
red line and a blue line that had never 
been seen before  appeared in the       
spectrum4 ,one knew immediately that an 
element1 hitherto  undiscovered1 was    
proclaiming its presence4 ,in this way  
in quick  succession the element ,csium 
was discovered1 then ,rubidium1         
,thallium1  ,indium1 ,argon1 ,helium1   
,neon1 ,krypton1 ,xenon--certainly      

things that were  already pre-formed in 
,nature1 just as the idea of a bridge   
from ,optics  to ,chemistry lay all     
ready in the heart of ,nature2 but no   
blame can be  given to the astonished   
contemporaries who regarded this        
fundamental  discovery of spectroscopic 
analysis as a creative achievement of   
the  intellect4    ,this ray of hope    
gave a glimpse of the degree of accuracy
 attainable4 ,in  this connexion the    
experiment confirmed infinitely more    
than the boldest  imagination could ever
 have dreamed4 ,a yellow line was       
detected in the  spectrum of sodium4    
,and it was found experimentally that   
the  three-millionth part of a          
thousandth of a gramme of a sodium salt 
is  sufficient to produce this sodium   
line in the spectrum of a ,bunsen       
burner4 ,there commenced a dizzying     
passage in the ,calculus of             
,probabilities for1 since it was found  
that in the sun's atmosphere  hydrogen1 
carbon1 iron1 aluminium1 calcium1       

sodium1 nickel1 chromium1  zinc1 and    
copper were present1 the question arose 
as to how great was  the possibility of 
an error in this observation4 ,kirchhoff
 calculated it  as a chance of a        
trillion to one that these substances   
are actually  present in the sun6       
,never before had an experiment verified
 to such an extreme degree a            
discoverer's idea4 ,it seems appropriate
 at this stage to deal with a  doctrine 
which seeks to shed light into the      
deepest recesses of the  connexion      
between experiment and discovery4 ,it   
teaches that an  experimentum crucis1 an
 experiment that verifies absolutely1 is
  impossible in physics4 ,that is to    
say1 every idea of a discoverer         
involves a hypothesis1 and1 however the 
experiment that follows may turn  out1  
there still remains the possibility that
 this hypothesis was false1  and may    
later have to make way for another      
essentially contradictory  hypothesis   
which will be valid again only for a    

limited time4    ,the chief exponent of 
this theory is the eminent scholar1     
,pierre ,duhem1  ,membre de l',institut4
 ,he draws a parallel between experiment
 and  mathematical proof1 particularly  
with the indirect1 apagogic form which  
has been so successfully applied in     
,euclidean geometry4 ,in this method  it
 is assumed that a certain statement is 
erroneous2 it is then shown  that it    
leads to an obvious contradiction2      
consequently the statement  was correct 
provided that a certain doubt be        
excluded4 ,thus in the  domain of       
mathematics we have a real experimentum 
crucis4    ,in accordance with this1    
,duhem tests the validity of two        
physical  theories1 both of which were  
put forward and claimed as discoveries4 
,newton had discovered the nature of    
light to consist in emission2 to  him1  
as well as to ,laplace and ,biot1 light 
consists of projectiles that  are       
emitted with very great velocity4 ,the  
discovery of ,huyghens1  supported by   

,young and ,fresnel1 substitutes        
wave-motion in place of  corpuscular    
emission4 ,hence1 according to ,duhem1  
we have1 or we had1  here two hypotheses
 which appear to be the only ones       
possible4  ,experiment was to pronounce 
a judgment1 and at first it decided     
irrefutably in favour of the            
wave-theory4 ,therefore1 the discovery  
of  ,huyghens is alone true1 and that of
 ,newton is shown to be an error2  there
 is no third outlet1 and so we have     
quite certainly an  experimentum crucis 
before us4    ,the term itself          
originates in ,bacon's ,novum ,organum4 
,contrary to  ,duhem's assumption1 it   
does not refer to a signpost at         
cross-roads  giving various routes1 nor 
is it connected with croix ou pile1     
heads  or tails4 ,experimentum crucis   
denotes rather a divine judgment at the 
cross1 that is a test that is absolutely
 decisive and beyond further  appeal4   
,but no6 adds ,duhem1 there is no room  
for a third judgment in the  case of two

 contradictory statements in geometry1  
but there is between  two contradictory 
statements in physics4 ,and1 in fact1   
this third  possibility has manifested  
itself in the discovery of ,maxwell1 who
 has  shown that the nature of light is 
founded on a process of periodic        
electromagnetic disturbances4 ,hence1 so
 concludes ,duhem1 experiment can  never
 decide whether a certain theory is     
alone valid4 ,the physicist is  never   
certain that he has exhausted all       
conceivable possibilities1 of  thought4 
,the truth of a physical statement1 the 
validity of a discovery1  cannot be     
confirmed by any experimentum crucis4   
,according to this argument1 therefore1 
it is also possible that the  scientific
 grounds of spectral analysis do not    
conform to truth4 ,a  contradictory     
hypothesis may1 indeed1 be set up1 with 
the result that  the same experiments   
that had led ,kirchhoff's discovery from
 one triumph  to another would have to  
be interpreted in a totally different   

sense4    ,i must frankly confess that  
,i cannot subscribe to such an extreme  
eventuality1 since1 in my opinion1      
,duhem's analogy with mathematics       
excludes this possibility4 ,for if a    
certain probability is expressed by  a  
trillion to one1 then ,i venture to     
state that even in the case of          
mathematical truths certainty reaches no
 higher degree of probability4  ,from   
the history of mathematics we know of   
theorems which were  enunciated and     
provided with complete proofs1 and yet  
did not succeed in  establishing        
themselves2 hence we see that1 however  
evident a  mathematical theorem may be1 
it is still only a matter of very great 
probability4    ,if1 following our usual
 habits of thought1 we take this for    
absolute  certainty1 then we may also   
consider the sum-total of experiments in
 the  realm of spectral analysis to be a
 great experimentum crucis for the      
correctness of the theory itself4       
,far removed from it1 and yet connected 

with it1 there is the ,periodic  ,system
 of the ,elements1 the discovery of     
,mendelejew and ,lothar ,meyer4  ,it1   
too1 offered prophetic glances into the 
future1 foretold the  unknown1 hinted at
 things that were present only in       
imagination in a  scheme of thought that
 assigned definite places of existence  
to  undiscovered things4 ,the ,periodic 
,system is represented by a table       
containing vertical and horizontal rows1
 in the squares of which the  elements  
are entered according to certain rules  
depending on their  atomic weights4 ,the
 discovery consisted theoretically in   
stating that  the physical and chemical 
properties of each element is the       
arithmetic  mean between the properties 
of its horizontal and vertical          
neighbours4  ,this gave rise to         
predictions concerning the unoccupied   
squares4 ,these  gaps1 these blank      
spaces in the table1 seem to say        
prophetically3 ,there  are elements     
missing here that must be discoverable4 

,the neighbours will  betray them1 and  
the empty space itself shows by what    
means they are to  be found4 ,with the  
shrewdness of a detective1 ,mendelejew  
was able to  say3 ,there must be        
elements of the atomic weights #dd1 #gj1
 and #gb2 we do  not know them yet1 but 
we are in a position to determine the   
properties  of these foundlings of the  
future1 and1 what is more1 the          
properties of  their compounds with     
other elements4 ,later researches1 which
 led to the  discovery of the elements4 
,scandium1 ,gallium1 and ,germanium1    
have  actually confirmed all these      
predicted properties4    ,the metal     
,gallium was discovered in #ahge by     
spectroscopic means4 ,its  properties   
are the mean of those of ,aluminium and 
,indium1 and this  places it in a       
position which had already been assigned
 to it in the  periodic table before its
 discovery2 for1 owing to a gap in the  
system1  ,mendelejew had asserted its   
existence five years previously1        

although he  then knew nothing of its   
characteristic spectral signs1 namely1  
two  beautiful violet lines4 ,radium1   
too1 which was discovered in #aijj and  
was found to have the atomic weight     
#bbf1 completely satisfied this test    
and fitted exactly into the place which 
this number reserved for it in  the     
table4 ,thus prediction and confirmatory
 discovery were fully  congruent in this
 case2 the experiment followed on the   
visionary insight  just as a ,euclidean 
proof follows on a mathematical         
assertion1 and we  have every reason to 
say that the system of ,mendelejew and  
,lothar ,meyer  has stood the crucial   
test4 ,future hypotheses will perhaps   
supplement  the system or enlarge our   
knowledge of it1 but will certainly not 
reduce  it ad absurdum4         99      
99     99     99     99     99     99   
99    ,apart from these cases1 there are
 achievements by men who may be called  
lucky discoverers1 although they        
displayed no genius for finding nor  for

 creating4 ,the philosopher-physicist1  
,ernst ,mach1 has devoted a  lecture to 
such intellects1 which seems to me very 
valuable1 if only for  the reason that  
he traces back the conceptions of       
discovery and  invention to one common  
root of knowledge1 and explains their   
difference  as being due only to a      
difference in the application of this   
discovery4    ,but when ,ernst ,mach in 
this lecture1 ,on the ,influence of     
,accidental  ,circumstances on the      
,development of ,inventions and         
,discoveries1 extends  the influence of 
chance to include accidental            
circumstances that can  only enter when 
the discoverer is closely attentive1 it 
seems to me that  certain limitations   
are advisable4 ,otherwise1 if we pursue 
,mach's line  of thought to its extreme1
 we could declare every discovery to be 
due to  chance1 and this would be the   
end of the intuitive-creative idea4     
,this  assertion would ultimately mean  
that genius owes its achievements to the

  accidental arrangement of the         
molecules in the brain-cells of its     
associated body4 ,this would be just as 
wrong as saying that chess is a  game of
 chance because we lose a game when1 by 
chance1 we come up  against a better    
player4    ,huyghens1 the great         
discoverer and inventor1 says1 in his   
,dioptrica1  that he would have to      
consider anyone who invented the        
telescope without  the favourable       
intervention of chance to be a          
superhuman genius4 ,why  should he      
choose just the telescope8 ,to many the 
invention of the  ,differential         
,calculus will appear grander and due to
 a higher degree of  ingenuity4 ,and    
since it was produced quite             
methodically1 and since  chance was     
excluded1 we may follow ,huyghens and   
with good reason  proclaim its authors  
superhuman geniuses4         99     99  
99     99     99     99     99     99   
,many a true inspiration is dependent on
 some impulse from without4 ,who        

discovered ,electromagnetism8 ,the      
world-echo answers1 ,oersted1 with the  
same confidence that it couples together
 the names ,america and ,columbus4      
,this shows how enormously important was
 the achievement4 ,next to  steam-power 
nothing has exerted such a revolutionary
 influence in all  branches as          
electromagnetism4 ,without it1 the world
 of to-day would  present a totally     
different aspect4 ,without it1 we should
 have no  dynamos1 no electric trams1 no
 telegraphy1 no electric-power stations1
  all of which are due to the work of   
,arago1 ,gay-,lussac1 ,ampre1 ,faraday1 
,gramme1 and ,siemens4 ,without it1     
there would be none of the abundance of 
brilliant discoveries that are          
associated with the names of ,maxwell1  
,hertz1 and ,einstein4 ,the fact that   
physics used to be divided into three   
parts--,mechanics1 ,optics1             
,electrodynamics--and that1 since then1 
the  coherent unity of the physical     
picture of the world has been developed1

  shows us a picture in the background  
of which we see the illuminating  figure
 of ,hans ,christian ,oersted4 ,it must 
not be overlooked1 however1  that in the
 case of his great discovery1 too1      
chance played a definite  part4 ,it     
occurred one day when ,oersted was      
holding a lecture in the  winter of     
#ahai-bj2 a magnetic needle situated    
near his ,volta-battery  began to       
vibrate irregularly4 ,this apparently   
unimportant trembling of  the metal     
points contained the key to a fact1 the 
whole consequences of  which could in no
 conceivable way have entered the mind  
of this observer  of a hundred years    
ago1 in spite of the genius of the      
,danish scientist1  which is documented 
in the classical and far-famed          
dissertation1  ,experimenta circa       
effectum conflictus electrici in ,acum  
magneticam1  which appeared in ,july    
#ahbj4 ,it cleared the way for          
intuitions that were  equally as        
fruitful for theory as for practice4    

,thirteen years after  this initial     
discovery the world saw the first very  
important  consequence in ,gauss' and   
,weber's electric telegraph1 and a      
little later  the eminent discoverer    
,fechner1 in ,leipzig1 proclaimed it as 
his  conviction that1 within two years1 
electromagnetism would entirely  reform 
the world of machines1 and would        
entirely supersede steam- and           
water-power4 ,of course1 his time       
estimate fell far short of the mark4 ,it
  has been reserved for the present     
generation to realize that we live in   
an electromagnetic world1 and that we   
have1 theoretically and  practically1 to
 spend our life electromagnetically4    
,the first indication  of this knowledge
 hung upon the quivering point of a     
magnetic needle1  and from it there     
evolved the electromagnetic ideas that  
we are so fond  of picturing as our     
handmaids1 but which1 in reality1 are   
sovereign over  us all4         99      
99     99     99     99     99     99   

99    ,a great deal of the history of   
discovery must be revised and corrected4
  ,the ,spiral of ,archimedes is not due
 to ,archimedes1 nor ,marriotte's ,law  
to ,marriotte1 nor ,cardan's formula to 
,cardan1 nor ,crookes' ,tube to         
,crookes1 and ,galvanism is only related
 to ,galvani by the following  anecdote4
 ,it arose from an accidental experience
 of ,madame ,galvani in  the kitchen3 a 
half-skinned frog that was to be fried  
for the evening  meal happened to rest  
between a scalpel and a tin plate1 which
 brought  it into metallic contact with 
an accidental discharge of electricity2 
the frog twitched2 the head of the house
 gave a very nave  interpretation to the
 phenomenon2 and it was under such      
auspices that  ,galvanism made its entry
 into the world4 ,it would be a futile  
task to  endeavour to trace the         
connexion between experiment and the    
underlying  idea1 which1 in this case1  
first came to life in ,alexander ,volta4
 ,what  would have remained a mere      

frog-dance if left to ,galvani now      
acquired  the rank of a discovery       
through the work of a thinking          
physicist1 who  set up a ,voltaic       
series2 this discovery then assumed     
power and dignity  in the hands of      
,nicholson1 ,davy1 ,thomson1 ,helmholtz1
 and ,nernst4 ,the  words ,galvanic     
,electricity should be made to give way 
entirely to  ,voltaic ,electricity1#d as
 in the case of many another expression 
for  which chance and insufficient      
thought have stood sponsor4    ,footnote
 #d3 ,the usual term in ,england is     
,voltaic ,electricity1 or1  simply1     
,current ,electricity4--,h4 ,l4 ,b4     
,it often happens that experiment acts  
as a corrective of the underlying  idea1
 neither confirming nor contradicting1  
but nursing it1 as it were1             
strengthening1 and purging it of errors4
 ,such experiments1 partly in           
conjunction with chance1 play an        
important1 sometimes a decisive1 rle  in
 the works of ,dufay1 ,bradley1         

,foucault1 ,fresnel1 ,fraunhofer1 and   
,rntgen4 ,faraday1 who was incapable of 
observing otherwise than  intensively1  
found himself compelled1 whilst studying
 induction  phenomena1 to alter his     
initial view1 and it is just this       
correction by  experiment that          
constitutes ,faraday's real discovery4  
,in many cases the  initial idea is     
corrected1 nay surpassed1 by the result4
 ,columbus worked  methodically when he 
set out to reach the ,east ,indies by   
travelling  westwards2 but what he      
discovered was not a confirmation of his
 nautical  idea only1 but something much
 greater1 which certainly did not lie in
  his calculation4 ,thus he became the  
archetype of all searchers1 who had     
thought out and anticipated essentially 
different conditions from those  that   
were afterwards discovered to be        
prevalent4 ,among these are to be       
counted ,priestley and ,cavendish1 who  
clung to the erroneous notion of        
phlogiston1 even when they had the      

evidence to the contrary in the         
elements they had themselves discovered1
 namely1 oxygen and hydrogen4  ,graham  
,bell1 the inventor1 was seeking        
something quite different from  what he 
later hit on3 as a teacher of the deaf  
and dumb he was trying to  give a visual
 picture of sounds1 in order to make    
clear the formation of  sounds to his   
pupils2 this led him to construct an    
electrical apparatus1  which finally led
 to the discovery of the telephone4     
,the truest and sharpest contrast with  
the experimentum crucis is  furnished by
 experiment when it shows the exact     
opposite of what the  explorer was      
expecting4 ,but since an absolute ,no   
entails a very decisive  ,yes--namely1  
in this case1 the affirmation of a      
relationship that was  previously held  
to be impossible--a negative experiment 
of this kind1  when it occurs1 will be  
followed by momentous consequences2     
these will  be the more important in    
proportion as the question1 the         

affirmation of  which was expected by   
the physicist1 is of a fundamental      
character4    ,the experiments of       
,michelson and ,morley1 directed at     
proving the  existence of the ether1 are
 to be regarded as the true classical   
instances of these experiments answering
 with an overwhelming negative4  ,their 
first effect was to produce a sense of  
helplessness1 a check to  thought1 a    
void in the chamber of ideas4 ,and to   
fill this void there  arose new views of
 the world in which we nowadays         
recognize the true  thought-pictures of 
the universe4 ,the great                
names--,lorentz1 ,minkowski1  ,albert   
,einstein--shone out6    ,as there are  
forerunners for almost every ,important 
event1 so also in  the case of the      
experimentum crucis of ,michelson and   
,morley4 ,henri  ,poincar1 the famous   
mathematician1 whilst still a student of
 the  cole ,polytechnique1 had initiated
 experiments with his fellow-student    
,fav1 which followed the same object4   

,the ,michelson-,morley experiment  was 
at least a hundred times more accurate4 
,in each case the conclusion  was that  
the laws of optics are not disturbed by 
a motion of  translation1 such as that  
of the earth through space this is1     
however1  contrary to what the old      
physical ideas lead us to expect4    ,if
 we assume the existence of a           
space-filling ether1 the earth1 owing to
  its own velocity of nineteen miles per
 second1 would have to pass  through a  
hurricane just as in the case of        
travellers sitting in an open  train    
rushing along at very great speed4 ,if  
we send out light rays in  all          
directions simultaneously from any point
 on the earth's surface1  some will     
travel in the teeth of the ether-storm1 
others will experience  only a part of  
the storm's power2 so that of two       
light-rays travelling  in exactly       
opposite directions the retardation of  
the one should be  equal to the         
acceleration of the other2 and yet they 

are not quite  equal1 for a simple      
calculation shows that in every case the
 retardation  is slightly more than the 
acceleration4    ,this may be made clear
 by means of a model of easy            
construction1 or1  better still1 by     
considering a ship that is subject to a 
constant  current and1 simultaneously1  
to a pressure of the wind4 ,the time    
taken  by the boat in making a trip up  
and down stream can never be the same   
for the cases when the wind is in the   
direction of the current1 and vice      
versa4    ,in the case of the ray of    
light1 which is sent backwards and      
forwards by  means of a contrivance of  
mirrors1 this fact should be clearly    
demonstrated by means of the            
interference-fringes1 which are able to 
show much smaller effects than the      
experiment demands4 ,the experimental   
oracle was to speak1 but it remained    
silent4 ,this portentous silence        
signified3 no interference-effect1 no   
action of the ether-current1 no         

influence due to translation--nothing6  
,this nothing compelled a decision of a 
very startling kind1 for the  result of 
this experiment was in direct           
contradiction to another famous         
experiment4 ,fizeau had proved that the 
ether is practically rigid and  remains 
fixed in interstellar space4 ,a decision
 had to be taken in  favour of ,fizeau  
or ,michelson and ,morley4 ,yet this was
 impossible1 for  both had operated with
 unsurpassable accuracy4 ,it was        
impossible to  reconcile both views as  
they were diametrically opposed4 ,this  
contradiction remains1 even if we assume
 a different hypothesis1 not  involving 
the ether1 for ,fizeau's experiment4 ,a 
solution was impossible  without        
undertaking revolutionary changes in the
 whole of physical  thought4    ,this   
radical change was effected by          
,einstein2 and this mysterious          
contradiction disappeared in the        
resulting revolution of thought4        
,einstein supplanted the absolute       

time-conception by a new relative       
conception1 and thus the perplexing     
problem disappeared4 ,two great         
principles arose as regulative factors  
in thought1 and wherever these  were    
applied1 they achieved wonders3 one was 
the new conception of time  that        
deprived the earth of her unique        
position as the sovereign of time  by   
the introduction of the principle that  
the rate at which time elapses  is      
different in media moving at different  
speeds2 the other is the  principle of  
the constancy of the velocity of light4 
,one feels a  temptation to apply a     
mythical allegory3 just as the world1   
according to  the ,biblical story1      
originated from nothing1 so there arose 
from the  nothing of the                
,michelson-,morley experiment a new     
world1 a world of  knowledge1 a cosmos  
of thought1 in which perfect harmony    
reigns4    ,its truth was contained in  
itself before the experimental proof was
  furnished4 ,and this realization of   

truth has become a fact in the          
experimentum crucis for which the sun   
and stars formed the material4  ,this   
will be discussed in another part of the
 book4    ,the really important factor  
is ultimately intuition1 ,einstein had  
said  to me4 ,it made me think of       
,huyghens' remark about the genius who  
would  have been able to create the     
telescope without the help of chance4   
,was  not this intellect1 imagined by   
,huyghens1 sitting opposite me at that  
moment8 ,an inner voice answered in the 
affirmative1 for ,einstein's            
thought-complex seemed to me at that    
moment a kind of telescope for the      
human mind1 a telescope that had arisen 
out of pure intuition1 and whose  range 
stretched to the limits of the universe4
          ,,chapter ,,vi    ,,of        
,,different ,,worlds    ,imaginary      
,experiment with                        
,lumen4--,impossibilities4--,a          
,destroyed  ,illusion4--,is the ,world  
,infinite8--,surface ,creatures and     

,shadow  ,rambles4--,what is the        
,beyond8--,action at a                  
,distance4--,ideas of                   
,multi-dimensional                      
,regions4--,hypnotism4--,recollections  
of ,zllner4--,science  and ,dogma4--,the
 ,trial of ,galilei4      ,,conversation
 held during ,april #aibj destroyed an  
illusion which had  become dear to me4  
,it concerned the fantastic figure1     
,lumen1 conceived as an actual  human   
being1 imagined as endowed with an      
extraordinary power of motion  and      
keenness of sight4 ,mr4 ,lumen is       
supposed to be the invention of the     
astronomer ,flammarion1 who produced him
 in the retort of fancy1 as ,faust      
produced ,homunculus1 to use him to     
prove the possibility of very           
remarkable happenings1 in particular1   
the reversal of ,time4    ,einstein     
declared outright3 ,firstly1 ,lumen is  
not due to ,flammarion1  who has derived
 him from other sources2 and secondly4  
,lumen can in no  way be used as a means

 of proving things4    ,,moszkowski3 ,it
 is at least very interesting to operate
 with him4 ,lumen  is supposed to have a
 velocity greater than that of light4   
,let us assume  this as given1 then the 
rest follows quite logically4 ,if1 for  
example1  he leaves the earth on the day
 of a great event1 such as the battle of
  ,waterloo1 and---- ,may ,i trace out  
this example1 at the risk of tiring     
you8    ,,einstein3 ,do repeat it1 and  
act as if you were telling something    
entirely new4 ,it is clear that the     
,lumen-story gives you great  amusement1
 so please talk quite freely4 ,but ,i   
cannot forgo the privilege  of showing  
later how the whole adventure and its   
consequences must be  demolished4       
,m43 ,well then1 the person1 ,lumen1    
sets off at the end of the battle of    
,waterloo to make an excursion into     
space with a speed of #bej1jjj miles    
per second4 ,he thus catches up all the 
light-rays that left the field of       
battle and moved in his direction4      

,after an hour he will already have     
attained a lead of about twenty minutes4
 ,this lead will be gradually           
increased1 so that at the end of the    
second day he will no longer be  seeing 
the end of the battle1 but the          
beginning4 ,what has ,lumen been  seeing
 in the meantime8 ,clearly he has been  
observing events happening  in the      
reverse direction1 as in the case of a  
cinematograph which is  exhibiting      
pictures backwards4 ,he saw the         
projectiles leaving the  objects they   
had struck1 and returning into the      
mouths of the cannon4 ,he  saw the dead 
come to life1 arise1 and arrange        
themselves into battalion  order4 ,he   
would thus arrive at an exactly opposite
 view of the passing  of time1 for what 
he observes is as much his experience as
 what we  observe is ours4 ,if he had   
seen all the battles of history and1 in 
fact1  all events happening in the      
reverse order1 then in his mind before  
and  after would be interchanged4 ,that 

is1 he would experience time  backwards2
 what are causes to us would be effects 
to him1 and our  effects would be his   
causes2 antecedents and consequents     
would change  places1 and he would      
arrive at a causality diametrically     
opposite to our  own4 ,he would be quite
 as justified in adopting his view of   
the  happening of things1 according to  
his experiences1 and of the causal      
nexus as it appears to him1 as we are   
justified in adopting ours4             
,,einstein3 ,and the whole story is mere
 humbug1 absurd1 and based on false     
premises1 leading to entirely false     
conclusions4    ,m43 ,but it is only to 
be taken as an imaginary experiment that
 plays  with fantastic impossibilities  
to direct our ideas on to the relativity
  of time by a striking illustration4   
,did not ,henri ,poincar adduce this    
extreme example to discuss the reversal 
of time8    ,,einstein3 ,you may rest   
assured that ,poincar1 even if he used  
this  example as an entertaining        

digression in his lectures1 took the    
same  view of ,lumen as ,i do4 ,it is   
not an imaginary experiment3 it is a    
farce1  or1 to express it more bluntly1 
it is a mere swindle6 ,these experiences
  and topsy-turvy perceptions have just 
as little to do with the  relativity of 
time1 such as it is taught by the new   
mechanics1 as have  the personal        
sensations of a man1 to whom time seems 
long or short  according as he          
experiences pain or pleasure1 amusement 
or boredom4 ,for1  in this case1 at     
least the subjective sensation is a     
reality1 whereas  ,lumen cannot have    
reality because his existence is based  
on nonsense4  ,lumen is to have a speed 
greater than that of light4 ,this is not
 only an  impossible1 but a foolish     
assumption1 because the theory of       
relativity  has shown that the velocity 
of light cannot be exceeded4 ,however   
great  the accelerating force may be1   
and for however long it may act1 it     
cannot cause this limit to be           

transcended4 ,lumen is supposed to be   
equipped with the organ of sight1 that  
is1 he is supposed to have a  corporal  
existence4 ,but the mass of a body      
becomes infinitely great when  it       
reaches the velocity of light1 so that  
it is quite absurd to go  beyond this   
stage4 ,it is admissible to operate with
 impossibilities in  imagination1 that  
is1 with things that contradict our     
practical  experience1 but not with     
absolute nonsense4 ,that is why the     
other  adventure of ,lumen1 in which he 
jumps to the moon1 is also an absurdity4
  ,in this1 he is supposed to leap with 
a speed greater than light1 and1  when  
he reaches the moon1 to turn round      
instantaneously1 with the result  that  
he sees himself jumping from the moon to
 the earth backwards6 ,this  jump is    
logically meaningless2 and if we try to 
make deductions of an  optical nature   
from such a nonsensical assumption1 we  
deceive ourselves4    ,m43              
,nevertheless1 ,i should claim          

extenuating circumstances for this case 
on the ground that ,i am enlisting the  
help of the conception of               
impossibility4 ,a journey even at a     
speed of only #ajjj miles per second  is
 impossible for a man or a homunculus4  
,,einstein3 ,yes1 according to our      
experience1 if we measure it against    
facts4 ,we cannot state definitely that 
a journey into the universe at an       
enormous yet limited velocity is        
absolutely impossible4 ,within the      
indicated bounds every play of thought  
that is argued correctly is  allowable4 
,m43 ,now1 suppose that ,i strip ,lumen 
of all bodily organs and take him as    
being a pure creature of thought1       
entirely without substance4 ,a velocity 
greater than that of light can be       
imagined1 even if it cannot be  realized
 physically4 ,if1 for example1 we think 
of a lighthouse with a  revolving light1
 and consider a beam of light about #fjj
 miles long1  which rotates #bjj times  
per second4 ,then we could represent to 

ourselves  that the light at the        
circumference of this beam travels with 
a speed of  nearly #gfj1jjj miles per   
second4    ,,einstein3 ,as for that1 ,i 
can give you a much better example of   
the same  thing4 ,we need only imagine  
that the earth is poised in space1      
motionless1 and non-rotating4 ,this is  
physically admissible4 ,then the  most  
distant stars1 as judged by us1 would   
describe their paths with  almost       
unlimited velocities4 ,but this projects
 us right out of the world  of reality  
into a pure fiction of thought1 which1  
if followed to its  conclusion1 leads to
 the most degenerate form of            
imagination1 namely1 to  pathological   
individualism4 ,it is in these realms of
 thought that such  perversities as the 
reversal of time and causality occur4   
,m43 ,dreams1 too1 are confined to the  
individual4 ,reality constrains all     
human beings to exist in one and the    
same world1 whereas1 in dreams1  each   
one has his own world with a different  

kind of causality4  ,nevertheless1      
dreams are a positive experience1 and   
signify a reality  for the dreamer4     
,even for waking reality it would be    
easy to construct  cases in which the   
causal relationship is shattered4       
,suppose a person  who has grown up in a
 confined retreat1 such as ,kaspar      
,hauser1 looks in  a mirror for the     
first time in his life4 ,as he knows    
nothing of the  phenomena of optical    
reflexion1 he sees in it a new1         
objective world  that gives a shock to1 
or even subverts1 his own idea of       
causality in so  far as it may have     
become developed in him4 ,lumen sees    
himself jump  backwards1 whereas ,kaspar
 ,hauser sees himself performing        
gestures on the  wrong side of his body2
 should it not be possible to draw a    
reasonable  parallel between these two  
cases8    ,,einstein3 ,quite impossible4
 ,however you set about it1 your ,lumen 
will  inevitably come to grief on the   
conception of time4 ,time1 denoted in   

physical expressions by the symbol t1   
may1 indeed1 be given a negative  value 
in these equations1 so that an event may
 be calculated in the  reverse          
direction4 ,but then we are dealing with
 pure matters of  calculation1 and in   
this case we must not allow ourselves to
 be drawn  into the erroneous belief    
that time itself may travel negatively1 
that  is1 retrogressively4 ,this is the 
root of the misapprehension3 that what  
is allowable and indeed necessary in    
calculations is confused with what  may 
be thought possible in ,reality4#e      
,whoever seeks to derive new  knowledge 
from the excursions of a creature like  
,lumen into space1  confuses the time of
 an experience with the time of the     
objective event2  but the former can    
have a definite meaning only if it is   
founded on a  proper causal relation of 
space and time4 ,in the above imaginary 
experiment the order of the experiences 
in time is the reverse of that  of the  
events4 ,and as far as causality is     

concerned1 it is a scientific           
conception that relates only to events  
ordered in space and time1 and  not to  
experiences4 ,in brief1 the experiments 
with ,lumen are swindles4    ,footnote  
#e3 ,perhaps an analogy will serve to   
make this clear4 ,suppose  that a       
certain quantity of some foodstuff is   
consumed by  head of  population4 ,the  
false inference would be that a         
population is possible  which has       
heads6 ,in the same way the statistics  
may be quite correct  in arriving at the
 figure  suicides1 but if we leave the  
realms of  calculation1 then the        
suicide loses its meaning entirely4     
,m43 ,i must resign myself to giving up 
these illusions4 ,i must frankly        
confess that ,i do so with a certain    
sadness1 for such bold flights of       
constructive fancy exert a powerful     
attraction on me4 ,at one time ,i was   
near outdoing ,lumen by assuming a      
,super-,lumen1 who was to traverse all  
worlds at once with infinite velocity4  

,he would then be in a position to  take
 a survey of the whole of universal     
history at a single glance4 ,from  the  
nearest star1 ,alpha ,centauri1 he would
 see the earth as it was four  years    
ago2 from the ,pole ,star1 as it was    
forty years ago2 and from the  boundary 
of the ,milky ,way1 as it was four      
thousand years ago4 ,at the  same moment
 he could choose a point of observation 
that would enable him  to see the ,first
 ,crusade1 the ,siege of ,troy1 the     
,flood1 and also the  events of the     
present day simultaneously4             
,,einstein3 ,and this flight of thought1
 which1 by the way1 has been  indulged  
in repeatedly by others too1 has much   
more sense in it than the  former one1  
because you may make an abstraction     
which disregards speed  altogether4 ,it 
is only a limiting case of reflection4  
,m43 ,i should like to touch on other   
limiting cases1 in particular two  that 
,i find it impossible to interpret4     
,lotze mentions them in his  ,logic4    

,the first concerns the infinitely long 
lever whose fulcrum1 or  turning-point1 
is at the confines of the universe4     
,according to the ,laws  of ,levers1 a  
mass of magnitude zero will suffice to  
keep in equilibrium  at the end of the  
other lever-arm any weight1 no matter   
whether it is a  million times heavier  
than the earth4 ,our imaginations cannot
 even  picture this4 ,yet ,i cannot feel
 satisfied with the mere explanation    
that  it is an exceptional case1 an     
extension of a general law to a case in 
which it is no longer applicable4 ,the  
second example is still more  perplexing
 because it does not require a journey  
into other worlds1 but  leads us into   
inconceivable consequences even if we   
remain on the earth4  ,lotze considers  
this second limiting case easier2 to me 
it seems more  difficult4 ,it is this3  
,the force that a wedge exerts is       
inversely  proportional to its          
thickness4 ,if it is infinitely thin1   
this formula  gives an infinitely great 

result1 whereas1 actually1 the force    
exerted  is nil4 ,this very thin wedge1 
transformed finally into a geometrical  
plane1 should be able to split in twain 
any wooden or even steel block4  ,and   
now1 consider a special arrangement of  
this wedge in which it is  resting with 
its extremely sharp edge vertically     
downwards1 whereas at  the top it       
broadens to a little ledge which        
supports a weight4 ,we then  get the    
incredible result that this wedge1 which
 can be imagined  concretely1 should be 
able to cut through the whole earth with
 its  extremely fine edge1 if placed on 
some base4 ,where is the fallacy in     
this case8    ,,einstein3 ,the          
mechanical facts have not been taken    
sufficiently into  consideration4--,he  
illustrated his further remarks by      
drawing a few  strokes with his pen1 and
 proved from his diagram that a wedge of
 this  sort would be able to perform    
what ,i assumed1 only if the base on    
which  it is placed is composed of      

separate laminae4 ,otherwise the        
assumption  that the force is infinitely
 great would be erroneous4         99   
99     99     99     99     99     99   
99    ,after this digression to a       
limiting case on the earth we returned  
to  more general problems1 and the      
question of the finitude or infinitude  
of  the universe4 ,shortly before1      
,einstein had given an address to the   
,berlin ,academy on this point1         
involving difficult calculations1 and ,i
  hoped to hear from him an easy        
explanation at least in general terms4  
,it is one of the ultimate problems4    
,whoever talks of the limits of the     
world endeavours also to mark off the   
bounds of the understanding4 ,the       
average person1 at first sight1 almost  
always decides in favour of an  infinite
 universe1 on the ground that a finite  
world is inconceivable4  ,he argues     
that1 if it were considered finite1 we  
should immediately be  confronted with  
the question3 ,what lies beyond the     

finite boundary8  ,something must be    
present1 even if it is only empty space4
 ,this brings  us into an inevitable    
conflict with the first of ,kant's      
antinomies1  with the thesis and        
antithesis1 from which there is no      
escape4 ,what is  the meaning of the    
fact that the apprehensive understanding
 seeks refuge  in ,infinity8 ,it        
signifies that he gets entangled in the 
folds of a  negative conception1 that   
furnishes him with no explanation at    
all1 and  expresses merely that his     
first assumption of finitude cannot be  
thought  out to its conclusion4         
,besides this1 a second disturbing      
question arises4 ,is there a finite or  
infinite number of stellar bodies8 ,if  
this question refers to an assumed      
infinite space1 even if such space is   
inconceivable1 then there are two       
possible answers4 ,for it would be      
possible to imagine a finite number of  
stars even if no limit could be found   
for space4    ,whereas the general      

question of space in the universe       
belongs  exclusively to speculative     
philosophy1 the star-question is not    
purely  metaphysical1 but is physical1  
too1 and has accordingly been treated by
  physicists4 ,the great astronomer     
,herschel imagined he could solve it by 
means of optical principles1 and he     
arrived at the conclusion that the      
number of heavenly bodies must be       
finite1 as otherwise the aspect of the  
starry firmament1 from the point of view
 of illumination1 would be  entirely    
different4 ,but this proof did not      
establish itself among  scientists1 for 
the number of stars of the type of the  
sun might be  finite1 whilst there was  
an infinite number of dark stars4    ,a 
further question presented itself3      
,would it be possible for a definite    
part of the heavens 7say1 that north of 
the ecliptic7 to contain an  infinite   
number of stars1 whilst other parts     
contained only a finite  number8 ,at    
first this sounds very extraordinary1   

but it is by no means  unreasonable1 as 
a concrete example will show3 ,if1 on a 
scale of  temperature1 we count the     
degrees of heat from a certain point1   
then  they stretch apparently to        
infinity in one direction1 whereas they 
extend only to -#bgc 7,centigrade7 in   
the other direction1 that is1 to  the   
absolute zero4 ,thus we can imagine an  
arrangement which stretches to  infinity
 only in one direction4    ,to get an   
insight into the discussion by ,einstein
 which is about to  follow1 we must     
first dispose of a certain arbitrariness
 of language1  lying in the customary   
indiscriminate use of the terms1        
infinite1  immeasurable1 and unbounded4 
,suppose we have a globe about one foot 
in  diameter1 the surface of which is   
inhabited by extremely small1           
ultramicroscopic creatures that can move
 about freely and can think4 ,the       
surface of the sphere constitutes the   
world of the micro-men1 and he has  a   
very good reason for considering it     

infinite1 for1 however far and in       
whatever direction he may move1 he never
 encounters a boundary4 ,but we1  who   
live in our space1 look on to this      
spherical surface1 and recognize  that  
his judgment is erroneous4 ,to us his   
spherical world seems  decidedly finite 
and quite measurable1 although it has no
 determinable  beginning and no end1 and
 thus must appear unbounded to the      
micro-man4  ,in fact1 we ourselves may  
regard it as boundless1 if we can       
succeed in  forming an abstraction that 
leaves out of account its limitations in
 our  own space4    ,now1 it might occur
 to a particularly intelligent          
micro-being to  undertake a voyage for  
the purpose of making measurements4 ,he 
carefully  marks his point of departure1
 walks ,straight ahead in a certain     
direction1 describing a circle on his   
sphere--a circle which he will          
necessarily regard as a straight line4  
,he continues ever onwards in the  firm 
conviction that he is getting farther   

and farther away from his               
starting-point4 ,suddenly1 he discovers 
that he has reached it again4 ,he       
discovers1 by the mark he made1 that he 
has not been describing a  straight     
line1 but a line that merges into       
itself4    ,the micro-professor would be
 compelled to declare3 ,our world1 the  
only  one known to me1 is not infinite1 
although in a certain sense boundless4  
,moreover1 it is not immeasurable1 since
 it can be measured in at least  one    
direction by the number of steps ,i have
 walked4 ,from this we may  infer that  
our former geometrical view was either  
wrong or incomplete1  and that1 in order
 to understand our world properly1 we   
must build up a  new geometry4    ,we   
may assume that the majority of the     
remaining micro-inhabitants would  at   
first protest strongly against this     
decision4 ,the idea that a line1  which 
appears to them to be pointing always in
 the same direction1 is  curved1 seems  
to them inconceivable and absurd4 ,they 

would only  gradually overcome their    
scruples of thought by getting an       
insight into  a newly developed geometry
 that makes clear to them for the first 
time  the conception of a sphere4    ,in
 our world of space1 which includes all 
stars1 we are the  micro-inhabitants4   
,we have been born with1 or have        
inherited1 the idea  of a straight and  
ever-advancing path in space1 and we    
become filled  with the utmost          
astonishment if some one asks us to     
believe that if we  undertake a voyage  
in one direction out into the universe1 
beyond ,sirius  and a million times     
farther1 we should finally arrive at our
  starting-point again1 although we had 
not changed our direction4 ,but the     
macro-being1 who belongs to a universe  
of higher dimensions and who  looks on  
our world as we looked on the above     
spherical world one foot in  diameter1  
sees the narrowness of our view4 ,we1   
too1 are in a position to  rise above   
this narrow view by means of a theory   

founded on our  experience1 which will  
lead us to an extended world-geometry1  
just as  the micro-professor used his   
experience to extend his theory of the  
circle to include the conception of a   
sphere4    ,after these preliminary     
remarks we shall endeavour to get an    
insight  into ,einstein's reasoning1 not
 in the form in which it was originally 
presented 7in the ,report of the        
,proceedings of the ,berlin ,academy of 
,science of #hth ,february #aiag71 but  
in a very easy description which was    
given to me during a conversation4      
,here1 too1 ,i shall try to preserve    
the sense of ,einstein's remarks without
 binding myself strictly to his  words4 
,for although ,i am indebted to him for 
his efforts to avoid  difficult points1 
yet the aim of this book is1 if         
possible1 to make the  explanation still
 easier4 ,any lack of accuracy arising  
from this last  simplification is to be 
debited to me4 ,the new form of         
representing the  argument1 which is as 

important as it is fascinating1 is1 of  
course1 due  to ,einstein4    ,the final
 result stated by ,einstein was3 ,the   
universe1 both as regards  extent and   
mass1 has finite limits and can be      
measured4 ,if anyone asks  whether this 
can be pictured1 ,i shall not deprive   
him of the hope4 ,all  that is required 
is a power of imagination that is great 
enough to  follow a pictorial           
description and that can take up the    
right attitude  towards a sort of       
figurative representation4    ,let us   
again imagine a sphere of modest        
dimensions with its  two-dimensional    
surface4 ,we are concerned only with the
 latter1 and not  with the cubical      
content4 ,the sphere is to be considered
 as resting on  an absolutely plane     
white table of unlimited extent in all  
directions4  ,the sphere touches the    
table at a single point which we shall  
call its  ,south ,pole2 on the top side 
directly opposite1 we have the ,north   
,pole4  ,to simplify matters we may make

 a sketch on paper of a vertical section
  through the centre of the sphere4     
,this profile-picture will show us the  
sphere as a circle1 and the white table 
as a straight line2 the line  joining   
the two poles is the axis of the globe1 
and the sectional circle  is a meridian4
    ,let us further suppose a creature  
7resembling1 say1 a ladybird in shape7  
having length and breadth1 but no       
thickness1 to crawl along this          
meridian4 ,although it has no thickness1
 we shall imagine it to have one        
property of a solid body1 that of being 
opaque1 so that it can throw a  shadow  
if properly illuminated4 ,we assume the 
globe itself to be  transparent4 ,at the
 ,north ,pole we suppose a very strong  
point-source of  light1 a little        
electric lamp1 that sends out rays      
freely in all  directions4    ,the      
insect begins its journey at the ,south 
,pole and sets out along the  meridian  
to reach the ,north ,pole4 ,it is       
illuminated by the lamp all the  way1 so

 that it continually throws a shadow on 
the white table4 ,the  shadow moves     
along the table farther and farther from
 the ,south ,pole1 in  proportion as the
 insect moves up the meridian1 with the 
difference that  while the insect is    
describing an arc of a circle1 its      
shadow moves  along a straight line4    
,the position of the shadow can be      
determined at  any moment by drawing the
 straight line connecting the lamp to   
the  insect1 and producing it to meet   
the white surface of the table2 the     
point of intersection is the projection 
of the insect on the plane4    ,at the  
beginning of the excursion the shadow is
 exactly as large as the  flat insect   
itself1 if we assume that its dimensions
 are negligible  compared with the      
surface of the sphere1 for it will then 
coincide with  its own shadow4 ,but when
 the insect crawls upwards1 its shadow  
will  increase1 because of the shortened
 distance between the insect and the    
lamp1 and because the points of         

projection on the table separate more   
and more as their distances from their  
corresponding points on the  sphere     
become greater4 ,there is thus a twofold
 increase4 ,the shadows  move away more 
and more rapidly1 and at the same time  
increase in size4    ,when the insect   
gets very near the ,north ,pole1 its    
shadow1 now of  enormous dimensions1 has
 moved to a very great distance2 and    
when  finally it reaches the ,pole1 its 
shadow becomes infinitely great and     
thus stretches to infinity4    ,but let 
the insect wander on along the meridian1
 past the ,north ,pole1  down towards   
the ,south4 ,at the moment when it      
passes the upper ,pole its  shadow jumps
 from the right side to the left4 ,its  
shadow now emerges  from an infinite    
distance to the left1 and1 instead of   
being infinite  size1 again becomes     
finite in dimensions as it approaches4  
,it contracts  as it approaches1 and1 in
 short1 the same process as occurred    
during the  first half of the journey   

now occurs in the reverse order4    ,if 
we fix on the critical moment of the    
jump from the right to the  left1 that  
is1 from plus infinity to minus         
infinity1 we may encounter              
difficulties4 ,for the surface-creature 
pursues its way without  interruption   
and continuously1 and we experience a   
wish to ascribe to it  a shadow-path    
that is also unbroken and continuous4   
,this is possible  only if we assume the
 two points at infinity to be connected1
 that is1  if we consider them          
identical4 ,this assumption will seem   
more natural if  we reason as follows4  
,in the profile-picture the table is    
represented as  a straight line1 and it 
is along this line that the shadow      
travels4 ,we  may regard this line as an
 infinitely great circle1 for an        
infinitely  great circle has zero       
curvature1 just as the straight line1   
from which  it is therefore             
indistinguishable4 ,the infinitely great
 circle has1  however1 only one point   

situated at an infinite distance1 that  
is1 it  associates together the two     
apparent points at infinity of the      
straight  line with which we identify   
it4 ,accordingly1 we preserve the       
continuity  of the shadow-journey1 too4 
,einstein considers it allowable to say 
that  the right and the left portion    
each represent a half of the infinite   
projection1 which becomes complete only 
when the two ends are joined4    ,now we
 must be prepared for an effort of      
thought which will need  considerable   
help from our imaginations4 ,firstly1   
instead of one  surface-creature1 we    
shall suppose several crawling about on 
different  meridians1 so that a series  
of shadows will be moving about along   
straight lines radiating from the ,south
 ,pole4 ,next1 let us imagine the  whole
 picture to have its dimensions         
increased by one1 that is1 we  transform
 the plane-picture into a space model4  
,the phenomena are to  remain the same1 
except that they are to be strengthened 

by one  dimension1 surface conditions   
becoming space conditions1 and surfaces 
becoming solids4    ,what we now see are
 actual insects with round bodies 7if we
 retain our  original type of           
creatures71 or1 since there is no       
restriction as to  their size--the      
shadows have assumed all possible       
sizes--we may assume  any solid bodies  
whatsoever1 stars or even star-systems4 
,their motions  take place in exactly   
the same way as those of the shadows    
previously  thrown by the flat bodies4  
,this means that1 if a stellar body     
moves1 its size increases until it      
reaches the spherical boundary of space1
 where it becomes infinitely  great1    
and1 at the same moment1 passes from    
plus infinity to minus  infinity1 that  
is1 it enters the universe from the     
opposite direction2  then1 if it        
continues moving in its original        
direction 7as it has been  doing all    
along71 it gradually becomes smaller in 
size until1 finally1  it reaches its    

original position and its original size4
 ,if we suppose  the body to be endowed 
with the power of sensation1 it would   
not be able  to observe its own changes 
of size1 since all its scale-measures   
would  be altered in the same           
proportion4 ,this whole complex of      
phenomena would  still be taking place  
in an infinite world of space1 but1     
according to  the ,general ,theory of   
,relativity1 the geometry that is valid 
in this  world would no longer be that  
of ,euclid2 it is replaced by a system  
of  laws that arise from physics as a   
geometric necessity4 ,in this new       
geometry1 a circle described with unit  
radius is a little smaller than  it     
would be in ,euclidean geometry1 with   
the result that the greatest            
conceivable circle in this world cannot 
assume an infinite size4    ,thus we    
have to imagine that our solid bodies1  
say stars1 arrive at a  point in their  
travels which we may term only          
enormously distant4 ,if  we call the    

directions right and left instead of    
positive and negative1  then the process
 reduces itself to this3 the moving body
 reaches the  point1 which is enormously
 distant on the right1 and which is     
identical  with the point enormously    
distant on the left2 this means that the
 body  never moves out of the space     
continuum of this world1 but returns to 
its  initial point of departure even    
when it moves ever onward in what is    
apparently a straight line4 ,it moves in
 a warped space4    ,einstein has       
succeeded in finding an approximate     
value for this  non-infinite universe1  
from the fact that there is a           
determinable  gravitational constant4   
,in the constitution of the universe it 
denotes  the same for the               
mass-relationships of the earth as the  
gravitational  constant of the earth    
denotes for us1 namely1 the quantity    
from which we  can calculate the final  
velocity attained by a freely falling   
body  during a unit of time4 ,he also   

assumes a probable average for the      
density of distribution of matter in the
 universe1 by supposing that it  is     
about the same as that of the ,milky    
,way4 ,on this basis ,einstein has      
arrived at the following result by      
calculation3    ,the whole universe has 
a diameter of #ajj million light-years1 
in round  numbers4 ,that amounts to     
about #gjj trillion miles4    ,m43 ,does
 this follow from the discussion you    
entered on just now8    ,,einstein3 ,it 
follows from the mathematical           
calculations which ,i  presented in     
,cosmological ,considerations arising   
from the ,general  ,theory of           
,relativity1 in which the figure ,i have
 just quoted is not  given4 ,the exact  
figure is a minor question4 ,what is    
important is to  recognize that the     
universe may be regarded as a closed    
continuum as far  as                    
distance-measurements are concerned4    
,another point1 too1 must not be        
forgotten4 ,if1 in deference to your    

wish1 ,i used an easy illustration1     
this must not be regarded otherwise than
 as an improvised bridge to  assist the 
imagination4    ,m43 ,nevertheless1 it  
will be very welcome to many1 who are   
unable to  grasp the difficult          
,cosmological ,considerations4 ,the     
number that you  mention is overwhelming
 in the extreme4 ,indeed1 it seems to me
 that a  diameter of #ajj million       
light-years suggests an infinitely great
  distance more than the word infinity  
itself1 mentioned per  definitionem1    
which conveys nothing to the ordinary   
mind4 ,it calls up a  regular carnival  
of numbers1 particularly in those to    
whom the immense  number alone gives a  
certain pleasure4 ,but you were going to
 give me the  number expressing the     
mass1 too8    ,and then ,i learned that 
the weight of the whole universe1       
expressed in  grammes1 was #aj          
multiplied by itself #ed times1 that is 
#ajed 7#dec  grammes  #a lb41 roughly74 
,this seems rather disappointing at     

first1 but  assumes a different aspect  
when we represent to ourselves what this
  figure signifies4 ,it means that the  
weight of the universe in  kilogrammes  
is high in the octillions4 ,the earth   
itself weighs six  quadrillion          
kilogrammes1 hence the weight of the    
,einstein universe bears  the same      
relation to the weight of the whole     
earth as the latter bears  to a         
kilogramme4 ,again1 the earth's weight  
to that of the sun is as #a is  to      
#cbd1jjj4 ,hence we should have to take 
at least a trillion1 that is1 a         
milliard times a milliard1 suns to get  
the weight of the universe4 ,and  as far
 as the linear extent is concerned1 let 
us consider the most  distant stars of  
the ,milky ,way1 which are at an        
inconceivable distance1  expressible    
only in light-years4 ,if we place       
#aj1jjj such ,milky ,ways end  to end we
 shall arrive at this diameter of the   
universe1 which1  accordingly1 will have
 a cubical content a thousand milliard  

times  greater than the region          
accessible to astronomical observation4 
,thus we have a very spacious universe4 
,yet it is not spacious enough to       
satisfy all the demands that a          
mathematician interested in permutations
  and combinations might make4 ,one of  
such combinations is exemplified in  the
 so-called ,universal ,book1 that       
originated in an imaginary  experiment  
of ,leibniz4 ,if we picture to ourselves
 the sum-total of all  books that can be
 printed by making all possible         
arrangements and  successions of our    
letters1 each book differing from any   
other even if  only in one symbol1 then1
 together1 they must contain all that   
can be  expressed in sense and nonsense1
 and everything that is ever realizable 
actually or in dreams4 ,hence1 among    
other things1 they would include all    
world-history1 all literature1 and all  
science1 even from the beginning  of the
 world to the end4 ,if we agree to the  
convention of operating with  #ajj      

different printed signs 7letters1       
figures1 stops1 spacings1 etc471  and of
 allowing each such book a million paces
 for signs1 so that each  book will     
still be of a handy size1 then the      
number of these books would  amount to  
exactly #aj to the two-millionth power1 
or1 in figures1 i4e4  #ajb1jjj1jjj4     
,this fully exhaustive universal library
 containing all wisdom would  consist of
 so many volumes that it could not be   
contained in a case of  the size of the 
entire stellar universe4 ,and1          
unhappily1 it must be  added that the   
closed universe1 just described by      
,einstein and having a  diameter of a   
hundred million light-years would be    
much too small to  contain this library4
    ,nevertheless1 said ,i1 your        
universe pictures something             
inconceivably  great2 one might call it 
an infinity expressed in figures4 ,for  
in your  world there still remains one  
property of infinity1 namely1 that it   
imposes no limitations on motion of any 

kind4 ,on the other hand1 the  figures  
proclaim a limited measure in the       
mathematical sense1 however  great this 
measure may be4 ,this calls up the old  
restlessness of mind1  due to the       
persistent question3 ,what lies beyond8 
,the absolute ,nothing8  ,or is it a    
something which yet does not occupy     
space8 ,descartes and many  other great 
thinkers have never overcome this       
difficulty1 and have  always affirmed   
that a closed world is impossible4 ,how1
 then1 is the  average person to        
reconcile himself with the dimensions   
you have  established8    ,einstein gave
 an answer which1 it seemed to me1      
offered a last escape to  apprehensive  
minds4 ,it is possible1 so he said1 that
 other universes  exist independently of
 our own4    ,that is to say1 it will   
never be possible to trace a connexion  
between  them4 ,even after an eternity  
of observation1 calculation1 and        
theoretical investigation1 no glimpse or
 knowledge of any of these  ultra-worlds

 will ever enter our consciousness4     
,imagine human creatures  to be         
two-dimensional surface-creatures1 he   
added1 and that they five  on a plane of
 indefinite extent4 ,suppose that they  
have organs1  instruments1 and mental   
attitude adapted strictly to this       
two-dimensional existence4 ,then1 at    
most1 they would be able to find out    
all the phenomena and relationships that
 objectify themselves in this  plane4   
,they would then have an absolutely     
perfect science of two  dimensions1 the 
fullest knowledge of their cosmos4      
,independent of this1  there might be   
another cosmic plane with other         
phenomena and  relationships1 that is1 a
 second analogous universe4 ,there would
 then be  no means of constructing a    
connexion between these two worlds1 or  
even  of suspecting such a connexion4   
,we are in just the same position as    
these plane-inhabitants except that we  
have one dimension more4 ,it is         
possible1 in fact1 to a certain degree  

probable1 that we shall by means  of    
astronomy discover new worlds far beyond
 the limits of the region so  far       
investigated1 but no discovery can ever 
lead us beyond the continuum  described 
above1 just as little as a discoverer of
 the plane-world would  ever succeed in 
making discoveries beyond his own world4
 ,thus we must  reckon with the finitude
 of our universe1 and the question of   
regions  beyond it can be discussed no  
further1 for it leads only to imaginary 
possibilities for which science has not 
the slightest use4         99     99    
99     99     99     99     99     99   
,einstein left me for a while to the    
tumult of ideas that he had roused  up  
in me4 ,after ,i had overcome the first 
shock1 ,i sought to gain a haven  in the
 idea that arose out of the first       
shadow-argument1 in which the  spherical
 bodies occurred that seek to escape    
towards infinity on the  right but      
reappear1 instead1 at enormous distances
 on the left4 ,has  anyone ever had     

presentiments of this kind of world8    
,perhaps something  of the sort is to be
 found in earlier books of science8 ,if 
so1 they have  escaped my notice4 ,yet1 
a passage of a poet occurs to me4 ,it is
 to be  found in a volume by ,heinrich  
von ,kleist2 it is a volume dealing only
  with earthly matter and bare of       
astronomical ideas4 ,imagine a book the 
subject of which is a puppet-show1      
containing1 in the middle of it1 a      
section foreshadowing ,einstein's       
universe6 ,quite by chance ,kleist comes
  to speak of the intersection of two   
lines which1 after passing through      
infinity1 suddenly appear on the other  
side1 like a picture in a concave       
mirror1 which moves away to infinity and
 suddenly returns again and is  quite   
close1 and1 quite in accordance with our
 new cosmology1 he  declares3 ,paradise 
is locked and barred1 and the cherub is 
behind us2  we must make a voyage round 
the world1 and see whether we cannot    
discover an exit elsewhere at the other 

end perhaps4    ,perhaps poets of the   
future will busy themselves with this   
universe2 not  lyrical poets1 but       
descendants of ,hesiod1 ,lucretius1 or  
,rckert4 ,they  will express in verse   
that ,einstein's world offers a source  
of  consolation to tormented spirits    
which have sickened of ,kant's          
antinomies4 ,for in this still almost   
immeasurable world the fateful          
conception infinite has been made       
bearable for the first time4 ,in a      
certain way it relieves us from what is 
quite inconceivable1 yet into  which we 
are usually driven1 and forms a bridge  
between the thesis  finite and the      
antithesis infinite4 ,we are brought to 
a common stream1  in which both         
conceptions peacefully flow together4   
,there was no mention  of this in our   
talk1 and ,i had good reason for being  
cautious about  following out the theme 
along these lines4 ,i must not allow any
 doubts  to arise on this point3        
,einstein1 himself1 clings with unerring

 logic to  the strict mathematically    
defined conception of infinity1 and     
allows no  compromise with the          
non-infinite4    ,when ,i1 on some      
previous occasion1 sought to lead him on
 to a  compromise1 involving a          
transition-boundary1 it availed me      
nothing that  ,i quoted ,helmholtz to   
support the possibility of such an      
operation3 my  effort came to an abrupt 
end4         99     99     99     99    
99     99     99     99    ,in pursuing 
these considerations about the universe1
 we arrived at  things which1 in        
ordinary language1 are usually called   
occult4 ,in  connexion with this1 these 
remarks ensued3 ,i am1 of course1 far   
from  trying to trace out a connexion   
between the four-dimensionality that you
  establish1 ,professor1 and the        
four-dimensionality of certain          
spiritistic  pseudo-philosophers1 yet it
 suggests itself to me that in such     
occult  circles efforts will be made to 
derive advantage from the fact that the 

same word is used in both cases4 ,this  
is more than a conjecture1 indeed1  for 
there are no misgivings among the       
ignorant1 and so we actually find  the  
name ,einstein quoted in connexion with 
mediumistic experiments that  are       
flavoured with four-dimensionality4     
,it will not be expected of me1 said    
,einstein1 to enter into  discussion    
with ignoramuses and misinterpreted4    
,discarding them1 then1  let us confine 
ourselves to a brief consideration of   
the conception  'occult1' as this has   
played a part in serious science4 ,the  
chief  example of this in history is    
gravitation4 ,huyghens and ,leibniz     
refused  to accept gravitation1 for1 so 
they said1 according to ,newton's view1 
it  is an action at a distance and hence
 belongs to the realm of the occult4    
,like everything occult1 it contradicts 
the causal order in ,nature4 ,we  must  
not regard ,huyghens' and ,leibniz's    
contradiction as being due to  lack of  
perspicacity2 rather1 they objected on  

grounds which1 as  investigators1 they  
had every right to uphold4 ,for1 as far 
as our  everyday experience is          
concerned1 every mutual influence of    
things in  ,nature occurs only by direct
 contact1 as by pressure or impact1 or  
by  chemical action1 as when a flame is 
lit4 ,the fact that sound and light     
apparently form exceptions is not       
usually felt as a contradiction to the  
postulate of contact4 ,the case of a    
magnet appears much more striking       
because its effect asserts itself as a  
direct manifestation of force4 ,i  must 
mention that when ,i1 as a child1 made  
my first acquaintance with a            
compass--and this was before ,i had ever
 seen a magnet--it created a  sensation 
in me1 which ,i consider to have been a 
dominant factor in my  life up to the   
very present4 ,there is1 indeed1 a      
fundamental difference  between pressure
 and impact on the one hand1 and what we
 hear and see on  the other1 even in    
everyday experience4 ,in the case of    

light and sound1  something must be     
'happening' continually1 if the effect  
is to occur and  continue4444    ,yet   
another difference seems to enter here1 
,i interposed4 ,is it  possible to give 
a full explanation of gravitation by    
using only the  conceptions pressure and
 impact8 ,perhaps 'pressure at a        
distance' would  not have seemed to     
contemporaries of ,newton as            
unintelligible as a  'tension or pull at
 a distance4' ,it seems to me that it is
 particularly  difficult to imagine a   
pull or an attraction towards a distant 
object4    ,einstein does not consider  
this difference considerable1 and       
regards it  as possible to overcome it  
even in a manner which can be directly  
pictured4 ,if the force is exerted by a 
corpuscular transmission1 he  explained1
 we may imagine a 'force-shadow' into   
which the bombarding  corpuscles cannot 
penetrate4 ,thus if an obstacle1 which  
produces such a  shadow1 becomes        
interposed between a body ,a and a body 

,b1 then there  will be a lesser        
pressure on the side of ,b facing ,a1   
and hence ,b will  experience a greater 
corpuscular pressure on the other side1 
with the  result that ,b will be forced 
in the direction of ,a1 and the observer
  would gain the impression of a pull   
from ,b to ,a4 ,nowadays1 when the      
theory of 'fields of force' dominates   
our physical views1 we need  trouble    
just as little about using corpuscular  
pressures and impacts as  about the     
vortices which ,descartes once          
considered as the ultimate  causes of   
the motions of the heavenly bodies4 ,the
 efforts of certain  reformers to       
reintroduce these vortices and          
whirlpools as explanations  must be     
regarded as futile4    ,nevertheless1 ,i
 answered1 it seems admissible to say   
that1  ultimately1 there is always an   
occult element in every physical        
explanation1 an absolutely final and    
elementary something which we  recognize
 as a principle1 without concealing from

 ourselves that we have  reached the    
limit of explanation1 and our knowledge 
avails no further4  ,this brings me to  
another question the discussion of      
which1 as ,i clearly  perceive1 leads us
 on to dangerous ground4    ,,einstein3 
,don't hesitate to say what is troubling
 you4 ,i cannot yet see  what you are   
aiming at4    ,m43 ,i am referring to   
certain phenomena which are also called 
occult--with the object of discrediting 
them4 ,they may at times  degenerate to 
hocus-pocus and fall into the category  
of dubious arts4 ,it  seems to me1      
however1 that scientists have not always
 drawn the line  with sufficient care1  
and that they have been disposed to     
reject as  humbug1 without examination1 
everything inexplicable that dares to   
present itself in the form of open      
display4    ,,einstein3 ,in general1    
they will be in the right1 for          
investigators  cannot be expected to    
occupy themselves with things bolstered 
up by  advertisement1 and which are     

supposed to be connected with some      
fabulous1 occult regions4    ,m43       
,nevertheless1 in my opinion even among 
such displays there sometimes  occur    
phenomena which scientists should not   
pass over with contempt4 ,i1  myself1   
have experienced such cases1 and have   
said to myself3 ,there are  stranger    
happenings here----    ,,einstein3--than
 are dreamt of in your philosophy1 you  
were about to say8    ,m43 ,exactly4    
,these are things that in the guise of  
sensationalism often  hide a physical   
truth well worthy of study4             
,,einstein3 ,but you must not overlook  
the fact that in such cases you have    
mostly played the part of an onlooker1  
and hence were exposed to all  possible 
manner of deception4 ,you are baffled on
 all sides by  undiscoverable tricks and
 by other persons1 whose collusion you  
do not  suspect4 ,this renders an       
objective criticism impossible4    ,m43 
,this presumes that the performing      
artist is not entirely isolated4  ,it is

 possible to bring about conditions that
 positively eliminate all  tricks from  
the very outset4    ,,einstein3 ,if you 
have experienced any such cases1 relate 
them by all  means4    ,m43 ,i shall be 
brief1 and shall state only facts4444   
,,einstein3 ,or1 expressed more         
accurately1 only things which seem to   
have  been facts as far as you can trust
 to memory4 ,well then1 you think that  
you have grounds for saying that you    
caught a glimpse of a mysterious  world 
at that time4    ,m43 ,it is certainly  
long ago1 more than thirty years4       
,hansen1 the freak1  one of the most    
eminent of his profession1 was showing  
hypnotic and  telepathic experiments    
that were partly identical with         
experiments that  the celebrated        
scientist ,charcot at ,paris was        
performing for purposes of  pathology4  
,,einstein3 ,well1 then1 why did you    
hesitate before8 ,these experiments     
come under the head of science1 and     
require no occult veil to appear in  the

 open4    ,m43 ,this touches the main   
issue4 ,hansen did not work in the      
interests of  science1 but wished1 above
 all1 to earn money4 ,nevertheless he   
had in  his own way produced marvellous 
results that were used later for        
scientific work4 ,unfortunately in his  
case1 owing to the fact that he  cloaked
 it in occultism at the outset1 he was  
brusquely repudiated by  scientists4    
,the result was that ,hansen was        
condemned to a long period of           
imprisonment in ,dresden1 thanks to the 
recommendation of scientists who        
declared that the experiments were only 
possible if deception was  practised1   
and hence that ,hansen was an impostor  
who should be made  harmless by being   
incarcerated4    ,,einstein3 ,and how   
did you yourself seek to discover       
whether his  experiments were genuine8  
,m43 ,very easily and with absolute     
certainty4 ,one of my acquaintances1    
the wealthy race-horse owner1 von       
,oelschlger1 had induced him by means   

of a high fee to experiment at his      
country house1 at some distance from    
,berlin1 in the presence of persons1 not
 one of whom ,hansen knew1 and in  the  
case of whom there could be no question 
of secret collaboration4 ,i  can assure 
you that everything succeeded without   
exception4 ,a single  second was        
sufficient for him to communicate his   
will to each subject of  experiment4 ,he
 operated like a supernatural being on  
those present4    ,,einstein3 ,i should 
like to hear examples4    ,m43 ,herr von
 ,oelschlger introduced four jockeys1   
and suggested a race  in the great      
salon4 ,hansen placed them astride over 
chairs1 hypnotized  them on the spot1   
described the shape of the course1      
giving distances in  kilometres1 curves1
 and even the value of the prizes4 ,he  
then gave the  signal for starting4 ,the
 jockeys immediately began treating     
their chairs  as race-horses1 exhibiting
 all the signs of extreme strain which  
accompany the actual ride4              

,,einstein3 ,this is not yet a positive 
proof4 ,the subjects of experiment  may 
have become cognizant of the fact that  
they were to serve some  eccentric      
display4 ,their acquiescence in a       
prescribed part need by no  means       
signify that they were subjectively     
convinced of the genuineness  of the    
affair4    ,m43 ,there could be not the 
slightest doubt on this point4 ,after a 
few  seconds perspiration was streaming 
over their faces as a result of the     
exertion1 a symptom that exhibits itself
 only when the participants are         
convinced of the absolute earnestness of
 their undertaking4 ,all that  gazed on 
this baffling ride made the acquaintance
 of a grotesque  reality1 and were      
looking into a strange world of dreams1 
which  transformed wooden chairs into   
living thoroughbreds4 ,in the course of 
his following experiments in the        
transference of his will-power1 ,hansen 
experimented with an actress who was    
famous at that time1 and with whom  he  

had no more acquaintance than with the  
others4 ,he again produced deep         
hypnosis1 and gave the order3 ,i shall  
ask you various questions1 all of  which
 you will be able to answer correctly1  
with one exception3 you will  have      
forgotten your name4 ,and so it         
happened4 ,in her trance the actress    
gave correct answers1 until1 when the   
question1 ,what is your name8 was       
asked1 her own name1 ,helene ,odilon1   
had vanished from her memory4 ,and      
immediately afterwards1 she told me     
herself that1 in spite of her state  of 
coma1 she had retained full             
consciousness1 had understood           
everything1  and had been possessed of  
her memory until it came to the critical
  moment when1 in spite of extreme      
efforts1 she could not recollect the    
words ,helene ,odilon4 ,but ,hansen did 
not stop at dictating his thoughts  to  
others1 he also transformed corporate   
things4 ,by a single motion of  his hand
 he converted a stable-boy into a rigid 

block1 devoid of  sensation4 ,never     
would ,i have thought such an intense   
state of cramp  possible4 ,he placed the
 boy with his feet and head alone       
resting on two  supports1 so that the   
body itself was poised in space4 ,he    
then stood on  the body with his whole  
weight1 without the rigid body of the   
boy  bending even an inch4              
,,einstein3 ,how did he1 in all these   
cases1 restore the normal state8    ,m43
 ,always by a single gesture1 which1    
like everything that he did1  worked at 
lightning speed4 ,i must admit that his 
display became a little  monotonous     
after a while1 and that his programme   
did not seem capable of  much variation4
 ,things were different1 however1 in the
 case of a man  who1 some years         
previously1 had toured the world as an  
exponent of  occult phenomena1 and to   
whom scientists will some time in the   
future  look back with regret4 ,when he 
appeared1 most academicians took only   
sufficient notice of him to reject him  

without having given him a trial4  ,it  
was ,henry ,slade1 the ,american1 who is
 not to be confused with other  ,slades 
who appropriated his name in order to   
dupe people whose  insatiable curiosity 
was aroused4    ,,einstein3 ,one might  
almost suppose that your genuine ,henry 
,slade served  as a model for them4     
,m43 ,for certain reasons ,i regard this
 as out of the question1 mainly  because
 the true ,slade gave demonstrations    
only occasionally1 his  chief object    
being to interest scientists4 ,he1      
himself1 repeatedly  asserted that he   
did not understand his own achievements1
 and he  unceasingly requested the      
supervision of professional physicists  
and  physiologists1 to whom the unusual 
phases in his nature were to serve as   
objects of study4 ,the result was that  
people like ,dubois-,reymond1           
,helmholtz1 and ,virchow refused to see 
him1 not to mention experiment  with    
him4    ,,einstein3 ,these men cannot be
 reproached for acting in this way4     

,slade  was regarded as a representative
 of a four-dimensional world in the     
spiritistic sense2 serious scientists   
must avoid all humbug of this  sort1    
since even slight interest in it can    
easily be misinterpreted by  the        
ignorant public4    ,m43 ,not every one 
was afraid of compromising himself4     
,after closed doors  had greeted ,slade 
in ,berlin1 he went to ,leipzig1 where  
he became an  object of study for one   
important scientist4    ,,einstein3 ,you
 are referring to ,friedrich ,zllner1   
who undoubtedly had a  reputation as an 
astrophysicist to preserve4 ,but he     
would have served  his reputation better
 if he had not entered into this        
adventure with the  ,american spiritist4
    ,m43 ,perhaps there will some day be
 cause for a revision of opinion on     
this point4 ,the documents are extant1  
even if1 half forgotten1 they are       
reposing in various libraries4 ,a       
renewed investigation of ,zllners       
,scientific ,dissertations1 dating from 

#ahgh to #ahia1 might lead to the       
judgment that his ghostly               
interpretations are to be regarded as   
occult  in the worst sense1 and yet one 
would marvel that a great scientist1    
such as he was1 should have felt himself
 at a complete loss with his  knowledge1
 so that he was forced to resort to     
abstruse methods in order  to escape    
from the mental confusion into which    
,slade had plunged him4    ,,einstein3  
,that merely shows that ,slade1 as a    
cunning practician1  surpassed him1 and 
that ,zllner did not succeed in seeing  
through his  machinations4    ,m43 ,this
 would lead one to assume that ,slade   
knew more physics than the  ,leipzig    
professor4 ,for in a great number of    
experiments ,zllner himself  had        
prescribed the conditions1 including all
 contrivances which made  deception so  
much the more unlikely1 since ,slade    
himself could not know  what ,zllner's  
intentions were4 ,it was a question of  
,electricity1  ,magnetism1 ,optics      

including prepared conditions of        
polarization1  involved ,mechanics1 in  
short1 things that ,zllner as a         
professional  physicist understood      
thoroughly1 and which1 moreover1 were   
controlled by  others of his profession4
 ,among the latter was the celebrated   
professor  of ,electricity1 ,wilhelm    
,weber1 who1 like ,zllner1 found himself
 faced  by phenomena that were utterly  
incomprehensible to him4 ,it would be a 
profitable undertaking to bring these   
dissertations to light again1 and  it   
would easily be recognized that the     
things described actually deal  with    
scientific problems and have not the    
remotest connexion with tricks  of      
magic4 ,for example1 there is an account
 of an incredible anatomical  feat4 ,on 
flour which had been placed carefully in
 a dish beforehand1  there suddenly     
appeared the imprint of a naked human   
foot1 whilst ,slade  was present at a   
certain distance1 being fully clothed   
and subject to  careful scrutiny4 ,the  

footprint showed all the surface-details
 of the  skin1 as was confirmed by      
authorities1 just as only a left foot   
could  produce them1 but not an         
artificial copy4    ,,einstein3 ,and    
from this ,zllner inferred the          
intervention of  supernatural beings8   
,he would have done better to measure   
the dimensions  of the foot4    ,m43 ,so
 he did--at once4 ,a difference of four 
centimetres between the  length of      
,slade's foot and the copy was          
disclosed4 ,this riddle1 like so  many  
others1 remained unexplained4 ,i must   
repeat that ,i am not in the  slightest 
degree disposed to assert that occult   
phenomena really occur1  but am         
interested only in seeing that they are 
investigated carefully by  qualified    
persons4    ,,einstein3 ,your remarks   
show that ,leipzig scientists did so at 
that time  with no better result than   
that ,zllners mental confusion became   
still  greater4    ,m43 ,the conjecture 
remains that the ,leipzig experiments1  

abundant as  they were1 did not suffice4
 ,allow me to ask a direct question1    
,professor4 ,supposing another such     
agent of miracles should appear1 would  
you yourself feel impelled to test him  
experimentally8    ,,einstein3 ,your    
question is misdirected4 ,i explained   
above that ,i share  the point of view  
taken up by ,dubois-,reymond and his    
colleagues4    ,m43 ,the following case 
may be conceived4 ,a certain man1 ,x1   
might  suddenly appear1 who has control 
of a certain natural force that has     
never before been investigated2 like one
 who knew how to use electricity  at a  
time when people had never experienced  
any electrical phenomenon4  ,he would be
 able to give hundreds of               
demonstrations1 all of which we  should 
relegate to the realm of inexplicable   
magic4 ,we should1 for  instance1 be    
much astonished if he were to draw      
sparks from a living  person4 ,now1     
suppose two professors express an       
opinion4 ,professor ,a  declares the    

whole thing to be a farce1 and refuses  
to look into it at  all4 ,professor ,b  
is ready to investigate the achievements
 of ,x only if  the latter subjects     
himself from the beginning to all the   
physical  conditions that are to be     
determined beforehand4 ,and suppose the 
professor arranges his conditions so    
that they make impossible the           
occurrence of electrical phenomena4 ,if1
 now1 all scientists were to  behave    
like ,a and ,b1 the consequences would  
be very depressing4 ,for here  was an   
important field of investigation1 which 
is cut off owing to the  distrust or    
obstinacy of scientists1 who should have
 been the first to  open it up4 ,it is  
quite irrelevant whether ,x had the     
character of a  charlatan or not1 for   
behind his charlatanism there were facts
 which  clamoured for investigation4    
,,einstein3 ,the most that ,i can grant 
is that your imagined case does not  lie
 outside the scope of possibility4 ,yet 
the chance that there is such  a natural

 force hitherto undiscovered by ,man1   
that is1 one that is a  secret force as 
far as we are concerned1 is so          
vanishingly small that  it may be set   
down as equal to impossible4 ,i should  
refuse to take part  in any such        
practices1 served up in the form of     
sensation1 for one  reason that ,i      
should regret the waste of time1 as     
there are better  things to do4 ,it is a
 different matter if the mood takes me  
to visit a  variety entertainment1 in   
order to derive amusement from such     
mystifications4 ,for example1 only      
yesterday ,i was in a little theatre1   
in which1 among diverse items1 a        
thought-reading woman was performing4   
,she correctly guessed the numbers #fa  
and #ei that ,i had in my mind4 ,but    
let no one mention this as a case of    
telepathic actions at a distance or     
wireless communication between minds1   
for an intermediate person1 the         
manager1 was present1 and ,i had to     
whisper the numbers to him4 ,the        

distance to the stage was certainly too 
great to allow the sound to be  conveyed
 directly to an audible degree4 ,hence  
there must have been a  different1 very 
cunningly arranged code of signals1     
which eluded the  notice of people in   
the stalls4 ,the process consists       
actually in an  extraordinary refinement
 of observation1 which does not1        
however1 seem  to me any more wonderful 
than the training of a reckoner who     
extracts  cubic roots mentally1 or than 
the practised muscles of a juggler all  
working in unison to enable him to      
perform feats with twelve plates        
simultaneously4    ,m43 ,it gives me    
enough satisfaction1 ,professor1 that   
you conceded me  before a certain       
limited chance of finding a last refuge 
in occultism4  ,and even if you1        
yourself1 as a representative of the    
most rigorous  research of physical     
reality1 refuse to consider it1 yet the 
fact that  many others are drawn        
irresistibly towards mysterious         

phenomena cannot  be denied4 ,should one
 feel shame on this account8 ,i believe 
that1 in  this matter1 we are touching  
on inner confessions that are quite     
independent of the standard of the mind 
in which they are embedded4  ,newton    
considered the key of the universe to be
 a personal ,god1 whereas  ,laplace     
proclaimed3 ,dieu--je n'avais pas besoin
 de cette hypothse3  this contrast      
allows no inference to be drawn as to   
their relative  keenness of mind4 ,and  
probably the same may be said of the    
question  whether there are other hidden
 universes besides the one in which we  
live4 ,in any case1 those who feel      
enthusiasm for such questions can  quote
 in their support good names from the   
learned world4 ,immanuel ,kant  occupied
 himself seriously and intensively with 
the wonders of  ,swedenborg1 ,kepler    
practised ,astrology1 in which he had a 
firm belief1  ,roger ,bacon1 ,cardanus1 
,agrippa1 ,nostradamus1 van ,helmont1   
,pascal1 and1  among the modern1        

,fechner1 ,wallace1 ,crookes1 are to be 
counted among the  mystics4 ,no matter  
whether the views they held were        
theosophical1  occult1 four-dimensional 
in the spiritistic sense1 or coloured by
 any  other superstition2 they          
proclaimed that things that could be    
rigorously  proved were1 alone1         
insufficient for them4 ,out of          
presentiment and  conjecture they       
constructed wings with which to fly into
 regions extra  naturam4 ,this is how it
 happened that1 as the common folk could
 not  find a place in science for many  
extraordinary achievements1 they        
assigned their authors to the realm of  
magicians1 as in the case of            
,paracelsus1 ,albertus ,magnus1         
,raimundus ,lullus1 ,sylvester ,,ii1 who
 were  regarded as sorcerers4 ,and this 
coin is still current3 to ,edison1 of   
our  times1 the term1 sorcerer of       
,menlo-,park1 has become attached4 ,in  
the  minds of the populace discovery and
 invention1 works of genius and         

supernatural phenomena1 become confused 
and indistinguishable2 it may  even     
happen to you4 ,professor1 that your    
works will become invested with  legend4
 ,i should not like to conjure up what  
your fate would have been  if your      
theory of relativity had originated at  
the time of the  ,inquisition4 ,for the 
views put forward by ,giordano ,bruno   
are mere  child's play compared with    
your theory of the universe as a        
quasi-spherical closed space of         
hyper-,euclidean character4 ,the        
tribunal  of the ,inquisition would not 
have understood your differential       
equation1  gravitational potentials1    
tensors1 and equivalence theory2 they   
would  abruptly have declared the whole 
theory to be a magical formula or a     
manifestation of the devil1 and would   
have honoured it and you with a  funeral
 pyre4    ,,einstein3 ,this is clearly a
 slight exaggeration4                   
,mathematico-physical  and astronomical 
works have never been attacked by the   

,papal courts1  but1 on the contrary1   
have been much encouraged by them down  
to the  present day4 ,this is abundantly
 clear from the fact that we can set up 
a  whole list of ,brothers of ,orders1  
particularly ,jesuits1 who have made    
eminent discoveries in natural science4 
,from my personal knowledge of  you1 ,i 
foresee that you will one day sketch a  
fantastic trial1 in which  the new      
world-system will have to defend itself 
against the ,sanctum  ,officium4    ,m43
 ,this would be a very grateful task1   
judged from the literary point  of view4
 ,what a splendid colouring could be    
obtained by bringing these  two worlds  
of thought into conflict with one       
another1 the ,relative  against the     
,absolute1 which has been established in
 tradition and dogma4  ,but we need not 
even call the historical fancy into     
action1 for1  actually1 the theory of   
the structure of the world is even now  
still at  variance with traditional     
ideas1 that act with dogmatic violence4 

,there  is no need to deny the fact that
 every person of education1 who makes   
the acquaintance of ,lorentz's1         
,minkowski's1 ,einstein's ideas for the 
first time1 feels excited to offer      
contradictions1 and becomes involved  in
 a tumult of pros and cons1 and each one
 experiences in himself the  excitement 
of an inquisitorial tribunal4 ,the      
triumph of the new theory  passes over  
the corpses of conceptions that lie at  
the cross-roads of  thought and1 long   
after1 retain a ghostly existence4 ,only
 very few of us  are aware of the       
further inner revolution that awaits us 
along the line  of development of       
,einsteinian ideas2 we have only vague  
presentiments  that whisper to us that  
the end of forms of thought once        
considered as  irrefragable is drawing  
nigh4 ,when once the principle of       
causality has  been set on a relative   
base1 and all properties have been      
resolved  into occurrence1 and all that 
is three-dimensional has come to be     

recognized as an abstraction from the   
four-dimensional world that is  alone   
valid1 then the time will have come to  
arrange for1 the death  procession of   
all the philosophies that once served as
 the main pillars  of thought4    ,a    
retrospect of the trials of ,giordano   
,bruno and of ,galileo ,galilei  offers 
certain parallels other than those      
usually discovered by  scholars4 ,and   
if1 to-day1 we proclaim ,einstein as the
 ,galilei of the  twentieth century1 it 
must be added that in character he is   
fortunately  a ,bruno and not a         
,galilei4 ,for it is not true that the  
latter came out  of the persecution as a
 moral victor with an eppur si muove1   
rather1  in spite of the protection of  
influential prelates and dignitaries1   
even  of the entourage of the ,pope1 he 
lacked courage and bowed his head1      
betraying his science and denying       
himself as well as ,copernicus4 ,are we 
to picture how ,einstein would have     
acted under similar circumstances1  even

 if they cannot recur again8    ,whoever
 has even an inkling of his character   
will entertain no doubts4  ,at that     
time1 three hundred years ago1 the      
materials for a magnificent  scene1 one 
world versus the other1 lay ready4 ,only
 one condition was  wanting1 the moral  
courage of the hero4 ,the lack of this  
one factor  spoilt the final act for the
 history of that time4 ,the fine ethical
  feelings of later generations have had
 to be propitiated by improvising  a    
legend iridescent with beautiful        
colours4          ,,chapter ,,vii       
,,problems    ,questions of the         
,future4--,problem of ,three            
,bodies4--,conception of                
,approximation4--,object of             
,mechanics4--,simplicity of             
,description4--,limits  of              
,proof4--,reflections about the         
,circle4--,from the ,history of         
,errors4--,causalities4--,relativity on 
a ,physiological ,basis4--,physicists   
as ,philosophers4      ,,we spoke of the

 objects and problems of science in     
general1 and touched  on certain        
recurrent questions with which reputed  
men of science are  confronted from time
 to time1 so that we may ascertain their
 opinions  about immediate as well as   
more remote aims1 and about worthy      
objects  and those within reach4        
,such stimuli1 said ,einstein1 may be   
quite interesting inasmuch as  they     
sharpen the appetite of the public for  
the works of investigators1  and give   
the latter the opportunity of making    
wider circles acquainted  with their    
plans4 ,yet the value of their          
suggestions must not be  overrated1 when
 they are directed at giving trustworthy
 information  about the future lines of 
development of science4 ,every          
scientist1 in  working out his own      
research1 gravitates to particular      
points on the  boundary which separates 
the known from the unknown1 and becomes 
inclined to take his particular         
perspective from these points4 ,it must 

not1 however1 be expected that these    
individual aspects will form a  complete
 picture1 and will indicate the only    
paths along which science  can or will  
advance4    ,may ,i suggest1 ,professor1
 ,i answered1 that we select certain    
answers  that have been given to these  
recurrent questions for discussion8 ,i  
have  brought along a whole series of   
them2 it would be of value to know what 
attitude you take up towards some of the
 statements that have been made  about  
future possibilities4    ,einstein      
acquiesced1 and so ,i read out a number 
of expressions of  opinion1 given by    
eminent authorities1 particularly in    
natural science  and mathematics4 ,they 
came under the heading1 ,the ,future    
,revolution of  ,science4 ,at the outset
 we encountered arguments by ,bailhaud1 
the  director of the ,paris             
,observatory2 he dealt with the         
so-called ,problem  of ,three ,bodies1  
and with ,the ,finitude or ,infinitude  
of the ,universe4    ,einstein          

elucidated these questions as follows4  
,the celebrated ,problem  of ,three     
,bodies is a special case of the general
 problem of ,many ,bodies1  the object  
of which is to discover the exact paths 
of the heavenly  bodies4 ,if we suppose 
that the planets and the comets are     
subject only  to the attraction of the  
central body1 the sun1 then their paths 
would  be exactly those given by        
,kepler's ,laws--that is1 they would    
move about  the central body1 or1 more  
precisely1 about the common centre of   
gravity  in perfectly elliptical orbits4
 ,the same result would happen if we    
regard the orbit of a moon to depend    
solely on its parent planet4 ,but  this 
assumption is not in agreement with     
reality1 since all the bodies  of our   
system are also subject to their mutual 
attraction depending on  their masses   
and distances4 ,consequently we have the
 so-called  disturbances1 perturbations1
 and divergences from the ideal paths2  
and  the problem of ascertaining these  

disturbances is essentially identical   
with the ,problem of ,three ,bodies4    
,regarded from the point of view of     
pure mechanics1 this problem may be     
considered solved in so far as we  are  
able to write down the equations of     
motion4 ,but1 in addition to this       
purely mechanical process1 there is a   
mathematical problem which has not  been
 completely solved--that is to say1 the 
integral expressions that  occur in it  
can be calculated only approximately4   
,this makes no  difference to the       
practical calculation1 since the degree 
of  approximation1 according to the     
present methods1 may be carried as far  
as we wish4 ,the error may be reduced to
 any desirable extent1 so that it  is   
probably wrong to expect new revelations
 on this point from future  upheavals in
 physics4 ,we read on and discovered    
that several of the  scientists         
mentioned did not stop at expecting all 
advances of the  future from pure       
theory4 ,they had visions of an optimum 

of happiness1 to  gain which the        
increase of knowledge alone did not     
suffice4 ,thus the  celebrated ,swedish 
astrophysicist ,svante ,arrhenius had   
summarized his  judgment in a few lines3
 ,after the stupendous progress that has
 been  made in the physical and chemical
 sciences in recent times1 it seems to  
me that the moment has come for         
attacking the most important problems of
  mankind with full success1 namely1    
those of biology1 and in particular  of 
the art of healing1 with the weapons    
that are furnished by the  arsenal of   
the exact sciences4 ,and the            
mathematician1 ,emile ,picard1  ,membre 
de l',acadmie1 expressed himself in     
still more hopeful terms3  ,there is no 
doubt but that the discoveries which the
 human race is  awaiting with impatience
 are those that are seeking to eliminate
  sickness and the decrepitude of old   
age4 ,injections giving immunity        
against all diseases1 an elixir of life 
7une eau de ,jouvence7 for  persons of  

advancing age--these are the discoveries
 that are longed for  by every one4     
,there are also sciences that are to be 
termed 'moral1'  from which we are      
impatiently expecting that guidance     
which will  diminish the hate which     
seems to be increasing from day to day  
among the  nations4 ,that would be a    
splendid discovery4    ,these are1      
indeed1 noble and inspiring words1 said 
,i4 ,it shows how  deeply rooted is the 
demand for ethical values in human      
nature1 when  even a mathematician1     
whose intellectual interests are        
directed  primarily towards exact       
results1 ranks the discoveries of ethics
 above  all others4    ,einstein        
answered3 ,we must carefully distinguish
 between what we wish  for in general   
and what we have to investigate as      
belonging to the world  of knowledge4   
,the question under consideration is not
 one of wishes and  feelings1 but was   
unmistakably aimed at the advances and  
revolutions in  the realm of science4   

,it does not come within the scope of   
science at  all to make moral           
discoveries6 ,its one aim is rather the 
,truth4 ,ethics  is a science about     
moral values1 but not a science to      
discover moral  'truths4' ,ethics1      
conceived as a science in the usual way1
 can therefore  serve to discover or to 
promote truth only indirectly4 ,to      
illustrate my  point of view ,i shall   
quote an example taken from a totally   
different  field2 it is merely to serve 
as an analogy4 ,let us consider the game
 of  chess4 ,its value and its meaning  
is not to be sought in scientific       
factors1 but in something entirely      
different1 in a struggle which takes    
place according to definite rules4 ,but 
even chess1 inasmuch as it  sharpens the
 intellect1 may exhibit an indirect     
value for promoting  truth4 ,it may1 for
 instance1 suggest examples in          
permutations1 which may  contain        
mathematical1 that is1 purely           
scientific1 truths4 ,i certainly  do not

 deny that there is an ethical factor in
 all genuine sciences4 ,for  being      
occupied with things for the sake of    
truth alone emancipates and  ennobles   
the mind4    ,this ennobling effect1 ,i 
interposed1 should surely show itself in
 a  moderation of the passions which    
were mentioned in the above expression  
of opinion4 ,with ,picard we should     
expect above all things to see a        
diminution in the feelings of hate      
between peoples1 the tragic             
consequences of which we have           
experienced4    ,einstein smiled1 and1  
with a touch of sarcasm1 said1 ,hate is 
presumably  a privilege of the          
'cultured1' who have the time and the   
energy for it1  and who are not the     
slaves of care4 ,his tone indicated     
clearly that he  used the generic term  
cultured to denote the ,philistines of  
culture1  its snobbish satellites1 but  
not those whose intensive work aimed at 
increasing and deepening the fields of  
culture4 ,in general he maintained  his 

view that it is an illusion to expect   
discoveries in the realm of  ethics1    
since every real discovery belonged     
alone to the sphere of truth  in which  
the division only into right and wrong1 
not that into good and  evil1 holds     
good4    ,this led us to the old        
question of ,pilate3 ,what is ,truth8   
,in seeking an  answer to this question 
,einstein first called special attention
 to the  conception of approximation1   
which plays a great part in the actual  
search for truth1 inasmuch as every     
physical truth1 expressed in  measures  
and numbers1 always leaves some         
remainder1 that marks its  distance from
 the unattainable truth of reality4     
,this conception1 which  manifests      
itself so prominently in the relation of
 ,einstein's own  researches to the     
older1 so-called classical1 mechanics1  
will be  developed here according to his
 line of thought as far as ,i can       
recollect from a number of              
conversations4    ,let us suppose that  

we overhear two people arguing about the
 shape of  the earth's surface4 ,the one
 affirms that it is an unlimited plane1 
whilst the other maintains that it is a 
sphere4 ,we should not hesitate a       
moment to say that the first is in      
error1 and that the second gives the    
true answer4 ,as long as the question   
was to be decided in favour of a  ,plane
 or a ,sphere1 the sphere would         
represent the absolute truth4 ,yet  it  
would be only relative1 for these two   
statements are contradictory  only      
between themselves1 but will no longer  
be so if a third assertion  is made     
which opposes a new alternative to      
sphere4    ,if this alternative         
objection is actually raised1 the third 
person would  be quite justified in     
saying that the sphere explanation is   
wrong4 ,for  the conception sphere      
requires that all diameters be equal1   
whereas we  know that they are not so1  
since the distance from pole to pole has
 been  proved to be smaller than that   

between opposite points on the equator4 
,the earth is an ellipsoid of rotation1 
and this truth is absolute in the  face 
of the errors which are expressed by the
 terms1 plane and sphere4    ,it would  
again have to be added that this        
absoluteness would stand only  as long  
as this contradiction is regarded as    
being one between a  definite sphere and
 a definite ellipsoid4 ,if1 as in the   
case of the  earth1 there are quite     
different diameters in the equatorial   
and the  diametral planes1 then there is
 complete contradiction between the two 
statements1 and as the supporter of the 
ellipsoid is right1 the one who         
supported the sphere must now give in1  
although he previously triumphed  over  
his first opponent4 ,his statement was  
true compared with the  latter1 but     
showed itself to be an error when       
compared with the  statement of the     
third person4    ,this does not run     
counter to the laws of elementary logic4
 ,one of these1  somewhat inadequately  

called the ,law of ,contradiction1      
states that two  directly contrary      
statements--e4g4 this figure is a       
circle1 and this  figure is not a       
circle--cannot both be true             
simultaneously4 ,the truth of  the one  
implies necessarily the falseness of the
 other4 ,as this cannot  be disputed1 it
 follows in our case that we cannot have
 been confronted  with contradictory    
judgments at all concerning the figure  
of the earth4    ,this is to be         
understood in a geometrical sense4 ,the 
sphere does not  entirely contradict the
 ellipsoid1 since it is a limiting case 
of the  latter3 and the plane is        
likewise a limiting case of the sphere1 
as well  as of the surface of           
ellipsoids4    ,but we are not concerned
 with purely geometrical considerations1
 for the  earth is a definite body1 and 
not a limiting configuration derived    
from  abstraction4 ,we are here dealing 
with measurable quantities1 whose       
difference can be proved1 and hence we  

must have one of the disputants         
proclaiming the absolute truth1 whilst  
the other proclaims an absolute  error4 
,this1 however1 again is incompatible   
with our result that the  second person 
is right in the one case and wrong in   
the other4    ,the logical ,law of      
,contradiction overcomes the dilemma in 
the simplest  way4 ,none of these       
assertions contains the truth1 hence    
none of these  judgments allows the     
falseness of the others to be deduced4  
,only this  may be said1 that there is a
 fraction of truth in each judgment4    
,the  true shape of the earth is given  
by the plane to a first1 the sphere to  
a second1 the ellipsoid of rotation to a
 third1 degree of approximation3  we    
reserve the right of further            
approximations1 each of which in        
succession approaches a higher degree of
 correctness1 but none attains  the     
absolute truth4    ,this reflection on a
 particular case may be generalized1 and
 remains  when we extend it to our      

attempts at grasping the states1        
changes1 and  occurrences of ,nature4   
,whenever we talk of physical laws1 we  
must bear  in mind that we are dealing  
with human processes of thought1 that   
are  subjected to a succession of       
judgments1 courts of appeal1 as it were1
  excluding1 however1 a final court     
beyond which no appeal is possible4     
,each new experience in the course of   
natural phenomena may render  necessary 
a new trial before a higher court1 whose
 duty is then to give  a more definite  
or different form to the law formulated 
by us1 so as to  attain a still higher  
degree of approximation to the truth4   
,if we call to mind some of the most    
valuable statements made by modern      
investigators about the nature of       
natural laws1 we recognize that they    
are all connected by a single thread of 
thought1 namely1 that even in  the most 
certain law there is left a remainder   
that has not been  accounted for1 and   
that obliges us to consider a greater   

approximation  to the truth as possible1
 even if a final stage is not           
attainable4    ,mechanics furnishes us  
with the expression of its laws in      
equations1  whose importance ,robert    
,kirchhoff explained in #ahgd by a      
definition that  has been considered    
conclusive by scientists4 ,according to 
him1 it is  the object of mechanics to  
describe completely 7and not to explain7
 in  the simplest manner the motions    
that occur in ,nature4    ,the postulate
 of simplicity is derived from the      
fundamental view of  science as an      
economy of thought4 ,it expresses the   
will of man's mind to  arrive at a      
maximum of result by using a minimum of 
effort1 and to  express the greatest sum
 of experience by using the smallest    
number of  symbols4 ,let us consider two
 simple examples quoted by ,mach4 ,no   
human  brain is capable of grasping all 
the possible circumstances of bodies    
falling freely1 and it may well be      
doubted whether even a supernatural     

mind like that imagined by ,laplace     
could succeed in doing so4 ,but if we   
take note of ,galilei's ,law for        
,falling ,bodies and the value of the   
acceleration due to gravity1 which is   
quite an easy matter1 we are  equipped  
for all cases1 and have a compendious   
formula1 accessible to  any ordinary    
mind1 that allows us to picture to      
ourselves all possible  motions of      
falling bodies4 ,in the same way no     
memory in the world could  retain all   
the different cases of the refraction of
 light4 ,instead of  trying to do the   
impossible task of grasping this        
infinite abundance1 we  simply take note
 of the sine law1 and the indices of    
refraction of the  two media in         
question2 this enables us to picture any
 possible case of  refraction1 or to    
complete it1 since we are free to       
relieve our memories  entirely by having
 the constants in a book4 ,thus we have 
here natural  laws that give us a       
comprehensive yet abbreviated statement 

of facts1  and satisfy the postulate of 
simplicity to a high degree4    ,but    
these facts are built up on experiences1
 and it is not impossible  that some new
 unexpected experience will reveal a new
 fact1 which is not  sufficiently taken 
into account in the law4 ,this would    
compel us to  correct the expression for
 the law1 and to seek a closer          
approximation  for the enlarged number  
of facts4    ,the ,law of ,inertia1     
according to our human standard1 seems  
unsurpassable  in simplicity and        
completeness2 it seems to us            
fundamental4 ,but this  law1 which      
prescribes uniform rectilinear motion to
 a body subject to no  external forces1 
selects only one possibility out of an  
infinite number  as being valid for us4 
,it does not seem evident to a child1   
and it is  easy to imagine a good       
scholar in some branch of knowledge     
other than  physics1 to whom it would   
likewise not seem evident4 ,for it is by
 no  means necessary a priori that a    

body will move at all when all forces   
are absent4 ,if the law were            
self-evident1 it would not need to have 
been  discovered by ,galilei in #afch4  
,nevertheless1 it appears to us1 now1 to
  be absolutely self-evident1 and we can
 scarcely imagine that it can ever  be  
otherwise4 ,this is simply because we   
are bound to the current set of  ideas  
that cannot extend beyond the sum of    
sense-data and experiences  that have   
been inculcated into us by heredity and 
environment4 ,at a very  distant date in
 the future the average mind may surpass
 that of ,galilei  to the same extent as
 ,galilei's surpasses that of a child1  
or of a  ,papuan native4 ,and of all the
 infinite possibilities one may occur to
 a  ,galilei of the distant future1     
which1 when formulated as a law1 may    
serve to describe motions of a body     
subject to no forces better than the    
law of inertia1 proposed in #afch4      
,these reflections are not mere         
hallucinations1 but have to do with     

scientific occurrences that we have     
observed in the twentieth century4      
,newton's equation that gives the ,law  
of ,attraction is beyond doubt a  model 
of simplicity1 and it would have        
occurred to no thinking person of  even 
the last generation to doubt its        
accuracy4 ,the easily grasped           
expression k 7m4m#ar#b7 apparently      
expresses truth in a law which is  valid
 for all eternity4 ,in this expression1 
he denotes a gravitational  constant1   
that is1 a quantity which is invariable 
in the whole universe2  m and m#a are   
two masses that act attractively on one 
another2 and  r is the distance between 
them4 ,but ,newton has been followed by 
,einstein1 who has proved that this     
expression represents only an           
approximate value1 that leaves a small  
remainder as an error that may be       
detected if the greatest refinement be  
made in our methods of  observation4    
,the equations that have been set up by 
,einstein represent  the approximation  

that is to be considered final for the  
present1 and  that may remain valid for 
thousands of years4 ,they are certainly 
very  complicated1 being included in a  
system of differential equations of     
awe-inspiring length1 and we may feel   
tempted to object with the  question3   
how do they agree with ,kirchhoff's     
postulate that the simplest  description
 of the motions must be sought8 ,but    
this objection falls to  the ground if  
we look carefully into the question4    
,for simplicity  consists not merely in 
being brief or in excluding difficulty  
from a  formula1 but rather in asserting
 the simplest relation to the universe  
as a whole1 which is independent of all 
systems of reference4 ,when this        
independence is proved--and in          
,einstein's case it is so--the          
complicated  aspect of the formula      
disappears entirely in the light of the 
higher  simplicity and unity of the     
world-system that presents itself--a    
world-system that is directed in        

conformity with the one fundamental law 
of general relativity as well in the    
motion of the electrons as in  motion of
 the most distant stars4 ,with regard to
 the other postulate1  that of          
completeness1 i4e4 absolute accuracy1 we
 have been furnished  with proofs that  
have rightly excited the wonder of the  
present  generation4 ,but are we then to
 recognize the ,principle of            
,approximation  in every direction8 ,is 
there then nothing that can be proved   
rigorously1  nothing that is            
unconditionally valid in the form of    
knowledge that  corresponds exactly to  
truth8    ,we are led to think of       
mathematical theorems1 which1 when they 
have once  been proved1 are evident to  
the same degree as the axioms from which
  they have been derived1 by virtue of  
logic which cannot be disputed  since a 
contradiction leads to absurdity4 ,it   
has been said that  mathematics est     
scientia eorum1 qui per se clara sunt1  
that is1 is  the science of what is     

self-evident4    ,but here again doubts 
arise4 ,if we should get to know only a 
single  case1 in which the self-evident 
came to grief1 the road to further      
doubts becomes open4 ,such a case will  
now be quoted4    ,as we know1 a tangent
 is a straight line1 which makes contact
 with a  curve at two coincident 7or    
infinitely near7 points without actually
  cutting the curve4 ,the simplest case 
of this is the perpendicular at the     
extremity of a radius of a circle4 ,and 
it agrees fully with what our  feeling  
leads us to expect when it is stated    
that every curved line that  is         
continuous1 that is1 which discloses no 
break and no sudden bend1  has a tangent
 at every point4 ,analysis1 which treats
 plane curves as  equations in two      
variables1 gives the direction of the   
tangent in terms  of the differential   
coefficient1 and declares accordingly   
that every  continuous function has a   
differential coefficient1 that is1 may  
be  differentiated1 at every point4 ,the

 one statement amounts to the same as   
the other1 since there must be an       
equivalent graphical picture            
corresponding to every functional       
expression4    ,but this apparently     
rudimentary theorem involves an error1  
which was not  discovered before the    
year #ahge4 ,the theory of curves has   
been in  existence for centuries1 but it
 occurred to no one to doubt the general
  validity of this theorem of tangents4 
,it was regarded as self-evident1  as a 
mathematical intuition4 ,and certainly  
neither ,newton1 nor ,leibniz1  nor     
,bernoulli1 not to mention the          
mathematicians of olden times1 even     
dreamed that a continuous curve without 
a tangent1 or a continuous  function    
without a differential coefficient1 was 
possible4    ,moreover1 a proof of the  
theorem had been accepted4 ,it appeared 
in  text-books1 and was often to be     
heard in lecture rooms2 nor was a shadow
  of a doubt suggested4 ,for it was not 
merely a demonstratio ad oculos1  but it

 appeared directly to our sense of      
intuition4 ,and we may safely  say that 
up to the present day no one has ever   
been able to imagine a  continuously    
curved line which has no tangent2 no one
 has been able to  picture even one     
point of such a curve at which no       
tangent could be  drawn4                
,nevertheless1 scientists appeared who  
began to entertain doubts4 ,in the  case
 of ,riemann and ,schwarz these doubts  
assumed a concrete form1 in  that they  
proved that certain functions are       
refractory at certain  points4 ,but     
,weierstrass was the first to make a    
real breach in the old  belief that was 
so firmly rooted4 ,he set up a function 
that is  continuous at every point1 but 
differentiable at no point4 ,the        
graphical  picture would thus have to be
 a continuous curve having no tangent at
  all4    ,what is the appearance of    
such a configuration8 ,we do not know1  
nor  shall we presumably ever get to    
know4 ,during a conversation in which   

this problem of ,weierstrass arose1     
,einstein said that such a curve lay    
beyond the power of imagination4 ,it    
must be remarked that1 although the     
mathematical expression of the          
,weierstrass function is not exactly    
simple1 it is not inordinately complex4 
,moreover1 seeing that one such         
function 7or curve7 exists1 others will 
soon be added to it 7,poincar  mentions 
that ,darboux actually gave other       
examples even in the same year  that the
 first was discovered72 there will1     
indeed1 be found an infinite  number of 
them4 ,we may go still further1 and say 
that1 corresponding to  each curve that 
has tangents1 there are an infinite     
number that have no  tangents1 so that  
the former form the exception and not   
the rule4 ,this  is an overwhelming     
confession that shakes the foundations  
of our  mathematical convictions1 yet   
there is no escape4    ,how may we apply
 the principle of approximation to these
  considerations8 ,may we say that the  

theorem that was believed earlier is  an
 approximation to a mathematical truth8 
,this is possible only conditionally1 in
 a certain extremely limited  sense1    
namely1 if we picture to ourselves that 
point in the development  of science at 
which the conception and properties of  
tangents first  began to be             
investigated4 ,compared with this stage 
of science1 the above  theorem denotes a
 first approximation to the truth1 in   
spite of its  incorrectness2 for it     
makes us acquainted with a great        
abundance of  curves that are very      
important for us and that exhibit       
tangents at every  point4 ,this         
knowledge brings us a step nearer to the
 more approximate  truth given by       
,weierstrass's example4 ,in the distant 
future1 the earnest  student will learn 
this theorem only as a curious anecdote1
 just as we  hear of certain            
astrological and alchemistic fallacies4 
,he will learn1  in addition1 other     
theorems that are looked on as proved by

 us of the  present day1 although       
actually they were proved only          
approximately4 ,for  what does it mean  
when ,gauss1 for example1 repudiated    
certain proofs of  earlier algebraists  
as being not sufficiently rigorous1 and 
replaced  them by more rigorous proofs8 
,it signifies no more than that1 in     
mathematics1 too1 what appears to one   
investigator as flawless1 strict1  and  
evident1 is found by another to have    
gaps and weaknesses4 ,absolute          
correctness belongs only to identities1 
tautologies1 that are absolutely  true  
in themselves1 but cannot bear fruit4   
,thus at the foundation of  every       
theorem and of every proof there is an  
incommensurable element of  dogma1 and  
in all of them taken together there is  
the dogma of  infallibility that can    
never be proved nor disproved4    ,it   
must appear extremely interesting that1 
at first sight1 this example  of the    
tangent has its equivalent in ,nature   
herself1 namely1 in  molecular motions  

the investigation of which is again     
largely due to  ,einstein4    ,jean     
,perrin1 the author of the famous book1 
,atoms1 describes1 in the  introduction1
 the connexion between this mysterious  
mathematical fact  and results that are 
visible and may be shown by experiment1 
to which we  have been led by the study 
of certain milky-looking 7colloidal7    
liquids4    ,if1 for example1 we look at
 one of those white flakes1 which we get
 by  mixing soap solution with common   
salt1 we at first see its surface       
sharply outlined1 but the nearer we     
approach to it1 the more indistinct  the
 outline becomes4 ,the eye gradually    
finds it impossible to draw a  tangent  
to a point of the surface2 a straight   
line which1 viewed  superficially1 seems
 to run tangentially1 is found on closer
 examination  to be oblique or even     
perpendicular to the surface4 ,no       
microscope  succeeds in dispelling this 
uncertainty4 ,on the contrary1 whenever 
the  magnification is increased1 new    

unevennesses seem to appear1 and we     
never succeed in arriving at a          
continuous picture4 ,such a flake       
furnishes us with a model for the       
general conception of a function which  
has no differential coefficient4 ,when1 
with the help of the microscope1  we    
observe the so-called ,brownian         
movement1 which is molecular by  nature1
 we have a parallel to the curve which  
has no tangent1 and the  observer is    
left only with the idea of a function   
devoid of a  differential               
coefficient4444 ,we find ourselves      
obliged1 ultimately1 to  give up the    
hope of discovering homogeneity at all  
in studying matter4  ,the farther we    
penetrate into its secrets1 the more we 
see that it1  matter1 is spongy by      
nature and infinitely complex2 all      
indications tend  to show that closer   
examination will reveal only more       
discontinuities4    ,i have not yet had 
an opportunity of seeing these ,brownian
 movements  under the microscope1 but ,i

 must mention that ,einstein has        
repeatedly  spoken to me of them with   
great enthusiasm1 of an objective kind1 
as it  were1 for he betrayed neither by 
word nor by look that he himself has    
done research leading to definite laws  
that have a recognized place in  the    
history of molecular theory4    ,as soon
 as we approach the question of         
molecular irregularities we  recognize  
that1 when we earlier spoke of the      
figure of the earth in  discussing the  
principle of approximation1 we were     
still very far from  the limit that may 
be imagined4 ,we had set up the three   
stages3  plane--sphere--ellipsoid of    
revolution1 as relative geometrical     
steps1  beyond which there must be still
 further geometrical approximations4 ,if
  we imagine all differences of level   
due to mountains and valleys to be      
eliminated1 for example1 and if we      
suppose the earth's surface to  consist 
entirely of liquid1 undisturbed by the  
slightest breath of wind1  even then1   

the ellipsoid is by no means the final  
description4 ,for now  the              
discontinuities from molecule to        
molecule begin1 the infinite number  of 
configurations without tangents1 the    
macroscopic parallels of what  the white
 flake soap solution showed as          
microscopically1 and no  conceivable    
geometry would ever be adequate to grasp
 these phenomena4 ,we  arrive at a      
never-to-be-completed list of functions 
which can never be  described either in 
words or in symbolic expressions of     
analysis4    ,but even if the ultimate  
geometrical truth is hidden behind the  
veils of  ,maya1#f we are yet left with 
the consolation that the method of      
approximation1 even when applied to a   
relatively modest degree1 produces      
remarkable results in the realm of      
numbers4 ,let us consider for a moment  
in the simple figure of a circle the    
ratio between the circumference and  the
 radius4    ,footnote #f3 ,maya         
appearance4    ,as we know1 this ratio  

is constant1 and is called in honour of 
the man  who first gave a trustworthy   
value for it1 ,ludolf's number1 namely1 
7pi74 ,thus it makes no difference      
whether we consider a circle as small   
as a wedding-ring1 or as large as a     
circus arena1 or even one the radius  of
 which is as great as the distance of   
,sirius4 ,and it makes just as  little  
difference what happens to the circle   
whilst it is being  measured2 the above 
ratio must remain constant4    ,but     
here1 too1 a contradiction makes itself 
heard1 issuing from one  section of     
modern science4 ,it calls to mind the   
saying of ,dove that when  professors   
are not quite sure about a thing they   
always preface their  remarks with the  
phrase3 it is well known that 444 ,we   
should be well  advised in avoiding this
 method of expression altogether1 for   
even when  we feel quite sure1 the ghost
 of the unknown lurks behind what we    
fain  would call well known4    ,the    
theorem that all circles without        

exception are subject to the same       
measure-relation belongs a priori to the
 synthetic judgments4 ,but  fields of   
thought have been discovered in which   
the a priori has lost  its power4       
,mathematics--once a quintessence of    
synthetic statements a  priori--is now  
regarded as being dependent on physical 
conditions4  ,physical conditions1      
however1 are empirical and subject to   
change4  ,therefore1 since the a priori 
is not subject to change1 we encounter a
  discrepancy4 ,it leads to the         
question3 ,is the ,euclidean geometry   
with  which we are familiar the only    
possible geometry8 ,or1 in particular3  
,is   the only possible                 
measure-relation8    ,einstein replies  
in the negative4 ,he not only shows how 
another geometry  is possible1 but he   
also discloses what once seemed         
inconceivable1  namely1 that if we wish 
to describe the course of the phenomena 
of  ,nature exactly by means of the     
simplest laws1 it is not only impossible

  to do so with the help of ,euclidean  
geometry alone1 but that we have to  use
 a different geometry at every point of 
the world1 dependent on the  physical   
condition at that point4    ,from the   
comparatively simple example of two     
systems rotating relatively  to one     
another1 ,einstein shows that the       
peripheral measurement of a  rotating   
circle1 as viewed from the other system1
 exhibits a peculiarity  which does not 
accompany the radial measurement4 ,for1 
according to the  theory of relativity1 
the length of a measuring rod is to be  
regarded as  being dependent on its     
orientation4 ,in the case quoted1 the   
rod  undergoes a relative contraction   
only when applied along the             
circumference1 so that we count more    
steps than when we measure the          
circumference of the same circle at     
rest1 that is1 in non-rotation4  ,since 
the radius remains constant in each     
case1 we get a relatively  greater value
 for 1 which shows that we are no longer

 using ,euclidean  geometry4    ,yet1   
formerly1 before such considerations    
could even be conceived in  dreams1 this
  was regarded as absolutely established
 and immutable2  and observers used     
every possible means of determining its 
value as  accurately as possible4    ,in
 ,byzantium there lived during the      
eleventh and twelfth centuries a        
learned scholar1 ,michael ,psellus1     
whose fame as the ,foremost of          
,philosophers stretched far and wide1   
and whose mathematical researches  were 
regarded as worthy of great admiration4 
,this grand master had  discovered by   
analytical and synthetical means that a 
circle is to be  regarded as the        
geometric mean between the circumscribed
 and the  inscribed square1 which gives 
to the above quantity1 as may easily be 
calculated1 the value #h1 that is1      
#b4hbhdbga4444 ,in other words1 the     
length of the circumference is not even 
three times that of the radius4    ,we  
have the choice of regarding the result 

of ,psellus as an  approximation1 or as 
mere nonsense4 ,every schoolboy who1 in 
a spirit of  fun1 measures a circular   
object1 say a top1 with a piece of      
string1  arrives at a better result1 but
 the contemporaries of ,psellus accepted
  this entirely wrong figure with       
credulous reverence1 and continued to   
burn incense at the feet of the famous  
master4 ,it is all very well for  us of 
the present to call him a donkey4 ,we   
have just as much right in  saying that 
mathematicians differ1 not in their     
natures1 but only in the  order of their
 brain functions4 ,if a man like        
,psellus missed the mark by  so much1 it
 is possible that men like ,fermat or   
,lagrange may also have  erred          
occasionally or even consistently4      
,no heavenly power will give us a       
definite assurance to the contrary1 and 
all of us may be just as false in our   
judgment of accepted celebrities  as    
were the ,byzantines eight hundred years
 ago in their estimate of  ,psellus4    

,whereas the latter had obtained a value
 less than #c1 there are learned        
documents of about the same date that   
have been preserved1 according to  which
 the value of  comes out as exactly #d4 
,compared with this  grandiose bungling1
 even the observations mentioned in the 
,old ,testament  are models of          
refinement4 ,for1 as early as three     
thousand years ago1 it  is stated of the
 mighty basin in the temple of ,solomon 
7,first ,book of  ,kings1 chapter       
,,vii473 ,and he made a molten sea1 ten 
cubits from the one  brim to the other3 
it was round all about1 and his height  
was five  cubits2 and a line of thirty  
cubits did compass it round about4 ,thus
   here appears as #c1 an approximation 
which no longer satisfied later         
generations4 ,the wise men of the       
,talmud went a step further1 in saying  
#c  plus a little more2 and this agrees 
roughly with the actual value4    ,the  
view became more and more deeply rooted 
that this  was a main  pillar of        

mathematical thought and calculation4   
,the more the problem of  the quadrature
 of the circle seized on men's minds1   
the greater were the  efforts made to   
find the exact value of this little more
 of the  ,talmud4 ,since #aggj we know  
that this is not possible1 for  is not  
rational1 that is1 it can be represented
 only as an infinite and  irregular     
7that is1 non-repeating7 decimal        
expression4 ,it occupies1  further1 a   
special rank as a transcendental        
quantity2 this fact was  proved by      
,lindemann as late as #ahhb for the     
first time4 ,yet1 even  nowadays1 there 
are incorrigible devotees of quadrature1
 who are still  hunting a solution      
because they cannot rid themselves of   
the  hallucination that such a simple   
figure as the circle must submit        
ultimately to a constructive process4   
,the correct way was to carry out an    
even more accurate determination of  the
 decimal figures4 ,the above-mentioned  
,ludolf van ,ceulen got as far as  the  

#ceth place of decimals2 at the turn of 
the eighteenth century the  #ajjth      
decimal place was reached4 ,since #ahdd1
 thanks to the lightning  calculator    
,dase1 we have its value to the #bjjth  
decimal place1 and this  should satisfy 
even the most extravagant demands4 ,this
 number1  associated with the circle1 is
 a classical example of how an          
approximation that is expressible in    
figures of very small value gives  an   
order of accuracy that can be described 
only by using fantastic  illustrations4 
,if we take a circle of the size of the 
equator1 and also multiply the  value of
 the diameter of the earth by 1 we know 
that the latter result  will not be     
exactly equal to the former1 and that   
there will always be a  small remainder4
 ,if this discrepancy were less than a  
metre1 the order  of exactness would be 
extraordinarily high1 for a metre is    
practically  insignificant compared with
 a mighty circle of the dimensions of   
the  earth's circumference4    ,let us  

stipulate still greater accuracy4 ,we   
demand that the error is to  be less    
than the thickness of the thinnest human
 hair4 ,we find1 then1  that we must    
take for  at most #ae places of         
decimals4 ,thus1 if we use              
#c4adaeibfecehigc1 we are applying a    
means of calculation that  reduces the  
possible error in all measurements of   
circles on the earth  to a degree beyond
 the limits of human perception4    ,if 
we pass beyond the world out into       
celestial space1 and consider  circles  
of the dimensions of a planetary orbit1 
nay1 further1 if we pass  on to the     
,milky ,way or even to the limit of     
visible stars1 to find space  for our   
circle1 and if in this case we still    
reduce the discrepancy so  as to be less
 than any length that is observable     
under a microscope1  then the last given
 value of  still suffices4 ,yet we must 
not forget  the proviso3 semper aliquid 
haeret1 something unsolved still clings 
to  the problem4    ,such numerical     

approximations1 however instructive they
 may be1  nevertheless retain a         
comparatively playful character1 and    
furnish only  a superficial analogy to  
the most important approximations that  
are  contained in our natural laws      
themselves4 ,it is these1 above all1    
that  manifest themselves so clearly in 
,einstein's life-work1 and they bear    
the same relation to the former as truth
 bears to correctness4 ,truth  comprises
 the greatest conceivable circle of     
ideas and passes far beyond  the sphere 
of correctness1 which deals only with   
measure-relations1 and  not with the    
things in themselves4 ,if ,einstein1 as 
we learn1  emphatically declares truth  
to be the only object of science1 he    
means  the strictly objective truth that
 is to be derived from ,nature1 the true
  relationship of phenomena and         
occurrences1 independently of whether   
restless philosophy assigns a question  
mark to this ultimate  objectivity4 ,a  
great discoverer in the realm of ,nature

 cannot and dare  not proceed otherwise4
 ,for him there is behind the veil of   
,maya not a  phantom that finally       
vanishes1 but something knowable1 that  
becomes ever  clearer and more real as  
he detaches each successive veil in his 
process  of approximation4    ,during   
this conversation1 when we were talking 
of the ,future of the  ,sciences1       
,einstein gave his ideas free rein1     
shooting far ahead of the  views and    
prognostications of the above-mentioned 
scientists3    ,hitherto we have        
regarded physical laws only from the    
point of view of  ,causality1 inasmuch  
as we always start from a condition     
known at a  definite cross-section of   
time1 that is1 by taking a time-section 
of  phenomena in the universe1 as1 for  
example1 a section corresponding to  the
 present moment4 ,but1 ,i believe1 he   
added1 with earnest emphasis1  that the 
laws of ,nature1 the processes of       
,nature1 exhibit a much higher  degree  
of uniformity of connexion than is      

contained in our  time-causality6 ,this 
possibility suggests itself to me       
particularly as  the result of certain  
reflections concerning ,planck's        
,quantum ,theory4  ,the following may be
 conceived3 ,what belongs to a definite 
cross-section  of time may in itself be 
entirely devoid of structure1 that is1  
it might  contain everything that is    
physically conceivable1 even such things
 7so  ,i understood him to say7 as1 in  
our ordinary physical thought1 we       
consider impossible of realization1 for 
example1 electrons of arbitrary  size1  
and having an arbitrary charge1 iron of 
any specific gravity1 etc4  ,by our     
causality we have adjusted our thought  
to a lower order of  structural         
limitations than seems realized in      
,nature4 ,real ,nature is  much more    
limited than our laws imply4 ,to use an 
allegory1 if we regard  ,nature as a    
poem1 we are like children who discover 
the rhyme but not  the prosody and the  
rhythm4 ,i interpret this as meaning    

that children  do not suspect the       
restrictions to which the form of the   
poem is  subject1 and just as little do 
we1 with our causality1 divine the      
restrictions which ,nature imposes on   
occurrences and conditions even  when we
 regard them as governed by the natural 
laws we have found4    ,thus a leading  
problem of science in the future will be
 to discover the  restrictions of       
,nature as compared with the apparent   
causality implied  in physical laws4    
,we have in this an example of the      
transcendental perspectives that are    
opened up when we accompany ,einstein on
 one of his excursions of  thought4 ,in 
this case it is actually a question of  
ultimate things1 of a  region of        
discovery of which we cannot yet form a 
conception1 and it  appears doubtful    
whether the problems latent in it are to
 be treated by  making investigations   
into physical nature1 or whether they   
are to be  allotted to speculative      
philosophy4    ,in the first place1     

,einstein's remark seems to aim at      
nothing less than  a revision of the    
conception of causality4 ,however much  
has been done to  purify this conception
 and to make it clear1 we have here1    
perhaps1 a  new possibility of refining 
it by making a synthesis of scientific  
and  abstract philosophical views4 ,we  
shall just touch very lightly and       
superficially on the possibility of a   
synthesis giving us an avenue to  truth4
 ,whoever has heard these words of      
,einstein1 feels the need of  getting on
 to firm ground to rescue himself out of
 the turmoil of ideas  into which he has
 been plunged4    ,what is ,causality8  
,a physiological answer may be given by 
saying that it  is the irrepressible    
animal instinct1 rooted in our          
brain-cells1 that  compels us to connect
 together things that we have           
experienced and  imagined4 ,poets have  
defined ,hunger and ,love as the        
fundamental elements  of our social     
lifes2 we need only add the thirst for  

causality to this  to complete the list 
of primary instincts4 ,for this mental  
thirst is not  less intense than our    
bodily hunger1 and is even greater in   
that it  never forsakes us for a moment4
 ,it is easier for the body to check    
breathing than for the soul to still the
 question of the why and  wherefore1 of 
the cause and effect1 of the antecedent 
and consequent4    ,this ceaseless      
search for a connexion between          
occurrences has become  organized into a
 fixed and immovable form of thought1   
which remains  mysterious even when we  
imagine that we have eliminated all the 
mystery  from it4 ,the relations that we
 seek and that we regard as being of an 
elementary character are totally foreign
 to ,nature herself4 ,david ,hume1  the 
first real1 and at the same time the    
most penetrating1 explorer into  this   
form of thought1 said that1 in the whole
 of ,nature not a single  case of       
connexion is disclosed which we are able
 to grasp4 ,all  happenings appear1 in  

reality1 disconnected and separate4 ,one
 follows  on another1 but we can never  
detect a connexion between them4 ,they  
appear co-joined1 but never connected4  
,and since we can form no idea  of what 
has never presented itself to our outer 
or inner perception1 the  necessary     
conclusion seems to be that we have     
absolutely no idea of  causal connexions
 or causative forces1 and that these    
expressions are  quite devoid of        
meaning1 however much they may be used  
in philosophical  discussions or in     
ordinary life4 ,this ,inquiry concerning
 ,human  ,understanding1 with its       
atmosphere of resignation1 has been     
elaborated  in manifold ways1           
particularly by ,kant and the ,kantians2
 for it is  impossible to take up a     
philosophic thread without entering on  
an  examination of the fundamental      
question concerning the existence of a  
causality which lies outside our        
instinct for causality4 ,it is also     
inevitable that1 whenever we start out  

in this direction1 we encounter  the    
further question3 ,what is ,time8 ,for  
causality directs itself to the  problem
 of succession1 both of sensations and  
phenomena1 consequently  the two        
questions are not only intimately       
connected1 but are really only          
different expressions of one and the    
same question4 ,time1 which  according  
to ,descartes and ,spinoza is a modus   
cogitandi1 not an  affectio rerum1 and1 
according to ,kant1 is an a priori form 
of  thought1 dominates our intelligence 
with the same sovereign power1 as  the  
imagined course of things3 what we      
perceive in the corresponding act  of   
thought is regarded as temporal and     
causal1 and impossible of further       
analysis4    ,now1 the conception of    
time has been entirely revolutionized by
 ,einstein  himself2 and it may be      
expected that the conception of         
causality1  too--which1 in accordance   
with custom1 we still endow with a      
separate  existence--will also be       

affected by this revolution4    ,we thus
 approach a relativization of causality1
 and we may advance a  step further in  
this direction1 if we call to mind the  
differences of  time-perception that    
,nature herself leaves open to us4 ,it  
must be  clearly understood that we are 
not dealing at present with the         
theoretical time of physics1 in the     
sense of ,einstein's theory1 but with   
something physiological that ultimately1
 however1 resolves itself into a        
relativization of time1 and hence also  
of the causal connexions in time4    ,to
 do this1 we have to follow the lines of
 reasoning developed by the  celebrated 
,st4 ,petersburg academician1 ,k4 ,e4   
von ,baer1 and we need  extend it only  
very little to get at the heart of      
causality1 if we start  from his address
 of #ahfj3 ,which ,view of ,living      
,nature is correct8 ,for  the human     
brain is a part of living nature1 and   
hence the processes of  thought may also
 be conceived as expressions of life4   

,the starting-point is a figment1 the   
fictitious character of which  vanishes 
as soon as we approach its results4 ,the
 bridge of thought may  be destroyed    
later2 it suffices to carry us          
temporarily1 as long as it  lands us in 
safety on the other side4    ,the       
rapidity of perception1 of the arbitrary
 motions1 of intellectual  life seems in
 the case of various animals to be      
proportional  approximately to the      
rapidity of their pulse-beats4 ,since1  
for example1  the pulse of a rabbit     
beats four times as quickly as that of a
 bull1 it  will1 in the same interval of
 time1 also perceive four times as      
quickly1  and will be able to execute   
four times as many acts of will1 and    
will  experience four times as much as  
the bull4 ,in the same astronomical     
length of time the inner life and       
perceptual world1 in the case of        
various animals1 including ,man1 will   
take place at different specific  rates1
 and it is on these rates that each of  

these living creatures  bases its       
subjective measure of time4 ,only when  
compared with our own  measure of time  
does an organic individual1 say1 a      
plant1 appear as  something permanent in
 size and shape1 at least within a short
 interval4  ,for we may look at it a    
hundred times and more in a minute1 and 
yet  notice no external change in it4   
,now1 if we suppose the pulse-beat1 the 
rate of perception1 the external course 
of life1 and the mental process  of     
,man1 very considerably accelerated or  
retarded1 the state of affairs  becomes 
greatly changed1 and phenomena then     
occur1 which we1 fettered by  our       
physiological structure1 should have to 
reject as being fantastic  and          
supernatural1 although1 on the          
supposition of a new structure they     
would be quite logical and necessary4   
,if we suppose human life from          
childhood to old age to be compressed   
into a thousandth part of its  present  
duration1 say1 into a month1 so that the

 pulse beats a thousand  times more     
quickly than occurs in our own          
experience1 we should be able  to follow
 the course of a discharged bullet very 
exactly from point to  point with our   
eyes1 more easily than we can at present
 observe the  flight of a butterfly4    
,for now the motion of the bullet in a  
second will  be distributed among at    
least #ajjj pulse-beats1 and will induce
 at least  #ajjj perceptions1 and       
accordingly1 in comparison with our     
everyday  perception1 it will appear    
#ajjj times slower4 ,if the duration of 
our  life were again to be reduced to a 
thousandth of its first reduced  value1 
that is1 shortened to about forty       
minutes1 then our flowers and  herbs    
would seem just as motionless and       
immutable as rocks and  mountains1 in   
which we only infer the changes without 
having directly  observed them4 ,we     
would in the course of our lifes see    
little more of  the growth and decay of 
a bud and a flower in full bloom than we

 at  present see of the geological      
changes in the earth's crust4 ,the acts 
of  animals would be much too slow to be
 seen2 at most1 we could infer them  as 
we do the motions of the stars at       
present4 ,if life were shortened  still 
further in the same way1 light would    
cease to be an optical  occurrence to   
us4 ,instead of seeing the things on    
which light falls1 we  should become    
aware of them as being audible1 and what
 we at present  call tones and noises   
would long have ceased to have an effect
 on the  ear4    ,if1 however1 we let   
our fancy roam in the opposite          
direction1 that is1  if1 instead of     
compressing the duration of human life1 
we expand it  enormously1 what a        
different picture of the world would    
present itself6  ,if1 for example1 the  
pulse-beat1 and hence the rate of       
perception1 were  to be made a thousand 
times slower1 so that the average human 
life would  be spread out over1 say1    
#hj1jjj years1 and that we should       

experience in  one whole year only as   
much as we now experience in a third of 
a day1  then1 in every four hours winter
 or any other season would pass by1     
vegetation would spring up and as       
rapidly die4 ,many a growth would not   
be perceptible1 on account of its       
relative rapidity compared with the     
rate of the pulse-beat4 ,for example1 a 
mushroom would suddenly come into       
existence1 like a newly formed spring4  
,day and night would alternate as  a    
light and a dark minute2 and the sun    
would appear to fly over the  heavens   
like a fiery projectile4 ,if we were    
again to make the duration  of human    
life a thousand times longer still1 and 
hence the rate of life  a thousand times
 slower still1 we should1 during the    
whole of an  ordinary year1 be able to  
have only #aij distinct perceptions1 so 
that  the difference between day and    
night would vanish entirely1 and the    
sun's path would be a glowing circular  
band in the heavens1 and all  changes of

 form that seem to us to happen quietly 
and regularly1 and to  preserve a       
certain permanency1 would melt together 
in the wild stream of  happening1       
engulfed in its onward rush4    ,are we 
justified in opposing to this relative  
perception of time our  own time1 which 
is something specific and dependent on  
our constitution  as human beings8      
,should we not rather adopt the view    
that this specific  time1 adapted to our
 particular pulse-beat1 gives only a    
very limited  picture of the world1     
which is conditioned and determined by  
the  limitations of our own definite    
intelligence8 ,is it1 perhaps1 only a   
distorted picture1 a caricature1 of     
actual occurrences8    ,an intelligence 
infinitely superior to our own would no 
longer be  dependent on the separate    
sensations such as are presented to us  
with  the rhythm of the pulse4 ,for such
 a mind there would be no metronomic    
foundation in the sequence of           
occurrences1 beyond what represents     

itself  as time to our understanding4   
,he would be situated outside of time in
  what ,thomas ,aquinas called the nunc 
stans1 in the stationary present1       
without a retrospect of the past and    
without expectation of a future4        
,without the ,before and the ,after1 the
 occurrences of the world would  acquire
 the clearest and simplest meaning1 like
 that given by an  equation of identity4
 ,what presents itself to us as a       
succession of  events would merge       
together into one whole1 just as a      
succession of  numerical calculations   
become summarized in a rule of          
calculation1 or as  a series of logical 
operations resolves into a logical      
self-evident  truth4 ,if the mind       
conceived by ,laplace actually existed1 
it would stand  above the necessity of  
introducing time as a quantity into its 
world-equations1 for time is a purely   
anthropomorphic quantity1 produced  by  
our perception1 and regulated by our own
 characteristic pulses4  ,accordingly1  

the conception of causality1 too1 which 
is indissolubly  connected with time1   
must be regarded as anthropomorphic1 as 
something  that we read into1 and not   
out of ,nature4 ,we should at least have
 to  recognize that if there is a       
causality outside ourselves1 then we can
  learn only a minimum about it1 and    
even this only in a world displaced  or 
distorted by the accidental rate of our 
pulse-beat4    ,let us now repeat       
,einstein's assertion that the laws of  
,nature1 the  processes of ,nature1     
exhibit a much higher degree of         
uniformity of  connexion than is        
contained in our time-causality6 ,it is 
possible that  what belongs to a        
definite cross-section of time may in   
itself be  entirely devoid of structure1
 that is1 it might contain everything   
that  is physically conceivable1 even   
such things as1 in our ordinary physical
  thought1 we consider impossible of    
realization1 for example1 iron of any   
arbitrary specific gravity4 ,it seems to

 me that the non-physicist will1        
perhaps1 gain a clearer insight into    
these highly significant words of       
,einstein1 now that he has received the 
assistance of these physiological       
considerations4 ,it must be granted that
 the philosophic grounds of  ,einstein  
are quite different and lie much deeper 
than those of von ,baer1  who starts    
from organic functions and ends by      
arriving at a mysterious  relativity    
that is yet consistent in itself4       
,nevertheless1 there is one  point of   
contact1 inasmuch as in each case       
possibilities that lie  apparently extra
 naturam are suggested4    ,einstein    
says3 ,hitherto we have regarded        
physical laws only from the  point of   
view of causality1 inasmuch as we always
 start from a  condition known at a     
definite cross-section of time1 as1 for 
example1 a  section corresponding to the
 present moment4 ,at our own risk an    
easy  paraphrase of his words will be   
attempted3    ,the time-section of the  

present contains for us the sum of all  
previous  experiences1 out of which the 
necessary course of our thought sifts   
out  the category of causality4    ,what
 is not present in experience cannot    
appear in our causality4 ,let us        
consider for a moment ,hume's example of
 the ,indian who has never known  ice4  
,without being told1 and if he is       
dependent only on his own  sensations1  
he would never learn that water freezes 
in cold climates4  ,the influence of    
cold on water is not gradual1           
corresponding to an  increase of cold1  
and not one that may be anticipated in  
all its  consequences1 but at the       
freezing-point water1 which a moment    
before was  a very mobile liquid1 passes
 into a very rigid solid4 ,the causality
 of  the ,indian cannot account for     
this4 ,if we tell him of this           
phenomenon1  he has two courses open to 
him4 ,either he refuses to believe      
it--and  this would be quite natural1   
since rigid water is to him as          

meaningless  as is a square circle to   
us4 ,or else he believes the story1 and 
then his  list of categories incurs a   
break1 passing through the middle of    
causality4 ,he has then to reconcile    
himself to the assumption that          
something that is meaningless to him and
 that stands outside the  connexion of  
cause and effect is possible of         
realization4 ,up to that  moment1 in his
 time-section of the present1 there was 
no room for it in  his causality4 ,to   
,torricelli the conception of liquid    
air1 which we have  been able to prepare
 only since #ahhc1 would have appeared  
impossible and  incompatible with his   
causality4    ,so there is no room in   
our causality for the idea of iron with 
the  specific gravity of air1 or with   
one several times that of gold4 ,for1   
reasoning along the lines of our        
causality1 we should conclude that a    
substance that is so light or so heavy  
may1 indeed1 exhibit chemical           
relationship with iron1 but it would not

 itself be sufficiently defined  by the 
term iron4    ,now ,einstein also said3 
,real ,nature is much more limited 7or  
bound7  than our laws imply4 ,a sceptic 
might be disposed to take these         
statements separately in order to       
construe a contradiction out of them4   
,for1 if there are limiting conditions  
in ,nature1 which are foreign to  the   
views expressed in our laws1 how would  
it then be possible for  phenomena1     
which cannot be imagined1 to become     
realized8 ,if ,nature can  do this1     
surely she must have more liberty than  
we seek to impose on  her4 ,this        
apparent contradiction vanishes if we   
treat the conception of  structural     
design or uniformity as something       
distinct from the measure  of all       
experience up to the present4 ,this     
would give us the following             
interpretation3    ,out of the manifold 
of occurrences that are possible in     
mechanical  ,nature1 real ,nature       
selects a very closely defined manifold4

 ,thus the  true laws imply a much      
greater degree of limitation than those 
known to  us4 ,for example1 the laws    
known to us at present would not be     
affected  if we should discover         
electrons of arbitrary size or iron of  
arbitrary  specific weight4 ,but ,nature
 realizes only electrons of a quite     
definite  size and iron of a definite   
specific weight4         99     99      
99     99     99     99     99     99   
,let us bear in mind that in aiming at  
ultimate truths we have no final  courts
 of appeal4 ,nor are the latter to be   
assumed even when1 in  pursuing a       
theory1 we encounter a difficulty1 which
 at first exhibits  all the signs of a  
direct conceptual contradiction4 ,it    
should rather be  realized that a       
fiction containing an initial but only  
provisional  contradiction serves as a  
starting-point for just those           
investigations  that are most subtle and
 that have far-reaching consequences4   
,we should  have no ,infinitesimal      

,calculus1 no ,algebra1 no ,atomic      
,theory1 no ,theory  of ,gravitation if1
 to avoid all initial contradictions1 we
 surrender the  fiction of              
differentials1 of imaginary quantities1 
of the atom1 of  action at a distance4  
,in short1 it may1 indeed1 be said that 
not only  knowledge1 but also life1 the 
holding together of people by           
convention1  law1 and duty1 would become
 impossible if we did not accept the    
fiction  of free will1 which directly   
contradicts the determinate character of
  all happening1 including actions and  
motives1 which1 physically1 alone  seems
 recognizable4    ,fiction 7not to be   
confused with hypothesis7 and           
anthropomorphism1 in  spite of their    
inner inconsistency1 are the two poles  
about which our  thoughts and our lives 
revolve4 ,and no doctrine will ever soar
 to such  heights that it will be able  
to deny completely its origin from these
  roots of all thought4 ,the            
,archimedean thought-centre of the      

universe1  which would enable us to lift
 the world out of its hinges1 is        
unattainable1 because it does not exist 
at all4    ,is this also to apply to the
 new physics1 whose results are to be   
regarded as the last word in scientific 
knowledge8 ,many a hypercritical        
thinker might be led away by the current
 of the preceding statement1 and  feel  
disposed to answer in the affirmative1  
were it not that1 here too1  a          
contradiction intrudes itself4 ,this is 
expressed in the fact that not  one of  
the present-day philosophers is in a    
position to pursue the  threads of this 
theoretical fabric to their hidden ends4
    ,thus we arrive at a parting of the 
ways4 ,whoever aims at becoming         
thoroughly familiar with ,einstein's new
 world-system finds that the  study of  
the theory claims so much attention that
 there is scarcely a  possibility left  
of proceeding to an ultimate            
philosophical analysis4  ,and whoever is
 absorbed only by the desire of making  

philosophic  investigations soon enough 
arrives at border-lines of thought1 at  
which  his conscience warns him to      
beware of insufficient scientific       
knowledge4  ,he will be attacked by     
doubts as to whether he has properly    
understood  the theory4 ,and he will be 
confronted with the question whether he 
is  justified in drawing ultimate       
philosophical conclusions before he has 
mastered all the mathematical details4  
,as far as can be judged at present1    
only one thinker has1 so far1 had       
sufficiently wide knowledge to enable   
him to correlate the physical  theory   
methodically with the theory of         
knowledge4 ,i mean ,professor  ,moritz  
,schlick of ,rostock1 who has set out   
his ideas systematically in  his book   
,erkenntnislehre1 which is extraordinary
 in itself and in its  great scope2 it  
takes us beyond ,kant4 ,in ,schlick's   
opinion ,einstein's  theory furnishes us
 with the key to new and unexpected     
chambers of  thought2 it is a wonderful 

instrument for opening up new avenues1  
and  would appear more wonderful still  
if we could use this instrument  without
 having recourse to anthropomorphism4   
,this limitation may lead to  a ,utopia1
 or may entail a circulus vitiosus4 ,but
 we have one  philosophy nowadays which 
applies to what cannot be fulfilled ,,as
 ,,if it  really is capable of          
fulfilment4 ,among the disciples of     
,vaihinger1 the  founder of the         
,as-,if-doctrine of thought1 we1        
however1 notice the  tendency to follow 
anthropomorphic and fictitious paths    
also in his  field of thought4    ,from 
numerous utterances of ,einstein1 ,i    
have gathered that he himself  does hot 
give his unqualified approval to all    
attempts at unravelling  the ultimate   
problems by means of philosophy1 that   
is1 by using  metaphysics alone4 ,he    
does not deprecate these endeavours1 but
 even  expresses admiration for some of 
the newer works1 as for that of         
,schlick1 yet he sees certain obstacles 

in the purely philosophical  methods1   
that at least restrain him from taking a
 systematic interest in  them4 ,this    
reluctant acceptance of1 and doubt in1  
the processes of  philosophy1 that has  
never forsaken the exact investigator1  
this  suspicious attitude which scents  
traces of sophistic and scholastic      
machinations in all metaphysical        
arguments1 also asserts itself in him   
in a noticeable form4 ,he feels the     
absence of rigour and of consistency  of
 direction1 which is a guarantee of     
progress in passing from one  result to 
another1 in the method of thought of    
those who are pure  philosophers3 and he
 deplores the spongy and murky          
appearance of certain  expressions of   
thought1 which1 it must be admitted1    
form a poor contrast  to the            
completeness and the crystal clearness  
of mathematico-physical  reasoning4     
,there was an inscription on the portals
 of the ,athenian  ,academy which stated
 that entrance was forbidden to all who 

had had no  mathematical training2 we   
may imagine next to it an academy of    
pure  transcendental philosophy1 bearing
 the inscription3 ,no exact research    
allowed6 ,i believe that this clear-cut 
distinction would tally with            
,einstein's view4    ,in the case of the
 great ,ernst ,mach1 for whom ,einstein 
has intense  admiration1 we observe a   
similar attitude1 or we may say that1 in
 the  language of allegory1 he sang     
openly the same refrain in another key4 
,he  never ceased reiterating that he   
was properly no philosopher at all1  but
 only an investigator of ,nature4 ,at   
the beginning of the  introduction to   
one of his works we read his confession3
 ,without in the  slightest degree being
 a philosopher1 or even wishing to be   
one 4442  and some lines further on he  
calls himself sarcastically a mere      
amateur  sportsman in philosophical     
regions4 ,yet1 ,mach's initial remark is
  followed by a remarkable result1 for  
the book in question1 ,knowledge  and   

,error 7,erkenntnis und ,irrtum71 is to 
be reckoned among the most  important   
works in philosophical literature2 and  
he himself1 the amateur  sportsman1 who 
did not even desire to be called a      
philosopher1 accepted  in #ahie the post
 of ,professor of ,philosophy at ,vienna
 ,university4 ,it was  merely his       
timidity in the face of the             
philosophical fraternity that had  made 
him emphasize repeatedly the distinction
 between his own work and  that of the  
philosophers1 whereas in his heart he   
had nourished a  passion for            
,philosophy1 the first mother of        
,science4 ,and in my opinion  such a    
moment may arrive for even the most     
rigorous investigator when he  succumbs 
to the siren strains from the shores of 
philosophy4    ,as far as ,einstein     
himself is concerned1 ,i cannot venture 
on a  prognostication4 ,even though he  
belongs to the category and rank of     
,descartes1 ,pascal1 d',alembert1 and   
,leibniz1 in whom ,mathematics and      

speculative ,philosophy are             
intermingled1 he is yet characterized by
 such  a pronounced individuality1 that 
it is quite inadmissible to draw        
conclusions about him from others4 ,he  
has no need to experience a day of      
,damascus1 for he carries the gospel of 
salvation in himself1 and it  radiates  
from him4 ,one thing seems possible1 in 
my opinion1 namely1 that  ,einstein will
 occasionally roam into the neighbouring
 realm merely from  sthetic motives4    
,although the means of philosophy are   
nebulous and  more indefinite than those
 of exact science1 which are almost     
glaringly  distinct1 philosophy itself  
for this reason is the more closely     
related  to ,art4 ,and a theory that    
applies to the whole universe must      
assuredly  contain many germs that may  
come to life if subjected to the methods
 of  ,art4 ,the connecting link between 
,kant and ,schiller shows in what sense 
this is to be understood4 ,even at      
present there are indications in ,art   

which tend to show that it is ready to  
establish points of contact with        
,knowledge4 ,in ,france symphonic poems 
were written on the measure  relations  
of the circle1 and on logarithms3 these 
are at present only  curiosities1 but   
may in future become models4 ,at a much 
later date1  perhaps1 the               
four-dimensional universe may become    
ripe for treatment by  such methods of  
,art4 ,on the way to this goal there is 
the treatment with  the symbolic1       
non-rigorous1 and semi-poetic means of  
expression used by  ,philosophy4 ,many  
will use their efforts to achieve this1 
and perhaps  they will come within      
closer range of success1 if ,einstein   
himself lends  a helping hand4 ,it will 
not be possible to arrive at new        
physical truths  by following this path1
 but those that are actually known will 
be traced  more readily to the great    
mainstream of philosophy4 ,to fathom the
  secrets of the world is the work of a 
recluse1 but to make it  comprehensible 

to a wide circle1 a preacher is         
necessary1 who uses the  beautiful      
methods of philosophical rhetoric4      
,cosmos denotes the ,world  and its     
,ornamentation2 its creator1 ,demiurge1 
is a master who fashions  his forms     
along the lines of ,art4    ,thus we    
have learned what ,einstein regards as  
the sole purpose of  ,science1 namely1  
the search after ,truth4 ,for him1 the  
latter is  something absolute in itself1
 and the possibility of getting nearer  
to  it is as great as the impossibility 
of deriving results of scientific  use  
from1 say1 ethical discoveries4 ,for    
ethics is a field which is  haunted by  
the conceptual ghosts1 and the manner of
 treatment1 ordine  geometrico1 that    
,spinoza wished to apply to it1 is      
reserved for  physics4 ,einstein leaves 
the inverse philosophical query3 ,is not
 ,truth  in itself only something that  
we have constructed in imagination8 to  
those who find pleasure in sauntering   
along paths of thought that are  totally

 unconnected1 whereas he himself        
advances in a straight line with  the   
consciousness that even if the goal is  
unattainable1 he will at  least not lose
 the right direction6          ,,chapter
 ,,viii    ,,highways ,,and ,,by-,,ways 
,practical ,aims of ,science4--,pure    
,search for ,truth4--,retrospective     
,considerations4--,the ,practical ,side 
of ,kepler4--,a ,saying of              
,kant4--,mathematics as a ,criterion of 
,truth4--,deductive and ,inductive      
,methods4--,conceptual and ,perceptual  
,knowledge4--,happiness and the         
,pleasures of ,theory4--,achievements of
 ,science and ,works of ,art4--,ethical 
,results4--,minor ,questions4           
,,again we chanced to refer to the great
 subject3 ,can or should  theoretical   
science also pursue practical aims8     
,it is impossible to overrate the       
importance of this question4 ,it haunts 
us daily and often enough looms up      
threateningly on the horizon of         
mankind4 ,observe what form the         

discussions of educated people take when
  the finest and most sublime           
achievements of mind are being debated3 
one  talks of the wonders of research in
 the remotest corners of astronomy      
where the structures of world-wide      
star-systems are being investigated2  we
 hear observations about the theories   
that aim at tracing the  cosmogonic     
development of universes from the       
original chaos of countless  ages ago4  
,we hear mention of exalted sciences1   
the ,theory of ,functions  and ,numbers1
 whose founders and representatives are 
just as remarkable  in propounding      
problems as in solving them1 and        
inevitably the following  question      
obtrudes itself3 ,of what use is it1    
ultimately8 ,what can one do  with it8  
,can it be admitted that theoretical    
science has an object of  its own1 or   
have we at least the right to maintain  
the hope that1 sooner  or later1 it will
 bring us a real ,utility expressible in
 practical  terms8    ,and just as the  

devotees of pure art have framed the    
expression1 ,l'art  pour l'art1 so      
,einstein proclaims that science is its 
own object1  ,science for its own sake6 
,it carries its aims absolutely in      
itself and  must not1 through aiming at 
other purposes1 stray from its own      
highways4  ,it is my inner conviction1  
said he1 that the development of science
  itself seeks in the main to satisfy   
the longing for pure knowledge1  which1 
psychologically1 asserts itself as      
religious feeling4    ,to yourself1     
,professor1 the practical aspect seems  
comparatively  insignificant8    ,i did 
not say that1 and it was not implied in 
the question4 ,we must not  lose sight  
of our premises4 ,as long as ,i am      
interested in working along  lines of   
research--this was the assumption--the  
practical aspect1 that  is1 every       
practical result that is found          
simultaneously or arises out of  it     
later1 is a matter of complete          
indifference to me4    ,far be it from  

me1 even in thought1 to wish to question
 this confession  of faith1 particularly
 as the fact that it comes from a       
searcher of the  truth gives it the more
 weight4 ,yet a certain uneasiness has  
crept over  me because voices have      
recently made themselves heard that     
demand for  science a totally different 
tendency4 ,they arise not only from the 
public at large1 but also from academic 
circles4 ,just a short time ago  ,i read
 an exposition by a well-known          
scientist1 ,w4 ,wien1 in which he       
indulged in a violent polemic against   
the view that purely scientific  objects
 are alone valid4 ,professor ,wien      
addressed himself particularly  to      
,german physicists1 reproaching them    
with underestimating technical  science1
 and with regarding it as a lowering of 
status when a  physicist enters into    
practical life4    ,to this ,einstein   
remarked3 ,i do not know at whom this   
reproach is  aimed1 but ,i venture to   
think that my own attitude can never    

have given  rise to an attack of this   
kind4 ,for ,i make no divisions of rank1
 and  recognize no higher and no lower  
status4 ,i affirm only what is the      
nature of science herself1 and the      
objects according to which she1         
objectively1 has to direct her gaze4    
,whatever further orientation           
individual investigators may seek for   
themselves depends on the  determining  
conditions of life of each1 although    
these conditions do not  serve as a     
means for deducing the main lines of    
research4 ,the accusation  that ,i am   
unwarranted in putting forward this view
 will1 ,i hope1 not be  levelled at me1 
for my connexions with practice are     
manifold enough1 and  up to the present 
moment ,i have often collaborated with  
practical  physicists4444    ,as ,i have
 regretfully observed when you were     
obliged to interrupt a  conversation    
with me to give an audience to impatient
 persons seeking  advice in technical   
matters6    ,my own associations with   

the world of practice are not1 indeed1  
of  recent date4 ,my own parents        
originally wanted me to become a        
technical  scientist1 and ,i was        
expected to choose this profession to   
earn my  livelihood4 ,i was not1        
however1 sympathetically inclined to it1
 for even  at an early age these        
practical aims were to me1 on the whole1
  indifferent and depressing4 ,my idea  
of human culture did not coincide  with 
the current view1 that cultural         
development is to be measured in  terms 
of technical progress4 ,doubts1 indeed1 
arose in me as to whether  technical    
improvements and advances would actually
 contribute to the  well-being of       
mankind4 ,i must add that1 later1 when  
,i came into actual  touch with         
technical science1 my opinion became    
somewhat modified1 for  the reason that1
 here too1 pleasures of theory often    
visited me4    ,the true position is    
probably that the technical worker who  
does not  merely think out improvements 

for machines1 but occupies himself with 
inventions on a higher plane1 never     
ceases to feel himself a theorist1      
since his achievements are dependent for
 their inspiration on the fruits  of    
theory4 ,the practical results of to-day
 are rooted in the theoretical  results 
of decades ago1 and what is nowadays    
regarded as an idea of pure  research   
may in later decades acquire practical  
value4 ,whether it  actually becomes of 
value1 or not1 is of little account in  
judging the  idea4 ,at any rate         
experience has shown that the beginning 
of theoretical  investigations hardly   
ever gives us the chance of making      
prognostications4 ,we spoke of the      
discoveries of ,volta1 ,ampre1 and      
,faraday4 ,when these were first known1 
the world might have asked3 ,why  have  
they been disclosed8 ,to what can they  
be applied8 ,of what use are  they8     
,nowadays we know the answers that still
 lay hidden at that time1  and we       
proudly point to modern dynamos4 ,but   

does a dynamo really  represent the     
significance of these discoveries8      
,would the importance  and rank of      
,volta1 ,ampre1 and ,faraday be less if 
the dynamo had not  come into existence8
 ,only an out-and-out materialist would 
affirm this1  and1 strictly speaking1   
the question should not even be raised4 
,for it  is in a sense equivalent to    
wishing to judge of the importance and  
significance of the ,polar ,star from   
its usefulness to the navigator on  the 
earth's surface in finding his bearings4
 ,we may put the question  7although    
only in the spirit of psychological     
curiosity1 and without  expecting much  
elucidation73 ,would these discoverers  
have been  particularly happy if they   
had divined the far-reaching            
consequences of  their work8 ,did they1 
indeed1 in the course of their abstract 
researches1 have a pre-vision of the    
future dominated by the dynamo8         
,einstein refused to answer this in the 
decisive negative4 ,he left room1  if   

ever so little1 for doubts--that is1 he 
considered that1 in all  probability1   
these three discoverers had no          
presentiment of these  consequences1 and
 even if they had in a dream caught a   
glimpse of our  present electrical age1 
their zest for discovery1 their pleasure
 in  theory1 could scarcely have been   
increased2 for they were discoverers  by
 nature1 who1 swept along by their own  
spirits1 did not need to wait  to       
satisfy the desires of practical        
application4    ,in ,einstein's opinion1
 the presentiment that a discovery may  
have  practical applications in the     
future may react on pure research4 ,he  
quoted bacteriology as a proof of this4 
,in the series of eminent               
bacteriologists1 ranging from           
,spallanzani to ,schwann and ,pasteur1  
there  were certainly some whose desire 
for knowledge was directed primarily    
towards discovering purely scientific   
relationships4 ,pasteur himself  started
 from the theoretical question of the   

creation of life1 that is1  from the    
problem of the origin of organic        
creatures from inorganic  matter without
 the medium of parent organisms4 ,as a  
pan-spermist he took  up a negative     
attitude1 that is1 he tried to prove    
that it is impossible  to discover a    
bridge between organic and inorganic    
matter4 ,yet he  doubtless knew that his
 theoretical efforts stretched out into 
practical  regions1 and he may easily   
have foreseen that they would exert a   
very  important influence on ,medicine  
and ,hygiene1 although he could not     
measure its full extent4 ,in this case1 
then1 we cannot fail to recognize  that 
a certain connexion between the desire  
for pure knowledge and the  impulse to  
apply it practically is possible1       
serviceable1 and justified  in itself4  
,an influence in the opposite direction 
is also possible1 and when1  during the 
course of our conversation1 we went in  
search of examples1 we  came across one 
of great interest4 ,it shows us that a  

question may arise  out of ordinary     
practice that may open up an immense    
field of pure  knowledge1 nay1 it may   
lead to a science of very wide scope4   
,as this  example is not well known1 ,i 
shall mention it here2 ,i do so with    
additional pleasure as the scientist    
involved is one of those whom  ,einstein
 quotes most frequently and for whom he 
has the greatest  admiration1 namely1   
,johannes ,kepler4 ,first we have the   
surprising fact  that ,kepler1 who1 even
 when at the height of his fame1 was not
 free from  care1 was once the possessor
 of some money4 ,in the year #afae1 his 
blessed year of fortune1 the great      
astronomer owned a comfortable home  in 
,linz1 and even dared to conceive the   
idea of placing some well-filled  casks 
in his cellar2 nay1 more1 he was in a   
position to publish a new  scientific   
work at his own expense1 and thus appear
 as his own  publisher4    ,this        
production of ,kepler and his casks of  
wine are directly connected1  as we see 

clearly from the title3 ,doliometrie1   
literally1 ,the  ,measurement of ,casks4
 ,but the title of the work gives not   
the slightest  hint of its importance4  
,for these investigations relating to   
wine-casks  actually became the         
foundation of a science of sovereign    
power1 the  ,infinitesimal ,calculus4   
,what was ,kepler's aim8 ,it was        
something entirely practical1 and       
directed  to a definite purpose1 quite  
independent of pleasures of theory1 to  
repeat ,einstein's expression4 ,his     
problem was a question of economy1 of   
using material sparingly and            
appropriately1 in accordance with the   
requirements of the careful head of a   
house4 ,how must such a cask be         
constructed from a minimum of wood to   
give the greatest cubical content8      
,his deliberations began by regarding   
wine as the precious content  enclosed  
by a figure in space1 and then          
conceiving the cask as  representing a  
particular class of bodies of           

revolution1 that is1 of  figures in     
space that may be regarded as produced  
by the revolution of a  curved line     
about an axis4 ,at this point he at     
first endeavoured to gain  a complete   
survey of the question4 ,he varied the  
boards along the sides1  the staves1 and
 formed successively ninety-two such    
bodies of  revolution1 some of which he 
named after the fruits which they       
resembled  in shape1 as1 for example1   
apple-shaped1 lemon-shaped1 olive-shaped
  bodies4 ,he started out by measuring  
casks1 and the final result was that    
his work1 ,doliometrie1 became the      
source of all future cubatures or       
measurements of volume4    ,now we come 
to the deciding point4 ,what conditions 
has the limiting  surface of such a     
cask-like body of revolution to fulfil1 
if the body is  to have a maximum       
volume8 ,an epochal discovery here came 
to light4 ,the  practical head of the   
house soars up into the sublime realms  
of the  theory of magnitudes4 ,kepler   

discovered the conception of changes in 
functions1 and their peculiarities at   
the maximum point4 7,he did not1 of     
course1 use these modern terms47 ,by    
this means1 long before ,newton and     
,leibniz1 he laid the foundations of    
,infinitesimal ,calculus1 which later   
became the heart and soul of            
mathematics1 of astronomy1 of           
theoretical  physics1 and of technical  
science1 in so far as it is founded in  
mechanical relations4    ,on the other  
hand1 ,einstein who now1 three hundred  
years later1 has set  up his            
differential equations1 and1 with them1 
a new world-system1  stands before us as
 a pure discoverer1 devoid of practical 
aims4 ,but in  these equations there are
 elements of analysis that once came to 
light  in a happy idyll4 ,this event did
 not come out of the grey obscurity of  
abstraction1 but out of a region of     
earthly happiness1 when a ray of  light 
found its way into ,kepler's gloomy     
existence4 ,no poet has yet  expressed  

this curious complex of events in a     
ballad1 telling how ,truth1  the only   
object of ,science1 was pressed out of  
the grape1 and how  ,practice1 inspired 
by the inquiry of a cooper1 found its   
way to a ,theory  that stretches to the 
confines of the ,universe4          ,,ii
      ,the conversation touched on      
famous expressions1 words carved in     
stone1  in particular a saying of ,kant 
which seeks to fix the foundation and   
the  limits of knowledge4 ,every science
 of ,nature1 the great philosopher of   
,knigsberg had said1 contains just as   
much ,truth as it contains  mathematics4
 ,and since1 ultimately4 ,nature        
includes everything--for a  demarcation 
between physical and mental science no  
longer seems  possible--then1 if we     
follow ,kant1 we should have to regard  
mathematics  as the sole measure of     
science4    ,it is certainly not yet    
possible to enter into a discussion on  
this  point with historians1 medical or 
legal practitioners4 ,they would be     

justified in refusing it1 since1 in     
their subjects1 truth is not the  sole  
factor1 and because we cannot see at    
present how the conception of  a        
comprehensive mathematical truth is to  
find a place in them4 ,but when  we     
question a physicist on this point1 who 
unceasingly uses mathematics  as his    
chief instrument1 we should surely      
expect him to answer with an            
unconditional affirmative4 ,at least1 ,i
 should not have been surprised if      
,einstein had answered in this way1 and 
if he had indeed claimed its  validity  
for every branch of science4    ,but    
,einstein considered this quotation to  
be true only conditionally1 in  that he 
accepted it as a principle1 but did not 
regard it as universal4  ,that is1 he   
does not recognize mathematics as the   
only test of truth4    ,the sovereignty 
of mathematics1 said ,einstein1 is based
 on very  simple assumptions2 it is     
rooted in the conception of magnitude   
itself4  ,its dominant position is due  

to the fact that it gives us much more  
delicate means of distinguishing between
 infinitely varied possibilities  than  
any other method of thought that        
expresses itself in language and  is    
restricted to the use of words4 ,the    
greater the field taken into            
consideration1 the clearer does this    
become2 but even in such a narrow  range
 as #a to #ajj1 an estimate such as #bg 
is incomparably more exact  than can be 
expressed in words in any other way4 ,if
 we think of a series  of sensations1   
ranging from pleasure to pain1 or from  
sweet to bitter1  we find that words    
leave us in an uncertain1 confused      
state1 and we do  not succeed in fixing 
on a point of the series with the same  
precision  as we above fixed on the #bg 
out of the #ajj4 ,but when the theory of
  magnitude plays a part in the         
question1 as1 for example1 in a series  
of  tones1 whose vibrations exhibit a   
mathematical sequence1 we immediately   
attain a much higher order of precision 

by using numbers4444    ,that is why    
there is a sort of scientific pleasure  
in the sequence of  tones1 so my        
thoughts ran on4 ,leibniz remarks that  
,music is the  pleasure of the human    
soul1 which arises from counting without
 knowing  that it is counting4 ,here    
,pythagoras' ,number is the essence of  
all  things is verified4 ,as soon as we 
arrive at the stage at which we feel    
the psychological essence of number1 we 
fall into a sort of ecstasy1  because1  
in our subconscious minds1 we experience
 not only the pleasure  of sense but    
also the underlying truth4    ,einstein 
resumed3 ,kant's remark is correct in   
the sense that it sets up  two things in
 clear contradiction to one another4 ,on
 the one hand1 he  has in view the      
fruits of knowledge of ordinary life1 in
 which our  ordinary perceptions and    
experiences are intermingled and cannot 
be  disentangled by inductive methods   
and deductive considerations4 ,opposed  
to these1 and to be regarded of higher  

rank1 are the properly scientific       
constructions--that is1 such in which we
 find a neat differentiation of         
connected thoughts that are based on    
regular foundations and that form  the  
links of a chain of deduction4 ,whenever
 our science succeeds in  detaching this
 logically ordered knowledge from its   
sense-sources1 it  has a mathematical   
character1 and the amount of truth      
contained in it  will accordingly be    
determined by ,kant's criterion4 ,but   
,kant demands too  much when he asks us 
to apply this scale to all attainable   
knowledge of  science4 ,it would seem   
advisable to draw limitations if his    
remark is to  serve as a regulative     
measure4 ,a great part of biological    
science will  in future still be obliged
 to make its way independently of purely
  mathematical considerations4    ,your 
reflections1 ,professor1 would then also
 apply to the saying of  ,galilei3 ,the 
book of ,nature lies open before us1 but
 is written in  letters other than those

 of our alphabet2 its characters are    
composed of  triangles1 quadrilaterals1 
circles1 and spheres4    ,with all due  
honour to the beauty of this            
observation1 ,i cannot refrain  from    
doubting its universal validity4 ,if we 
were to accept it  unconditionally we   
should have to regard the paths of all  
research as  purely mathematical1 and   
this would exclude certain very         
important  possibilities1 above all1    
certain forms of intuition that have    
shown  themselves to be extremely       
fruitful4 ,thus1 according to ,galilei's
  interpretation1 the book of ,nature   
would have been illegible for ,goethe1  
for his spirit was entirely             
non-mathematical1 indeed                
anti-mathematical4  ,but he possessed a 
particular form of intuition that       
expressed itself as  a feeling which put
 him into direct contact with ,nature1  
with the result  that he obtained a     
clearer vision than many an exact       
investigator4    ,do you then consider  

intuitive gifts to be separable at all  
in form and  in kind8    ,it would be   
pedantic to seek to establish a         
fundamental difference1  even if we may 
regard the non-mathematical intuition of
 ,goethe as a very  striking case4      
,moreover1 as ,i have often emphasized1 
all great  achievements of science start
 from intuitive knowledge1 namely1 in   
axioms1 from which deductions are then  
made4 ,it is possible to arrive at  such
 axioms only if we gain a true survey of
 thought-complexes that are  not yet    
logically ordered2 so that1 in general1 
intuition is the  necessary condition   
for the discovery of such axioms4 ,and  
it cannot be  denied that1 in the great 
majority of minds with a mathematical   
tendency1 this intuition exhibits itself
 as a characteristic of their  creative 
power4    ,from these remarks it would  
appear that you value deduction         
considerably higher than induction4     
,perhaps in using these catchwords ,i   
am expressing myself a little vaguely2  

it seems to me that great things  have  
been achieved1 too1 by using inductive  
processes4    ,let us first define what 
each of these terms means4 ,deduction is
 the  derivation of the particular from 
the general1 whereas induction is the   
process of deriving the general from the
 particular case4 ,now1 quote any       
example of a brilliant achievement1     
which you feel illustrates the power  of
 the inductive method4 ,of whatever kind
 your example may be1 you will  soon    
become aware of the difference in the   
significance of the two  processes4     
,for me the most perfect example of     
induction is given by certain  reasoning
 of ,euclid4 ,the question was whether  
there is a finite or an  infinite number
 of primes 7that is1 numbers that cannot
 be divided  without leaving a remainder
 except by unity74 ,euclid found an     
elegant  proof that the total number is 
infinite by the following strictly      
inductive reasoning4 ,if the total      
number were finite there would have to  

be a greatest prime4 ,let us call it n1 
and then form the product of  all primes
 up to n and including it1 finally      
adding one1 thus3  #b x #c x #e x #g x  
#aa x #ac 444 n1 plus #a4 ,this new     
number1 say ,y1 is  certainly greater   
than n1 and now there are two           
possibilities1 either  n is prime or it 
is not prime4    ,if it is not prime1 it
 must be divisible by some existing     
prime4 ,but  the primes up to and       
including n cannot divide exactly into  
,y1 as  there is always a remainder1    
namely1 #a4 ,hence ,y must be divisible 
by an  existing prime ,x greater than n4
 ,this contradicts the assumption that  
n is the greatest prime1 for ,x is shown
 to be greater than n4    ,secondly1 if 
,y is a prime1 it immediately follows   
that n cannot be  the greatest prime1   
for ,y is greater than n4 ,hence1       
however great may  be any prime that we 
may assume1 there will always be one    
that is  greater1 and even if we do not 
succeed in expressing it in figures1 we 

see that it must certainly exist4 ,thus 
by studying carefully a  particular     
case--the prime n1 which was assumed to 
be the greatest  possible one--we have  
arrived at a general theorem which      
states that  there is no limit to the   
number of primes4 ,is not that1 too1 a  
triumph  of intuition8    ,certainly1   
said ,einstein4 ,but you must not       
overlook the fact that a  theorem of    
this kind cannot be ranked with a       
theorem of a fundamentally  axiomatic   
character4 ,the one you have discussed  
has been derived by a  clever process of
 reasoning1 but it does not exhibit the 
characteristic  of a momentous          
discovery4 ,this theorem of ,euclid can 
be imagined absent  from science without
 the content of truth in science being  
essentially  effected4 ,compare with it 
a theorem of axiomatic significance1    
such as  ,galilei's ,law of ,inertia1 or
 ,newton's ,law of ,gravitation4        
,theorems such  as the latter are       
characterized by being starting-points  

of knowledge  that are inexhaustible in 
the consequences that may be deduced    
from  them4 ,your question1 earlier1 as 
to whether ,i consider the deductive    
method superior to the inductive1 was   
not formulated in correct terms4  ,to   
this ,i answered above that the         
inductive method as a means of          
discovering general truths usually      
appears over-estimated4 ,the proper     
form of the question is3 ,which truths  
are of the higher order1 those  that are
 found inductively1 or those that lead  
to further deduction8  ,there can       
scarcely be doubt about the answer4     
,no1 that is certainly true4 ,if ,i     
understand your meaning rightly1 the    
answer may be expressed by an allegory4 
,intuition of the highest order  creates
 treasure-mines1 those of lesser degree 
individual articles of  value that are  
significant in themselves1 although they
 cannot be  compared with the           
inestimable value of the mines4 ,the    
fact that the  highest intuition is     

found in minds with a mathematical trend
 makes it  appear possible that ,kant's 
remark may gain more and more credence  
in  the future4 ,it already applies in a
 measure to subjects to which it  seemed
 inapplicable during ,kant's lifetime1  
for example1 in ,psychology1  in which  
the relations between stimulus and      
response have been  established         
mathematically only since the           
,weber-,fechner ,law was set up2  and   
also1 since the time of ,quetelet1 in   
,moral ,science and ,sociology1 we      
learn from mathematical methods of      
statistics and probability that even    
,man as an active being is subjected to 
mechanical causality4 ,at any rate  it  
seems manifest that ,kant's remark1 that
 in every science there is  just as much
 truth as there is mathematics1 has     
received additional  support in recent  
times4    ,that may be admitted1        
concluded ,einstein1 without recognizing
 his  remark as an axiom4 ,it is still  
far removed from making possible        

unassailable deductions1 and will never 
quite succeed in doing so2 yet  it may  
claim equal significance as a           
beautifully expressed idea with  that of
 ,pythagoras1 which asserts number to be
 the nature of all  things4             
,,iii      ,the lines of demarcation    
between 'conceptual knowledge'          
7,erkennen7  and 'perceptual knowledge' 
7,kennen7 are being drawn more and more 
closely nowadays4 ,the former is        
regarded as being the exclusive         
possession of the highly developed human
 mind1 and the latter as being          
characteristic of the lower intelligence
 of other living creatures4 ,is  this   
not a pronounced case of                
anthropomorphism1 and does it not       
mislead  us to form opinions that we    
should at once disown if we succeed in  
stepping out of our human frames even   
for a moment8    ,we have to rest       
satisfied with anthropomorphism once and
 for all1  answered ,einstein1 and there
 is no sense in wishing to escape from  

it1  for the arguments about            
anthropomorphism are necessarily also   
diffused  with it1 itself4 ,we are thus 
moving in a circle if we imagine we can 
deduce something outside of human       
knowledge4 ,as soon as we have argued   
around the circle1 we find ourselves    
again at the starting-point1 and so  we 
are compelled to mark clear lines of    
division between instinctive  knowledge1
 derived directly by perception1 from   
conceptual knowledge1  derived by       
processes of abstraction and reflection2
 in this way we award  the palm of      
supremacy to the human mind4    ,but    
what if the following contradiction were
 to assert itself8 ,suppose  that the   
logical 'circle' is not a circle at all1
 but a spiral1 so that  the final point 
of the argument lies just a trifle above
 the initial  point4 ,i feel            
instinctively that such apparently      
fruitless circuitous  arguments might   
finally lead to a definite piece of     
knowledge4 ,for  example1 a certain     

insect1 the ichneumon-fly1 although     
devoid of a  knowledge of science in our
 sense1 infallibly plants its sting in a
  definite point in the rings of a      
caterpillar1 at just the point that     
serves its purpose of paralysing the    
caterpillar without killing it4 ,it     
acts instinctively1 and it is open to me
 to interpret this occurrence in  other 
words4 ,the fly discloses that it       
'knows' the anatomy of the  foreign     
creature1 although it has no conceptual 
knowledge of it in our  sense4 ,but it  
immediately follows from this analogy   
that1 from the point  of view of the    
fly1 its perceptual intelligence stands 
higher than our  conceptual             
intelligence--that is1 by changing the  
perspective1 ,i am  led to declare the  
anatomical knowledge of the fly to be of
 higher rank  than the analogous        
knowledge of the most learned anatomist4
 ,in the same  way ,i might persuade    
myself that the mathematics of a bird of
 passage  stands above the cartographic 

knowledge of any human explorer4 ,the   
migratory bird that flies from the      
interior of ,africa in a straight fine  
to its nest in ,mecklenburg must have   
something in the nature of a            
co-ordinate system in its organism4 ,the
 real reason that we assign a  higher   
position to our conceptual knowledge is 
that we are equally proud  of our       
intelligence as of our science2 this is 
perhaps a deception  depending on some  
compromise1 a sort of illicit deal in   
which the mind  draws bills of exchange 
on science1 and1 as a return1 science   
meets its  obligations by paying in     
cheques drawn on the mind6    ,i must   
confess that these hazardous suggestions
 received no welcome from  ,einstein1   
and were not even met with the friendly 
smile with which he  usually accompanies
 his refutations4 ,nor do ,i disguise   
from myself that  the question of       
conceptual or perceptual knowledge can  
in no way serve  as a basis of proof2 we
 may at most base certain conjectures on

 the  difference of these types of      
knowledge1 conjectures that suggest in  
words what eludes our clear             
comprehension4 ,einstein's refusal to   
allow  this possibility certainly rests 
on much firmer ground than the somewhat 
,bergsonian views that ,i tried to      
present4 ,perhaps they are of a         
hair-splitting nature1 and deal with    
things lying on different planes2  and  
are deduced by unjustifiably altering   
the perspective with a sort of          
sophistic somersault2 perhaps ,i may be 
reproached with seeking1 like           
,mnchhausen1 to reach a higher          
standpoint without having a support from
  which to start4 ,yet how is it that ,i
 find it impossible to free myself  from
 this chain of thought8 ,no reason is   
forthcoming1 for it is a purely         
metaphysical question1 and there has    
never yet been a clear system of        
metaphysics free from ambiguities and   
sophism4    ,let us rather confine      
ourselves to the conceptual intelligence

  characteristic of human beings1 with  
which1 according to ,einstein1 so  many 
pleasures of theory are available4 ,i   
asked him whether he would  recognize   
differences of degree in these          
pleasures1 dependent on their           
intensities4 ,although ,i rightly felt  
that he would answer in the             
affirmative1 his answer took a totally  
different turn from what ,i had         
expected4 ,it was1 indeed1 a great      
surprise1 for in the matter of          
happiness of spirit he expressed a view1
 according to which he--a great         
discoverer6--does not regard ,science as
 the deepest source of happiness6       
,personally1 said ,einstein1 ,i         
experience the greatest degree of       
pleasure in getting contact with works  
of ,art4 ,they furnish me with  happy   
feelings of an intensity such as ,i     
cannot derive from other  realms4       
,this is indeed a remarkable revelation1
 ,professor6 ,i exclaimed4 ,not  that ,i
 have ever doubted your receptivity for 

products of art1 for ,i  have often     
enough observed how you are affected by 
good music1 and with  what interest you 
yourself practise music4 ,but even at   
such moments when  you gave yourself up 
to the pleasures of the ,muses1 and were
 soaring in  regions far removed from   
the earth1 ,i used to say to myself3    
,this is a  delightful arabesque in     
,einstein's existence2 but ,i should    
never have  surmised that you regard    
this decorative side-issue as the       
greatest  source of happiness4 ,but your
 confession seems to go further1 perhaps
  even beyond music8    ,at the moment  
,i was thinking particularly of         
literature4    ,do you mean literature  
in general8 ,or had you a definite      
writer in  mind1 when you were speaking 
of the felicitous effect of works of    
art8    ,i meant it generally1 but if   
you ask in whom ,i am most interested at
  present1 ,i must answer3 ,dostojewski6
 ,he repeated the name several times    
with increasing emphasis4 ,and1 as if to

 deal a mortal blow at every            
conceivable objection1 he added3        
,dostojewski gives me more than any     
scientist1 more than ,gauss6    ,if1    
,professor1 said ,i1 after a pause that 
may easily be accounted  for--if you    
mention in the same breath the names of 
two such powerful  but essentially      
different intellects1 you open the way  
to a discussion  that cannot be settled 
by a mere positive assertion4 ,it is    
possible to  admire intensely           
,dostojewski as one who moulds          
personalities and who  analyses the     
inner struggles of the soul1 and yet to 
deny him perpetual  fame4 ,this depends 
on individual judgment1 and1 as for my  
own1 ,i believe  that ,dostojewski1 in  
spite of his direct artistic appeal1    
will not have  his name perpetuated     
through the centuries like that of many 
another  member of ,parnassus4 ,it seems
 to me to be a more important matter    
whether a common measure can be found   
for ,art and ,discovery at all4         

,perhaps the test of how far a work can 
be replaced may be regarded as  valid   
for each4 ,when you say that            
,dostojewski gives you more than ,gauss1
  this probably corresponds with the    
feeling that without ,dostojewski you   
would have no ',karamasoffs' and hence  
would lack a certain life-value  that   
cannot be replaced4 ,but if ,gauss had  
failed to produce one of his            
fundamental theorems of ,algebra1       
probably some other ,gauss would have   
appeared1 who would have achieved this  
result4 ,according to this1 then1  our  
instinct increases the value of a work  
of art1 as we feel that we  are         
dependent on one being alone for its    
creation4    ,but this is only to be    
admitted conditionally1 said ,einstein1 
for the  best that ,gauss has given us  
was likewise an exclusive production4   
,if he  had not created his geometry of 
surfaces1 which served ,riemann as a    
basis1 it is scarcely conceivable that  
anyone else would have discovered  it4  

,i do not hesitate to confess that to a 
certain extent a similar  pleasure may  
be found by absorbing ourselves in      
questions of pure  geometry4    ,perhaps
 we may use a different characteristic  
as a means of  comparison1 ,i suggested1
 namely1 the permanency of the          
impression  produced on the subject     
receiving it4 ,for example1 a fine piece
 of music  never loses its influence4   
,we can listen to the first movement of 
,beethoven's ,ninth ,symphony a hundred 
times1 and1 although we know at  every  
beat what will follow1 the state of     
pleasure continues unweakened2  indeed1 
it might rather be said that the        
expectation of pleasure  increases from 
one hearing to the next4    ,this       
characteristic1 too1 answered ,einstein1
 cannot be claimed as the  exclusive    
property of works of art4 ,its existence
 cannot be doubted1  inasmuch as it     
belongs to every eminent example of art4
 ,yet we encounter  it outside the realm
 of art1 too1 in great advances of      

science1 with  which we never cease     
occupying ourselves1 and yet the        
impression  continues unweakened4    ,do
 you include among them the impressions 
that a discoverer experiences  when he  
reviews in his mind the progress due to 
his own efforts8    ,naturally1 and     
these1 indeed1 quite particularly2 and  
if this question  were put to me        
directly1 ,i should answer              
unhesitatingly that ,i find  pleasure in
 reflecting on my own discoveries1 and  
never experience  feelings of weariness 
in passing over them again4 ,so that1 to
 return to  our original thesis1 we must
 adopt a new basis of value if we wish  
to  account for the fact that the       
greatest degree of happiness is to be   
expected of a work of art4 ,it is the   
moral impression1 the feeling of        
elevation1 that takes hold of me when   
the work of art is presented4 ,and  ,i  
was thinking of these ethical factors   
when ,i gave preference to              
,dostojewskis works4 ,there is no need  

for me to carry out a literary          
analysis1 nor to enter on a search for  
psychological subtleties1 for all       
investigations of this kind fail to     
penetrate to the heart of a work  such  
as ,the ,karamasoffs4 ,this can be      
grasped only by means of the  feelings1 
that find satisfaction in passing       
through trying and difficult            
circumstances1 and that become          
intensified to exultation when the      
author  offers the reader ethical       
satisfaction4 ,yes1 that is the right   
expression1 'ethical satisfaction'6 ,i  
can find no other words for it4    ,his 
whole face lit up1 and ,i was deeply    
touched by his expression4 ,at  that    
moment it seemed to me that he had drawn
 the last veil from his  soul to allow  
me to share in his ecstasy4 ,was that   
the same physicist  who interprets the  
events of the world in terms of         
mathematics1 and  whose equations       
encompass phenomena from electrons to   
universes8 ,if so1  it was a different  

soul2 one which gave utterance1 like    
that of ,faust1  to the words3          
,and when in the feeling wholly blest   
thou art1      ,call it then what thou  
wilt4      ,call it ,bliss6 ,heart6     
,love6 ,god6      ,i have no name for   
it6      ,feeling is all in all6        
,name is but sound and reek1      ,a    
mist round the glow of heaven6          
,and1 certainly1 the book need not have 
been one of ,dostojewski's to  excite   
this feeling in him4 ,he chose the      
latter to give expression to a  mood    
that may change according to what he    
reads1 but undergoes no  fluctuations in
 its ethical foundation4 ,from other    
occasions we know how  little ethics1   
that is conducted along systematic      
lines1 signifies to  him1 and that he   
does not even include it in the         
sciences4 ,but at the  same time we see 
now that his inner life is dominated    
entirely by the  ethical principle4 ,his
 deep love of ,art is characterized by  
it1 and  receives full satisfaction from

 the source of ethical joy of which ,art
  is the centre4          ,,iv          
,during the autumn of #aiah ,einstein   
was feeling indisposed1 and1 on the     
advice of his doctor1 did not leave his 
bed4 ,when ,i entered his room1 ,i  saw 
at once that there was no reason for    
alarm1 for pieces of paper  covered with
 mysterious symbols were lying about1   
and he was absorbed in  making additions
 to some of them4 ,nevertheless1 ,i     
considered it my duty  to treat him as a
 patient under medical care1 and did not
 conceal my  intention of leaving him   
after having inquired about his         
condition4 ,but  he would not accept my 
visit as a mere call to ascertain his   
progress  towards recovery1 and insisted
 that ,i should remain with him a while1
 to  converse about amusing little      
problems as usual4    ,i pointed out to 
him that there were two objections to   
this1 the first  being that he was      
unwell1 and the second that ,i was      
intruding on his  work4    ,how         

illogical6 he answered4 ,if ,i interrupt
 my work to chat with you1  ,i am       
putting aside exactly what the doctor   
would deny me if ,i were to  allow him4 
,so1 let us make a start4 ,you have     
probably some conundrum  weighing on    
your mind4    ,that may not be far      
wrong4 ,i have been troubled by         
something in  connexion with ,kepler's  
second law4 ,it almost robbed me of my  
night's  sleep4 ,my thoughts kept       
returning to a certain question1 and ,i 
should  like to know whether there is   
any sense in the question itself at all4
    ,let us hear it6    ,the law in     
question states that every planet in    
describing its elliptic  path1 sweeps   
out with its radius vector equal        
sectorial areas in equal  intervals of  
time4 ,but this seems only half a law1  
for the radius  vectors are only        
considered drawn from the one focus of  
the ellipse1  namely1 the gravitational 
centre4 ,now1 another focus exists1 that
 may be  situated in space somewhere1   

perhaps far away in totally empty       
regions1  if we assume the orbit to be  
very eccentric4 ,my question is3 ,what  
form  does this law take if the radius  
vectors are drawn from this second      
focus and if the corresponding sectorial
 areas are considered1 instead  of these
 quantities being referred to the first 
focus exclusively8    ,this question is 
not devoid of sense1 but it serves no   
useful purpose4  ,it may be solved      
analytically1 but would probably lead to
 very  complicated expressions1 that    
would be of no interest for celestial   
mechanics4 ,for the second focus is only
 a constructive addition1 that  has     
nothing real in space corresponding to  
it4 ,what else is troubling  you8    ,my
 next difficulty is a little problem    
that sounds quite simple and yet  is    
sufficiently awkward to make one rack   
one's brains4 ,it was suggested  to me  
by an engineer who certainly has a keen 
mind for such things1 and  yet1 as far  
as ,i could judge1 he did not get a     

solution for it4 ,it  concerns the      
position of the hands of a clock4       
,you surely are not referring to the    
children's puzzle of how often and  when
 both hands coincide in position8    ,by
 no means4 ,as ,i said just now1 it is  
really quite perplexing4 ,let us  assume
 the position of the hands at twelve    
o'clock1 when both hands  coincide4 ,if 
they are now interchanged1 we still have
 a possible  position of the hands1     
giving an actual time4 ,but1 in another 
case1 say1  exactly six o'clock1 we get 
a false position of the hands1 if we    
interchange them1 for on a normal clock 
it is impossible for the large  hand to 
be on the six whilst the small hand is  
on the twelve4 ,the  question is now3   
,when and how often are the two hands   
situated so that  when they are         
interchanged1 the new position gives a  
possible time on  the clock8    ,there1 
you see1 said ,einstein1 that is just   
the right kind of  distraction for an   
invalid4 ,it is quite interesting1 and  

not too easy4  ,but ,i am afraid the    
pleasure will not be of great duration1 
for ,i  already see a way to solve it4  
,supporting himself on his elbow1 he    
sketched a diagram on a sheet of  paper 
that gave a clear picture of the        
conditions of the problem4 ,i can  no   
longer recollect how he arrived at the  
terms of his equation4 ,at any  rate1   
the result soon came to hand in a time  
not much longer than ,i had  taken to   
enunciate the problem to him4 ,it was a 
so-called indeterminate  7,diophantic7  
equation between two unknowns1 that was 
to be satisfied by  simple integers     
only4 ,he showed that the desired       
position of the hands  was possible #adc
 times in #ab hours1 an equal interval  
separating each  successive position2   
that is1 starting from twelve o'clock1  
the two  hands may be interchanged every
 #e minutes  seconds1 and yet give a    
possible time4         99     99     99 
99     99     99     99     99    ,i    
mention this little episode1 which is   

insignificant in itself1 merely  to give
 an example of how a great discoverer1  
too1 finds amusement in  such           
distractions4 ,in ,einstein's case this 
tendency to practise his  ingenuity on  
unimportant trifles is so much the more 
pronounced from the  fact that he       
requires an outlet for his virtuosity in
 calculation1 and  gratefully welcomes  
every suggestion that helps him to      
relieve his  mental tension4 ,similar   
characteristics are reported of the     
great ,euler1  as well as of ,fermat1   
whereas many another eminent            
mathematician feels  decidedly unhappy  
if he drifts within reach of the realm  
of actual  numerical calculation4 ,in my
 mind's eye ,i still see ,ernst ,kummer1
 the  splendid savant 7who1 in his time1
 conferred distinction on ,berlin       
,university by his very presence71      
suffering agonies whenever ordinary     
arithmetical tables threatened to appear
 in the working-out of his  formulae4   
,as a matter of fact1 these two things1 

a mastery over  mathematics and a talent
 for ingenious calculation1 are to be   
considered  as quite independent1 even  
if we now and then find them present in 
the  same person4    ,in the case of    
,einstein this tendency is a symptom of 
an incredible  universality of spirit4  
,it moreover presents itself in the     
pleasantest  forms1 and a               
character-sketch of ,einstein would be  
incomplete if this  trait were not      
mentioned4 ,every problem which is in   
any way amusing  excites in him a       
willing interest and enthusiasm4 ,i once
 directed our  conversation to the      
so-called ,scherenschnitte4 ,these are  
made from  long strips of paper or      
canvas1 the ends of which are caused to 
overlap  a little and then pasted       
together1 but instead of being fixed so 
that a  flat wheel results1 which rolls 
on one side of the strip1 the strip is  
twisted one or more times before the    
ends are fastened together4 ,if now  the
 strip is cut lengthwise right along its

 centre1 various unexpected  results    
occur1 depending on the number of twists
 that have been made  before pasting4   
,some very complex geometrical          
difficulties are involved in these      
problems4 ,this is shown by the fact    
that learned mathematicians have        
written extensive disquisitions on these
 curious constructions 7for  example1   
,dr4 ,dingeldey's book1 published by    
,teubner1 ,leipzig74 ,einstein  had     
never taken notice of these wonders of  
the scissors1 but when ,i  began to form
 these strips1 to paste them1 and to cut
 them1 he  immediately became interested
 in the underlying problem1 and         
predicted  in a flash what puzzling     
chain constructions would result in each
 case1  with a certainty that would lead
 one to imagine that he had spent days  
at it4 ,on another occasion a           
space-problem dealing with dress came up
  for discussion3 ,can a properly       
dressed man divest himself of his       
waistcoat without first taking off his  

coat8 ,one would not have dared to      
confront ,copernicus or ,laplace with   
such a problem4 ,einstein at once       
attacked it with enthusiasm1 as if it   
were an exercise in mechanics1 the  body
 being the object2 he solved it in a    
trice1 practically1 with a  little      
energetic manipulation1 much to the     
amazement and joy of the  beholder1 who 
asked himself3 ,is this the same        
,einstein who developed the  work of    
,copernicus and ,newton8 ,a little      
later1 perhaps1 the conversation        
centres around some serious point drawn 
from politics1 political  economy1      
sociology1 or jurisprudence4 ,whatever  
it may be1 he knows how  to spin out the
 suggested thread1 to establish contact 
with his partner  in conversation1 to   
open up his own perspectives without    
ever insisting  on his point of view1   
always stimulating and showing a ready  
sympathy  for the subject of discussion 
and for all the ideas which it          
crystallizes1 the prototype of the      

scientist1 in the mouth of whom         
,terence put the words3 ,i am a human   
being2 nothing that is human is  alien  
to me6          ,,chapter ,,ix    ,,an  
,,experimental ,,analogy    ,forms of   
,physical ,laws4--,aids to              
,understanding4--,popular               
,descriptions4--,optical                
,signals4--,simultaneity4--,experiments 
in ,similes4      ,i ,,wish to ask you4 
,professor1 to help me over a difficulty
 and to treat  me as the spokesman of a 
great number who are similarly troubled4
 ,in  most accounts of your theory of   
relativity1 there is a dearth of        
definite1 concrete1 illustrative        
examples on which we can fix our minds  
whenever the theorem is to be applied   
generally without limitation4 ,let  me  
express this more precisely3 ,your      
simplified picture of the structure  of 
the universe is achieved in the theory  
of relativity by emancipating  all      
observations from fixed co-ordinate     
systems1 and by proclaiming the         

equivalence of all systems of reference4
 ,one of your earliest theorems  states 
that physical laws describing how the   
states of physical systems  alter1      
remain the same1 no matter to which of  
two co-ordinate systems  these states   
are referred1 provided that the         
co-ordinate systems are  moving         
rectilinearly and uniformly relatively  
to one another4 ,this  theorem entails  
the following statement4 ,if            
we--erroneously--adopt a                
non-relativistic view1 we shall come to 
the conclusion that physical  laws      
depend on the particular system of      
reference chosen1 and will thus  assume 
a different form for each different     
system4 ,at this point we  experience a 
desire to hear definite examples4 ,what 
varying forms may a  certain given      
physical law1 known under a definite    
form1 assume1 and how  can we use this  
law to show that it must adapt itself to
 the postulate  of relativity8          
,einstein explained that such examples  

cannot be given in special cases1  but  
only in very general terms4 ,if we were 
to suggest the elliptic  orbits of the  
planets 7at which ,i had hinted in my   
remarks71 we should  fall into error1   
for the law of elliptic orbits is no    
such law4 ,for1  from another point of  
view1 the elliptic paths of the planets 
might be  drawn out into wavy lines1 or 
into spirals1 and they would remain     
ellipses only as long as the lines of   
motion are referred to the central      
attracting body4 ,but the constancy of  
the velocity of light is such a  law1 as
 also is the law of inertia1 according  
to which a body that is  left to itself 
moves uniformly in a straight line4     
,i confessed to him that this limitation
 to a few very general laws would  be a 
painful matter for many an enthusiast of
 average attainments1 who  has great    
difficulty in distinguishing the laws   
that are generally  valid from those    
that hold only within circumscribed     
limits4 ,but if this  were not so1 we   

should have to alter our conception of  
what is conveyed  by a popular          
exposition4 ,for it is called popular1  
not because it now  and then uses the   
patronizing words dear reader1 but      
because it  anticipates the questions   
and doubts of the man of average sense1 
and  examines them1 proving some to be  
unjustified and others to be  reasonable
 or unreasonable1 as the case may be4   
,then there is a further  matter that   
troubles me1 ,i continued4 ,let us      
suppose an ordinary  reader of such a   
popular account to get a first insight  
into the new  conception of ,time4 ,he  
is glad to feel the ideas dawning in    
him1 and1 to  get a more lasting view of
 the idea1 he repeats the arguments     
through  which he has just threaded his 
way1 and1 in doing so1 again encounters 
the phrase 'uniform motion4' ,at the    
first reading he imagined that he       
understood the expression quite well1   
but the second time he pauses and       
considers4 ,for now that he knows how   

much depends on it1 he is anxious  to   
find out the exact meaning of a 'uniform
 motion4' ,he looks for a  definition1  
and if he cannot find one in the book he
 is perusing1 he  endeavours to reason  
it out for himself4 ,with good luck he  
arrives at  the usual statement3 a body 
moves with 'uniform motion' if it       
traverses  equal distances in equal     
intervals of time4 ,but equal intervals 
of time  are clearly those during which 
a body in uniform motion traverses equal
  distances4 ,in other words1 he        
explains ,a by means of ,b1 and ,b by   
means  of ,a1 so that he has involved   
himself in a vicious circle from which  
he  cannot escape4 ,this is his hour of 
need1 due to the difficulty of  'time4' 
,he hopes that further study will remove
 this obstacle4 ,he meets with  the     
conception of 'simultaneity1' which is  
defined for him anew1 and is  disclosed 
as being 'relative4' ,he manuvres       
further towards the  fundamental theorem
 that every body of reference has its   

own particular  time4    ,his popular   
booklet makes this clear to him by      
quoting the example of a                
flying-machine1 or1 better still1 a     
railway train that is rushing along  an 
embankment at a very great speed1 and   
that carries a passenger4 ,two  strokes 
of lightning ,i and ,,ii are to take    
place at two widely distant  points on  
the embankment4 ,the question is then3  
,when are these two  flashes of         
lightning to be considered              
'simultaneous'8 ,what conditions  must  
be fulfilled to ensure this8 ,it is     
found--incontrovertibly--that  the      
light-rays starting out from the two    
strokes of lightning must meet  at the  
mid-point of the embankment4    ,it now 
follows from a short chain of argument  
that the observer in the  train will see
 flash ,,ii earlier than flash ,i1 if   
they reach the  observer1 who is at     
rest1 at the same moment4 ,that is1 two 
events that  are simultaneous with      
respect to the embankment are not       

simultaneous for  a moving system 7such 
as a train or a flying-machine72 the    
converse is1  of course1 also true4     
,here1 again1 the eager layman          
encounters difficulty1 for he asks      
himself3 ,why should the two events be  
characterized or defined by             
lightning-flashes in particular8 ,if    
acoustic signals were used instead1     
nothing would be altered in the         
fundamental determination1 for the sound
  rays 7sound-waves7 would likewise meet
 at the mid-point of the line  joining  
the sources of disturbance4 ,what is the
 reason that the  relativity of time    
arises only when phenomena are regarded 
optically1  and that rays of light play 
the deciding part in all later          
developments8    ,and this particular   
query is followed by one which is more  
general3 ,why  does the popular pamphlet
 not read this question in my mind8 ,i  
know that  the author of it is more     
skilled in these matters than ,i1 but   
just this  superiority should help him  

to divine what is passing in my mind    
when ,i  make efforts to follow his     
reasoning4    ,einstein had listened to 
me patiently1 and then he explained to  
me at  considerable length why in this  
case optical signals cannot be replaced 
by sound signals3 light is the only mode
 of motion that shows itself to  be     
entirely independent of the carrier of  
the motion1 of the  transmitting medium4
 ,thus the constancy of velocity is     
assumed in the  above argument1 and as  
this constancy is an exclusive property 
of light1  every other method must be   
discarded as unallowable for            
investigating  the conception           
simultaneity4 ,furthermore1 he showed me
 how1 on the  basis of relativity1      
starting from the embankment-experiment1
 we may  arrive at a perfectly          
consistent representation of the        
conception of  ,time4 ,he certainly did 
this by applying subtle physical        
arguments that  exceed the scope of the 
present book4#g ,he added1 in substance1

 that it  was futile and impossible to  
discuss in detail all the conceivable   
objections that might arise in the mind 
of one reading a popular work of  this  
kind3 it was a futile undertaking1      
because the true purpose was  defeated1 
inasmuch as a clear development of the  
fundamental thought  would be almost    
impossible under the cross-fire of so   
many random  questions4    ,footnote #g3
 ,in these arguments1 arrangements of   
synchronous clocks  occur1 which are    
fixed into the co-ordinate systems1 the 
positions of  their hands being compared
 with one another4 ,the time of an event
 is  then defined as the position of the
 hands of a clock immediately  adjacent 
to the scene of the event4    ,thus1 in 
this matter1 ,einstein takes the same   
stand as ,schopenhauer in  the preface  
of his chief work1 in which he says3 ,to
 understand this  work no better way can
 be advised than to read it twice 7at   
least71  inasmuch as the beginning      
assumes the end1 almost as much as the  

end  assumes the beginning2 the smallest
 part cannot be understood if the  whole
 has not already been understood4       
,whoever accepts and follows this       
advice will find that the intermediate  
objections will gradually balance  and  
cancel one another1 and that it is not  
necessary that they should  interrupt   
the steady and consistent line of       
development4    ,the position would be  
different if a disciple of the new      
theory should  resolve to dispense with 
strictly scientific reasoning           
altogether1 and  should wish to meet the
 wishes of his readers or hearers by    
discarding  accuracy entirely4 ,such a  
programme seems quite feasible4    ,this
 would be merely following the sketchy  
method of a magazine1  ,einstein        
remarked1 but you do not seriously think
 that it would lead to  anything8    ,it
 would not be a true explanation1 which 
is reserved for technical  productions4 
,but ,i can imagine that it would not be
 unprofitable to help  one who is       

entirely ignorant on these questions by 
using makeshifts1 in  the form of       
allegories or analogies1 which will     
serve as supports if he  should take    
fright during the course of his earlier 
studies4 ,these  shocks are bound to    
occur1 as1 for instance1 when he learns 
that a  moving rigid rod undergoes      
contraction in the direction of motion4 
,but this is proved to him6             
,nevertheless1 he does not easily accept
 it4 ,for the general reader will  say  
to himself3 ',a superhuman effort is    
imposed on my mind4 ,a rigid rod  is the
 most constant of all things1 and never 
before has one been  compelled to regard
 something that is constant as          
variable4'    ,if he does not grasp it1 
no analogy will teach him4    ,but      
perhaps it is possible4 ,the analogy is 
to show him that the effort  is not     
superhuman1 and that thinking ,man has  
already had occasion to  become familiar
 with such transformations from constant
 to variable  factors4    ,i am afraid  

your analogy will prove a failure4      
,from the scientific point of view this 
is probably true1 inasmuch as  all      
comparisons are imperfect1 but the      
analogy may yet be of service as  a last
 resort4 ,for example1 ,i should say to 
my general reader3 ',picture  to        
yourself a savant of the ,middle ,ages  
who reflects on the constitution  of    
animals and plants4 ,one fact seems to  
him to be irrevocably true1  namely1    
that the species are unchangeable6 ,a   
palm tree is a palm tree1 a  horse is a 
horse1 a worm a worm1 and what is once a
 reptile remains a  reptile4 ,a species 
in itself denotes something absolutely  
invariant4'    ,the expression is wrong 
when taken in this connexion2 you mean  
invariable4    ,a little inaccuracy more
 or less does not affect the analogy4   
,for the  sake of my picture ,i should  
like to retain the conception-couple1   
variable and invariant4 ,well1 then1 the
 species give our savant the  impression
 of invariance1 as in the view that was 

held by ,linn and  ,cuvier4 ,this view  
necessarily has its counterpart in his  
thought4 ,he  argues that every species 
has its own original root1 and that1 in 
this  sense1 there is very extensive    
variation4 ,the fundamental roots are   
extremely manifold2 ,nature has produced
 innumerable variations in her          
individual acts of creation4 ,but now   
the ,theory of ,descent of ,lamarck1    
,goethe1 ,oken1 ,geoffroy ,st4 ,hilaire1
 enters the field and produces a        
complete inversion of these two         
elements2 the two parts of the earlier  
point of view change places4 ,our savant
 has to revise his whole world of       
thought4 ,now all organisms are to be   
traced back to a single original  root3 
the latter1 which was variable before1  
becomes an invariable  unicellular      
primitive organism1 but the apparently  
unchangeable species  now becomes       
variable1 in the widest possible sense4 
,and even if this  savant should        
exclaim3 ',how am ,i to reconcile myself

 to this view8' his  descendants later  
find no difficulty in accepting the idea
 that the  organic roots are uniform1   
and that it is the species that are     
subject  to all manner of variation as a
 compensating feature4    ,einstein     
expressed himself very little pleased   
with this attempt at an  analogy1 and   
found that it was so far fetched that it
 could not be  considered admissible4   
,then ,i must ask your permission to    
continue my attempt2 perhaps  something 
useful may yet result from it4 ,i now   
picture to myself a human  being who    
lived in classical times and who1       
following ,ovid and the great  majority 
of his contemporaries1 regards the earth
 as a disc4 ,on this  disc1 each        
inhabitant of the earth has his own     
particular position1 for  the disc has a
 centre with reference to which the     
position of a person  can be specified  
if his distance and his angular         
displacement from a  given initial      
radius is specified4 ,thus1 there is a  

variation of  position if various       
persons are considered4 ,on the other   
hand1 the  ,above and the ,below is     
absolutely invariable for all persons1  
for  the lines running between ,above   
and ,below are all parallel for them1   
since they all have uniformly the same  
disc under their feet and the  same     
heaven above their heads4 ,ovid would   
therefore have refused to  entertain for
 a moment the suggestion that           
,above-,below is a variable4  ,but his  
distant descendants accepted the view   
that the earth is  spherical and that   
there are antipodes as self-evident1 and
 they found  not the slightest          
difficulty in considering the line      
,above-,below to  vary with their own   
position1 making all possible angles    
with an initial  line extending to      
direct oppositeness4 ,referred to the   
centre of the  sphere1 all people have  
now an 'invariant' position1 whereas1 in
  compensation1 the ,above-,below is    
subject to every conceivable  variation4

 ,and now ,i again address myself to the
 average reader1 and say  that the      
meaning of these analogies is that every
 doctrine that leads to  a great        
uniformity converts what was formerly   
invariant into a  variable quantity1 and
 vice versa4 ,the theory of relativity  
makes all  considerations about the     
physical world independent of all       
co-ordinate  systems2 it establishes    
completely invariable uniformity1       
removed from  all changes due to varying
 points of view4 ,hence what was        
previously  invariable--such as a rigid 
measuring-rod--will now become variable4
 ,it  is not surprising that this       
requires a new method of thought1 a     
revision  of our mode of reasoning1 for 
the above analogies show that these     
radical adjustments are                 
characteristically necessary in the case
 of  comprehensive theories1 and that   
such theories are able to overcome      
apparently firmly established ideas4    
,the parallels that ,i drew above  will 

at least inspire the average reader with
 a certain confidence1 for  they show   
him how results of reasoning that were  
once considered  incredible were        
regarded as self-evident by later       
generations4    ,i have already         
emphasized sufficiently that ,einstein  
regards as  inadequate these auxiliary  
pictures that have presented themselves 
to  me4 ,yet in the course of the       
conversation ,i gained the impression   
that  his judgment grew somewhat milder1
 and that1 with certain reservations1   
he was disposed to let them pass as     
tolerably useful helps--and they are    
not intended to be more than this4 ,i   
think1 therefore1 that ,i am not  acting
 counter to his wishes in citing these  
allegorical examples here1  particularly
 as they arose in the course of our     
talks4    ,since then1 ,i have had many 
opportunities of testing these examples 
on  certain persons1 and may mention    
that they proved quite useful4          
,analogies of this kind may offer a     

friendly help in moments when the       
uninitiated feel themselves in peril1   
and encounter a difficulty which  they  
imagine to be insurmountable4 ,they do  
not remove the difficulty1  but they    
impart a certain power of expansion to  
the intellect and  encourage a          
continuation of effort1 which would     
probably otherwise be  relaxed at the   
first sign of something which is        
imagined to be  inconceivable4 ,there is
 thus no room in textbooks for such     
helps1 but  they may justifiably find a 
place in a book that departs from the   
methodical route1 and hopes to discover 
in by-ways things that are  suggestive  
and instructive4          ,,chapter ,x  
,,disconnected ,,suggestions            
,conditionality and ,unconditionality of
 ,physical ,laws4--,conception of       
,temperature4--,grain of ,sand and      
,universe4--,are ,laws                  
unalterable8--,paradoxes of             
,science4--,rejuvenation by             
,motion4--,gain of a                    

,second4--,deformed ,worlds4--,atomic   
,model4--,researches of ,rutherford and 
,niels ,bohr4--,microcosmos and         
,macrocosmos4--,brief ,statement of the 
,principle  of ,relativity4--,science   
with reduced ,sense-,organs4--,eternal  
,repetition4--,higher ,types of         
,culture4      ,,in all branches of     
reasoning1 no word and no conception has
 played a  more important part than that
 of law4 ,physical laws denote the      
barrier  that separates strictly chance 
and arbitrariness from necessity1 and it
  seems to us that the region of the    
latter must ever extend so that  finally
 nothing will be left of the former1    
which will have become  amalgamated with
 necessity4 ,we shall be constrained to 
believe more and  more in a supreme law 
that will be a complete expression of   
all the  partial laws which science     
presents to us as more or less permanent
  results of individual researches4     
,our conversation was centred about     
these individual laws1 such as those    

that are taught in the theory of gases1 
optics1 etc41 and that are  associated  
with the names1 ,boyle1 ,gay-,lussac1   
,dalton1 ,marriotte1  ,huyghens1        
,fresnel1 ,kirchhoff1 ,boltzmann1 and   
others4 ,in connexion with  these ,i    
asked ,einstein whether he regarded the 
laws as things  unconditioned in        
themselves1 and capable of proof under  
every set of  circumstances2 and whether
 absolutely valid laws existed or could 
exist4    ,einstein's answer was        
essentially in the negative4 ,a law     
cannot be  final1 if only for the reason
 that the conceptions1 which we use to  
formulate it1 show themselves to be     
imperfect or insufficient as science    
progresses4 ,let us consider1 for       
example1 an elementary law such as      
,newton's ,law of ,force4 ,from our more
 recent point of view we find the       
conception of direct action at a        
distance to be inexact in ,nature4 ,for 
it has been shown that action at a      
distance is not an ultimate factor1  but

 must be resolved into a multiplicity of
 actions between immediately            
neighbouring points 7,the ,theory of    
,action by ,contact or ,contiguous      
,action74 ,another example is provided  
by the conception ,temperature4  ,this  
conception becomes meaningless if we    
endeavour to apply it to  molecules3 it 
leads to no result if we try to impose  
it on the smallest  parts of matter as  
such4 ,the reason is that the state1 the
 velocity1 and  the inner energy of the 
individual molecules fluctuates between 
very  wide limits4 ,the conception      
'temperature' is applicable only to a   
configuration composed of many          
molecules1 and even then it is not      
applicable quite generally4 ,for let us 
picture to ourselves an extremely       
rarefied gas contained in a closed      
receiver4 ,two opposite walls are to  be
 at different temperatures1 the one     
being cold and the other being hot  ,in 
a gas at such very low pressure the     
molecules come into collision so  seldom

 that1 practically1 we have to take into
 account only the  collisions of the    
molecules with the confining walls4 ,the
 molecules that  rebound from the hot   
wall have greater velocities than those 
coming from  the colder wall1 and hence 
the conception of temperature becomes   
untenable for this gas4    ,would the   
temperature-scale on the thermometer    
then denote nothing8 ,i  asked4 ,the    
greater or lesser degree of warmth of a 
body1 in this case  of the mass of gas1 
depends on the more rapid or less rapid 
motion of  its smallest parts4 ,the     
motions are in any case present1 so what
 would a  thermometer indicate8    ,it  
would betray only that it had nothing to
 indicate4 ,if a thermometer  that is   
blackened on one side were inserted into
 the vessel containing  the gas1 then   
different temperatures would be recorded
 if the  thermometer were gradually     
turned about its own axis2 and this     
signifies  that the conception of       
temperature has become meaningless for  

this  configuration of molecules4 ,and  
passing beyond the quoted examples1 ,i  
should maintain that all our            
conceptions1 however subtly they may    
have  been thought out1 are shown in the
 course of progressive knowledge to be  
too rough hewn1 that is1 too little     
differentiated4         99     99     99
     99     99     99     99     99     
,we spoke of the ,properties of ,things1
 and of the degree to which these       
properties could be investigated4 ,as an
 extreme thought1 the following         
question was proposed3    ,supposing it 
were possible to discover all the       
properties of a grain  of sand1 would we
 then have gained a complete knowledge  
of the whole  universe8 ,would there    
then remain no unsolved component of our
  comprehension of the universe8        
,einstein declared that this question   
was to be answered with an              
unconditional affirmative4 ,for if we   
had completely and in a scientific      
sense learned the processes in the grain

 of sand1 this would have been  possible
 only on the basis of an exact knowledge
 of the laws of  mechanical events in   
time and space4 ,these laws1            
differential equations1  would be the   
most general laws of the universe1 from 
which the  quintessence of all other    
events would have to be deducible4      
,this thought may be spun out in yet    
another direction4 ,every piece of      
research1 however specialized it may    
appear and of whatever minor  importance
 it may be1 retains a relationship with 
researches into the  universe1 and may  
prove to be valuable for this latter    
task4 ,if we  accept the view that      
science is capable of realizing         
perfection1 then  every contribution to 
knowledge1 even the most insignificant1 
is  essentially indispensable for       
attaining this goal4         99     99  
99     99     99     99     99     99   
,can a physical law alter with time8 ,in
 more precise language1 can time1  as   
such1 enter explicitly into laws1 so    

that1 for example1 an experiment  that  
is carried out at different times leads 
to different results8 ,this  question   
has been treated several times1 among   
others1 by ,poincar1 who  answered it   
with an emphatic ,no6 but also by others
 to whom the  invariability of physical 
laws did not seem to hold for all       
eternity4 ,if  my memory does not play  
me false1 ,helmholtz once expressed     
faint doubts  about the constancy of    
laws4    ,einstein answered this        
question with a decided negative4 ,for a
 law of  physical nature is1 by         
definition1 a rule to which events      
conform  wherever and whenever they take
 place4 ,thus1 if we were to be         
compelled  as a result of experience to 
make a law dependent on time1 it would  
be a  necessary step to seek a law      
independent of time1 which would include
 in  itself the law dependent on the    
time as a special case4 ,the latter     
would  be excluded from the category of 
physical laws1 and would henceforward   

play the part only of a result deduced  
from the law which is independent  of   
the time4         99     99     99      
99     99     99     99     99    ,what 
attitude should we adopt if1 in studying
 a scientific doctrine1 we  encounter   
paradoxical results even though the     
inferences have been drawn              
correctly--that is1 if we meet with a   
deduction to which our reasoning  powers
 object1 although no fallacy is         
discoverable in the argument8    ,before
 we deal with cases which seem to me1   
personally1 to be  interesting1 let us  
hear what is ,einstein's attitude in    
general4 ,as  soon as a paradox presents
 itself1 we may1 as a rule1 infer that  
inaccurate reasoning is the cause1 and  
should thus examine in each  particular 
case whether an error of logic is       
discoverable1 or whether  the           
paradoxical result denotes only a       
violent contrast with our present       
views4    ,let us first take examples   
from an entirely modern science1 from   

the  ,theory of ,aggregates founded by  
,georg ,cantor of ,halle4 ,we shall     
follow  the argument by the only        
possible method for this book1 namely1  
by rough  indications that will serve   
our purpose and do not claim to be      
accurate  in expression or in sense4    
,if we take an aggregate of three       
objects1 for example1 an apple1 a pear1 
and a plum1 we may1 by definition1 form 
six partial aggregates1 namely3         
the apple      the pear      the plum   
the apple and the pear      the apple   
and the plum      the pear and the plum4
    ,the aggregate of the partial       
aggregates1 which contains six elements1
 is  thus greater than 7actually twice  
as great as7 the original aggregate1  in
 which only three elements occur4    ,if
 the original aggregate contains an     
additional element1 for example1 a  nut1
 the following partial aggregates may be
 formed3        the apple      the pear 
the plum      the nut      the apple and
 the pear      the apple and the plum   

the apple and the nut      the pear and 
the plum      the pear and the nut      
the plum and the nut      the apple1 the
 pear1 and the plum      the apple1 the 
pear1 and the nut      the apple1 the   
plum1 and the nut      the pear1 the    
plum1 and the nut4    ,thus1 in this    
case1 the aggregate of the partial      
aggregates is already  considerably     
greater than the original aggregate4    
,this numerical excess  increases       
rapidly with each successive increase in
 the original  aggregate1 so that if we 
apply the same reasoning to an infinite 
aggregate1 the aggregate of partial     
aggregates becomes an infinity of a     
higher order4 ,this is expressed by     
saying that the infinite aggregate  of  
partial aggregates has a greater        
potentiality than the infinity of  the  
elements of the original aggregate4     
,so we see that the one infinity is1 in 
popular language1 much more             
comprehensive1 more powerful than the   
other4 ,our minds do not find it        

impossible to grasp this4 ,but in a     
definite imaginary experiment it is     
found that this theorem of progression  
not only fails in its  application1 but 
leads to flagrant contradiction4    ,for
 if we start from the primary aggregate 
of all conceivable things1  its infinity
 can certainly not be transcended by any
 other infinity4 ,but  according to the 
above theorem the aggregate of all      
partial aggregates  would have a greater
 potentiality1 although it itself cannot
 extend  further than to the conception 
of the maximum of all conceivable       
things4  ,we thus arrive at an insoluble
 paradox1 a typical example of how1 in  
the  system of conceptions involved1    
something is insufficient or not in     
conformity with logical thought4 ,and   
this sceptical view receives  support   
from various remarks of ,descartes1     
,locke1 ,leibniz1 and  particularly     
,gauss1 who1 long before the advent of  
the ,theory of  ,aggregates1 raised a   
protest against inexact definitions of  

infinity4    ,in another case1 however1 
the same theory seems to arise by       
perfectly  logical processes1 although  
it again leads to a statement that does 
not  seem correct to common sense4 ,for 
it shows by a very subtle and  ingenious
 method that all the surface-points of a
 surface infinitely  extended in all    
directions may be brought to correspond 
in a reversible  single manner to the   
linear points of a line1 however small2 
so that to  every point of the unlimited
 plane there corresponds a definite     
point of  the line1 and vice versa4 ,the
 same theorem may be extended to        
three-dimensional space1 with the result
 that we have to reconcile  ourselves   
with the incredible fact that1 expressed
 in popular language1  a straight line  
of however small length exhibits the    
same potentiality  with regard to the   
number of its points1 as all the points 
in the  universe4    ,for my own part1  
,i must confess that no means suggests  
itself to me to  make this paradox      

intelligible4 ,but the sacrificium      
intellectus comes  within dangerous     
proximity4 ,einstein1 who values and    
marvels at the  theory of aggregates as 
a science1 or perhaps more as a work of 
art  built up from the materials of     
science1 gives whole-hearted support to 
the proof4 ,he refuses to accept the    
notion of a paradox--that is1 he        
recognizes a contradiction not in our   
process of reasoning1 but only in  a    
habit of thought that is open to        
correction4 ,i should give much to      
discover the means of correction6       
99     99     99     99     99     99   
99     99    ,a third example arises out
 of the special theory of relativity4   
,it has a  mysterious paradoxical       
character that vanishes when a clear    
view of the  relationships involved has 
been obtained4    ,according to this    
theory the rate at which events happen  
alters  according to the state of motion
 of the system under consideration4 ,let
  us now consider two twins ,a and ,b1  

that1 although born at one place on  the
 earth1 are immediately separated1 ,b   
remaining at rest1 whilst ,a  rushes out
 into space at an enormous rate1        
describing what1 viewed from  the earth1
 is an inconceivably great circle4 ,in  
this way the rate of  happening of all  
events is reduced very considerably for 
,a in a manner  that may be calculated4 
,if ,a then returns to ,b1 it may happen
 that the  twin who stayed at home is   
now sixty years old1 whereas the        
wanderer is  only fifteen years of age1 
or is perhaps only an infant still4     
,the first introduction to this flight  
of imagination naturally causes         
profound perplexity4 ,nevertheless1 we  
are dealing not with a realm of         
miracles1 but with something that is    
within the range of comprehension4      
,in the case of these two twins1        
,einstein declared1 we have merely a    
paradox of feeling4 ,it would be a      
paradox of thought only if no           
sufficient ground could be suggested for

 the behaviour of these two  creatures4 
,this ground1 which accounts for the    
comparative youth of ,a1  is given1 from
 the point of view of the special theory
 of relativity1 by  the fact that the   
creature in question1 and only this     
creature1 has been  subject to          
accelerations4 ,a proper grasp of the   
reason is furnished only  when we adopt 
the general theory of relativity1 which 
tell us that1  from the point of view of
 ,a1 a centrifugal field exists1 whereas
 it is  absent from the point of view of
 ,b4 ,this field exerts an influence on 
the relative rate of happening of the   
events of life4    ,it certainly        
requires a prodigious mechanism to allow
 the moving twin to  gain even only one 
second of time4 ,if he were to spend a  
year in a  merry-go-round whose         
circumference were about #ai milliard   
miles in  length1 he would have to      
travel in it at the rate of over #fjj   
miles per  second if he is to gain a    
second on his brother4    ,this         

inevitable result that is immediately   
apparent to a trained  scientific mind  
throws light on the nature of common    
sense1 the  validity of which1 as an    
ultimate criterion1 ,kant too has       
refused to  recognize1 in so far as this
 common sense is incapable of passing   
beyond the examples offered in its own  
experience4 ,it circulates1 as          
,einstein says1 in the realms of feeling
 and analogy4 ,it finds no  analogy for 
a phenomenon like that described above1 
and since it can  apply rules only      
concretely1 many things appear to it    
paradoxical that1  in the light of      
intensified abstraction1 appear logical 
and necessary4         99     99     99 
99     99     99     99     99    ,let  
us speculate on the following question4 
,if all things in the  universe should  
increase or decrease enormously in      
dimensions1 and if1  at the same time1  
in a manner totally concealed from us1  
certain  physical conditions should     
become changed1 we should lack all means

 of  discovering the difference between 
things before and after the change4     
,for since all measuring-rods1 including
 those furnished by our senses1  would  
have become changed in the same         
proportion1 the two conditions  could   
not be differentiated from one another4 
,it may easily be shown  that this would
 necessarily occur1 if an extramundane  
power were  non-uniformly to displace1  
deform1 compress1 or bend all things in 
the  universe1 provided that our        
instruments and senses participated in  
this  transformation4 ,accordingly it is
 permissible also to regard the         
universe known to us as one that is     
deformed1 and one that is derived  from 
another1 the original form of which will
 ever remain a secret to  us4    ,is    
there any connexion between this        
grotesque speculation and the theory  of
 relativity8    ,we can establish only  
one that is negative and that arises e  
contrario4 ,these deformations1 said    
,einstein1 are in themselves            

abstractions that are physically        
meaningless4 ,only relations between    
bodies have a physical meaning1 for     
example1 the relation between           
measuring-rods and the objects they     
measure4 ,therefore1 it is reasonable   
to talk of deformations only when we are
 dealing with the deformations  of two  
or more bodies with respect to one      
another1 whereas the  conception of     
deformation has no sense1 unless a real 
object is  specified1 to which it is    
referred4 ,the philosophical merit of   
the  general theory of relativity1 as   
compared with previous views of         
physics1 consists in the fact that the  
former avoids entirely these            
meaningless abstractions with respect to
 space and time4    ,according to this1 
it is not purposeless to enter on these 
grotesque  trains of thought1 even if   
they are untenable physically4 ,for     
since the  new physics teaches us to    
avoid these false tracks1 it seems of   
value to  know what it is that is to be 

avoided4 ,just as we must study         
scholastic  thought if we wish to grasp 
thoroughly the philosophy which sprang  
up  after the scholastic fetters were   
burst4 ,moreover1 these reflections on  
concealed universes are not without a   
certain attraction1 reminiscent of  the 
sorcerer's wand1 if they pursued any    
other goal than that of making          
universes distorted4 ,it is true that   
they hold out latent temptations  that  
may in some cases lead us on to         
dangerous ground1 in encouraging us  to 
venture on analogies beyond the scope of
 geometry and physics4 ,would  it be    
possible to enter suddenly into a world 
that is distorted and  deformed with    
respect to its ethics1 its culture1 and 
its reasoning  intellects1 without our  
observing the difference8 ,are we       
ourselves  perhaps living under such    
deranged conditions1 of which we cannot 
become  aware1 because our perceptual   
organs have likewise become deformed8 ,i
  must frankly confess that ,i do not   

regard it as quite inconceivable that   
this argument of deformation may be spun
 out in this direction1 but ,i  must add
 that ,einstein rejects absolutely all  
such extensions1 since1  as he          
emphasizes1 they lead to regions that   
are merely fields for the  exhibition of
 verbal gymnastics4         99     99   
99     99     99     99     99     99   
,the question whether ,nature makes     
leaps or not is very old4 ,in the       
theory of descent it forms the          
foundation of the difference between    
revolutionists and the evolutionists1   
who uphold the axiom natura non  facit  
saltus1 with all its consequences4      
,recently attempts have been  made1     
particularly by psychologists1 to       
propound and justify a natural          
principle of discontinuity4 ,they assert
 that our own perceptions and           
sensations are discontinuous in         
themselves1 and that the mechanism of   
every perception is akin to that of a   
cinematograph with its extremely  rapid 

interruptions4 ,if this should actually 
be the case1 we should  scarcely have a 
means of solving definitely the question
 whether  continuity reigns1 or not1 in 
,nature4    ,einstein does not recognize
 the possibility of this alternative for
 a  moment4 ,if a doubt had ever arisen1
 the researches of ,maxwell would in    
themselves have been sufficient to      
dispel it4 ,our universe that is to be  
described in terms of differential      
equations is absolutely continuous4     
,but1 ,i interjected1 does not modern   
physics offer a certain support  to the 
assumption of a discontinuity8 ,does not
 the ,quantum ,theory point  to an      
atomistic structure of energy1 and hence
 also of events that are  to be imagined
 as happening in jerks and as involving 
relations  expressible in whole numbers8
    ,einstein gave an answer of         
epigrammatic brevity and flavour4 ,the  
fact  that these phenomena are          
expressible in whole numbers must not be
  construed into an argument against    

continuous happening4 ,just imagine to  
yourself for a moment that beer is sold 
only in whole litres2 would you  then   
infer that beer1 as such1 is            
discontinuous8         99     99     99 
99     99     99     99     99    ,what 
achievements are to be expected of      
astronomy in the present era8    ,this  
question would have a special meaning if
 it were assumed that the  astronomer   
who works in observatories is surrounded
 by solved problems1  and can no longer 
hope to solve problems having the       
universal  significance of those of     
,copernicus or ,kepler4 ,this           
assumption1 however1  would not be in   
agreement with the actual state of      
affairs4    ,einstein indicated to me a 
number of fundamental problems that     
present  themselves to modern astronomy1
 and the solution of which he expected  
of  future times4    ,above all1 the    
geometrical and physical constitution of
 the stellar  systems will1 in the main1
 become revealed4    ,at present we do  

not yet know whether ,newton's ,law of  
,attraction holds1  at least            
approximately1 for configurations of the
 type of the ,milky ,way  and of the    
spherical clusters of stars--that is1 in
 extents of space in  which the         
influence of space-curvature would      
become appreciable4 ,the  rapid progress
 of recent astronomy justifies our great
 hopes that the  solution of this       
universal problem will be found within  
the coming  decades4    ,in distant     
connexion with this we also touched on  
the question of the  habitability of    
other worlds4 ,this theme of            
,fontenelle1 la pluralit  des mondes    
habits1 which has again become a centre 
of public  interest1 owing to           
investigations of ,mars1 has evoked a   
storm of  discussion4 ,we hear the noisy
 war-cries of geocentric scientists who 
wish to regain for the earth her        
shattered supremacy in astronomy1 and   
who claim the existence of organic forms
 as the sole prerogative of our  planet4

 ,it is scarcely necessary to mention   
that ,einstein rejects the  motives of  
these human and all-too-human           
individuals as small-minded and         
short-sighted4 ,creatures in distant    
worlds are derived from1 and are        
subject to1 conditions of organic       
nature1 of which we can form no idea  by
 deductions from the world which we     
inhabit4 ,but to deny their  existence  
on numberless constellations1 or to     
demand an ocular proof of  their        
presence1 is no better than to assume   
the point of view of an  infusoria to   
whom there is no life other than that in
 a dirty drop of  ditch-water4          
99     99     99     99     99     99   
99     99    ,the idea of the atom as   
the ultimate structural element involves
 a  philological as well as a conceptual
 contradiction4 ,for atomos  signifies  
the indivisible1 the                    
no-further-divisible1 whereas the idea  
of  a body1 however small1 an element of
 structure differing from zero1         

demands1 at least geometrically1 further
 divisibility4 ,even the original       
founders of the theory of atoms1        
,leukippus1 ,epicurus1 and ,democritus1 
assigned definite forms to the ultimate 
components1 and we may read in  the     
splendid work of ,lucretius how he      
infers from the nature of  substance    
that the ultimate particles are smooth1 
round1 or rough1 or  have the shapes of 
hooks and eyes4 ,the further analysis   
pressed forward1  the more the          
simplicity of the original idea         
vanished4 ,microcosms came  to be       
regarded as copies of macrocosms1 and   
the atoms of present-day  science       
actually exact from us that we should   
regard them as worlds in  themselves4   
,einstein acceded to my request that he 
might give a sketch of the latest       
achievements of science sufficient to   
provide an approximate idea of the      
atomic model4 ,according to the         
researches of ,rutherford and ,niels    
,bohr1 we are to picture it as a        

planetary system4    ,the central body  
of this system is represented by a      
positively charged  nucleus1 which      
constitutes almost the whole mass of the
 atom1 surrounded  by a certain number  
of electrons1 negative charges1 that    
move in uniform  circular or elliptic   
orbits about the nucleus4 ,there is thus
 a certain  analogy that allows us to   
regard the nucleus as the sun1 and the  
electrons as the planets of this system4
    ,the number of these electrons      
varies between the limits #a and #ib1   
according to the chemical constitution  
of the element4 ,the smallest  number   
occurs in the case of helium 7in which  
there are two71 and of the  hydrogen    
atom1 in which only one electron-planet 
describes its circular  path about the  
nucleus4 ,in other atoms there are      
probably more  complicated orbits1      
although they are more or less          
approximately  circular4 ,according to  
this still very new theory1 which is    
supported by  very convincing facts1 the

 electrons are to be imagined as        
arranged in  concentric shells 7like the
 layers of an onion71 among which the   
innermost shell plays a distinctive part
 inasmuch as the number of the          
electrons arranged in it decides the    
chemical character of the atom in       
question4 ,it sometimes occurs that     
electrons spring1 under external        
influence1 from one orbit to another2   
when the electron jumps back to  the    
original orbit1 light is emitted4 ,an   
essential fact is to be noted3  ,whereas
 any arbitrary orbits of any arbitrary  
radius may occur in a  planetary system 
of the celestial regions1 the manifold  
of these orbits  in the case of the     
electrons is restricted1 in that only   
certain orbits  are possible1 namely1   
those that are determined mathematically
 by the  quantum condition4    ,perhaps1
 ,i interrupted1 the whole analogy may  
be inverted4 ,if the  atom is considered
 analogous to a planetary system in the 
model1 it  should be admissible to      

regard our true planetary system as a   
cosmic  atom4 ,and then1 long after we  
have become accustomed to regard our    
earth  as playing the part of a grain of
 sand1 the sovereignty of the sun1 too1 
would be past4 ,the whole majesty of the
 solar system as far as the orbit  of   
,neptune would then shrink to a         
configuration compared with which the   
world of a grain of sand would be       
infinitely complex4    ,this fantastic  
inversion is permissible up to a certain
 extent1 said  ,einstein1 but we must   
not lose sight of the fact that there is
 a  cardinal difference4 ,if we         
disregard the enormous disparity in     
dimensions1 the analogy is far from     
exact owing to the circumstance that    
the atom is only an element of          
structure1 whereas the true planetary   
system is an extraordinarily complex    
structure in itself4 ,thus the          
difference between a simple thing and   
one that is very highly complex  still  
remains4    ,but1 ,professor1 may not a 

similar complexity yet be discovered in 
the  atom8 ,it may be merely a          
difference of philosophical view from   
the  primary idea to that of regarding  
the electrons as circulating like       
planets4 ,may we not conjecture that in 
each successive step we are  merely     
carrying out a true regressus in        
infinitum8    ,that seems highly        
improbable1 he replied1 although1 of    
course1  structural investigations can  
never cease4 ,at first they are directed
 at  the more remote object of finding  
out why certain atoms are radioactive1  
that is1 exhibit a tendency to          
disintegrate4 ,it has already been      
established that this tendency is a     
property of the positive nucleus1 of    
which little is as yet known4 ,this     
means that the nucleus is not simple1   
yet it does not open up the possibility 
of an unending regression4 ,our  aim    
must be to get a clear insight into the 
constitution of the nucleus1  as regards
 the positive and negative charges1 and 

it is my opinion1 he  concluded1 that   
beyond this there will be no further    
subdivision of  matter4    ,when ,goethe
 writes of the immovable pole in the    
flux of phenomena1 we  recognize that   
his beautiful remark pronounces an elegy
 to the  possibility of attaining       
ultimate simplicity4 ,einstein's        
utterance1 if ,i  understand him aright1
 converts this elegy into a song of     
hope4 ,if the  subdivision of matter    
actually has an end somewhere1 then we  
are now on  the threshold of ultimate   
things1 we are near the immovable pole1 
which  we are capable of reaching4      
99     99     99     99     99     99   
99     99    ,every new truth of science
 must be such that1 in ordinary writing1
 it  may be communicated completely     
within the space of a quarto leaf4      
,kirchhoff made this remark1 and gave a 
sufficient1 if not literal1             
demonstration of its truth4 ,when       
,bunsen and he published the first      
notice about spectral analysis1 they    

compressed their publication into  the  
small space of three printed pages4     
,but what is to happen if the new truth 
should be built up of very              
comprehensive materials1 when it        
requires many links1 of which none can  
be omitted if the truth is to be made   
intelligible8 ,would ,kirchhoffs  quarto
 page still be sufficient8              
,certainly1 said ,einstein1 provided1 of
 course1 that it is addressed  to a     
reader who has already mastered what    
went before--that is1 to one  who is so 
far acquainted with the older facts that
 he has to learn only  the really new   
part of the new truth4    ,that sounds  
very hopeful1 ,i remarked1 for then it  
should also be  possible to describe    
very briefly the theory of relativity4  
,let us rather say its essentials--the  
heart of the matter4 ,well1 then1  get  
your ,kirchhoff page ready4 ,we shall   
see whether we can set out on it  the   
special theory of relativity4    ,the   
totality of our experience compels us to

 assume that light travels  with a      
constant velocity in empty space4       
,likewise1 our whole experience  in     
optics compels us to recognize that all 
inertial systems are  equivalent2 these 
are systems that are produced from an   
allowable one by  means of a uniform    
translation4 ,an allowable system is one
 in which  ,galilei's and ,newton's ,law
 of ,inertia holds4 7,this law states   
that a  moving body that is left to     
itself retains its direction and        
velocity  permanently47    ,now1 the law
 of the constancy of light propagation  
seems to conflict  with the classical   
principle of relativity1 according to   
which the  velocity of a ray of light   
assumes different values in the moving  
system  according to the direction of   
the ray4    ,this apparent              
incompatibility arises from the         
following unproved  assumptions3    7a7 
,if two events are simultaneous with    
regard to one inertial system1  they are
 also simultaneous with regard to any   

other inertial system4    7b7 ,the      
length of a measuring-rod1 the shape and
 size of a rigid body1  and the rate of 
a clock are independent of their motion 
with respect to  the system of reference
 used1 provided this motion is          
rectilinear and  non-rotational4        
,these assumptions must be discarded if 
this disagreement is to be  eliminated4 
,if we substitute for them the          
assumption that all inertial  systems   
are equivalent and that the velocity of 
light in vacuo is  constant1 we get3    
7#a7 ,that the dimensions of bodies and 
the rate of clocks have a  functional   
relation to the motion4    7#b7 ,that   
the equations of motion of ,newton      
require to be modified2 this            
modification leads to results that1 for 
rapid motions1 differ  appreciably from 
those of ,newton4    ,this is1 in a very
 compressed form1 the meaning of the    
special theory of  relativity4      ,as 
there is still some space left on our   
quarto page1 we may add a  remark that1 

it is hoped1 will make a little clearer 
the above-mentioned  discrepancy4       
,let us choose as our system of         
reference an express train #ah miles    
long4  ,there are two passengers--,mr4  
,front1 right at the front of the train1
  and ,mr4 ,back1 at the extreme end of 
the train1 so that a rigid distance  of 
#ah miles separates the two passengers4 
,the carriages are transparent1  so that
 the two passengers can signal to one   
another4 ,they are1  moreover1 furnished
 with ideal clocks that run at exactly  
the same rate4    ,first1 suppose that  
the train is at rest4 ,back is just     
opposite  milestone #ajj1 whilst ,front 
is opposite milestone #aah4 ,by means of
 a  flash1 ,back signals to ,front his  
time1 exactly #ab o'clock4 ,it takes    
light very nearly  second to traverse   
the length of  the train--#ah miles2    
hence the flash will reach ,front at #ab
 o'clock   second4 ,exactly the same    
result would have come  about if ,front 
had signalled his time to ,back4 ,light 

makes no difference  in travelling      
forwards and backwards4 ,if the train   
moves at a great  speed1 the two        
travellers can conduct the same         
experiment as when the  train was at    
rest4 ,they will then set the time that 
light takes to  travel from ,back to    
,front equal to the time that it takes  
to traverse  the same way in the reverse
 direction4 ,but this phenomenon will   
assume a  different aspect if viewed    
from the railway embankment4 ,an        
observer on  the latter would affirm    
that light does not take the same time  
in  travelling the length of the train  
in one direction as it does when        
travelling in the opposite direction4   
,for the ray of light moving in the     
forward direction has to traverse not   
only the distance between ,back and     
,front1 but also the very short         
distance that ,front has moved forward  
during the interval that the light  has 
been moving2 whereas1 inversely1 the    
flash sent out by ,front to ,back  will 

traverse a distance that is             
correspondingly less than that between  
the passengers1 since ,back is moving   
towards the signal4    ,thus the        
duration of the two phenomena of light  
propagation is the same  or different1  
respectively1 according as it is judged 
from the train or  from the embankment4 
,in other words1 the judgment of the    
length of time  depends on the state of 
motion of the observer4    ,all further 
pronouncements of the special theory of 
relativity are based  on the preceding  
arguments of the relativity of time4    
99     99     99     99     99     99   
99     99    ,would ,man be able to     
construct a ,science if he possessed one
 sense less  than at present--for       
example1 if he were deprived of sight8  
,let us apply  this to a definite case4 
,in the new physics the velocity of     
light plays  a decisive part as a       
world-constant4 ,at first sight it would
 appear  impossible for us to determine 
it and recognize its importance1 if we  

had not at our disposal some organ which
 enabled us to become aware of  optical 
phenomena4    ,but1 as ,einstein        
explained to me1 even under such        
difficult  circumstances1 it would be   
possible to build up a science1 for the 
reason that phenomena1 as far as they   
are perceptible1 may be  transformed so 
that they become manifest to other      
senses if one sense  should be absent4  
,for example1 the electrical            
conductivity of selenium  is strongly   
influenced by the amount of illumination
 that falls on it4  ,thus light acts on 
a selenium cell1 causing changes of     
current  intensity1 which in their turn 
may be perceived by feeling1 or by      
chemical action on the mucous fluid of  
the tongue4 ,ultimately we are          
concerned only with a differentiation   
that enables us to refer identical      
experiences to identical events4 ,we    
should certainly encounter enormous     
difficulties in endeavouring to form a  
physical picture of our  surrounding    

world if the number of our senses should
 become less than  the organs with which
 we actually operate4 ,yet1 in          
principle1 we should  be able to        
overcome all difficulties by means of   
much lengthened and  complicated lines  
of research1 even if we should have only
 a single  sense left1 or if we had only
 one at the very outset4 ,the           
construction  of a ,science would then  
be possible1 and would give the same    
results1  although it might be          
propounded only after a delay of perhaps
 millions  of years4    ,it is naturally
 assumed that the intellect is retained1
 as this is the  necessary condition for
 all scientific research4 ,since the    
degree of  understanding depends on the 
senses--nihil est in intellectu1 quod   
non  prius fuerit in sensu--we may      
conjecture that a human being with only 
one sense organ would work with a       
minimum degree of understanding1 which  
would be insufficient for the           
acquirement of any knowledge whatsoever4

  ,this transcendental question1 which  
lies almost beyond the bounds of        
discussion1 was not touched on in our   
conversation1 as the subject was        
restricted so that it should not drift  
into metaphysical regions4              
,nevertheless1 ,i should like to mention
 that a speculation of this kind  is    
recorded in the history of science4     
,condillac1 in a study teeming  with    
ideas1 investigates the behaviour of a  
,statue1 that he represents  as a human 
being1 with the assumption that there is
 at first no idea in  the soul of this  
statue-person4 ,this living creature is 
enclosed in a  marble envelope1 the sole
 exterior organ of which is at first the
 organ  of smell4 ,he then shows that by
 means of this single sense all manner  
of  sensations and expressions of will  
may develop in his statue4  ,condillac  
does not1 however1 undertake to give a  
convincing proof that  this creature1   
restricted to the organ of smell1 would 
be able to  discover physically the     

relationships that hold in physical     
nature1 and  thus to build up a         
scientific system4 ,thus ,einstein1 in  
his discussion1  goes considerably      
further than the author of this statue4 
99     99     99     99     99     99   
99     99    ,has the eternal           
repetition1 as outlined by ,nietzsche1  
any meaning8    ,the sage of            
,sils-,maria tells us that this         
revelation came to him midway  between  
tears and ecstasy1 as a fantasy with a  
real meaning4 ,the crux of  his idea is 
a finite world built up of a finite     
number of atoms4 ,from  the fact that   
the present state emerges out of the    
immediately preceding  one1 the latter  
from the one just before1 and so on1 he 
concludes that  the present state       
exhibits repetition both forwards and   
backwards4 ,all  becoming recurs and    
moves in a multiple cycle of absolutely 
identical  states4    ,let us discard   
for the moment all philosophical        
objections1 above all  this1 that the   

recurrence of the same disposition of   
atoms may not  necessarily entail the   
recurrence of the same psychical states4
  ,furthermore1 let us suppress the     
cynical thought that in the return to   
the same state the world would have     
reason to enjoy extreme happiness  only 
for moments1 but to lament for aeons4   
,then we are left with the              
comparatively simple question3 ,is this 
repetition1 from the point of  view of  
physics1 conceivable and possible8      
,it would be the death-knell of         
,nietzsche's idea if the answer of a    
great  physical research scientist were 
entirely in the negative4 ,but ,einstein
  still allows it a small measure of    
life4 ,eternal repetition1 so he        
expressed himself1 cannot be denied by  
science with absolute  certainty4 ,the  
disciples of ,nietzsche will have to    
rest satisfied with  this very small    
concession4 ,for what1 in ,nietzsche's  
eyes1 is a logical  necessity becomes   
transformed by ,einstein's supplementary

 remark into a  vague assumption1 the   
product of fantasy4 ,from the point of  
view of  physics the recurrence of the  
same condition is to be regarded as     
enormously improbable4 ,this statement  
is founded chiefly on the famous  second
 ,law of ,thermodynamics1 according to  
which the processes of ,nature  are in  
the main irreversible1 so that a        
one-sided tendency is expressed  in     
natural phenomena4 ,the fact that the   
course of phenomena is in only  one     
sense or direction speaks in favour of  
the view that the events of  the world  
are to be regarded as occurring only    
once4    ,so that when ,nietzsche1 in   
contradistinction to this1 vigorously   
supported the doctrine of repetition1 he
 contradicted at least one  important   
recognized theorem of physics4 ,the fact
 that he did not become  conscious of   
this contradiction1 but that1 on the    
contrary1 he regarded  his idea as the  
most important event in the development 
of his  intellect1 may be regarded as an

 example of a docta ignorantia4 ,but it 
is allowable1 too1 that philosophic     
fantasies that complete the poetical    
picture of the universe should be given 
expression4 ,and ,nietzsche would       
presumably have been deprived of a      
degree of pleasure if he had been  aware
 of this second law4    ,truth is the   
most expedient error2 this statement may
 be traced back  to a sequence of       
thought developed by ,nietzsche4 ,but   
the ,eternal  ,repetition is shattered  
by just this remark1 for judged by its  
consequences it would be a very         
inexpedient error4         99     99    
99     99     99     99     99     99   
,supposing we should succeed in         
exchanging thoughts with the inhabitants
  of distant worlds and should1 through 
them1 acquire the elements of a         
civilization superior to our own1 would 
this knowledge prove a  blessing to us  
or the reverse8    ,the word superior   
must1 of course1 be treated             
circumspectly4 ,it is to  denote only   

that1 relatively1 this distant          
civilization bears somewhat  the same   
relation to our civilization of to-day  
as our own bears to that  of an         
,australasian negro or an anthropoid    
ape4 ,there are fanatics of  progress   
whose wishes plunge headlong and without
 restraint into the  future1 and to whom
 nothing could be more desirable than   
the sudden  appearance of a civilization
 that1 as they opine1 would at one      
stroke  carry us forward many thousands 
of years4    ,but the view of these     
magicians with their seven-league boots 
is  untenable4 ,let me cite a mere      
outline of the many opposing arguments  
in  a few words of ,einstein4 ,every    
sudden change in the conditions of      
existence1 even if it occurred in the   
form of a higher development1  would    
come upon us like a doom1 and would     
probably annihilate us1 just  as the    
,indians succumb to the civilization    
that has outstripped them4  ,the tragedy
 of our own highly civilized times is   

that we cannot create  the social       
organizations that have become necessary
 as a consequence of  the technical     
advances of the last century4 ,this has 
given rise to the  crises1 impasses1 and
 senseless competition between nations1 
and to the  impoverishment of           
defenceless individuals4 ,these         
deplorable conditions  would become     
inconceivably accentuated if we were to 
be invaded by  extra-mundane technical  
sciences of a higher order4         99  
99     99     99     99     99     99   
99    ,nevertheless1 there is still a   
possibility that the superior           
civilization might contain indications  
of the organizations which we  lack4    
,instead of entering on the question of 
this ,utopia1 we confined  ourselves to 
comparing past conditions in our world  
with present ones4  ,did we not have the
 most promising preliminaries for an    
organization  that was devoid of        
friction and tended to reduce the       
competition between  nations in the     

numerous international institutions that
 drew together a  great section of the  
intellectual world to work in           
co-operation8 ,are  there hopes that    
this international coalition will be    
resumed8    ,einstein expressed himself 
optimistically1 not to do homage to an  
organization artificially formed1 but to
 extol the world-wide mastery of        
intellect4 ,even if international       
congresses were to be swept away1 he    
said1 international co-operation would  
not be abolished1 as it effects  itself 
automatically4 ,i should venture to     
assert that if all these  congresses    
were to cease1 we should not even have  
cause to fear that  there would be an   
appreciable diminution in the combined  
effort of  research4 ,if certain        
developments are hindered by political  
conditions1  it is only due to the      
resulting economic hardships affecting  
individuals  in their work and robbing  
them of their intellectual freedom4 ,the
 real  friends of ,truth have always    

clung together1 and do so actually now2 
indeed1 many feel the tie to be closer  
than that connecting them to  their own 
country4 ,in spite of all obstacles and 
boundaries they will  never cease to    
find contact with one another6          
,,chapter ,,xi    ,,einstein',s ,,life  
,,and ,,personality      ,,we know from 
the biographies of great thinkers that  
they seldom  personify the character of 
a dramatic ideal4 ,they are not heroes  
of  fiction who pass through complex    
experiences and struggle with           
mysterious problems of existence that   
may unduly excite the imagination  of   
observers4 ,whoever follows their       
development remarks in the majority  of 
cases the predominance of the inner     
life1 the course of which is            
discoverable only by study of their     
works1 no clue being given in the       
confusion of ordinary exterior          
manifestations4 ,an eminent man of      
thought1 whose energies are concentrated
 on mental effort1 rarely finds  time to

 present in addition an interesting     
figure in the epic sense4 ,the  poet who
 moulds his forms from life finds little
 scope in him as a  model1 and only in  
exceptional cases has he succeeded in   
idealizing the  savant in a work of art4
    ,it would be a fruitless undertaking
 to treat ,einstein's life as one of    
these exceptional cases4 ,it is possible
 to trace the various phases of  his    
development1 yet neither the writer nor 
the reader must disguise  from himself  
the fact that such outlines give only   
the external picture  of the man and    
chronological events of importance4     
,nevertheless1 a book  of which he forms
 the theme cannot pass over the task of 
giving his  curriculum vit4 ,and if it  
should partly appear aphoristic and     
disjointed1 it must be borne in mind    
that this account originated from       
conversations and scraps of conversation
 that touched on various  episodes of   
his life1 according as they had a       
bearing on the subject  under           

discussion4    ,the story of ,einstein's
 life begins at ,ulm1 the town which    
possesses the  highest building in      
,germany4 ,gladly would ,i stand on the 
belfry of the  ,ulm ,cathedral in order 
to obtain a general survey of           
,einstein's youth4  ,but the view       
discloses nothing beyond the bare fact  
that he was born  there in ,march #ahgi4
 ,the detail which has already been     
mentioned above1  namely1 that it was   
something physical that first arrested  
the child's  attention1 remains to be   
noted4 ,his father once showed the      
infant1 as he  lay in his cot1 a        
compass1 simply with the idea of amusing
 him--and in  the five-year-old boy the 
swinging metal needle awakened for the  
first  time the greatest wonderment     
about unknown cohesive forces1 a        
wonderment  that was an index of the    
research spirit that was still lying    
dormant in  his consciousness4 ,the     
remembrance of this psychical event has 
a  significant meaning for the ,einstein

 of to-day4 ,in him all the  impressions
 of early childhood seem to be still    
vivid1 the more so as  all other        
physical occurrences1 such as the       
falling of an unsupported  body1 left no
 impression on him4 ,his attention was  
fixed on the compass1  and the compass  
alone4 ,this instrument addressed him in
 oracular  language1 indicating to him  
an electromagnetic field that was in    
later  years to serve him as a domain   
for fruitful research4    ,his father1  
who had a sunny1 optimistic temperament1
 and was inclined  towards a somewhat   
aimless existence1 at this time moved   
the seat of the  family from ,ulm to    
,munich4 ,they here lived in a modest   
house in an  idyllic situation and      
surrounded by a garden4 ,the pure joy of
 ,nature  entered into the heart of the 
boy1 a feeling that is usually foreign  
to  the youthful inhabitants of cities  
of dead stone4 ,nature whispered song   
to him1 and at the coming of the        
spring-tide infused his being with joy1 

to which he resigned himself in happy   
contemplation4 ,a religious             
undercurrent of feeling made itself     
manifest in him1 and it was             
strengthened by the elementary stimulus 
of the scented air1 of buds and  bushes1
 to which was added the educational     
influence of home and school4  ,this was
 not because ritualistic habits reigned 
in the family4 ,but it  had so happened 
that he learned simultaneously the      
teachings of the  ,jewish as well as the
 ,catholic ,church2 and he had extracted
 from them  that which was common and   
conducive to a strengthening of faith1  
and not  what conflicted4    ,youthful  
impetuosity1 which in boys of a similar 
age usually expresses  itself in rash   
enterprises and loose tricks1 did not   
appear in him4 ,his  spirit was adjusted
 to contemplation1 and an inborn        
fatalism1 diffused  with a              
super-sensuous element appertaining to  
dreams1 restrained him  from responding 
to external impulses4 ,he reacted slowly

 and  hesitatingly1 and he interpreted  
what his senses offered him and all the 
little experiences of early days in     
terms of a reverence reflected from     
within4 ,words did not easily rise from 
his lips1 and measured by the  ordinary 
scale of rapidity of learning and       
readiness in answering  questions1 he   
would scarcely have been judged to      
possess unusual gifts4  ,as an infant he
 had started to talk so late that his   
parents had been in  some alarm about   
the possibility of an abnormality in    
their child4 ,at  the age of eight or   
nine years he presented the picture of a
 shy1  hesitating1 unsociable boy1 who  
passed on his way alone1 dreaming to    
himself1 and going to and from school   
without feeling the need of a  comrade4 
,he was nicknamed ,biedermaier1 because 
he was looked on as  having a           
pathological love for truth and justice4
 ,what at that time  seemed to be       
pathological1 to-day appears as a deeply
 rooted and  irrepressible natural      

instinct4 ,whoever has got to know      
,einstein as a  man and as a scientist  
knows that this failing of his boyhood  
was but  the forerunner of a very       
healthy outlook4    ,signs of his love  
for music showed themselves very early4 
,he thought out  little songs in praise 
of ,god1 and used to sing them to       
himself in the  pious seclusion that he 
preserved even with respect to his      
parents4  ,music1 ,nature1 and ,god     
became intermingled in him in a complex 
of  feeling1 a moral unity1 the traces  
of which never vanished1 although  later
 the religious factor became extended to
 a general ethical outlook  on the      
world4 ,at first he clung to a faith    
free from all doubt1 as had  been       
infused into him by the private ,jewish 
instruction at home and the  ,catholic  
instruction at school4 ,he read his     
,bible without feeling the  need of     
examining it critically2 he accepted it 
as a simple moral  teaching and found   
himself little inclined to confirm it by

 rational  arguments inasmuch as his    
reading extended very little beyond its 
circle4    ,painful inner conflicts were
 not wanting4 ,jewish children formed a 
small  minority in the school1 and it   
was here that the boy ,albert felt the  
first ripples of the anti-semitic wave  
that1 sweeping on from without1  was    
threatening to overwhelm master and     
pupil alike4 ,for the first time  he    
felt himself oppressed by something that
 was not in harmony with his  simple    
temperament4 ,his modesty made him a    
prey to injustice1 and in  defending    
himself his originally gentle and       
restrained nature gained a  certain     
independence and individuality4    ,if  
one may speak of achievements at all in 
a preparatory school1 those  of ,albert 
were of the average modest level4 ,he   
was careful as a pupil1  generally      
satisfied requirements1 but in no way   
betrayed special  talents3 indeed1 so   
much the less1 as he showed himself to  
be possessed  of a very uncertain memory

 for words4 ,the methodic plan of the   
elementary school that he attended to   
his tenth year was1 however1 not  other 
than the usual scheme mapped out by     
drill-masters2 it made up for  what was 
lacking in an understanding of the      
pupils by applying drastic  strictness4 
,the beautiful sentence of ,jean ,paul3 
,memory is the only  paradise from which
 we cannot be banished1 finds no echo in
 ,einstein's  school memories1 of which 
he has often spoken to me without a     
shadow of  regret for a lost paradise4  
,he told me with bitter sarcasm that his
  teachers had the character of         
sergeants--those later in the gymnasium 
7secondary school7 were of the nature of
 lieutenants4 ,both terms are  used in  
the pre-armistice sense1 and his words  
were directed against the               
self-opinionated tone and customs of    
these garrison-schools of earlier  days4
    ,the next stage of his development  
was a course of study at the            
,luitpold-,gymnasium in ,munich1 which  

placed him in the second class4 ,in     
,einstein's retrospect of these days    
more friendly recollections present     
themselves1 connected1 however1 only    
with particular persons1 and not        
breathing praise in general2 on the     
contrary1 from his account1 it is  clear
 that although he conceived affection   
for individual teachers1 he  felt the   
tone of the institute as a whole to be  
rough4 ,as we know1 many  things have   
been changed in these schools since     
then1 following on a  revulsion from the
 convict atmosphere that used to        
characterize them1  and which meant     
suffering enough for the pupils4 ,the   
result was that the  schoolboy ,einstein
 developed a contempt for human         
institutions and  assigned little value 
to the subjects of study which he was   
obliged to  absorb in schematic form    
without the application of his own      
mental  energy4 ,this gloomy picture is 
relieved at points by the presence of   
several teachers1 above all1 one called 

,russ1 who took pains in  exposing the  
beauty of classical antiquity to the    
fourteen-year-old boy4  ,we learn       
elsewhere that ,einstein at present     
admits the humanistic ideal  for the    
school of the future only under very    
restricted limitations4 ,but  when he   
thinks of this teacher and his          
influence1 a warm appreciation of       
classical study vibrates in his words1  
occasionally rising1 indeed1 to  an     
unbounded enthusiasm for the treasures  
of ,greek history and  literature4 ,his 
instruction was not restricted to the   
acquisition of a  perspective of the    
antique4 ,under the direction of the    
same teacher1 he  was introduced into   
the poetic world of his native country1 
and learned  the magic of ,goethe in his
 ,hermann and ,dorothea2 this poem1 as  
he  confesses1 was explained to him in a
 really model manner4 ,thus there  were 
some oases in the desert of schematic   
teaching3 they served as  refreshing    
halts for the spirit of the eager young 

searcher after  knowledge4    ,we must  
go back one or two years to note a      
weighty experience1 which  occurred when
 he made his first acquaintance with    
elementary  mathematics2 this subject   
presented itself to him with the        
intensity of  a revelation4 ,it did not 
happen in the ordinary course of        
school-work1  but was due to a sort of  
wizard-like inquiring inner spirit that 
plied  him with questions and that gave 
him inward thrills of joy when he found 
a sharp-witted solution4 ,from the very 
beginning ,albert proved himself  to be 
a good solver of problems1 even before  
he achieved an arithmetical  virtuosity1
 and before he knew the technique of    
equations4 ,he helped  himself by means 
of little tricks1 experimented          
roundabout inventions1  and was happily 
excited when they led to the goal4 ,one 
day he asked his  uncle1 ,jacob         
,einstein1 an engineer who lived in     
,munich1 a certain  question4 ,he had   
heard the word algebra and surmised that

 his uncle  would be able to explain the
 term to him4 ,uncle ,jacob answered3   
,algebra  is the calculus of indolence4 
,if you do not know a certain quantity1 
you  call it x and treat it as if you do
 know it1 then you put down the         
relationship given1 and determine this x
 later4 ,that was quite  sufficient4    
,the boy received a book containing     
algebraic problems that  he solved all  
alone in accordance with this not       
exhaustive but expedient  direction4 ,on
 another occasion ,uncle ,jacob told him
 the enunciation of  ,pythagoras'       
theorem without giving him a proof4 ,his
 nephew understood  the relationship    
involved1 and felt that it had to be    
founded on some  reasoning4 ,again he   
set about all alone to furnish what was 
wanting4  ,this was1 however1 not a case
 for the calculus of indolence with an  
x that was to be determined4 ,here it   
was a question of developing a  facility
 for geometric argument1 such as very   
few possess at such an  early stage of  

development4 ,the boy plunged himself   
for three weeks into  the task of       
solving the theorem1 using all his power
 of thought4 ,he came  to consider      
similarity of triangles 7by dropping a  
perpendicular from  one vertex of the   
right-angled triangle on to the         
hypotenuse71 and was  thus led to a     
proof for which he had so ardently      
longed6 ,and although it  concerned only
 a very old well-known theorem1 he      
experienced the first  joy of the       
discoverer4 ,the proof that he had found
 proved that the  ingenuity of the      
worrying young mind was awakening4    ,a
 new world was opened for him when he   
made the acquaintance of ,a4            
,bernstein's comprehensive popular books
 on scientific subjects4 ,this  work is 
looked on nowadays as being somewhat    
antiquated and1 in the eyes  of many a  
professional scientist1 has sunk to the 
level of a  pseudo-scientific shocker2  
even when ,einstein as a boy made       
explorations in it1 there were signs of 

rust and decay in the work1 for  it     
originated in the fifties of the        
previous century and1 in point of       
subject-matter1 had long been           
transcended4 ,yet it could be read      
then--and even now--as a story          
containing thousands of interspersed    
physical1 astronomical1 and chemical    
wonders1 and for the boy ,einstein  it  
came to be a true book of ,nature1 which
 presented to his mind1 greedy  for     
knowledge1 as much as it did to his     
imagination4    ,other vistas were      
opened up to him by ,bchner's ,kraft und
 ,stoff  7,force and ,substance71 a book
 the cheapness of which he could not yet
  discern1 but which called up wonder in
 him without rousing his  criticism4 ,in
 addition1 his attention was chiefly    
occupied by a handbook  of elementary   
planimetry1 containing an abundance of  
geometrical  exercises1 which he        
fearlessly attacked and within a very   
short time  solved almost in their      
entirety4 ,his delight grew when he     

ventured into  the difficulties of      
analytical geometry and infinitesimal   
calculus quite  apart from the          
curriculum of his school-work4 ,lbsen's 
textbook had  fallen into his hands1 and
 these directions sufficed for his      
audacious  spirit4 ,whereas many of his 
school companions were still standing   
undecidedly before the pools of theorems
 of congruence and repeating  decimals1 
he was already disporting himself freely
 in the ocean of  infinitesimals4 ,his  
work did not remain concealed1 and      
gained  appreciation4 ,his mathematical 
teacher declared that the               
fifteen-year-old boy was ripe for       
university study4    ,yet he was not to 
find a way into the open by             
matriculating very early1  but through  
an event that unexpectedly threw him    
into new surroundings  of life4 ,in     
#ahid his parents transferred their     
abode to ,italy4 ,the  chronicler has   
nothing to report of pangs of separation
 in ,albert when  he left ,bavarian     

soil4 ,he was glad to get away from the 
drill academy1  ,luitpold1 and1 as an   
inhabitant of ,milan1 he enjoyed the    
change in his  existence1 and was not   
encumbered by attacks of home-sickness4 
,all in  all1 he had felt himself in an 
unhappy position under school compulsion
  in ,munich1 in spite of the           
mathematical delights he had provided   
for  himself1 and in spite of the       
rapturous moments that musical          
revelations  had created for him since  
his twelfth year4 ,defiance and distrust
  against outside influences had        
remained active in him as forces that   
did  not allow the happy disposition    
proper to his age to assert itself4 ,but
  now the fetters had fallen and the    
pent-up joy of life burst forth as if   
through opened sluices4 ,the sun and    
landscape of the ,south1 ,italian       
manners of life1 art freely displayed in
 the market-place and on the  street1   
realized for him dream-pictures that had
 appeared to him earlier  during the    

hours of oppression4 ,whatever he saw1  
felt1 and experienced  lay outside the  
ordinary course of his life1 awakened   
his sense for  natural and human things1
 and set his spirit free from all bonds4
 ,there  was no question of his going to
 school in the first six months4 ,he    
enjoyed complete freedom1 occupied      
himself with literature1 and  undertook 
extended excursions4 ,starting from     
,pavia1 he wandered all  alone over the 
,apennine to ,genoa4 ,whilst he was     
being intoxicated with  the sublime     
,alpine landscape1 he came into contact 
with the lower  stratum of the people1  
who aroused his deepest sympathy4 ,the  
tour took  him over a short stretch of  
the ,italian ,riviera1 the beauties of  
which1 as depicted by ,bcklin1 do not   
seem to have revealed themselves  to    
him4 ,at that time he was probably      
subject to a feeling of upward  striving
 such as possessed ,zarathustra4        
,with all their joys and inspirations   
the experiences in ,italy remained  but 

a short episode4 ,einstein resolved on a
 new tour1 which was not  without a     
professional purpose4 ,he made a        
pilgrimage to ,switzerland with  the    
intention of studying mathematics and   
physics at the ,zrich  ,polytechnical   
,institute4 ,but he was not to be       
successful in his first  effort to gain 
entrance4 ,the conditions of entry      
required a standard in  descriptive     
sciences and modern languages that he   
had not yet reached4  ,so he turned to  
,aarau1 where he was allowed to extend  
his knowledge with  the help of         
excellent methods at the ,canton school4
 ,even it the present  day ,einstein    
talks with extreme enthusiasm of the    
organization of this  model school that 
corresponds in rank approximately to a  
,german  ,realgymnasium 7or an ,english 
,grammar ,school74 ,there was nothing to
  remind him of the continual           
manipulation of the sceptre of authority
 at  the ,luitpold school barracks2 he  
easily obtained his leaving             

certificate1 and now the portals of the 
,zrich ,polytechnicum were open  for    
him4    ,he himself was probably not    
aware that he carried a marshal's baton 
in  his own mathematical equipment4     
,but1 in looking back1 we come across   
astounding things4 ,for it is a fact    
that even in the pupil at ,aarau        
problems had taken root that already lay
 in the vanguard of research at  that   
time4 ,he was not yet a finder1 but what
 he sought as a  sixteen-year-old boy   
was already stretching into the realms  
of his later  discoveries4 ,we have here
 simply to register facts1 and to       
abstain from  making an analysis of his 
development1 for how are we to trace out
 the  intermediate steps1 and to        
discover the sudden phases of thought   
that  lead a very young ,canton pupil to
 feel his way into a still undiscovered 
branch of physics8 ,the problem that    
occupied him was the optics of  moving  
bodies1 or1 more exactly1 the emission  
of light from bodies that  move         

relatively to the ether4 ,this contains 
the first flash of the  grandiose       
complex of ideas that was later to lead 
to a revision of our  picture of the    
world4 ,and if a biographer should state
 that the first  beginnings of the      
doctrine of relativity occurred at that 
time1 he would  not be making an        
objectively false statement4    ,the    
ambitions of the youth by no means      
reached these flights of  imagination1  
for whereas the latter signified the    
coming power of his  wings1 he himself  
set a modest goal4 ,he wished to become 
a schoolmaster1  and imagined that in   
choosing this career he was allowing his
 hopes to  run high4 ,this was in       
conformity with the esteem in which he  
held the  status of teachers4 ,in the   
,zrich ,technical ,school there is a    
section  equipped as a department for   
preparing teachers1 and in this         
,einstein  studied from the age of      
seventeen to the age of twenty-one1     
perfectly  satisfied with the thought of

 sitting1 not on the pupil's bench1 but 
at  the master's desk1 and of exercising
 a beneficial if limited influence  as a
 preceptor of the young4    ,he was     
still under the sway of the feeling that
 he was not sufficiently  experienced in
 life and that he dare not venture out  
into the light for  existence in the    
great turmoil of the world4 ,he saw in  
this struggle1  which pitted man against
 man1 led to exhibitions of violence1   
and  aroused ambition for glittering    
unrealities1 cause only for disgust and 
alienation4 ,the prospect of personal   
success did not lure him to try  force  
against force4 ,thus1 for the time      
being1 it was his ideal to lead  a very 
modest existence4 ,from various quarters
 he had been given hopes  of a position 
as assistant to some professor of       
physics or mathematics4  ,but for       
unknown reasons he was everywhere       
refused4 ,these apparently  obscure     
grounds1 it must be said with regret1   
become clearer when we  bear in mind his

 confession of faith4 ,nor did his hopes
 of teaching at a  gymnasium seem near  
fulfilment1 as certain conditions of    
birth raised  obstacles4 ,in the first  
place1 he was not a ,swiss2 in fact1    
since his  stay in ,milan he was without
 a nationality at all in the            
bureaucratic  sense1 and then he had no 
personal connexions1 without which1 at  
least  at that time1 there was no chance
 of progress even for a talented        
person4 ,yet the young student who was  
entirely without protection of any  sort
 had to overcome the cares and satisfy  
the needs of daily life4 ,he  could not 
rely on material help from his parents1 
who themselves lived  in restricted     
circumstances1 and thus we find him a   
little later in  ,schaffhausen and      
,bern1 where he earned a small pittance 
as a private  tutor4    ,he found       
consolation in the fact that he         
preserved a certain  independence1 which
 meant the more to him as his instinct  
for freedom  led him to discover the    

essential things in himself4 ,thus1     
earlier1 too1  during his studies at    
,zrich he had carried on his work in    
theoretical  physics at home1 almost    
entirely apart from the lectures at the 
,polytechnic1 plunging himself into the 
writings of ,kirchhoff1 ,helmholtz1     
,hertz1 ,boltzmann1 and ,drude4         
,disregarding chronological order1 we   
must  here mention that he found a      
partner in these studies who was working
 in  a similar direction1 a ,southern   
,slavonic student1 whom he married in   
the  year #aijc4 ,this union was        
dissolved after a number of years4      
,later he  found the ideal of domestic  
happiness at the side of a woman whose  
grace  is matched by her intelligence1  
,else ,einstein1 his cousin1 whom he    
married in ,berlin4    ,in #aija1 after 
living in ,switzerland for five years1  
he acquired the  citizenship of ,zrich1 
and this at last gave him the           
opportunity of  rising above material   
cares4 ,his ,university friend1 ,marcel 

,grossmann1  lent him a helping hand by 
recommending him to the ,swiss ,patent  
,office1  the director of which was his 
personal friend4 ,einstein occupied     
himself  here from #aijb to #aije as a  
technical expert1 that is1 as an        
examiner of  applications for patents1  
and this position gave him the chance of
  moving about in absolute freedom in   
the realms of technical science4        
,whoever has a strong predilection for  
discovery will perhaps feel  estranged  
to find ,einstein so long in the sphere 
of invention1 but1 as  ,einstein himself
 emphasizes very strongly1 both regions 
make great  demands on clearly defined  
and accurate thought4 ,he recognizes a  
definite relationship between the       
knowledge that he gained at the ,patent 
,office and the theoretical results that
 appeared at the same time as  products 
of intensive thought4    ,in #aije1 in  
the midst of his work1 the storm broke  
loose in him with the  suddenness of a  
hurricane4 ,in quick succession his mind

 disburdened  itself of the abundance of
 ideas that had stored themselves up in 
the  work of the preceding years1 and   
these ideas signify more to us than a   
definite stage in the development of an 
individual4 ,what physicists have  come 
to regard as an elaboration of the      
heritage of ,galilei and ,newton  had   
matured in him4 ,we merely record the   
title of dissertations1 which  appeared 
in #aije in the ,annalen der ,physik3   
,concerning a ,heuristic  ,standpoint   
towards the ,production and             
,transformation of  ,light--,concerning 
the ,inertia of ,energy--,the ,law of   
,brownian  ,movement4--,then the most   
important contribution3 ,the            
,electrodynamics  of ,moving ,bodies1   
that contained the revolutionary ideas  
underlying the  special theory of       
relativity4 ,to these is to be added a  
dissertation for  his doctorate in the  
same year3 ,a ,new ,determination of    
,molecular  ,dimensions4    ,in all1    
these represent a life-work that belongs

 to the history of  science4 ,it was    
certainly some considerable time before 
his work began  its triumphal march in  
the sight of the world1 and it may be   
added that  treasures were hidden in    
these disquisitions that were not       
understood  till long years afterwards4 
,yet the youthful discoverer was not    
passed  over without signs of friendly  
appreciation4 ,he received a letter1    
couched in very warm terms1 from the    
celebrated physicist1 ,max ,planck1  who
 was a complete stranger to him at that 
time2 it spoke in glowing  words of his 
essay1 ,the ,electrodynamics of ,moving 
,bodies4 ,this letter  was the first    
diploma1 the forerunner of all the      
honours that later  swept over him like 
a tidal wave4    ,it was his intention  
to obtain a tutorial position at the    
,university4 ,an  appointment to ,bern  
was at first again hindered by certain  
obstacles  which he would probably have 
overcome if he had applied himself      
energetically to attaining his goal4 ,he

 finally received his  appointment1 but 
exercised his duties for only a very    
short time1 as  ,zrich now opened her   
arms to him4 ,in #aiji he accepted the  
position of  ,professor extraordinarius 
there for theoretical physics1 and soon 
assembled a grateful audience about     
himself4 ,nevertheless1 during the      
earlier stages of his professorship he  
found it difficult to suppress a        
longing for the quiet1 unexcited life of
 his patent-office work1 in  which he   
seemed to have had a still greater      
degree of independence4 ,in  #aiaa he   
accepted a new appointment as ,professor
 ,ordinarius to ,prague1  which offered 
him more favourable emoluments as an    
inducement4 ,in the  autumn of #aiab he 
returned to ,zrich as a ,professor at   
the ,polytechnic1  and in the early part
 of #aiad he was drawn into the strong  
magnetic  field of the northern capital2
 he arrived at the ,spree1 and has1     
since  then1 lived among us4 ,he is now 
a ,swiss by nationality1 a world citizen

  by conviction1 and1 professionally1 a 
member of the ,berlin ,academy and      
attached in a lecturing capacity to the 
,university4 ,here he perfected  his    
works on relativity1 ending in the      
superlative elaboration of the  theory  
of gravitation1 the beginnings of which 
stretch back to the year  #aijg4 ,he had
 spent eight years in a concentrated    
effort of severe  thought to bring it to
 completion1 and perhaps centuries will 
be  necessary before the world will gain
 a complete perspective of all the      
consequences of his theory4    ,for the 
theory asks us to brush aside habits of 
thought that have  claimed an hereditary
 position in pre-eminent minds4 ,one of 
the foremost  physicists1 ,henri        
,poincar1 had confessed as late as #aiaj
 that it  caused him the greatest effort
 to find his way into ,einstein's new   
mechanics4 ,another whole year passed   
before he gave up his last doubts4      
,then he passed with flying colours into
 ,einstein's camp1 and recommended      

,einstein's appointment to the          
,professorship at ,zrich1 in conjunction
  with the discoverer of radium1 ,madame
 ,curie1 in an exuberant letter  which  
may add its note of appreciation here3  
,herr ,einstein1 so wrote the great     
,poincar1 is one of the most  original  
minds that ,i have ever met4 ,in spite  
of his youth he already  occupies a very
 honourable position among the foremost 
savants of his  time4 ,what we marvel at
 in him1 above all1 is the ease with    
which he  adjusts himself to new        
conceptions and draws all possible      
deductions  from them4 ,he does not     
cling tightly to classical principles1  
but sees  all conceivable possibilities 
when he is confronted with a physical   
problem4 ,in his mind this becomes      
transformed into an anticipation of  new
 phenomena that may some day be verified
 in actual experience4444 ,the  future  
will give more and more proofs of the   
merits of ,herr ,einstein1  and the     
,university that succeeds in attaching  

him to itself may be  certain that it   
will derive honour from its connexion   
with the young  master4    ,we may be   
tempted to look back and ask whether the
 criteria that ,wilhelm  ,ostwald once  
set up as a test of great men are       
verified in ,einstein's  case4 ,he has  
certainly not broken the first and most 
general rule1 the  principle of early   
maturity4 ,this showed itself clearly   
when his  impulse towards mathematical  
knowledge and discovery asserted itself1
  and when he penetrated far into the   
future with his optical problems4  ,the 
history of science and of art may offer 
more striking examples in  this         
connexion1 but at any rate in           
,einstein's case the indications are    
sufficient to serve as a confirmation of
 the rule4 ,on the other hand1  the     
second test of ,ostwald seems to be     
valid only conditionally when  applied  
to ,einstein4 ,for ,ostwald takes up    
arms against a gradual  intensification 
of ability1 and proclaims it as an      

almost universal  rule that the         
exceptional achievement is the privilege
 of quite young  persons3 what he       
achieves later is seldom as impressive  
as his first  brilliant achievement4    
,thus1 in ,einstein's case1 the         
exception is  evident4 ,for if we fix on
 only two chief discoveries1 passing    
over many  others1 there is no doubt    
that the second 7the theory of          
gravitation7  surpasses the first       
7special relativity7 in both range and  
significance4  ,indeed1 we cannot escape
 from the idea of a gradual             
intensification1  for the second        
discovery could come about only as a    
result of the first4  ,moreover1 it is  
not yet night1 and there is nothing to  
refute the  assumption that there will  
be a further progression4               
,furthermore1 ,ostwald takes into       
consideration the tempo of the          
intellectual pulse of inspiration to    
divide the main types of great men  into
 a classical and a romantic category3   

this classification cannot1  however1 be
 applied to ,einstein4 ,he is decidedly 
classical1 in so far as  his work seems 
calculated to serve later generations as
 a classical  foundation for all        
mechanical investigations of the        
macrocosm of the  heavens and the       
microcosm of atoms4 ,on the other hand1 
his versatility1  the mobility and      
resource of his highly imaginative mind1
 stamp him as a  romantic spirit4 ,his  
delight in teaching would also assign   
him to this  category1 for in the case  
of many classical spirits there is a    
decided  aversion to imparting          
instruction4 ,so that1 although we might
 well be  able to speak of a synthesis  
of these two forms1 it seems better to  
estimate ,einstein1 not in the light of 
a ready scheme1 but rather as a  type of
 which he is the unique representative4 
99     99     99     99     99     99   
99     99    ,just as the external      
contour of his life is on the whole     
regular and  unbroken1 so also his inner

 life is attuned to simplicity4         
,nowhere1 it  might almost be said1 do  
we observe a break1 a spasmodic turn1 or
 a  sudden intensification4 ,although he
 has grasped and suggested so many      
problems1 he himself presents no        
psychological riddle1 and we meet with  
no singularities in analysing his       
personality4 ,it has already been       
remarked several times that ,art plays a
 part in his life4 ,what ,i learned     
from him himself about his affection for
 music coincides exactly with  what     
observation clearly discloses4 ,the     
expression of his countenance  when he  
is listening to music is a sufficient   
indication of the  resonances induced in
 him4 ,he is confessedly a classicist1  
and a sincere  devotee of the           
revelations of ,bach1 ,haydn1 and       
,mozart4 ,what fascinates  and          
enraptures him above all is that which  
is directed inwards1 which is           
contemplative and erected on a religious
 basis4 ,the simple masterful  flow in  

musical development and invention is    
all-important for him4 ,the             
architectonic structure that we marvel  
at in ,bach1 the ,gothic tendency       
towards heavenly heights1 perhaps calls 
up in him sensations that  emanate from 
his hidden wealth of constructive       
mathematical ideas4 ,it  seems to me    
that this possibility is not unworthy of
 remark4 ,it suggests  a reason for the 
fact that he gives himself up only      
unwillingly to the  nervous strain of   
drama directed at emotional upheaval4   
,he does not  gladly overstep the       
boundary that separates the simple from 
the  psychologically subtle1 and        
whenever his desire to understand art   
requires him to venture beyond it1 his  
appreciation is not accompanied  by     
genuine pleasure4 ,his subjectivity does
 not fix this boundary in  accordance   
with the ordinary rules of concert      
sthetics1 which are  actually not rules 
at all1 but only changeable valuations  
and  crystallizations of the feelings of

 certain groups of people4 ,he gives    
himself up quietly and freely to what is
 presented1 but makes no special  effort
 to assimilate experiences to which his 
being does not  spontaneously react4    
,there would be no meaning in seeking to
 mark off  the limits of his receptivity
 in accordance with this1 and to tell   
him  that it is too limited1 and that it
 should be enlarged1 and that he  should
 not regard as an opinionated           
exaggeration what appears to others  to 
be a deep and mighty revelation1 or     
seems to be possessed of divine         
sweetness4 ,he would be able to point   
out that even in the case of  masters of
 the musical art a change of faith was  
not a rare occurrence1  and that they   
learned anew1 or rejected what they once
 idolized1 and  very often found no     
permanent haven in their own faith4     
,whoever1 like  ,einstein1 gives himself
 up to the simply contemplative1 and    
feels no  impulse towards               
sensationalism1 is spared the task of   

learning afresh1  and finds still one   
world left for him even if many other   
worlds are  inaccessible4 ,to mention   
only the main features1 then1 neither   
,beethoven  as a composer of symphonies1
 nor ,richard ,wagner1 denote the       
pinnacles of  music for him2 he could   
live without the ,ninth ,symphony1 but  
not without  ,beethoven's ensemble      
music4 ,the number of composers and     
compositions  which are not a necessity 
of life for him is very considerable4   
,it  includes the majority of           
romanticists1 the erotically inclined   
school of  ,chopin and ,schumann1 which 
revels in sensation1 and1 as already    
mentioned1 the neo-,german dramatic     
composers4 ,he has much objective       
admiration for them1 yet he does not    
conceal the fact that he also feels     
lively opposition in the gamut of his   
sensations4 ,he regards the  properly   
modern productions as interesting       
phenomena1 and has various  degrees of  
disapproval for them1 extending to      

complete aversion4 ,it  costs him an    
effort to hear an opera of ,wagner1 and 
when he has done so1  he returns home   
bearing with him the leitmotiv of       
,meister ,eckhard3  ,the lust of        
creatures is intermingled with          
bitterness4 ,in general he  seems to    
take up approximately the point of view 
of ,rossini4 ,wagner  gives him         
wonderful moments1 followed1 however1 by
 periods of acute  emotional distress4  
,i need hardly add that ,i myself1 who  
confess to  being an ultra-,wagnerite1  
never strove in my conversations with   
,einstein  to make my opinion prevail   
against his4 ,for ,i am deeply convinced
 that  in this matter there is no       
question of right and wrong1 and that   
every  musical valuation represents no  
more than an accidental judgment        
dependent on one's own nature1 entirely 
egocentric and thus objectively  of no  
account4    ,einstein also occupies     
himself in an active sense with music1  
and has  developed into a very fair     

violinist1 without claiming higher      
degrees of  achievement4 ,among other   
things ,i once heard him play the violin
 part of  a ,brahms ,sonata1 and his    
performance approached concert standard4
 ,he  draws a beautiful tone1 infuses   
expression into his rendering1 and knows
  how to overcome the technical         
difficulties4 ,among the supreme artists
 of  his instrument who have exerted a  
personal influence on him1 ,joachim     
assumes the first place4 ,einstein still
 speaks with great enthusiasm of        
,joachim's performance of ,beethoven's  
,tenth ,sonata and of ,bach's           
,chaconne4 ,he himself plays the latter 
piece1 for which the purity and         
accuracy of his double and multiple     
stopping fits him4 ,whoever chooses  the
 right moment--this good fortune has not
 yet befallen me--may  overhear         
,einstein at his pianistic studies4 ,as 
he confessed to me1  improvisation on   
the piano is a necessity of his life4   
,every journey  that takes him away from

 the instrument for some time excites a 
home-sickness for his piano1 and when he
 returns he longingly caresses  the keys
 to ease himself of the burden of the   
tone experiences that have  mounted up  
in him1 giving them utterance in        
improvisations4    ,the regular run of  
concerts in which displays of bravura   
play an  important part finds little    
favour with him2 above all1 he is not a 
worshipper of the orchestral conductor1 
whom he regards only as an  interpreter 
and not as a virtuoso on the orchestral 
instrument4 ,he  expressed this idea in 
unmistakable words3 ,the conductor      
should keep  himself in the background4 
,i believe that his dearest wish would  
be to  breathe in the tones without a   
personal or material medium1 merely out 
of the air or out of space4             
,furthermore1 ,i believe that there is  
an  unfathomable connexion between his  
musical instinct and his nature as a    
research scientist4 ,for the ear1 as we 
know from ,mach1 is the true organ  that

 enables us to experience space1 and    
thus things may occur within  the ear of
 the investigator of space that may have
 a different  significance from that of 
music which is representable in tones4  
,i  strongly doubt whether traces of    
compositional form occur in ,einstein's 
tone-monologues1 but perhaps they       
contain examples of an art for which    
the sthetics of a distant future may    
find a name4         99     99     99   
99     99     99     99     99    ,with 
regard to higher literature1 and indeed 
all writings not connected  with        
science1 ,einstein has little to say4   
,he himself rarely directs  conversation
 on to this topic1 and still less rarely
 does he give vent  to an enthusiastic  
outburst that betrays warm interest4 ,he
 restricts  himself to making short1    
aphoristic comments1 and now and then   
allows  his listener to gather that he  
can easily imagine an existence without 
literature4 ,the number of accepted     
novels1 tales1 and poetic works which   

he has not read is legion1 and all the  
pretentiously artistic1  historical1 and
 critical writings that are added to    
them have attracted  only a very        
momentary interest from him4    ,i have 
never seen him attracted in any way by  
the promising aspect of  some new book  
intended for diversion4 ,if such a one  
happens to get into  his hands1 he      
merely places it among the others4 ,at  
times ,i was  constrained to think of   
,caliph ,omar's words3 ,if the book     
contains what  is already in the ,koran1
 it is unnecessary2 if it contains      
something  else1 it is harmful4 ,it is  
harmful at least in the sense that it   
robs  us of time that may be better     
spent in another way4 ,i am purposely   
exaggerating here to make it quite clear
 that ,einstein finds full  satisfaction
 in a narrow circle of literature1 and  
that he experiences  no loss if numerous
 new works pass by and escape his       
notice4    ,nevertheless1 he speaks with
 reverence of a series of authors1 to   

whom  he owes enrichment3 among them are
 the classical writers1 who naturally   
occupy the highest position1 with       
certain exceptions1 which he equally    
naturally wishes to be taken as a       
personal opinion and not in the sense   
of a critical valuation4 ,with him the  
difference reveals itself in the        
intonation from which we may read a     
greater or lesser measure of  affection4
 ,when he says ,shakespeare1 the eternal
 greatness seems to be  inherent in the 
actual sound of the name4 ,when he says 
,goethe1 we  notice a slight undertone  
of dissonance1 which may be interpreted 
without difficulty4 ,he admires him with
 the pathos of distance1 but no  warmth 
glows through this pathos4    ,i had    
ventured to deduce from my knowledge of 
his nature the men and the  works which1
 in my opinion1 should awaken strong    
echoes in him4 ,a fairly  clearly       
defined line leads to the true path4    
,outside of any systematic  series1 ,i  
may mention ,dostojewski1 ,cervantes1   

,homer1 ,strindberg1  ,gottfried ,keller
 in the positive sense1 ,emile ,zola and
 ,ibsen in the  negative sense4 ,taken  
as a whole1 this prognostication does   
not disagree  seriously with his own    
statement1 excepting that he lays still 
greater  emphasis on ,don ,quixote and  
the ,brothers ,karamasoff than ,i had   
surmised4  ,he expressed himself with   
reserve about ,voltaire4 ,he has no     
belief in  ,voltaire's poetic qualities1
 and sees in him only a subtle-minded   
and  amusing writer4 ,perhaps if        
,einstein were to devote himself a      
little more  intensively to ,voltaire   
and ,zola1 he would assign a higher     
value to  these related spirits4 ,but   
there is little hope of this occurring1 
as  the wide range of ,voltaire's works 
tends to restrain him4 ,time1 which  the
 physicist ,einstein has shown to be    
relative1 has an absolute value  for him
 when measured in hours1 and whoever    
seeks to persuade him to  read thick    
volumes is not likely to gain his       

goodwill4    ,our philosophical         
literature is not received with         
acclamation by him4 ,if  some one wished
 to undertake the task of ascertaining  
,einstein's  attitude towards           
philosophy1 he would be well advised to 
plunge into  ,einstein's works rather   
than to ask him personally4 ,in them the
  questioner would find ample hints1    
pointing towards a new theory of        
knowledge1 the first indications of     
which are already perceptible4 ,a  great
 portion of philosophic doctrine will   
yet have to pass through the  ,einstein 
filter to be purified4 ,he himself1 it  
seems to me1 leaves this  process of    
filtering mostly to other thinkers1 but 
we must not lose  sight of the fact that
 these others derive their views of     
space1 time1  and causality from        
,einstein's physics4 ,it is thus        
immediately evident  that he does not   
find revelations about ultimate things  
in already  extant literature1 for the  
simple reason that they are not to be   

found  there4 ,for him famous works     
represent1 in ,kant's language1         
,prolegomena  to every future system of 
metaphysics which can claim to rank as a
  science4 ,the accent is to be put on  
the future that has not yet become  the 
present4 ,he praises many1 particularly 
,locke and ,hume1 but will  grant       
finality to none1 not even to the great 
,kant1 not to mention  ,hegel1          
,schelling1 and ,fichte1 whom he barely 
mentions in this connexion4  ,to        
,schopenhauer and ,nietzsche he assigns 
a high position as writers1 as  masters 
of language and moulders of impressive  
thoughts4 ,he values them  for their    
literary excellence1 but denies them    
philosophic depth4 ,as far  as          
,nietzsche is concerned1 whom1 by the   
way1 he regards as too  glittering1     
,einstein certainly experiences ethical 
objections against  this prophet of the 
aristocratic cult whose views are so    
diametrically  opposed to ,einstein's   
own opinion of the relations between man

 and man4    ,earlier when we were      
talking of classical poetry he had      
particularly  emphasized ,sophocles as  
one who was dear to him4 ,and this name 
leads us  to the innermost source of    
,einstein as a man4 ,i am not here to   
hate  with you but to love with you1 is 
the cry of ,sophocles' ,antigone1 and   
this cry is the keynote of ,einstein's  
emotional existence4 ,i shall not  give 
way to the temptation to follow those   
who in the turmoil of the  present day  
refer to ,einstein as a political       
figure4 ,that would lead to  a          
description of policy and party         
arguments that lie beyond the scope of  
this book2 so much the less am ,i       
inclined to do so as ,einstein's        
convictions may be expressed very       
clearly without reference to schematic  
terms of a very elastic nature4 ,an     
individuality such as his cannot be     
compressed into a party programme4 ,and 
if anyone should insist on  placing him 
among the radicals or on assigning him  

far to the left1 ,i  should suggest that
 it would be better to choose1 instead  
of the  classification right and left1  
that of above and below4 ,i look up     
towards his idealism1 whose altitude may
 perhaps be reached one day by  the     
raising of our ethical standards4 ,but  
not by means of paragraphs of  laws4 ,i 
have seldom heard him talk of such      
schematic recipes1 but so  much the more
 have ,i noted utterances which bore    
witness to a very  intense and          
ever-present sympathy with every human  
creature4 ,his  programme1 which is     
written not in ink but in heart's-blood1
 proclaims  in the simplest manner the  
categorical imperative3 ,fulfil your    
duty to  your fellow-being3 offer help  
to every one3 ward off every material   
oppression4 ,well1 then1 he is a        
socialist1 so the cry runs4 ,if it is   
your pleasure to call him so1 he will   
not deny you it4 ,but to me this  term  
seems to denote too narrow limits for   
him4 ,i see no contradiction  in        

applying the term1 but there is no      
perfect congruence4 ,if one word is     
necessary1 ,i should be rather more     
inclined to say that he is in the       
widest sense a democrat of liberal      
trend4    ,for him the ,state is not its
 own aim1 nor does he imagine himself to
 be  the possessor of a panacea4 ,the   
attitude of the individual to           
socialism1 he said1 is uncertain owing  
to the fact that we can never  ascertain
 clearly how much of the iron compulsion
 and blind working of  our economic     
system may be overcome by appropriate   
institutions4 ,and ,i  should like to   
add that such institutions would        
scarcely have a  permanent result1 but  
that more may be expected from the      
ethical example  of those who have the  
power of renunciation4 ,whoever realizes
 the motto  of ,antigone1 ,i am here to 
love with you1 brings us nearer the     
goal4  ,all in all1 our longing         
continually flees from the confusion of 
political considerations to simple      

morality4 ,for ,einstein this is the    
primary element1 that which is directly 
evident and not open to                 
misrepresentation4 ,it includes         
sympathy1 and1 what is more important1  
joy in conjunction with others4 ,the    
best that life has to offer1 he  once   
exclaimed1 is a face glowing with       
happiness6    ,this look is expressed on
 his own face when he discusses his     
ideals1  above all the internationality 
of all intellectual workers and the     
realization of eternal peace among the  
nations4 ,to him pacifism is a  matter  
of mind as well as of heart1 and he is  
of the opinion that the  course of      
history so far is but the prelude to its
 realization4 ,the  past1 with its      
bloodstained fingers that reach into the
 present1 does  not discourage him ,he  
points to the endless city wars of the  
,middle ,ages  in ,italy1 which had     
finally to cease in answer to the       
increasing feeling  of solidarity4 ,so  
he believes in the victory of peace1    

which the unified  consciousness of all 
humanity will one day win over the      
demonic powers  of tyranny and conquest4
    ,the pacifistic goal seems to him to
 be attainable without the              
peculiarities of the various ,states    
being destroyed4 ,national              
characteristics arising from tradition  
and hereditary influences do not        
signify in his eyes a contradiction to  
the internationalism that  embraces the 
common intellectual factors of civilized
 peoples4 ,thus the  desire for the     
preservation and care of particularities
 directs him to  the secondary goal of  
,zionism4 ,his blood asserts itself when
 he supports  the foundation of a ,state
 in ,palestine1 which seems to him to be
 the  only means of preserving the      
national individuality of his race      
without  the freedom of the individual  
being affected4    ,we had left ,art to 
talk of the ,state1 and then returned to
 the former  theme to touch lightly on  
the pictorial arts4 ,painting was       

allowed to  pass with merely a fleeting 
remark4 ,it plays no considerable part  
in  ,einstein's existence1 and he would 
not suffer great grief if it were to    
vanish from the plane of culture1 a     
consummation to which definite signs    
seems to point4 ,i have described these 
signs in other writings 7as in  ,kunst  
in #ajjj ,jahren71 and maintain the     
point of view that the latest  branches 
of painting as represented by           
expressionism and cubistic  futurism    
denote1 in essence1 the last convulsions
 of a dying surface  art4 ,and even the 
chief representatives of former         
flourishing periods  are beginning to   
fade away1 and ,einstein will not be the
 only one who  will relegate this art1  
as compared with music1 to a lower plane
 among  the inspired arts that bring joy
 to humanity4 ,he is only more frank    
than  others when he freely confesses   
that he cannot convince himself that a  
life without the joys of pictorial art  
would be hopelessly impoverished4  ,but 

he bows his head to sculpture1 and1 for 
him1 architecture is a  goddess4 ,it is 
again his deeply rooted piety that      
asserts itself when  memory recalls to  
him the ,gothic dome with its pinnacles 
striving  towards heaven4 ,goethe and   
,schlegel have called architecture      
frozen  music1 and this picture is      
present in his mind when he sees ,gothic
  architecture as frozen music of ,bach4
 ,it is open to anyone to analyse  this 
specific impression in another way by   
seeking the fundamental  elements1 in   
which the essence of the art is to      
provide support for a  weighty structure
 and to overcome gravitation4 ,for a    
spirit that works  with mechanics and   
that feels within itself the pressures  
and tensions  occurring in external     
nature1 architecture is a kind of       
statics and  dynamics transformed into a
 thing of beauty1 a ravishing picture of
 his  own science4         99     99    
99     99     99     99     99     99   
,einstein has told me many a story of   

his travels1 and these reports were     
characterized by an absence of definite 
purpose4 ,the conception of  something  
worth seeing in the tourists' sense does
 not exist for him1  and he does not set
 out in eager pursuit of those things   
that are marked  with two asterisks in  
,baedeker4 ,the intense romanticism of  
,swiss  scenery1 that lay within such   
easy reach for him1 has never enticed   
him  into its magic circle1 and he has  
nothing to do with the abysmal terrors  
of glaciers and the world of snow-peaks4
 ,his enthusiasm for landscape  beauty  
conforms with the behaviour of the      
barometer3 the greater the  altitude1   
the lower the mercury4 ,in simple       
contact with ,nature he  prefers the    
lesser mountains1 the seashore1 and     
extensive plains1  whereas brilliant    
panoramic contours like those of the    
,vierwaldstetter  ,see do not rouse him 
into ecstasy4 ,it is unnecessary to     
remark that he  does not arrange his    
living on the standard of the ,grand    

,palace ,hotels  en route4 ,it is nearer
 the truth to picture him as a vagrant  
who tramps  along without a sense of    
time and without a goal1 in the fairy   
atmosphere of a joyous wanderer who has 
unconsciously adopted the old  rule of  
,philander3 ,walk with a steady step3   
make your burden small3  start early in 
the morn1 and leave home all care6      
,am ,i to record the list of pleasures  
and hobbies that are foreign to  him8   
,the list would be very long1 and ,i    
should arrive at my goal more  quickly  
by setting his sporting tendencies equal
 to zero4 ,i once  suspected him of     
being given to aquatic sport1 as ,i     
learned that he had  taken part in      
several yachting excursions4 ,but ,i was
 mistaken4 ,he sails  in the same way as
 he walks on his tours1 without a set   
purpose1  dreaming1 and uninterested in 
what is regarded by members of sailing  
clubs as a feat4 ,in the negative list  
of his games we see even chess1  that   
usually exerts a strong attraction on   

natures with a mathematical  tendency4  
,the particular types of combination    
offered by this game have  never tempted
 him1 and the world of chess has        
remained terra incognita  for him4 ,he  
is just as little interested in every   
kind of collection1  even that of books4
 ,i have seldom or never met a savant   
who attaches so  little value to the    
personal possession of numerous and     
valuable books4  ,this statement may be 
extended as far as saying that he       
experiences no  pleasure at all in      
possession as such3 he says so himself1 
and his whole  manner of life proves it4
 ,there seems to me to be an element of 
resignation in his amiable hedonism1 a  
kind of monkish asceticism4 ,he  never  
rids himself of the feeling that he is  
only paying a visit in this  world4     
,i do not know whether ,einstein        
considers that his life-work can be     
completed within the span of this visit4
 ,at any rate he makes no attempt  to   
extract more out of the day by following

 a rigid programme of work  than the day
 voluntarily offers4 ,he does not compel
 himself to cover a  definitely         
circumscribed piece of ground with      
chronological exactitude4  ,there are   
brain-workers1 especially artists1 who  
actually never shake  off the fetters of
 the twenty-four hours day of work      
inasmuch as they  spin on the threads of
 daily effort into the nightly fabric of
 dreams4  ,einstein can make a pause1   
interrupt his work1 or divert himself   
into  side-channels at leisure and      
according to the demands of the hour1   
but  dreams offer him no inspiration and
 do not waylay him with problems4    ,on
 the other hand1 however1 he is waylaid 
so much the more during the  day by     
things and persons that make an assault 
on him4 ,this starts as  soon as the    
first post arrives1 to see through which
 requires a special  bureau4 ,in        
addition to the communications of a     
professional or official  nature there  
appear innumerable letters from         

everywhere and anywhere  asking him to  
grant a little of his time4 ,whatever   
each individual  writer has thought     
about the principle of relativity1 all  
his thoughts  and doubts1 additions1    
and1 above all1 that which he has not   
been able  to understand1 all this is to
 be answered by ,einstein4 ,has he1 the 
child  of fame1 even a quarter of an    
hour for himself8 ,there they wait in   
the  hall1 the painter1 the             
photographer1 the sculptor1 and the     
interviewer2  with whatever powers of   
persuasion and argumentative subtlety   
his  attentive wife may seek to defend  
his hours of rest1 some of these        
visitors will yet succeed in gaining the
 upper hand1 and will produce  something
 in oil-colours1 in plaster of ,paris1  
in black and white1 in  water-colours1  
or in print4 ,fame1 too1 demands her    
sacrifices1 and if we  talk of a hunt   
after fame1 then ,einstein is certainly 
not the hunter1  but the hunted4    ,he 
sighs under the burden of his           

correspondence1 not only as the         
recipient1 but also with the sender1    
whose letter has to remain  unanswered4 
,yet he is never roused to anger by the 
intruder on his time4  ,if this were not
 so1 the aphorism of ,cyrus that        
patience is the panacea  of all ills    
would not hold for him1 and how would ,i
 myself otherwise  have dared to claim  
so many hours of him8 ,a sense of guilt 
falls on me6    ,but even ,einstein's   
patience can come to an end1 and this is
 at the  point where society begins3 ,i 
mean the congregation of persons in a   
salon1 society entertainments to which  
one is invited to be seen1 and so  that 
one may claim to have been there4 ,a    
solemn representation in which  he is to
 be made the cynosure of all eyes is a  
torture to him4 ,if in a  very          
exceptional case he is compelled to     
participate in such a  gathering1 the   
joy of his hosts will not be entirely   
unmixed1 for it  does not require a     
thought-reader to recognize the longing 

for solitude  imprinted on his          
countenance3 ,could ,i but escape6      
,so much the happier does he feel       
himself in the narrow circle of his     
friends1 who offer what means to him    
much more than admiration1 namely1      
affection1 and an appreciation of his   
human self4 ,he is what one wishes  him 
to be4 ,he is happy when he can forget  
the doctor profundus1 and can  yield    
himself up to the atmosphere of         
stimulating and unconstrained  converse4
 ,he is a master in the art of          
listening1 and is not averse to         
contradiction2 when possible1 he even   
emphasizes the arguments of his         
opponent4 ,audiatur et altera pars6     
,this is a further manifestation of  his
 altruistic personality1 which rejoices 
when he extracts the true  kernel from  
the husk of the opposing opinion4 ,here 
he also displays a  characteristic which
 one does not usually expect to find    
among abstract  thinkers1 a sense of    
humour that runs through the whole gamut

 from a  gentle smile to hearty         
laughter1 and that is the happy source  
of many a  striking sally4 ,it may      
happen that the subject of conversation 
excites  his anger1 especially in       
political debates when he calls to mind 
militaristic or feudal misgovernment4   
,he then becomes roused1 and1 as a      
cynical philosopher1 sarcastically      
attacks personalities and points out    
the primary source of perennial hate1   
immediately afterwards soaring up  to   
happy speculations of the future4    ,it
 is a matter for regret that the        
subjects that he has discoursed on      
lightly have not been fixed             
phonographically4 ,such records would   
form an  interesting supplement to the  
conversations outlined in this book4 ,it
  would never occur to him to set down  
in permanent literary form the          
inspiration of the moment4 ,what he     
writes emanates from other regions1  and
 is1 to use his own expression1 a       
precipitate of thick ink4 ,this is      

obvious1 for what he has to proclaim as 
a scientist cannot be presented  in a   
thin form4 ,but many a so-called writer 
would have reason to  congratulate      
himself1 if so much thinly flowing      
matter occurred to him  in writing as to
 ,einstein in speaking4         99      
99     99     99     99     99     99   
99    ,the record of these conversations
 was begun in the summer of #aiai1 and  
completed in the autumn of #aibj4       
,,index    ,aristoteles1 #da            
,arrhenius1 #add    ,babinet1 #be       
,bach1 #hh1 #bce  ,bacon1 #df  ,baer1   
,k4 ,e4 von1 #afb  ,bailhaud1 #add      
,beethoven1 #ii1 #bcd1 #bce  ,bell1     
,graham1 #be1 #aaa  ,branger1 #hd       
,bergson1 #ia  ,bernoulli1 #dh          
,bernstein1 #bbe  ,bessel1 #cb  ,bohr1  
,niels1 #eg1 #baj  ,brahe1 ,tycho1 #id  
,bruno1 ,giordano1 #ada  ,bchner1 #bbe  
,bulwer1 #gf  ,bunsen1 #afd  ,byron1 #i 
,cantor1 #eb1 #bjc  ,cavendish1 #aaa    
,ceulen1 ,ludolf van1 #aeh  ,condillac1 
#baf  ,copernicus1 #f1 #ij  ,cosmati1   

#dh  ,curie1 ,madame1 #gi1 #bca         
,cuvier1 #aif    ,darboux1 #aeb  ,dase1 
#aeh  ,descartes1 #dg1 #acc1 #afb       
,dingeldey1 #aij  ,dostojewski1 #ahe1   
#ahg  ,dove1 #ba1 #aee  ,duhem1 #aje1   
#ajf  ,dhring1 #ed1 #ef    ,eckermann1  
#ej1 #he  ,edison1 #adj  ,euclid1 #ahj  
,euler1 #ih  ,euripides1 #he            
,faraday1 #ci1 #fa1 #hd  ,fechner1 #aaj1
 #ahb  ,fermat1 #ig1 #aij  ,fizeau1 #aac
  ,flammarion1 #aae  ,franklin1 #ajb    
,fresnel1 #de    ,galilei1 #f1 #dj1     
#aej1 #agi1 #aha  ,galle1 #f  ,galvani1 
#aaj  ,gauss1 #ee1 #ahe1 #ahf  ,goethe1 
#ac1 #bc1 #agi1 #aig1 #bab1 #bcf    #bdj
  ,grillparzer1 #ie  ,grossmann1 #bbi   
,hansen1 #acd  ,hebbel1 #gg1 #hf        
,hegel1 #db  ,heine1 #di  ,helmholtz1   
#be1 #bf1 #ec1 #gc  ,heraclitus1 #bc    
,herschel1 #hd  ,hertz1 #fj  ,hooke1 #da
  ,horace1 #c  ,humboldt1 #di  ,hume1   
#afa  ,huyghens1 #ef1 #aji1 #acb        
,jean ,paul1 #hf1 #bbc  ,joule1 #hd     
,jung ,stilling1 #hd    ,kant1 #ce1     
#aba1 #agj1 #agg1 #agi1 #bcg  ,kepler1  

#f1 #db1 #hd1 #agf1 #agg  ,kirchhoff1   
#ajd-ajg1 #adh1 #bab  ,kleist1 #acj     
,kummer1 #aij    ,lamarck1 #aig  ,lange1
 #dg  ,laplace1 #dj1 #de1 #adj1 #afe    
,leibniz1 #bf1 #abh  ,leonardo da       
,vinci1 #aa1 #ej-ed  ,leverrier1 #f1 #aj
  ,liebig1 #ee  ,lindemann1 #aeh  ,linn1
 #aif  ,lorentz1 #eg1 #gb  ,lothar      
,meyer1 #ajg  ,lucretius1 #baj    ,mach1
 #df1 #gg1 #ajh1 #adi1 #afi  ,mauthner1 
#ie  ,maxwell1 #ci1 #fj  ,mayer1        
,robert1 #be1 #ee1 #ef  ,melanchthon1   
#hb  ,menander1 #hf  ,mendelejew1 #ajg  
,mezzofanti1 #fc  ,michelangelo1 #di    
,michelson and ,morley1 #aab  ,mill1 #de
    ,mithridates1 #fc  ,montaigne1 #gg  
,mozart1 #bcc    ,newton1 #b1 #f1 #h1   
#ci1 #dj1 #dc1 #if  ,nietzsche1 #fc1    
#bag1 #bcg  ,nollet1 #ajc    ,odilon1   
,helene1 #ace  ,oersted1 #aji  ,ostwald1
 #hc1 #bca1 #bcb  ,ovid1 #aig           
,pascal1 #ic1 #ih  ,pasteur1 #age       
,perrin1 #aed  ,pflger1 #ce  ,philander1
 #bda  ,picard1 #add  ,planck1 #eg1 #ei1
 #ia1 #bcj  ,poincar1 #a1 #g1 #aab1     

#aaf1 #bca  ,pope1 #ed  ,priestley1 #aaa
  ,psellus1 #aef  ,pyrrhon1 #ib         
,pythagoras1 #aja1 #agi    ,quetelet1   
#ahb    ,regiomantus1 #eb  ,reis1 #be   
,riemann1 #ahf  ,riggenbach1 #be  ,russ1
 #bbd  ,rutherford1 #cf1 #baj           
,schiller1 #gd1 #id1 #agj  ,schlegel1   
#bdj  ,schlick1 ,moritz1 #afh           
,schopenhauer1 #da1 #bcg  ,schwann1 #age
  ,shakespeare1 #bcf  ,siemens1 #be1    
#bg-cj  ,slade1 #acf  ,sophocles1 #bch  
,spinoza1 #hd1 #afb  ,stephenson1 #be   
,terence1 #aia  ,thomas ,aquinas1 #afe  
,torricelli1 #aff    ,vaihinger1 #dc1   
#afi  ,vitruvius1 #aja  ,volta1 #aaj1   
#aaa  ,voltaire1 #dg1 #bcg    ,wagner1  
#bcd  ,weber1 #ahb  ,weierstrass1 #aeb  
,weyl1 #cd  ,whewell1 #de  ,wien1 #agc  
,zelter1 #hd  ,zllner1 #acg