,transcriber's ,note3 ,this e-text was  
produced from ,astounding ,science      
,fiction1 ,june1 #aiee4 ,extensive      
research did not uncover any evidence   
that the ,u4,s4 copyright on this       
publication was renewed4    ,,as ,,long 
,,as ,,you ,,wish  ,if1 somehow1 you get
 trapped in a circular time system 444  
how long is the circumference of an     
infinitely retraced circle8   ,by ,,john
 ,o',,keefe  ,illustrated by van ,dongen
   ,the patient sat stiffly in the      
leather chair on the other side of the  
desk4 ,nervously he pressed a coin into 
the palm of one hand4  ,just start      
anywhere1 ,i said1 and tell me all about
 it4  ,as before8 ,without waiting for  
an answer1 he continued1 the coin       
clutched tightly in one hand4 ,i'm      
,charles ,j4 ,fisher1 professor of      
,philosophy at ,reiser ,college4  ,he   
looked at me quickly4 ,or at least ,i   
was until recently4 ,for a second his   
face was boyish4 ,professor of          
,philosophy1 that is4  ,i smiled and    

found that ,i was staring at the coin in
 his hand4 ,he gave it to me4 ,on one   
side ,i read the words3 ,,the           
,,statement ,,on ,,the ,,other ,,side   
,,of ,,this ,,coin ,,is ,,false4 ,the   
patient watched me with an              
expressionless face2 ,i turned over the 
coin4 ,it was engraved with the words3  
,,the ,,statement ,,on ,,the ,,other    
,,side ,,of ,,this ,,coin ,,is ,,false4 
,that's not the problem1 he said1 not my
 problem4 ,i had the coin made when ,i  
was an undergraduate4 ,i enjoyed reading
 one side1 turning it over1 reading the 
other side1 and so on4 ,a fiendish      
enjoyment like boys planning where to   
put the tipped-over outhouse4  ,i looked
 at the patient4 ,he was thirty-eight1  
single1 medium build1 had an ,m4,a4 and 
,ph4,d4 from an eastern university4 ,i  
knew this and more from the folder on my
 desk4  ,eight months ago1 he continued1
 ,i read about the sphere found on      
,paney ,island4 ,he stopped1 looking at 
me questioningly4  ,yes1 ,i know1 ,i    

said4 ,i opened my desk drawer1 took out
 a clipping from the newspaper1 and     
handed it to him4  ,that's it4  ,i read 
the clipping before putting it back in  
the drawer4      ,manila1 ,sept4 #bd    
7,,ins7 ,archeologists from ,university 
of ,california     have discovered in   
earth fault of recent quake a sphere two
 feet in     diameter of an             
unidentifiable material4      ,dr4 ,karl
 ,schwartz1 head of the group1 said the 
sphere was returned     to the          
,university for study4 ,he declined to  
answer questions on the     cultural    
origin of the sphere4  ,there wasn't any
 more in the newspapers about it1 he    
said4 ,i have a friend in ,california   
who got me the photographs4  ,he looked 
at me intently4 ,you won't believe any  
of this4 ,he pressed the coin into the  
palm of his hand4 ,you won't be able to4
  ,the photographs1 he continued1 as if 
lecturing1 were of characters projected 
by the sphere when placed before a      
focused light4 ,the sphere was          

transparent1 you see1 imbedded with dark
 microscopic specks4 ,by moving the     
sphere a certain distance each time1    
there was a total projection of three   
hundred and sixty different characters  
in eighteen different orderings4 ,or    
nineteen different orderings if you     
count one which was a list of all the   
characters4  ,i made a mental note of   
the numbers4 ,i felt they were          
significant4  ,as ,i said1 he continued1
 ,i obtained the photographs of the     
characters4 ,very strange shapes1       
totally unlike the characters of        
,oriental languages1 but yet that is the
 closest way to describe them4 ,he      
jerked forward in his chair1 ,except1 of
 course1 ostensively4  ,later1 ,i said4 
,i wanted to get through the            
preliminaries first4 ,there would be    
time later to see the photographs4      
99      99      99      99      99  ,the
 characters projected by the sphere1 he 
said1 weren't like the characters of any
 known language4 ,he paused             

dramatically4 ,there was reason to      
believe they had origin in an unknown   
culture4 ,a culture more scientifically 
advanced than our own4  ,and the reasons
 for this supposition8 ,i asked4  ,the  
material 444 the material of the sphere4
 ,it could only be roughly classified as
 ferro-plastic4 ,totally unknown1       
amazing imperviousness4 ,a synthetic    
material1 hardly the product of a former
 culture4  ,from ,mars8 ,i said1        
smiling4  ,there were all kinds of      
conjectures1 but1 of course1 the        
important thing was to see if the       
projection of characters was a message4 
,the message1 if any1 would mean more   
than any conjecture4  ,you translated   
it8  ,he polished the coin on his       
jacket4 ,you won't dare believe it1 he  
said sharply4  ,he cleared his throat   
and stiffened into a more rigid posture4
 ,it wasn't exactly translation4 ,you   
see1 to us none of the characters had   
designation4 ,they were just characters4
  ,so it was a problem of decoding8 ,i  

asked4  ,as it turned out1 no4 ,decoding
 is dependent on knowledge of language  
characteristics--characteristics of     
known languages4 ,decoding was tried1   
but without success4 ,no1 what we had to
 find was a key to the language4  ,you  
mean like the ,rune ,stone8  ,more or   
less4 ,in principle1 we needed a picture
 of a cow1 and a sign of meaning        
indicating one of the characters4  ,for 
me1 there was no possibility of finding 
similarities between the characters and 
characters of other languages--that     
would require tremendous linguistic     
knowledge and library facilities4 ,nor  
could ,i use a decoding approach--that  
would require special knowledge of      
techniques and access to electronic     
computers and other mechanical aids4    
,no1 ,i had to work on the assumption   
that the key to the sphere was implicit 
in the sphere4  ,you hoped to find the  
key to the language in the language     
itself8  ,exactly4 ,you know1 of course1
 some languages do have an implicit key8

 ,for example hieroglyphics or picture  
language4 ,the word for cow is a picture
 of a cow4  ,he looked at the toes of   
his shoes4 ,you won't be able to believe
 it4 ,it's impossible to believe4 ,i use
 the word impossible in its logical     
sense4  ,in most languages1 he          
continued1 looking up from his shoes1   
the sound of some words themselves      
indicates the meaning of the word4      
,onomatopoetic words like bowwow1 buzz4 
,and the key to the unknown language8 ,i
 asked4 ,how did you find it8           
99      99      99      99      99  ,i  
watched him push the coin against the   
back of his arm1 then lift it to read   
the backward letters pressed into his   
skin4 ,he looked up at me and smiled4   
,i built models of the characters4 ,big 
material ones1 exactly proportionate to 
the ones projected4 ,then--quite by     
accident--,i viewed one of them through 
a glass globe the size of the original  
sphere4 ,what do you think ,i saw8      
,what8 ,i noticed he had the boyish look

 again4  ,a distortion of the model4    
,but that's not what's important4 ,the  
distortions1 on study1 gave specific    
visual entities4 ,like when looking at  
one of those trick pictures and suddenly
 seeing the lion in the grass4 ,the     
lines outlining the lion are there all  
the time1 only the observer has to view 
them as the outline of a lion4 ,it was  
the same with the models of the         
characters1 except the shapes that      
appeared were not of lions or other     
recognizable things4 ,but they did      
suggest4  ,he pressed the coin against  
his forehead1 closed his eyes and       
appeared to be thinking deeply4 ,yes1   
impossible to believe4 ,no one can      
believe it4  ,in addition to the visual 
response1 the distortions gave me       
definite feelings4 ,not mixtures of     
feelings1 but one definite emotional    
experience4  ,how do you mean8  ,one    
character when viewed through the globe 
gave me a visual image and1 at the same 
time1 a strong feeling of light         

hilarity4  ,i take it then that these   
distortions seemed to connote meanings1 
rather than denote them4 ,you might say 
that their meaning was conveyed through 
a ,gestalt experience on the part of the
 observer4  ,yes1 each character gave a 
definite ,gestalt4 ,but1 the ,gestalt   
was the same for each observer4 ,or at  
least for thirty-five observers there   
was an eighty per cent correlation4  ,i 
whistled softly4 ,and the translation8  
,doctor1 what would you say if ,i told  
you the translation was unbelievable2   
that it couldn't be seriously           
entertained by any man8 ,what if ,i said
 that it would take the sanity of any   
man who believed it8  ,i would say that 
it might well be incorrect4  ,he took   
some papers from his pocket and laughed 
excitedly1 slumping down in the chair4  
,this is the complete translation in    
idiomatic ,english4 ,i'm going to let   
you read it1 but first ,i want you to   
consider a few things4  ,he hid the     
papers behind the back of his chair2 his

 face became even more boyish1 almost as
 if he were deciding on where to put the
 tipped over outhouse4  ,consider first1
 doctor1 that there was a total         
projection of three hundred and sixty   
different characters4 ,the same number  
as the number of degrees in a circle4   
,consider also that there were eighteen 
different orderings of the characters1  
or nineteen counting the alphabetical   
list4 ,the square root of three hundred 
and sixty would lie between eighteen and
 nineteen4  ,yes1 ,i said4 ,i remembered
 there was something significant about  
the numbers1 but ,i wasn't at all sure  
that it was this4  ,consider also1 he   
continued1 that the communication was   
through the medium of a sphere4         
,moreover1 keep in mind that physics    
accepts the path of a beam of light as  
its definition of a straight line4 ,yet1
 the path is a curve2 if extended       
sufficiently it would be a circle1 the  
section of a sphere4  ,all right1 ,i    
said4 ,by now the patient was pounding  

the coin against the sole of one shoe4  
,and1 he said1 keep in mind that in some
 sense time can be thought of as another
 dimension4 ,he suddenly thrust the     
papers at me and sat back in the chair4 
,i picked up the translation and began  
reading4 ,the patient sat stiffly in the
 leather chair on the other side of the 
desk4 ,nervously he pressed a coin into 
the palm of one hand4  ,just start      
anywhere1 ,i said1 and tell me all about
 it4  ,as before8 ,without waiting for  
an answer1 he continued1 the coin       
clutched tightly in one hand4 ,i'm      
,charles ,j4 ,fisher1 professor of      
philosophy at ,reiser ,college4  ,he    
looked at me quickly4 ,or at least ,i   
was until recently4 ,for a second his   
face was boyish4 ,professor of          
philosophy1 that is4  ,i smiled and     
found that ,i was staring at the coin in
 his hand4 ,he gave it to me4 ,on one   
side ,i read the words3 ,,the           
,,statement ,,on ,,the ,,other ,,side   
,,of ,,this ,,coin ,,is ,,false4 ,the   

patient watched4444   ,,the ,,end