,transcrib]'s ,notes3 ,und]scores 80 be=e & aft] a ^w or phrase indicate italics 9 ! orig9al text4 ,a s+le und]score aft] a symbol indicates a subscript4 ,small capitals h be5 conv]t$ to ,,solid capitals4 ,illu/rations h be5 mov$ s !y d n break up p>agraphs4 ,typographical & punctuation errors h be5 sil5tly correct$4 ,,giant ,,bra9s ,,or ,,ma*9es ,,t ,,?9k ,,edmund ,,callis ,,b]keley ,consultant 9 ,mod]n ,te*nology ,presid5t1 ,e4 ,c4 ,b]keley & ,associates ,,john ,,wiley ,,sons1 ,,inc41 ,,new ,,york ,,*apman ,,hall1 ,,limit$1 ,,london ,copyright1 #aidi by ,,edmund ,,callis ,,b]keley ,all ,rights ,res]v$ ,?is book or any "p !re( mu/ n be reproduc$ 9 any =m )\t ! writt5 p]mission ( ! publi%]4 ,second ,pr9t+1 ,febru>y1 #aiej ,pr9t$ 9 ! ,unit$ ,/ates ( ,am]ica ,to my fri5ds1 ^: help & in/ruction made ?is book possible ,,preface ,! ,subject1 ,purpose1 & ,me?od ( ?is ,book ,! subject ( ?is book is a type ( ma*9e t comes clos] to be+ a bra9 t ?9ks ?an any ma*9e ev] did be=e #aidj4 ,^! new ma*9es are call$ sometimes me*anical bra9s & sometimes sequ5ce-controll$ calculators & sometimes by o!r names4 ,ess5tially1 ?\gh1 !y are ma*9es t c h&le in=mation ) great skill & great spe$4 ,& t p[] is v simil> to ! p[] ( a bra94 ,^! new ma*9es are important4 ,!y d ! "w ( hundr$s ( human be+s = ! wages ( a doz54 ,!y are p[]ful in/rum5ts = obta9+ new k4 ,!y apply 9 sci5ce1 bus9ess1 gov]nm5t1 & o!r activities4 ,!y apply 9 reason+ & comput+1 &1 ! h>d] ! problem1 ! m useful !y are4 ,along ) ! release ( atomic en]gy1 !y are "o ( ! great a*ievem5ts ( ! pres5t c5tury4 ,no "o c af=d to be unaw>e ( _! significance4 ,9 ?is book ,i h s\ght to tell a "p ( ! /ory ( ^! new ma*9es t ?9k4 ,p]haps y1 z y />t ?is book1 may n agree ) me t a ma*9e c ?9k3 ! fir/ *apt] ( ?is book is devot$ to ! discussion ( ?is "q4 ,my purpose has be5 to tell en\gh ab\t ^! ma*9es s t we c see 9 g5]al h[ !y "w4 ,i h s\ght to expla9 "s giant bra9s t h be5 built & to %[ h[ !y d ?9k+ op]ations4 ,i h s\ght also to talk ab\t :at ^! ma*9es c d 9 ! future & to judge _! significance = u4 ,x seems to me t !y w take a load (f m5's z great z ! load t pr9t+ took (f m5's writ+3 a trem5d\s burd5 lift$4 ,we ne$ to exam9e sev]al ( ! new me*anical bra9s3 ,massa*usetts ,in/itute ( ,te*nology's diff]5tial analyz]1 ,h>v>d's ,,ibm automatic sequ5ce-controll$ calculator1 ,moore ,s*ool's ,,eniac 7,electronic ,num]ical ,integrator & ,calculator71 & ,bell ,laboratories' g5]al-purpose relay calculator4 ,^! are describ$ 9 ! sequ5ce 9 :i* !y 7 f9i%$ betwe5 ! ye>s #aidb & #aidf4 ,we also h to g on "s excursions--= in/ance1 ! nature ( language & ( symbols1 ! mean+ ( ?9k+1 ! human bra9 & n]v\s sy/em1 ! future design ( ma*9]y t c ?9k1 & a little algebra & logic4 ,i h also s\ght to discuss ! relations betwe5 ma*9es t ?9k & human society--:at we c =esee z likely to happ5 or be ne$$ z a result ( ! rem>kable inv5tion ( ma*9es t c ?9k4 ,,read+ ,,?is ,,book ,?is book is int5d$ = ev]yone4 ,i h s\ght to put x toge!r 9 su* a way t any read] c select f x :at he wants4 ,p]haps at fir/ read+ y want only ! ma9 ?read ( ! /ory4 ,!n read only :at seems int]e/+1 & skip :atev] seems un9t]e/+4 ,! subhead+s %\ld help to tell y :at to read & :at to skip4 ,ne>ly all ! *apt]s c be read ) little ref]5ce to :at goes be=e1 al?\gh "s ref]5ce to ! supplem5ts 9 ! back may at times be useful4 ,p]haps y\r memory ( physics is dim1 l m9e4 ,! little k ( physics ne$$ is expla9$ "h & !re ?r\gh\t ! book1 & ! index %\ld tell :]e to f9d any explanation y may want4 ,p]haps x is a long "t s9ce y did any algebra4 ,!n ,supplem5t #b on ma!matics may hold some?+ ( use to y4 ,two sections 7"o 9 ,*apt] #e & "o 9 ,*apt] #f7 label$ z conta9+ "s r ma!matical details may be skipp$ ) no great loss4 ,p]haps y are unacqua9t$ ) logic t uses symbols--! bran* ( logic call$ ma!matical logic4 ,9 fact1 v few p are famili> ) x4 ,no discussion 9 ! book h+es on und]/&+ ?is subject1 except = ,*apt] #i :]e a ma*9e t calculates logical tru? is describ$4 ,9 all o!r *apt]s y may freely skip all ref]5ces to ma!matical logic4 ,b1 if y are curi\s ab\t ! subject & h[ x c be usefully appli$ 9 ! field ( me*anical bra9s1 !n beg9 ) ! introduction to ! subject 9 ,*apt] #i1 & note ! sugge/ions 9 ! section entitl$ 8,algebra ( ,logic0 9 ,supplem5t #b4 ,9 any case1 glance at ! table ( cont5ts1 ! *apt] head+s & subhead+s1 & ! supplem5ts at ! back4 ,^! %\ld give an idea ( h[ ! book is put toge!r & h[ y may select :at may be int]e/+ to y4 ,please d n read ?is book /raight f beg9n+ to end unless t way proves to be cong5ial to y4 ,if y are n int]e/$ 9 te*nical details1 skip mo/ ( ! middle *apt]s1 :i* describe exi/+ me*anical bra9s4 ,if1 on ! o!r h&1 y want m details ?an ?is book conta9s1 look up ref]5ces 9 ,supplem5t #c4 ,"h are li/$1 ) a few comm5ts1 ov] #bej books1 articles1 & pamphlets relat$ to ! subject ( ma*9]y = comput+ & reason+4 ,^! cov] _m p>ts ( ! field2 "s p>ts1 h[ev]1 are n yet cov]$ by any publi%$ in=mation4 ,!re are no photographs 9 ?is book1 al?\gh !re are ov] #hj draw+s4 ,photographs ( ^! complicat$ ma*9es c really %[ v little3 panels1 lights1 swit*es1 wires1 & o!r k9ds ( h>dw>e4 ,:at is important is ! way ! ma*9e works inside4 ,?is _c be %[n by a photograph b may be %[n by s*ematic draw+s4 ,9 ! same way1 a photograph ( a human be+ %[s almo/ no?+ ab\t h[ he ?9ks4 ,,und]/&+ ,,?is ,,book ,i h tri$ to write ?is book s t x c\ld be und]/ood4 ,i h attempt$ to expla9 ma*9]y = comput+ & reason+ )\t us+ te*nical words any m ?an necess>y4 ,to d ?is seem$ to be easy 9 "s places1 mu* h>d] 9 o!rs4 ,z a te/ ( ?is attempt1 a c\nt has be5 made ( all ! diff]5t words 9 ! book t h two syllables or m1 t are us$ = expla9+1 & t are n !mselves def9$4 ,!re are few] ?an #ahjj ( ^! words4 ,9 ,supplem5t #a1 entitl$ 8,words & ,ideas10 ,i h digress$ to discuss fur!r ! problem ( explanation & und]/&+4 ,e n[ & !n 9 ! book1 along comes a ^w or a phrase t has a special mean+1 = example1 ! "n ( some?+ new4 ,:5 x fir/ appe>s1 x is put 9 italics & is expla9$ or def9$4 ,9 addition1 all ! words & phrases hav+ special mean+ appe> aga9 9 ! index1 & next to ea* is ! page numb] ( its explanation or def9ition4 ,9 _m places1 ,i h talk$ ( me*anical bra9s z if !y 7 liv+4 ,= example1 in/ead ( 8capacity to /ore in=mation0 ,i h spok5 ( 8memory40 ,( c\rse1 ! ma*9es are n liv+2 b !y d h individuality1 responsiv5ess1 & o!r traits ( liv+ be+s1 j z a political p>ty pictur$ z a liv+ elephant does4 ,besides1 to treat ?+s z p]sons is a help 9 mak+ any subject vivid & und]/&able1 z e song writ] & c>tooni/ illu/rates4 ,we speak ( 8,old ,man ,riv]0 & 8,fa!r ,"t02 we may speak ( a %ip or a locomotive z 8%e02 & ! crew on ! fir/ ,h>v>d sequ5ce-controll$ calculator has (t5 call$ h] 8,bessy1 ! ,bessel eng9e40 ,let u pause a little long] on ! subject ( und]/&+4 ,:at is ! und]/&+ ( some?+ new8 ,x is a /ate ( kn[+1 a process ( kn[+ m & m4 ,! m we "k ab\t some?+ new1 ! bett] we und]/& x4 ,x is possible = almo/ anybody to und]/& almo/ any?+1 ,i believe4 ,:at is ma9ly ne$$ 9 ord] to grasp an idea is a good collection ( true /atem5ts ab\t x & "s practice 9 us+ ^? /atem5ts 9 situations4 ,= example1 no "o has ev] se5 or t\*$ ! sep>ate scraps ( electricity call$ electrons4 ,b electrons h be5 describ$ & measur$2 hundr$s ( ?\s&s ( p "w ) electrons2 !y "k & use true /atem5ts ab\t electrons4 ,9 effect1 ^! p und]/& electrons4 ,probably ! h>de/ task ( an au?or is to make 8 /atem5ts und]/&able yet accurate4 ,x is too mu* to hope = complete success4 ,i %all be v grateful to any read] :o po9ts out to me ! /atem5ts t he has n und]/ood or t are 9 error4 ,z to ! views ,i h express$1 ,i d n expect e read] to agree ) me4 ,9 fact1 ,i %all be glad if _m a read] disagrees ) me4 ,= !n someone else may say to bo? ( u1 8,y're bo? "r & bo? wrong--! tru? lies atwixt & atwe5 y40 ,?\ghtful & tol]ant disagreem5t is ! f9e/ climate = sci5tific progress4 ,,basic ,,facts ,_m ( ! me*anical bra9s describ$ 9 ?is book w d good "w = ye>s2 b _! design is already out ( date4 ,_m organizations are h>d at "w f9d+ new tricks 9 electronics1 mat]ials1 & eng9e]+ & mak+ new me*anical bra9s t are bett] & fa/]4 ,9 spite ( future developm5ts1 ?\gh1 ! basic facts ab\t me*anical bra9s w endure4 ,^! basic facts are drawn f ! pr9ciples ( ?9k+1 ( ma!matics1 ( sci5ce1 ( eng9e]+1 etc4 ,^! facts gov]n all h&l+ ( in=mation4 ,!y d n dep5d v mu* on human or me*anical en]gy4 ,!y d n dep5d v mu* on signs4 ,!y d n dep5d v mu* on ! c5tury1 or ! language1 or ! c\ntry4 ,= example1 8,,ii et ,,iii ,v sunt10 ! ,romans may h said2 8deux et trois font c9q10 say ! ,fr5*2 8#b #c #e10 say ! ma!maticians2 & we say1 8two & ?ree make five40 ,! ma9 ef=t 9 ?is book has be5 to make cle> ! basic facts ab\t me*anical bra9s1 = !y are n[ a ma/]ly in/rum5t = obta9+ new k4 ,,edmund ,,callis ,,b]keley ,new ,york #aa1 ,n4 ,y4 ,june #cj1 #aidi ,,ackn[l$gm5ts ,?is book has be5 ov] sev5 ye>s 9 ! mak+ & has evolv$ ?r\gh _m diff]5t plans = its cont5ts4 ,x spr+s ess5tially f ! desire to see human be+s use _! k bett]3 we "k en\gh1 b h[ are we to use :at we "k8 ,ma*9es t h&le in=mation1 t make k accessible1 are a long /ep 9 ! direction ( us+ :at we "k4 ,= help 9 caus+ ?is desire to come to fruition1 ,i %\ld l to express my indebt$ness especially to ,pr(essor 7!n ,comm&]1 ,u4,s4,n4,r47 ,h[>d ,h4 ,aik5 ( ,h>v>d ,univ]sity1 ^: /imulus1 :ile ,i 0 /ation$ = t5 mon?s 9 #aide-df 9 8 laboratory1 0 v great4 ,i %\ld also l to express my appreciation to ,mr4 ,h>ry ,j4 ,volk1 ^: vision & en?usiasm greatly enc\rag$ me 9 ! writ+ ( ?is book4 ,= c>eful reviews & helpful comm5ts on ! *apt]s deal+ ) exi/+ me*anical bra9s1 ,i am especially grateful to ,dr4 ,franz ,l4 ,alt1 ,mr4 ,e4 ,g4 ,&rews1 ,pr(essor ,samuel ,h4 ,caldwell1 ,dr4 ,grace ,m4 ,hopp]1 ,mr4 ,!odore ,a4 ,kal91 & ,dr4 ,john ,w4 ,mau*ly1 :o are exp]ts 9 _! fields4 ,dr4 ,ru? ,p4 ,b]keley1 ,dr4 ,rudolf ,fles*1 ,mr4 ,j4 ,ross ,macdonald1 ,dr4 ,z4 ,i4 ,mosesson1 ,mr4 ,irv+ ,ros5?al1 ,mr4 ,max ,s4 ,we9/e91 & _m o!rs h be5 true fri5ds 9 read+ & comm5t+ ^u _m p>ts ( ! manuscript4 ,mr4 ,frank ,w4 ,kell] devot$ mu* "t & skill to conv]t+ my r\gh sket*es into illu/rations4 ,mr4 ,murray ,b4 ,ritt]man has be5 ( invaluable help 9 prep>+ & *eck+ mu* ( ! bibliography4 ,miss ,m>jorie ,l4 ,black has help$ v greatly 9 turn+ scraps ( pap] be>+ s5t5ces into an excell5t manuscript = ! pr9t]4 ,= p]mission to use ! quotations on v>i\s pages 9 ,*apt]s #aa & #ab1 ,i am indebt$ to ! k9dness (3 ,e4 ,p4 ,dutton ,co41 = quotations f ,frank5/e91 by ,m>y ,w4 ,%elley1 ,ev]yman's ,libr>y1 ,no4 #faf4 ,samuel ,fr5*1 = quotations f ,r4 ,u4 ,r41 by ,k>el apek4#a ,mod]n ,indu/ry1 = a quotation f ! issue ( ,febru>y #ae1 #aidg4 #a ,copyright #aibc by ,d\bl$ay1 ,page & ,co42 all rights res]v$2 quotations repr9t$ by p]mission ( ,k>el apek & ,samuel ,fr5*4 ,responsibility = ! /atem5ts & op9ions express$ 9 ?is book is solely my own4 ,^! /atem5ts & op9ions d n necess>ily repres5t ! views ( any organization ) :i* ,i may be or h be5 associat$4 ,to ! be/ ( my k & belief no in=mation conta9$ 9 ?is book is classifi$ by ! ,dep>tm5t ( ,def5se ( ! ,unit$ ,/ates4 ,,edmund ,,callis ,,b]keley ,,cont5ts #a4 ,,c ,,ma*9es ,,?9k8 ,:at ,is a ,me*anical ,bra98 #a #b4 ,,languages3 ,sy/ems = ,h&l+ ,in=mation #aj #c4 ,a ,,ma*9e ,,t ,,w ,,?9k3 ,! ,design ( a ,v ,simple ,me*anical ,bra9 #bb #d4 ,,c\nt+ ,,holes3 ,pun*-,c>d ,calculat+ ,ma*9es #db #e4 ,,measur+3 ,massa*usetts ,in/itute ( ,te*nology's ,diff]5tial ,analyz] ,no4 #b #fe #f4 ,,accuracy ,,to #bc ,,digits3 ,h>v>d's ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator #hi #g4 ,,spe$--#ejjj ,,additions ,a ,,second3 ,moore ,s*ool's ,,eniac 7,electronic ,num]ical ,integrator & ,calculator7 #aac #h4 ,,reliability--,,no ,,wrong ,,results3 ,bell ,laboratories' ,g5]al-,purpose ,relay ,calculator #abh #i4 ,,reason+3 ,! ,kal9-,burkh>t ,logical-,tru? ,calculator #add #aj4 ,,an ,,excursion3 ,! ,future ,design ( ,ma*9es ,t ,?9k #afg #aa4 ,,! ,,future3 ,ma*9es ,t ,?9k1 & ,:at ,!y ,might ,d = ,m5 #ahj #ab4 ,,social ,,control3 ,ma*9es ,t ,?9k1 & ,h[ ,society ,may ,control ,!m #aif ,,supplem5ts #a4 ,words & ,ideas #bji #b4 ,ma!matics #bad #c4 ,ref]5ces #bbh ,,index #beg ,*apt] #a ,,c ,,ma*9es ,,?9k8 ,,:at ,,is ,a ,,me*anical ,,bra98 ,rec5tly !re has be5 a good deal ( news ab\t /range giant ma*9es t c h&le in=mation ) va/ spe$ & skill4 ,!y calculate & !y reason4 ,"s ( !m are clev]] ?an o!rs--able to d m k9ds ( problems4 ,"s are extremely fa/3 "o ( !m does #ejjj additions a second = h\rs or days1 z may be ne$$4 ,:]e !y apply1 !y f9d answ]s to problems mu* fa/] & m accurately ?an human be+s c2 & s !y c solve problems t a man's life is f> too %ort to p]mit him to d4 ,t is :y !y 7 built4 ,^! ma*9es are simil> to :at a bra9 w\ld be if x 7 made ( h>dw>e & wire in/ead ( fle% & n]ves4 ,x is !re=e natural to call ^! ma*9es me*anical bra9s4 ,also1 s9ce _! p[]s are l ^? ( a giant1 we may call !m giant bra9s4 ,sev]al giant me*anical bra9s are n[ at "w f9d+ out answ]s nev] be=e kn[n4 ,two are 9 ,cambridge1 ,mass42 "o is at ,massa*usetts ,in/itute ( ,te*nology1 & "o at ,h>v>d ,univ]sity4 ,two are 9 ,ab]de51 ,md41 at ! ,army's ,balli/ic ,rese>* ,laboratories4 ,^! f\r ma*9es 7 f9i%$ 9 ! p]iod #aidb to #aidf & are describ$ 9 lat] *apt]s ( ?is book4 ,m giant bra9s are be+ con/ruct$4 ,c we say t ^! ma*9es really ?9k8 ,:at d we mean by ?9k+1 & h[ does ! human bra9 ?9k8 ,,human ,,?9k+ ,we d n "k v mu* ab\t ! physical process ( ?9k+ 9 ! human bra94 ,if y ask a sci5ti/ h[ fle% & blood 9 a human bra9 c ?9k1 he w talk to y a little ab\t n]ves & ab\t electrical & *emical *anges1 b he w n be able to tell y v mu* ab\t h[ we add #b & #c & make #e4 ,:at m5 "k ab\t ! way 9 :i* a human bra9 ?9ks c be put d[n 9 a few pages1 & :at m5 d n "k w\ld fill _m libr>ies4 ,injuries to bra9s h %[n "s ?+s ( importance2 = example1 !y h %[n t c]ta9 p>ts ( ! bra9 h c]ta9 duties4 ,!re is a "p ( ! bra91 = in/ance1 :]e sights are record$ & comp>$4 ,if an accid5t damages ! "p ( ! bra9 :]e c]ta9 in=mation is /or$1 ! human be+ has to rele>n--halt+ly & badly--! in=mation de/roy$4 ,we "k also t ?9k+ 9 ! human bra9 is done ess5tially by a process ( /or+ in=mation & !n ref]r+ to x1 by a process ( le>n+ & rememb]+4 ,we "k t !re are no little :eels 9 ! bra9 s t a :eel /&+ at #b c be turn$ #c m /eps & ! result ( #e read4 ,in/ead1 y & ,i /ore ! in=mation t #b & #c are #e1 & /ore x 9 su* a way t we c give ! answ] :5 que/ion$4 ,b we d n "k ! regi/] 9 our bra9 :]e ?is p>ticul> piece ( in=mation is /or$4 ,nor d we "k h[1 :5 we are que/ion$1 we are able automatically to pick up ! n]ve *annels t lead into ?is regi/]1 get ! answ]1 & report x4 ,s9ce !re are _m n]ves 9 ! bra91 ab\t #aj billion ( !m1 9 fact1 we are c]ta9 t ! network ( connect+ n]ves is a ma9 "p ( ! puzzle4 ,we are !re=e mu* int]e/$ 9 n]ves & _! prop]ties4 ,,n]ves ,,& ,,_! ,,prop]ties ,a s+le n]ve1 or n]ve cell1 consi/s ( a cell nucleus & a fib]4 ,?is fib] may h a l5g? ( any?+ f a small fraction ( an in* up to sev]al feet4 ,9 ! laboratory1 successive impulses c be s5t along a n]ve fib] z (t5 z #ajjj a second4 ,impulses c travel along a n]ve fib] 9 ei!r direction at a rate f #c feet to #cjj feet a second4 ,because ! spe$ ( ! impulse is f> less ?an #ahf1jjj miles a second--! spe$ ( an electric curr5t--! impulse 9 ! n]ve is ?\ght by "s inve/igators to be m *emical ?an electrical4 ,we "k t a n]ve cell has :at is call$ an all-or-none response1 l ! trigg] ( a gun4 ,if y /imulate ! n]ve up to a c]ta9 po9t1 no?+ w happ52 if y rea* t po9t1 or cross x1--bang6--! n]ve responds & s5ds out an impulse4 ,! /r5g? ( ! impulse1 l ! %ot ( ! gun1 has no relation :atev] to ! am\nt ( ! /imulation4 ,illu/ration3 ,,fig4 #a4 ,s*eme ( a n]ve cell4 ,! /ructure betwe5 ! end ( "o n]ve & ! beg9n+ ( ! next is call$ a synapse 7see ,fig4 #a74 ,no "o really kn[s v mu* ab\t synapses1 = !y are extremely small & x is n easy to tell :]e a synapse /ops & o!r /uff beg9s4 ,impulses travel ?r\gh synapses 9 f to #c ?\s&?s ( a second4 ,an impulse travels ?r\gh a synapse only 9 "o direction1 f ! head 7or axon7 ( "o n]ve fib] to ! foot 7or d5drite7 ( ano!r4 ,x seems cle> t ! activity 9 a synapse is *emical4 ,:5 ! head ( a n]ve fib] br+s 9 an impulse to a synapse1 app>5tly a *emical call$ acetyl*ol9e is releas$ & may affect ! foot ( ano!r fib]1 ?us transmitt+ ! impulse2 b ! process & ! conditions = x are /ill n well und]/ood4 ,x is ?\ght t ne>ly all in=mation is h&l$ 9 ! bra9 by gr\ps ( n]ves 9 p>allel pa?s4 ,= example1 ! eye is e/imat$ to h ab\t #ajj million n]ves s5sitive to light1 & ! in=mation t !y ga!r is report$ by ab\t #a million n]ves to ! "p ( ! bra9 t /ores sights4 ,n mu* m is yet kn[n1 h[ev]1 ab\t ! op]ation ( h&l+ in=mation 9 a human bra94 ,we d n yet "k h[ ! n]ves are connect$ s t we c d :at we d4 ,probably ! greate/ ob/acle to k is t s f> we _c obs]ve ! detail$ /ructure ( a liv+ human bra9 :ile x p]=ms1 )\t hurt+ or kill+ x4 ,,behavior ,,t ,,is ,,?9k+ ,!re=e1 we _c yet tell :at ?9k+ is by obs]v+ precisely h[ a human bra9 does x4 ,in/ead1 we h to def9e ?9k+ by describ+ ! k9d ( behavior t we call ?9k+4 ,let u consid] "s examples4 ,:5 y & ,i add #ab & #h & make #bj1 we are ?9k+4 ,we use our m9ds & our und]/&+ to c\nt #h places =w>d f #ab1 = example1 & f9i% ) #bj4 ,if we c\ld f9d a dog or a horse t c\ld add numb]s & tell answ]s1 we w\ld c]ta9ly say t ! animal c\ld ?9k4 ,) no tr\ble a ma*9e c d ?is4 ,an ord9>y #aj-;column add+ ma*9e c be giv5 two numb]s l #a1cgh1iag1gff & #b1cee1gii1hfg & ! in/ruction to add !m4 ,! ma*9e w !n give ! answ]1 #c1gcd1gag1fcc1 mu* fa/] ?an a man4 ,9 fact1 ! me*anical bra9 at ,h>v>d c add a numb] ( #bc digits to ano!r numb] ( #bc digits & get ! "r answ] 9 _/ ( a second4 ,or1 suppose t y are walk+ along a road & come to a =k4 ,if y /op1 read ! signpo/1 & !n *oose left or "r1 y are ?9k+4 ,y "k be=eh& :]e y want to g1 y comp>e y\r de/9ation ) :at ! signpo/ says1 & y decide on y\r r\te4 ,?is is an op]ation ( logical *oice4 ,a ma*9e c d ?is4 ,! me*anical bra9 n[ at ,ab]de5 :i* 0 built at ,bell ,laboratories c exam9e any numb] t comes up 9 ! process ( a calculation & tell :e!r x is bigg] ?an #c 7or any /at$ numb]7 or small]4 ,if ! numb] is bigg] ?an #c1 ! ma*9e w *oose "o process2 if ! numb] is small] ?an #c1 ! ma*9e w *oose ano!r process4 ,n[ suppose t we consid] ! basic op]ation ( all ?9k+3 9 ! human bra9 x is call$ le>n+ & rememb]+1 & 9 a ma*9e x is call$ /or+ in=mation & !n ref]r+ to x4 ,= example1 suppose y want to f9d #cje ,ma9 ,/reet 9 ,kalamazoo4 ,y look up a map ( ,kalamazoo2 ! map is in=mation k9dly /or$ by o!r p = y\r use4 ,:5 y /udy ! map1 notice ! /reets & ! numb]+1 & !n f9d :]e ! h\se %\ld be1 y are ?9k+4 ,a ma*9e c d ?is4 ,9 ! ,bell ,laboratories' me*anical bra91 = example1 ! map c\ld be /or$ z a long li/ ( ! blocks ( ! city & ! /reets & numb]s t apply to ea* block4 ,! ma*9e w !n hunt = ! city block t conta9s #cje ,ma9 ,/reet & report x :5 f\nd4 ,a ma*9e c h&le in=mation2 x c calculate1 conclude1 & *oose2 x c p]=m reasonable op]ations ) in=mation4 ,a ma*9e1 !re=e1 c ?9k4 ,,! ,,def9ition ,,( ,a ,,me*anical ,,bra9 ,n[ :5 we speak ( a ma*9e t ?9ks1 or a me*anical bra91 :at d we mean8 ,ess5tially1 a me*anical bra9 is a ma*9e t h&les in=mation1 transf]s in=mation automatically f "o "p ( ! ma*9e to ano!r1 & has a flexible control ov] ! sequ5ce ( its op]ations4 ,no human be+ is ne$$ ar\nd su* a ma*9e to pick up a physical piece ( in=mation produc$ 9 "o "p ( ! ma*9e1 p]sonally move x to ano!r "p ( ! ma*9e1 & !re put x 9 aga94 ,nor is any human be+ ne$$ to give ! ma*9e in/ructions f m9ute to m9ute4 ,in/ead1 we c write out ! :ole program to solve a problem1 translate ! program into ma*9e language1 & put ! program into ! ma*9e4 ,!n we press ! 8/>t0 button2 ! ma*9e />ts :irr+2 & x pr9ts out ! answ]s z x obta9s !m4 ,ma*9es t h&le in=mation h exi/$ = m ?an #bjjj ye>s4 ,^! two prop]ties are new1 h[ev]1 & make a deep break ) ! pa/4 ,h[ %\ld we imag9e a me*anical bra98 ,"o way to ?9k ( a me*anical bra9 is %[n 9 ,fig4 #b4 ,we see "h a railroad l9e ) f\r /ations1 m>k$ input1 /orage1 comput]1 & output4 ,^! /ations are jo9$ by little gates or swit*es to ! ma9 railroad l9e4 ,we c imag9e t numb]s & o!r in=mation move along ?is railroad l9e1 load$ 9 freight c>s4 ,input & output are /ations :]e numb]s or o!r in=mation g 9 & come out1 respectively4 ,/orage is a /ation :]e !re are _m plat=ms & :]e in=mation c be /or$4 ,! comput] is a special /ation some:at l a factory2 :5 two numb]s are load$ on plat=ms #a & #b ( ?is /ation & an ord] is load$ on plat=m #c1 !n ano!r numb] is produc$ on plat=m #d4 ,illu/ration3 ,,fig4 #b4 ,s*eme ( a me*anical bra94 ,we see also a t[]1 m>k$ control4 ,?is t[] runs a telegraph l9e to ea* ( its little wat*m5 /&+ by ! gates4 ,! t[] tells !m :5 to op5 & :5 to %ut :i* gates4 ,n[ we c see t1 j z soon z ! "r gates are %ut1 freight c>s ( in=mation c move betwe5 /ations4 ,actually ! freight c>s move at ! spe$ ( electric curr5t1 ?\s&s ( miles a second4 ,s1 by clos+ ! "r gates ea* fraction ( a second1 we c fla% numb]s & in=mation ?r\gh ! sy/em & p]=m op]ations ( reason+4 ,?us we obta9 a me*anical bra94 ,9 g5]al1 a me*anical bra9 is made up (3 #a4 ,a quantity ( regi/]s :]e in=mation 7numb]s & in/ructions7 c be /or$4 #b4 ,*annels along :i* in=mation c be s5t4 #c4 ,me*anisms t c c>ry out ari?metical & logical op]ations4 #d4 ,a control1 :i* guides ! ma*9e to p]=m a sequ5ce ( op]ations4 #e4 ,input & output devices1 :]eby in=mation c g into ! ma*9e & come out ( x4 #f4 ,motors or electricity1 :i* provide en]gy4 ,,! ,,k9ds ,,( ,,?9k+ ,a ,,me*anical ,,bra9 ,,c ,,d ,!re are _m k9ds ( ?9k+ t me*anical bra9s c d4 ,among o!r ?+s1 !y c3 #a4 ,le>n :at y tell !m4 #b4 ,apply ! in/ructions :5 ne$$4 #c4 ,read & rememb] numb]s4 #d4 ,add1 subtract1 multiply1 divide1 & r\nd (f4 #e4 ,look up numb]s 9 tables4 #f4 ,look at a result1 & make a *oice4 #g4 ,d long *a9s ( ^! op]ations "o aft] ano!r4 #h4 ,write out an answ]4 #i4 ,make sure ! answ] is "r4 #aj4 ,"k t "o problem is f9i%$1 & turn to ano!r4 #aa4 ,det]m9e mo/ ( _! own in/ructions4 #ab4 ,"w unatt5d$4 ,!y d ^! ?+s mu* bett] ?an y or ,i4 ,!y are fa/4 ,! me*anical bra9 built at ! ,moore ,s*ool ( ,electrical ,eng9e]+ at ! ,univ]sity ( ,p5nsylvania does #ejjj additions a second4 ,!y are reliable4 ,ev5 ) hundr$s ( ?\s&s ( p>ts1 ! exi/+ giant bra9s h work$ successfully4 ,!y h rem>kably few me*anical tr\bles2 9 fact1 = "o ( ! giant bra9s1 a me*anical failure is ( ! ord] ( once a mon?4 ,!y are p[]ful4 ,! big ma*9e at ,h>v>d c rememb] #gb numb]s ea* ( #bc digits at "o "t & c d #c op]ations ) ^! numb]s e second4 ,! me*anical bra9s t h be5 f9i%$ are able to solve problems t h baffl$ m5 = _m1 _m ye>s1 & !y ?9k 9 ways nev] op5 to m5 be=e4 ,me*anical bra9s h remov$ ! limits on complexity ( r\t9e3 ! ma*9e c c>ry out a complicat$ r\t9e z easily z a simple "o4 ,already1 processes = solv+ problems are be+ work$ out s t ! me*anical bra9 w itself det]m9e m ?an #ii p] c5t ( all ! r\t9e ord]s t x is to c>ry out4 ,b1 y may ask1 c !y d any k9d ( ?9k+8 ,! answ] is no4 ,no me*anical bra9 s f> built c3 #a4 ,d intuitive ?9k+4 #b4 ,make bright guesses1 & leap to conclusions4 #c4 ,det]m9e all its own in/ructions4 #d4 ,p]ceive complex situations outside itself & int]pret !m4 ,a clev] wild animal1 = example1 a fox1 c d all ^! ?+s2 a me*anical bra91 n yet4 ,!re is1 h[ev]1 good reason to believe t mo/1 if n all1 ( ^! op]ations w 9 ! future be p]=m$ n only by animals b also by ma*9es4 ,m5 h only j begun to con/ruct me*anical bra9s4 ,all ^? f9i%$ are *ildr52 !y h all be5 born s9ce #aidj4 ,soon !re w be mu* m rem>kable giant bra9s4 ,,:y ,,are ,,^! ,,giant ,,bra9s ,,important8 ,mo/ ( ! ?9k+ s f> done by ^! ma*9es is ) numb]s4 ,!y h already solv$ problems 9 airplane design1 a/ronomy1 physics1 ma!matics1 eng9e]+1 & _m o!r sci5ces1 t previ\sly c\ld n be solv$4 ,to f9d ! solutions ( ^! problems1 ma!maticians w\ld h _h to "w = ye>s & ye>s1 us+ ! be/ kn[n me?ods & l>ge /affs ( human comput]s4 ,^! me*anical bra9s n only calculate1 h[ev]4 ,!y also rememb] & reason1 & ?us !y promise to solve "s v important human problems4 ,= example1 "o ( ^! problems is ! application ( :at mank9d kn[s4 ,x takes too long to f9d und]/&able in=mation on a subject4 ,! libr>ies are full ( books3 mo/ ( !m we c nev] hope to read 9 our lifetime4 ,! te*nical j\rnals are full ( cond5s$ sci5tific in=mation3 !y c h>dly be und]/ood by y & me4 ,!re is a big gap betwe5 somebody's kn[+ some?+ & employm5t ( t k by y or me :5 we ne$ x4 ,b ^! new me*anical bra9s h&le in=mation v swiftly4 ,9 a few ye>s ma*9es w probably be made t w "k :at is 9 libr>ies & t w tell v swiftly :]e to f9d c]ta9 in=mation4 ,?us we c see t me*anical bra9s are "o ( ! great new tools = f9d+ out :at we d n "k & apply+ :at we d "k4 ,*apt] #b ,,languages3 ,,sy/ems ,,= ,,h&l+ ,,in=mation ,z ev]yone kn[s1 x is n always easy to ?9k4 ,by ?9k+1 we mean comput+1 reason+1 & o!r h&l+ ( in=mation4 ,by in=mation we mean collections ( ideas--physically1 collections ( m>ks t h mean+4 ,by h&l+ in=mation1 we mean proce$+ logically f "s ideas to o!r ideas--physically1 *ang+ f "s m>ks to o!r m>ks 9 ways t h mean+4 ,= example1 "o ( y\r h&s c express an idea3 x c /ore ! numb] #c = a %ort :ile by turn+ #c f+]s up & #b d[n4 ,9 ! same way1 a ma*9e c express an idea3 x c /ore in=mation by arrang+ "s equipm5t4 ,! ,h>v>d me*anical bra9 c /ore #acb numb]s betwe5 #j & #ii1iii1iii1iii1iii1iii1iii1iii = days4 ,:5 y want to *ange ! numb] /or$ by y\r f+]s1 y move !m3 p]haps y ne$ a half second to *ange ! numb] /or$ by y\r f+]s f #c to #b1 = example4 ,9 ! same way1 a ma*9e c *ange a /or$ numb] by *ang+ ! arrangem5t ( "s equipm5t3 ! electronic bra9 ,eniac c *ange a /or$ numb] 9 _/ ( a second4 ,,languages ,s9ce x is n always easy to ?9k1 m5 h giv5 mu* att5tion to devices = mak+ ?9k+ easi]4 ,!y h work$ out _m sy/ems = h&l+ in=mation1 :i* we (t5 call languages4 ,"s languages are v complete & v]satile & ( great importance4 ,o!rs cov] only a n>r[ field--su* z numb]s alone--b 9 ?is field !y may be rem>kably effici5t4 ,j :at is a language8 ,e language is bo? a s*eme = express+ mean+s & physical equipm5t t c be h&l$4 ,= example1 let u take spok5 ,engli%4 ,! s*eme ( spok5 ,engli% consi/s ( m ?an #aej1jjj words express+ mean+s1 & "s rules = putt+ words toge!r mean+fully4 ,! physical equipm5t ( spok5 ,engli% consi/s ( 7#a7 s\nds 9 ! air1 & 7#b7 ! e>s ( millions ( p1 & _! m\?s & voices1 by :i* !y c he> & speak ! s\nds ( ,engli%4 ,= ano!r example1 let u take numb]s express$ 9 ! ,arabic num]als & ! rules ( ari?metic4 ,! s*eme ( ?is language conta9s only t5 digits #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i or _! equival5ts1 & "s rules = comb9+ !m4 ,suffici5t physical equipm5t = ?is language might v well be a t5-column desk calculat+ ma*9e ) its c\nt] :eels1 ge>s1 keys1 etc4 ,if we tri$ to ex*ange ! physical equipm5t ( ^! two languages1 we w\ld be block$3 ! desk calculat+ ma*9e _c possibly express ! mean+ful comb9ations ( #aej1jjj words1 & s\nds 9 ! air are n p]man5t en\gh to express ! /eps ( division ( "o l>ge numb] by ano!r4 ,,s*emes ,,= ,,express+ ,,mean+s ,if we exam9e languages t h exi/$1 we c obs]ve a numb] ( s*emes = express+ mean+s4 ,9 ! table on pp4 #ab-ac is a r\gh li/ ( a doz5 ( !m4 ,f among ^! we c *oose ! s*emes t are likely to be useful 9 me*anical bra9s4 ,s*emes #aa & #ab are ! s*emes t h be5 pr$om9antly us$ 9 ma*9]y = comput+4 ,s*eme #ab consi/+ ( comb9ations ( j two m>ks1 1 1 provides "o ( ! be/ codes = me*anical h&l+ ( in=mation4 ,?is s*eme1 call$ b9>y cod+ 7see ,supplem5t #b71 is also useful = measur+ ! quantity ( in=mation4 ,,quantity ,,( ,,in=mation ,h[ %\ld we measure ! quantity ( in=mation8 ,! smalle/ unit ( in=mation is a 8yes0 or a 8no10 a *eck m>k 77 or a cross 771 an impulse 9 a n]ve or no impulse1 a #a or a #j1 black or :ite1 good or bad1 etc4 ,?is tw(old diff]5ce is call$ a b9>y digit ( in=mation 7see ,supplem5t #b74 ,x is ! conv5i5t unit ( in=mation4 ,,s*emes ,,= ,,express+ ,,mean+s ,,example3 _/-------------------------------------- ---------------------------- ,,pr9ciple ,,sign ,,us$ ,,9 ,,significance ,,"n ,,( ,,no4 ,,( ,,s*eme ,,s*eme 7#a7 7#b7 7#c7 7#d7 7#e7 7#f7 ,s\nds #a4 ,s\nd ( new ,bob:ite#b ,spok5 k9d ( quail1 ,imitative2 ^w is l ,engli% s call$ b[w[ s\nd ( f its note !ory ref]5t #b4 ,an utt]ance ,pooh6#b ,spok5 ,! speak] ,pooh-pooh becomes a ,engli% expresses !ory new ^w disda9 #c4 ,new ^w is ,*ortle#b ,spok5 8,*uckle0 ,analogical l ano!r ,engli%2 & ^w inv5t$ by 8snort0 ,lewis ,c>roll1 bl5d$ #ahif #d4 ,^w has ,"m#b ,spok5 ,female ,hi/orical be5 us$ ,engli% p>5t ?r\gh ! ages ,sights #e4 ,picture picture ,egyptian2 ,picture ( ,imitative2 is l ( eye ,ojibwa eye & pictographic ref]5t 7,am]ican te>s1 to ,indian7 mean grief #f4 ,patt]n is #e ,engli%2 ,five2 ,ideographic2 symbol ( ,fr5*2 c9q2 ma!matical2 an idea ,g]man2 fnf2 symbolic2 etc4 etc4 num]ic ,mapp+ ( ,s\nds #g4 ,object picture ,possible ,picture ( ,rebus- pictur$ ( knot ,engli% a knot to writ+2 has ! mean 8n0 phonographic want$ s\nd #h4 ,patt]n is picture ,anci5t ,sign = ,syllable- symbol = ( /> ,cypriote ! writ+ a l>ge 7isl& ( syllable s\nd unit ,cyprus7 mu #i4 ,patt]n is ,int]national ,! s\nd ,phonetic symbol = ,phonetic zh1 z writ+ a small ,alphabet ( s 9 alphabetic s\nd unit #hg *>act]s 8measure0 writ+2 ,mapp+ ( ,sights or ,symbols #aj4 ,sy/ematic ,,eniac ,abbreviations1 ,initial ,alphabetic comb9ations etc4 lett]s cod+ ( #bf ( a lett]s #e-^w title #aa4 ,sy/ematic #ace-jc-abbh ,abbreviations1 ,social ,num]ic comb9ations nom5clature1 ,security cod+ ( #aj digits etc4 ,no4 ( a p]son #ab4 ,sy/ematic 1111 ,*eck+ 8yes10 ,b9>y comb9ations li/s1 8no10 cod+ ( #b m>ks etc4 8no10 8yes10 8yes10 respectively #b ,! prec$+ ^w is ! spok5 ^w1 n ! writt5 "o4 ,) #b units ( in=mation or #b b9>y digits 7#a or #j7 we c repres5t #d pieces ( in=mation3 #jj1 #ja1 #aj1 #aa ,) #c units ( in=mation we c repres5t #h pieces ( in=mation3 #jjj1 #jja1 #jaj1 #jaa1 #ajj1 #aja1 #aaj1 #aaa ,) #d units ( in=mation we c repres5t #af pieces ( in=mation3 #jjjj #jjja #jjaj #jjaa #jajj #jaja #jaaj #jaaa #ajjj #ajja #ajaj #ajaa #aajj #aaja #aaaj #aaaa ,n[ #d units ( in=mation are suffici5t to repres5t a decimal digit #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i & all[ #f possibilities to be left ov]2 #c units ( in=mation are n suffici5t4 ,= example1 we may h3 #j #jjjj #e #jaja #a #jjja #f #jaaj #b #jjaj #g #jaaa #c #jjaa #h #ajjj #d #jajj #i #ajja ,we say1 !re=e1 t a decimal digit #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i is equival5t to #d units ( in=mation4 ,?us a table conta9+ #aj1jjj numb]s1 ea* ( #aj decimal digits1 is equival5t to #djj1jjj units ( in=mation4 ,"o ( ! #bf lett]s ( ! alphabet is equival5t to #e units ( in=mation1 =1 #e b9>y digits 7#a or #j7 h #cb possible arrangem5ts1 & ^! are en\gh to provide = ! #bf lett]s4 ,any pr9t$ in=mation 9 ,engli% c be express$ 9 ab\t #hj *>act]s consi/+ ( #aj num]als1 #eb capital & small lett]s1 & "s #ah punctuation m>ks & o!r types ( m>ks2 #f b9>y digits 7#a or #j7 h #fd possible arrangem5ts1 & #g b9>y digits 7#a or #j7 h #abh possible arrangem5ts4 ,ea* "* 9 a pr9t$ book1 !re=e1 is r\ghly equival5t to #g units ( in=mation4 ,x c be det]m9$ t a big telephone book or a big ref]5ce diction>y /ores pr9t$ in=mation at ! rate ( ab\t #a billion units ( in=mation p] cubic foot4 ,if ! #aj billion n]ves 9 ! human bra9 c\ld indep5d5tly be impuls$ or n impuls$1 !n ! human bra9 c\ld conceivably /ore #aj billion units ( in=mation4 ,! l>ge/ libr>y 9 ! _w is ! ,libr>y ( ,congress1 conta9+ #g million volumes includ+ pamphlets4 ,x /ores ab\t #ajj trillion units ( in=mation4 ,we c ?us see ! significance ( a quantity ( in=mation f #a unit to #ajj trillion units4 ,no di/9ction is "h made betwe5 in=mation t reports facts & in=mation t does n4 ,= example1 a book ( fiction ab\t p]sons :o nev] exi/$ is /ill c\nt$ z in=mation1 &1 ( c\rse1 mu* in/ruction & ent]ta9m5t may be f\nd 9 su* a s\rce4 ,,physical ,,equipm5t ,,= ,,h&l+ ,,in=mation ,! fir/ ?+ we want to d ) in=mation is /ore x4 ,! second ?+ we want to d is comb9e x4 ,we want equipm5t t makes ^! two processes easy & effici5t4 ,we want equipm5t = h&l+ in=mation t3 #a4 ,co/s little4 #b4 ,holds mu* in=mation 9 little space4 #c4 ,is p]man5t1 :5 we want to keep ! in=mation4 #d4 ,is erasable1 :5 we want to remove in=mation4 #e4 ,is v]satile1 holds easily any k9d ( in=mation1 & all[s op]ations to be done easily4 ,! am\nt ( human ef=t ne$$ to h&le in=mation correctly dep5ds v mu* on ! prop]ties ( ! physical equipm5t express+ ! in=mation1 al?\gh ! laws ( correct reason+ are indep5d5t ( ! equipm5t4 ,= example1 ! great difficulty ) spok5 s\nds z physical equipm5t = h&l+ in=mation is ! tr\ble ( /or+ !m4 ,! te*nique = do+ s 0 ma/]$ only ab\t #ahgg :5 ,?omas ,a4 ,edison made ! fir/ phonograph4 ,ev5 ) ?is advance1 no "o c glance at a s\ndtrack & tell quickly :at s\nds are /or$ !re2 only by turn+ back ! ma*9e & li/5+ to a groove c we det]m9e ?is4 ,x 0 n possible = ! m5 ( #bjjj ,b4,c4 to wait ?\s&s ( ye>s = ! /or+ ( spok5 s\nds4 ,! problem ( /or+ in=mation 0 accord+ly tak5 to o!r types ( physical equipm5t4 ,,physical ,,equipm5t ,,= ,,h&l+ ,,in=mation ,,physical ,,arrang$ ,,op]at$ ,,or ,,l[ ,,little ,,p]m- ,,eras- ,,v]s- ,,no4 ,,objects ,,9 ,,or ,,on ,,produc$ ,,by ,,co/8 ,,space8 ,,an5t8 ,,able8 ,,atile8 7#a7 7#b7 7#c7 7#d7 7#e7 7#f7 7#g7 7#h7 7#i7 ,m9d #a4 ,n]ve ,human ,body cells bra9 ,s\nds #b4 ,s\nds ,air ,voice #c4 ,s\nd- ,wax ,ma*9es tracks cyl9d]s1 & phonograph motors records ,sights #d4 ,m>ks ,s& ,/ick #e4 ,color$ ,cave ,pa9tbru% pa9t+ walls1 & pa9ts canvases1 etc4 #f4 ,m>ks1 ,clay1 ,/ylus1 inscript- /one *isel ions #g4 ,m>ks ,slate ,*alk #h4 ,m>ks ,pap]1 ,p5 p>*m5t1 & ink1 etc4 p5cil #i4 ,lett]s1 ,pap]1 ,pr9t+ etc4 books1 press1 etc4 movable type1 motor1 & h&s #aj4 ,photo- ,film1 ,cam]a graphs pr9ts1 etc4 #aa4 ,lett]s1 ,pap]1 ,typewrit] etc4 mimeograph & /5cil1 f+]s etc4 ,body #ab4 ,ge/ures ,space ,body #ac4 ,f+]s ,h&s ,body ,objects #ad4 ,pebbles ,slab ,h&s #ae4 ,knots ,/r+ ,h&s #af4 ,tallies1 ,/ick ,knife not*es #ag4 ,beads ,rods 9 ,h&s a frame1 abacus #ah4 ,rul$ ,rul]s1 ,h&s1 l9es1 scales1 pressure1 po9t]s dials etc4 ,ma*9es #ai4 ,c\nt] ,desk ,motor :eels1 calculat+ & ge>s1 ma*9es1 h&s keys1 fire-control lights1 in/rum5ts1 etc4 etc4 #bj4 ,pun*$ ,pun* c>d ,motor c>ds ma*9]y1 & & teletype1 input pap] etc4 in/ructions tape #ba4 ,relays ,dial ,motor telephone1 & o!r input ma*9]y in/ructions #bb4 ,elect- ,ma*9]y ,motor ronic & tubes input in/ructions #bc4 ,magnetic ,ma*9]y ,motor surfaces3 & wire1 input tape1 in/ructions discs #bd4 ,delay ,ma*9]y ,motor l9es3 & electric1 input ac\/ic in/ructions #be4 ,electro- ,ma*9]y ,motor /atic & /orage input tubes in/ructions yes1 v4 yes1 adequately4 n g5]ally4 n at all4 ,:at are ! types ( physical equipm5t = h&l+ in=mation1 & :i* are ! good ones8 ,9 ! table on pp4 #af-ag is a r\gh li/ ( #be types ( physical equipm5t = h&l+ in=mation4 means 8yes1 v20 means 8yes1 adequately20 means 8n g5]ally20 means 8n at all40 ,= example1 our f+]s 7see ,no4 #ac7 z a device = h&l+ in=mation are v exp5sive = mo/ cases4 ,!y take up a good deal ( space4 ,c]ta9ly !y are v tempor>y /orage2 any in=mation !y may express is v erasable2 & :at we c express ) !m alone is v limit$4 ,yet1 ) a typewrit] 7see ,no4 #aa71 our f+]s become v]satile & effici5t4 ,9 fact1 our f+]s c make #d /rokes a second2 we c select any "o ( ab\t #ch keys2 &1 s9ce ea* key is equival5t to #e or #f units ( in=mation1 ! effective spe$ ( our f+]s may be ab\t #hjj units ( in=mation a second4 ,,languages ,,( ,,physical ,,objects ,! use ( pebbles 7see ,no4 #ad7 = keep+ track ( num]ical in=mation is %[n 9 ! hi/ory ( ! words conta9+ ! root calc-( ! ^w calculate4 ,! ,lat9 ^w calcis meant p]ta9+ to lime or lime/one1 & ! ,lat9 ^w calculus d]iv$ f x meant fir/ a small piece ( lime/one1 & lat] any small /one1 p>ticul>ly a pebble us$ 9 c\nt+4 ,all ?ree ( ^! mean+s h left desc5dants3 8*alk10 8calcite10 8calcium10 relat+ 9 "o way or ano!r to lime2 9 m$ic9e1 8calculus10 ref]r+ to /ones 9 ! kidneys or else:]e 9 ! body2 & 9 ma!matics1 8calculate10 8calculus10 ref]r+ to computations1 once done ) pebbles4 ,! pebbles1 & ! slab 7= :i* ! anci5t ,greek ^w is abax7 on :i* !y 7 arrang$ & c\nt$1 7 lat] replac$1 = ease 9 h&l+1 by gr\ps ( beads /rung on rods & plac$ 9 a frame 7see ,no4 #ag74 ,^! con/itut$ ! abacus 7see ,supplem5t #b & ! figure !re74 ,?is 0 ! fir/ calculat+ ma*9e4 ,x is /ill us$ all ov] ,asia2 9 fact1 ev5 today m p use ! abacus = acc\nt+ ?an use p5cil & pap]4 ,! skill ) :i* ! abacus c be us$ 0 %[n 9 ,novemb] #aidf 9 a well-publiciz$ conte/ 9 ,japan4 ,kiyo%i ,ma/uzaki1 a cl]k 9 ! ,japanese communications dep>tm5t1 us+ ! abacus1 *all5g$ ,private ,?omas ,wood ( ! ,u4 ,s4 ,army1 us+ a mod]n desk calculat+ ma*9e1 & defeat$ him 9 a spe$ conte/ involv+ additions1 subtractions1 multiplications1 & divisions4 ,! heaps ( small pebbles1 ! not*es 9 /icks1 & ! abacus _h ! advantage ( be+ visible & comp>atively p]man5t4 ,/or+ & read+ 7 relatively easy4 ,!y 7 r compact & easy to manipulate1 c]ta9ly mu* easi] ?an spok5 words4 ,b !y 7 subject to disadvantages also4 ,mov+ correctly f "o arrangem5t to ano!r 0 difficult1 s9ce !re 0 no good way = /or+ int]m$iate /eps s t ! process c\ld be easily v]ifi$4 ,fur!rmore1 ^! devices appli$ to specifi$ numb]s only4 ,also1 !re 0 no natural provision = record+ :at ! sev]al numb]s belong$ to4 ,?is _h to be record$ ) ! help ( ano!r language1 writ+4 ,! language ( physical objects 0 pick$ up f obscurity by ! inv5tion ( motors & ! dem&s ( comm]ce & bus9ess4 ,comm5c+ 9 ! late #ahjj's1 desk calculat+ ma*9es 7see ,no4 #ai7 7 con/ruct$ to meet mass calculation requirem5ts4 ,!y w\ld add1 subtract1 multiply1 & divide specific numb]s ) great accuracy & spe$4 ,b until rec5tly !y /ill 7 adjuncts to ! o!r languages1 = !y provid$ figures "o at a "t = ins]tion 9 ! spaces on ! l$g] pages or calculation %eets :]e figures 7 call$ =4 ,beg9n+ 9 ! #aibj's1 a rem>kable *ange has tak5 place4 ,in/ead ( p]=m+ s+le op]ations1 ma*9es h be5 develop$ to p]=m *a9s ( op]ations ) _m k9ds ( in=mation4 ,"o ( ^! ma*9es is ! dial telephone3 x c select "o ( #g million telephones by successive sort+ accord+ to ! lett]s & digits ( a telephone numb]4 ,ano!r ( ^! ma*9es is a fire-control in/rum5t1 a me*anism = controll+ ! fir+ ( a gun4 ,= example1 9 a mod]n anti-aircraft gun ! me*anism w obs]ve an enemy plane fly+ at sev]al hundr$ miles an h\r1 conv]t ! obs]vations into gun-aim+ directions1 & det]m9e ! aim+ directions fa/ en\gh to %oot d[n ! plane4 ,pun*-c>d ma*9]y1 ma*9es h&l+ in=mation express$ z pun*$ holes 9 c>ds1 enable ! fulfillm5t ( social security legislation1 ! production ( ! c5sus1 & c\ntless op]ations ( banks1 insurance companies1 dep>tm5t /ores1 & factories4 ,&1 f9ally1 9 #aidb ! fir/ me*anical bra9 0 f9i%$ at ,massa*usetts ,in/itute ( ,te*nology4 ,,! ,,crucial ,,devices ,,= ,,me*anical ,,bra9s ,let u consid] ! two mod]n physical devices = h&l+ in=mation :i* make me*anical bra9s possible4 ,^! are relays & electronic tubes 7,nos4 #ba & #bb74 ,! la/ ?ree k9ds ( equipm5t li/$ 9 ! table 7magnetic surfaces1 ,no4 #bc2 delay l9es1 ,no4 #bd2 & electro/atic /orage tubes1 ,no4 #be7 7 n includ$ 9 any me*anical bra9s function+ by ! middle ( #aidh4 ,! discussion ( !m is !re=e put (f to ,*apt] #aj1 :]e we talk ab\t ! future design ( me*anical bra9s4 ,illu/ration3 ,,fig4 #a4 ,relay ,figure #a %[s a simple relay4 ,!re are two electrical circuits "h4 ,"o has two t]m9als--,pickup & ,gr\nd4 ,! o!r has ?ree t]m9als--,common1 ,normally ,op51 & ,normally ,clos$4 ,:5 curr5t fl[s ?r\gh ! coil ( wire ar\nd ! iron1 x makes ! iron a magnet2 ! magnet pulls d[n ! flap ( iron above1 ov]com+ ! =ce ( ! spr+4 ,:5 !re is no curr5t ?r\gh ! coil1 ! iron is n a magnet1 & ! flap is held up by ! spr+4 ,n[ suppose t !re is curr5t 9 ,common4 ,:5 !re is no curr5t 9 ,pickup1 ! curr5t f ,common w fl[ ?r\gh ! upp] contact1 to ! t]m9al m>k$ ,normally ,clos$4 ,:5 !re is curr5t 9 ,pickup1 ! curr5t f ,common w fl[ ?r\gh ! l[] contact1 to ! t]m9al m>k$ ,normally ,op54 ,?us we see t a relay expresses a 8yes0 or a 8no10 a #a or #j1 a b9>y digit1 a unit ( in=mation4 ,a relay co/s #e to #aj4 ,x is r exp5sive = /or+ a s+le unit ( in=mation4 ,! fa/e/ x c be *ang$ f #a to #j1 or vice v]sa1 is ab\t _/ ( a second4 ,illu/ration3 ,,fig4 #b4 ,electronic tube4 ,figure #b %[s a simple electronic tube4 ,x has ?ree p>ts--! ,ca?ode1 ! ,grid1 & ! ,plate4 ,! ,grid actually is a co>se net ( metal wires4 ,electrons c fl[ f ! ,ca?ode to ! ,plate1 provid$ ! voltage on ! ,grid is su* z to p]mit !m to fl[4 ,s we c see t an electronic tube is a v simple on-(f device & expresses a 8yes0 or a 8no10 a #a or #j1 a b9>y digit1 a unit ( in=mation4 ,a simple electronic tube suitable = calculat+ purposes co/s #ej c5ts to a #a1 only ! co/ ( a relay4 ,x c be *ang$ f #a to #j1 or back aga91 9 #a million? ( a second4 ,relays h be5 widely us$ 9 ! me*anical bra9s s f> built1 & electronic tubes are ! ess5ce ( ,eniac4 ,9 ! next *apt]1 we %all see h[ physical equipm5t = h&l+ in=mation c be put toge!r to make a simple me*anical bra94 ,*apt] #c ,a ,,ma*9e ,,t ,,w ,,?9k3 ,,! ,,design ,,( ,a ,,v ,,simple ,,me*anical ,,bra9 ,we %all n[ consid] h[ we c design a v simple ma*9e t w ?9k4 ,let u call x ,simon1 because ( its pr$ecessor1 ,simple ,simon4 ,,simon1 ,,! ,,v ,,simple ,,me*anical ,,bra9 ,by design+ ,simon1 we %all see h[ we c put toge!r physical equipm5t = h&l+ in=mation 9 su* a way z to get a v simple me*anical bra94 ,at e po9t 9 ! design ( ,simon1 we %all make ! simple/ possible *oice t w /ill give u a ma*9e t3 h&les in=mation1 transf]s in=mation automatically f "o "p ( ! ma*9e to ano!r1 & has control ov] ! sequ5ce ( op]ations4 ,simon is s simple & s small1 9 fact1 t x c\ld be built to fill up less space ?an a groc]y-/ore box1 ab\t #d cubic feet4 ,if we "k a little ab\t electrical "w1 we w f9d x r easy to make ,simon4 ,:at d we d fir/ to design ! v simple me*anical bra91 ,simon8 ,,simon',s ,,fle% ,,& ,,n]ves--,,repres5t+ ,,in=mation ,! fir/ ?+ we h to decide ab\t ,simon is h[ in=mation w be repres5t$3 z we put x into ,simon1 z x is mov$ ar\nd inside ( ,simon1 & z x comes out ( ,simon4 ,we ne$ to decide :at physical equipm5t we %all use to make ,simon's fle% & n]ves4 ,s9ce we are tak+ ! simple/ conv5i5t solution to ea* problem1 let u decide to use3 pun*$ pap] tape = putt+ in=mation 91 relays 7see ,*apt] #b7 & wires = /or+ & transf]r+ in=mation1 & lights = putt+ in=mation out4 ,illu/ration3 ,,two-,,hol$ ,,tape ,,read]3 ,simon's left e> t li/5s to numb]s & op]ations4 ,,f\r-,,hol$ ,,tape ,,read]3 ,simon's "r e> t li/5s to in/ructions4 ,,light ,,bulbs3 ,simon's eyes t w9k answ]s4 ,,fig4 #a4 ,simon1 ! v simple me*anical bra94 ,= ! equipm5t inside ,simon1 we c\ld *oose ei!r electronic tubes or relays4 ,we *oose relays1 al?\gh !y are sl[]1 because x is easi] to expla9 circuits us+ relays4 ,we c look at a relay circuit laid out on pap] & tell h[ x works1 j by see+ :e!r or n curr5t w fl[4 ,examples w be giv5 bel[4 ,:5 we look at a circuit us+ electronic tubes laid out on pap]1 we /ill ne$ to "k a good deal 9 ord] to calculate j h[ x w "w4 ,h[ w ,simon p]ceive a numb] or o!r in=mation by means ( pun*$ tape1 or relays1 or lights8 ,) pun*$ pap] tape hav+1 = example1 #b spaces :]e holes may be1 ,simon c be told #d numb]s--#jj1 #ja1 #aj1 #aa4 ,"h ! b9>y digit #a means a hole pun*$2 ! b9>y digit #j means no hole pun*$4 ,) #b relays toge!r 9 a regi/]1 ,simon c rememb] any "o ( ! #d numb]s #jj1 #ja1 #aj1 & #aa4 ,"h ! b9>y digit #a means ! relay pick$ up or en]giz$ or clos$2 #j means ! relay n pick$ up or n en]giz$ or op54 ,) #b lights1 ,simon c give z an answ] any "o ( ! #d numb]s #jj1 #ja1 #aj1 #aa4 ,9 ?is case ! b9>y digit #a means ! light gl[+2 #j means ! light (f4 7,see ,fig4 #a47 ,we c say t ! two lights by :i* ,simon puts out ! answ] are 8 eyes & say t he tells 8 answ] by w9k+4 ,we c say also t ! two me*anisms = read+ pun*$ pap] tape are ,simon's e>s4 ,"o tape1 call$ ! input tape1 takes 9 numb]s or op]ations4 ,! o!r tape takes 9 in/ructions & is call$ ! program tape4 ,,simon',s ,,m5tality--,,possible ,,range ,,( ,,in=mation ,we c say t ,simon has a m5tality ( #d4 ,we mean n age #d b j ! simple fact t ,simon kn[s only #d numb]s & c d only #d op]ations ) !m4 ,b ,simon c keep on do+ ^! op]ations 9 all sorts ( r\t9es z long z ,simon has in/ructions4 ,we decide t ,simon w "k j #d numb]s1 #j1 #a1 #b1 #c1 9 ord] to keep our model me*anical bra9 v simple4 ,!n1 = any regi/]1 we ne$ only #b relays2 = any answ]1 we ne$ only #b lights4 ,any calculat+ ma*9e has a m5tality1 consi/+ ( ! :ole collection ( diff]5t ideas t ! ma*9e c ev] actually express 9 "o way or ano!r4 ,= example1 a #aj-place desk calculat+ ma*9e c h&le numb]s up to #aj decimal digits )\t additional capacity4 ,x _c h&le bigg] numb]s4 ,illu/ration3 ,,fig4 #b4 ,f\r directions4 ,:at are ! #d op]ations ) numb]s :i* ,simon c c>ry out8 ,let u consid] "s simple op]ations t we c p]=m ) j #d numb]s4 ,suppose t !y /ood = #d directions 9 ! ord] ea/1 nor?1 we/1 s\? 7see ,fig4 #b74 ,or suppose t !y /ood = a turn c\nt]clockwise ?r\gh "s "r angles z foll[s3 #j3 ,turn ?r\gh #j1 or no "r angles4 #a3 ,turn ?r\gh #ij1 or #a "r angle4 #b3 ,turn ?r\gh #ahj1 or #b "r angles4 #c3 ,turn ?r\gh #bgj1 or #c "r angles4 ,!n we c\ld h ! op]ations ( addition & negation1 def9$ z foll[s3 ,,addition ,,negation c a b c -a b3 #j #a #b #c ac a ------------------ ---------------- #j #j #a #b #c #j #j #a #a #b #c #j #a #c #b #b #c #j #a #b #b #c #c #j #a #b #c #a ,= example1 ! fir/ table says1 8#a plus #c equals #j40 ,?is means t1 if we turn #a "r angle & !n turn 9 ! same direction #c m "r angles1 we face 9 exactly ! same way z we did at ! />t4 ,?is /atem5t is cle>ly true4 ,= ano!r example1 ! second table says1 8#b is ! negative ( #b40 ,?is means t1 if we turn to ! left #b "r angles1 we face 9 exactly ! same way z if we turn to ! "r #b "r angles1 & ?is /atem5t also is1 ( c\rse1 true4 ,) only ^! two op]ations 9 ,simon1 we %\ld probably f9d him a little too dull to tell u mu*4 ,let u1 !re=e1 put into ,simon two m op]ations4 ,let u *oose two op]ations involv+ bo? numb]s & logic3 9 p>ticul>1 7#a7 f9d+ :i* ( two numb]s is great] & 7#b7 select+4 ,9 ?is way we %all make ,simon a little clev]]4 ,x is easy to tea* ,simon h[ to f9d :i* ( two numb]s is ! great] :5 all ! numb]s t ,simon has to "k are #j1 #a1 #b1 #c4 ,we put all possible cases ( two numb]s a & b into a table3 b3 #j #a #b #c a------------------ #j #a #b #c ,!n we tell ,simon t we %all m>k ) #a ! cases :]e a is great] ?an b & m>k ) #j ! cases :]e a is n great] ?an b3 ,,great] ,,?an b3 #j #a #b #c a------------------ #j #j #j #j #j #a #a #j #j #j #b #a #a #j #j #c #a #a #a #j ,= example1 8#b is great] ?an #c0 is false1 s we put #j 9 ! table on ! #b l9e 9 ! #c column4 ,we see t1 = ! #af possible cases1 a is great] ?an b 9 #f cases & a is n great] ?an b 9 #aj cases4 ,!re is a neat way ( say+ :at we h j said1 us+ ! language ( ma!matical logic 7see ,*apt] #i & ,supplem5t #b74 ,suppose t we consid] ! /atem5t 8a is great] ?an b0 :]e a & b may be any ( ! numb]s #j1 #a1 #b1 #c4 ,we c say t ! tru? value p ( a /atem5t ,p is #a if ! /atem5t is true & t x is #j if ! /atem5t is false3 p #a if ,p is true1 #j if ,p is false ,! tru? value ( a /atem5t ,p is conv5i5tly d5ot$ z ,t7,p7 7see ,supplem5t #b73 p ,t7,p7 ,n[ we c say t ! table = ! op]ation great] ?an %[s ! tru? value ( ! /atem5t 8a is great] ?an b03 p ,t7a b7 ,let u turn n[ to ! op]ation selection4 ,by select+ we mean *oos+ "o numb] a if "s /atem5t ,p is true & *oos+ ano!r numb] b if t /atem5t is n true4 ,z be=e1 let p be ! tru? value ( t /atem5t ,p1 & let x be equal to #a if ,p is true & to #j if ,p is false4 ,!n ! op]ation ( selection is fully express$ 9 ! foll[+ table & logical =mula 7see ,supplem5t #b73 ,,selection c ap b7#a - p7 p3 #j #j #j #j #a #a #a #a b3 #j #a #b #c #j #a #b #c a------------------------------------ #j #j #a #b #c #j #j #j #j #a #j #a #b #c #a #a #a #a #b #j #a #b #c #b #b #b #b #c #j #a #b #c #c #c #c #c ,= example1 suppose t a is #b & b is #c & ! /atem5t ,p is ! /atem5t 8#b is great] ?an #j40 ,s9ce ?is /atem5t is true1 p is #a1 & ap b7#a - p7 #b7a7 #c7j7 #b ,?is result is ! same z select+ #b if #b is great] ?an #j & select+ #c if #b is n great] ?an #j4 ,?us we h f\r op]ations = ,simon t d n ov]/ra9 8 m5tality2 t is1 !y d n require him to g to any numb]s o!r ?an #j1 #a1 #b1 & #c4 ,^! f\r op]ations are3 addition1 negation1 great] ?an1 selection4 ,we label ^! op]ations also ) ! numb]s #jj to #aa z foll[s3 addition1 #jj2 negation1 #ja2 great] ?an1 #aj2 selection1 #aa4 ,,simon',s ,,memory--,,/or+ ,,in=mation ,! memory ( a me*anical bra9 consi/s ( physical equipm5t 9 :i* in=mation c be /or$4 ,usually1 ea* section ( ! physical equipm5t :i* c /ore "o piece ( in=mation is call$ a regi/]4 ,ea* regi/] 9 ,simon w consi/ ( #b relays4 ,ea* regi/] w hold any ( #jj1 #ja1 #aj1 #aa4 ,! in=mation /or$ 9 a regi/] #jj1 #ja1 #aj1 #aa may express a numb] or may express an op]ation4 ,illu/ration3 ,s#a-b ,relay en]giz$ ,illu/ration3 ,s#a-a ,relay n en]giz$ ,,fig4 #c4 ,regi/] ,s#a /or+ #aj4 ,h[ _m regi/]s w we ne$ to put into ,simon to /ore in=mation8 ,we %all ne$ "o regi/] to read ! input tape & to /ore ! numb] or op]ation record$ on x4 ,we %all call ?is regi/] ! input regi/] ,i4 ,we %all ne$ ano!r regi/] to /ore ! numb] or op]ation t ,simon says is ! answ] & to give x to ! output lights4 ,we %all call ?is regi/] ! output regi/] ,o4 ,we %all ne$ #e regi/]s = ! "p ( ,simon :i* does ! comput+1 :i* we %all call ! comput]3 we %all ne$ #c to /ore numb]s put into ! comput] 7,c#a1 ,c#b1 ,c#c71 #a to /ore ! op]ation gov]n+ ! comput] 7,c#d71 & #a to /ore ! result 7,c#e74 ,suppose t we decide to h #h regi/]s = /or+ in=mation1 s z to provide "s flexibility = do+ problems4 ,we %all call ^! regi/]s /orage regi/]s & "n !m ,s#a1 ,s#b1 ,s#c1 ,s#h4 ,!n ,simon w h #ae regi/]s3 a memory t at "o "t c hold #ae pieces ( in=mation4 ,h[ w "o ( ^! regi/]s hold in=mation8 ,= example1 h[ w regi/] ,s#a hold ! numb] #b 7see ,fig4 #c78 ,! numb] #b 9 ma*9e language is #aj4 ,regi/] ,s#a consi/s ( two relays1 ,s#a-b & ,s#a-a4 #aj /or$ 9 regi/] ,s#a means t relay ,s#a-b w be en]giz$ & t relay ,s#a-a w n be en]giz$4 ,,! ,,control ,,( ,,simon ,s f> we h said no?+ ab\t ! control ( ,simon4 ,is he docile8 ,is he /ubborn8 ,we "k :at 8 capacity is1 b we d n "k h[ to tell him to d any?+4 ,h[ d we connect our desires to 8 behavior8 ,h[ d we tell him a problem8 ,h[ d we get him to solve x & tell u ! answ]8 ,h[ d we arrange control ov] ! sequ5ce ( 8 op]ations8 ,= example1 h[ d we get ,simon to add #a & #b & tell u ! answ] #c8 ,on ! outside ( ,simon1 we h said1 !re are two e>s3 little me*anisms = read+ pun*$ pap] tape4 ,also !re are two eyes t c w9k3 light bulbs t by %9+ or n %9+ c put out in=mation 7see ,fig4 #a74 ,"o ( ! e>s--let u call x ! left e>--takes 9 in=mation ab\t a p>ticul> problem3 numb]s & op]ations4 ,"h ! problem tape or input tape is li/5$ to4 ,ea* l9e on ! input tape conta9s space = #b pun*$ holes4 ,s1 ! in=mation on ! input tape may be #jj1 #ja1 #aj1 or #aa--;ei!r a numb] or an op]ation4 ,! o!r e>--let u call x ! "r e>--takes 9 in=mation ab\t ! sequ5ce ( op]ations1 ! program or r\t9e to be foll[$4 ,"h ! program tape or r\t9e tape or control tape is li/5$ to4 ,ea* l9e on ! program tape conta9s space = #d pun*$ holes4 ,we tell ,simon by in/ructions on ! program tape :at he is to d ) ! in=mation t we give him on ! input tape4 ,! in=mation on ! program tape1 !re=e1 may be #jjjj1 #jjja1 #jjaj1 1 #aaaa1 or any numb] f #j to #ae express$ 9 b9>y notation 7see ,supplem5t #b74 ,h[ is ?is accompli%$8 ,9 ! fir/ place1 ,simon is a ma*9e1 & he behaves dur+ "t4 ,he does diff]5t ?+s f "t to "t4 ,8 behavior is organiz$ 9 cycles4 ,he repeats a cycle ( behavior e second or s4 ,9 ea* cycle ( ,simon1 he li/5s to or reads ! input tape once & he li/5s to or reads ! program tape twice4 ,e complete in/ruction t goes on ! program tape tells ,simon a regi/] f :i* in=mation is to be s5t & a regi/] 9 :i* in=mation is to be receiv$4 ,! fir/ "t t he reads ! program tape he gets ! "n ( ! regi/] t is to receive c]ta9 in=mation1 ! receiv+ regi/]4 ,! second "t he reads ! program tape he gets ! "n ( ! regi/] f :i* in=mation is to be s5t1 ! s5d+ regi/]4 ,he f9i%es ea* cycle ( behavior by transf]r+ in=mation f ! s5d+ regi/] to ! receiv+ regi/]4 ,= example1 suppose t we want to get an answ] out ( ,simon's comput] into ,simon's output lights4 ,we put d[n ! in/ruction ,s5d in=mation f ,c#e into ,o or1 m briefly1 ,c#e ,o ,b he does n und]/& ?is language4 ,we mu/ translate into ma*9e language1 9 ?is case pun*$ holes 9 ! program tape4 ,naturally1 ! pun*$ holes 9 ! program tape mu/ be able to specify any s5d+ regi/] & any receiv+ regi/]4 ,!re are #ae regi/]s1 & s we give !m pun*$ hole codes z foll[s3 ,,regi/] ,,code ,,regi/] ,,code ,i #jjja ,c#a #ajaj ,s#a #jjaj ,c#b #ajaa ,s#b #jjaa ,c#c #aajj ,s#c #jajj ,c#d #aaja ,s#d #jaja ,c#e #aaaj ,s#e #jaaj ,o #aaaa ,s#f #jaaa ,s#g #ajjj ,s#h #ajja ,to translate ! direction ( transf] ( in=mation1 :i* we %[$ z an arr[1 we put on ! program tape ! code = ! receiv+ regi/] fir/--9 ?is case1 output1 ,o1 #aaaa--;& ! code = ! s5d+ regi/] second--9 ?is case1 ,c#e1 #aaaj4 ,! in/ruction becomes #aaaa1 #aaaj4 ,! fir/ "t 9 any cycle t ,simon li/5s ) 8 "r e>1 he kn[s t :at he he>s is ! "n ( ! receiv+ regi/]2 & ! second "t t he li/5s1 he kn[s t :at he he>s is ! "n ( ! s5d+ regi/]4 ,"o reason = ?is sequ5ce is t any p]son or ma*9e has to be prep>$ be=eh& to absorb or take 9 any in=mation4 ,n[ h[ d we tell ,simon to add #a & #b8 ,on ! input tape1 we put3 ,add #jj #a #ja #b #aj ,on ! program tape1 we ne$ to put3 ,i ,c#d ,i ,c#a ,i ,c#b ,c#e ,o :i* becomes3 #aaja1 #jjja2 #ajaj1 #jjja2 #ajaa1 #jjja2 #aaaa1 #aaaj ,,! ,,usefulness ,,( ,,simon ,?us we c see t ,simon c d su* a problem z3 ,add #j & #c4 ,add #b & ! negative ( #a4 ,f9d :i* result is great]4 ,select #c if ?is result equals #b2 o!rwise select #b4 ,to "w out ! cod+ = ?is & l problems w\ld be a good ex]cise4 ,simon1 9 fact1 is a r clev] little me*anical bra91 ev5 if he has only a m5tality ( #d4 ,x may seem t a simple model ( a me*anical bra9 l ,simon is ( no great practical use4 ,on ! contr>y1 ,simon has ! same use 9 in/ruction z a set ( simple *emical exp]im5ts has3 to /imulate ?9k+ & und]/&+ & to produce tra9+ & skill4 ,a tra9+ c\rse on me*anical bra9s c\ld v well include ! con/ruction ( a simple model me*anical bra9 z an ex]cise4 ,9 ?is book1 ! prop]ties ( ,simon may be a good introduction to ! v>i\s types ( m complicat$ me*anical bra9s describ$ 9 lat] *apt]s4 ,! re/ ( ?is *apt] is devot$ to su* que/ions z3 ,h[ d transf]s ( in=mation actually take place 9 ,simon8 ,h[ does ! comput] 9 ,simon "w s t calculation actually occurs8 ,h[ c\ld ,simon actually be con/ruct$8 ,:at foll[s %\ld be skipp$ unless y are int]e/$ 9 ^! que/ions & ! burd5some details ne$$ = answ]+ !m4 ,,simon',s ,,?9k+--,,transf]r+ ,,in=mation ,! fir/ basic ?9k+ op]ation = any me*anical bra9 is transf]r+ in=mation automatically4 ,let u see h[ ?is is done 9 ,simon4 ,illu/ration3 ,,fig4 #d4 ,s*eme ( ,simon4 ,let u fir/ take a look at ! s*eme ( ,simon z a me*anical bra9 7see ,fig4 #d74 ,we h #a input1 #h /orage1 #e comput]1 & #a output regi/]s1 :i* are connect$ by means ( transf] wires or a transf] l9e along :i* numb]s or op]ations c travel z electrical impulses4 ,?is transf] l9e is (t5 call$ ! bus1 p]haps because x is always busy c>ry+ some?+4 ,9 ,simon ! bus w consi/ ( #b wires1 "o = c>ry+ ! "r-h& digit & "o = c>ry+ ! left-h& digit ( any numb] #jj1 #ja1 #aj1 #aa4 ,simon also has a numb] ( neat little devices t w d ! foll[+3 ,:5 any numb] goes into a regi/]1 ! coils ( ! relays ( ! regi/] w be connect$ ) ! bus4 ,:5 any numb] goes out ( a regi/]1 ! contacts ( ! relays ( ! regi/] w be connect$ ) ! bus4 ,= example1 suppose t 9 regi/] ,c#e ! numb] #b is /or$4 ,9 ma*9e language ?is is #aj4 ,t means ! left-h& relay 7,c#e-b7 is en]giz$ & ! "r-h& relay 7,c#e-a7 is n en]giz$4 ,suppose t we want to transf] ?is numb] #b into ! output regi/] ,o1 :i* has be5 cle>$4 ,:at d we d8 ,let u take a look at a circuit t w transf] ! numb] 7see ,fig4 #e74 ,fir/ we see two relays 9 ?is circuit4 ,!y belong to ! ,c#e regi/]4 ,! ,c#e-b relay is en]giz$ s9ce x holds #a2 curr5t is fl[+ ?r\gh its coil1 ! iron core becomes a magnet1 & ! contact above x is pull$ d[n4 ,! ,c#e-a relay is n en]giz$ s9ce x holds #j2 its contact is n pull$ d[n4 ,! next ?+ we see is two rectifi]s4 ,! sign = ^! is a triangle4 ,^! are "s mod]n electrical equipm5t t all[ electrical curr5t to fl[ 9 only "o direction4 ,9 ! diagram1 ! direction is %[n by ! po9t+ ( ! triangle along ! wire4 ,rectifi]s are ne$$ to prev5t undesir$ circuits4 ,next1 we see ! bus1 consi/+ ( two wires4 ,"o c>ries ! impulses = left-h& or #b relays1 & ! o!r c>ries impulses = ! "r-h& or #a relays4 ,next1 we see two relays1 call$ ! entrance relays = ! ,o regi/]4 ,curr5t f ,s\rce #a may fl[ to ^! relays1 en]gize !m1 & close _! contacts4 ,:5 ! fir/ l9e ( ! program tape is read1 specify+ ! receiv+ regi/]1 ! code #aaaa causes ,s\rce #a to be en]giz$4 ,?is fact is %[n s*ematically by ! arr[ runn+ f ! program tape code #aaaa to ,s\rce #a4 ,f9ally1 we see ! coils ( ! two relays = ! ,output or ,o regi/]4 ,we ?us see t we h a circuit f ! contacts ( ! ,c#e regi/] ?r\gh ! bus to ! coils ( ! ,o regi/]4 ,illu/ration3 ,,fig4 #e4 ,transf] circuit4 ,we are n[ ready to transf] in=mation :5 ! second l9e ( ! program tape is read4 ,?is l9e holds #aaaj & designates ,c#e z ! s5d+ regi/] & causes ,s\rce #b to be en]giz$4 ,?is fact is %[n s*ematically by ! arr[ runn+ f ! second l9e ( ! program tape to ,s\rce #b4 ,:5 ! second l9e is read1 curr5t fl[s3 #a4 ,f ,s\rce #b4 #b4 ,?r\gh ! contacts ( ! ,c#e regi/] if clos$4 #c4 ,?r\gh ! rectifi]s4 #d4 ,?r\gh ! bus4 #e4 ,?r\gh ! entrance relay contacts ( ! ,o regi/]4 #f4 ,?r\gh ! coils ( ! ,o regi/] relays1 en]giz+ su* ( !m z mat* ) ! ,c#e clos$ contacts2 & f9ally #g4 ,into ! gr\nd4 ,?us relay ,o-#b is en]giz$2 x receives curr5t because contact ,c#e-b is clos$4 ,& relay ,o-#a is n en]giz$2 x receives no curr5t s9ce contact ,c#e-a is op54 ,s we h actually transf]r$ in=mation f ! ,c#e regi/] to ! ,o regi/]4 ,! same process 9 pr9ciple applies to all transf]s3 ,! patt]n ( electrical impulses1 =m$ by ! position+ ( "o regi/]1 is produc$ 9 ! position+ ( ano!r regi/]4 ,,simon',s ,,comput+ ,,& ,,reason+ ,n[ s f> ! comput+ regi/]s 9 ,simon are a my/]y4 ,we h said t ,c#a1 ,c#b1 & ,c#c take 9 numb]s #jj1 #ja1 #aj1 #aa1 t ,c#d takes 9 an op]ation #jj1 #ja1 #aj1 #aa1 & t ,c#e holds ! result4 ,:at process does ,simon use s t he has ! correct result 9 regi/] ,c#e8 ,let u take ! simple/ comput+ op]ation fir/ & see :at sort ( a circuit us+ relays w give u ! result4 ,! simple/ comput+ op]ation is negation4 ,9 negation1 a numb] #jj1 #ja1 #aj1 #aa goes into ! ,c#a regi/]1 & ! op]ation #ja mean+ negation goes into ! ,c#d regi/]1 & ! correct result mu/ be 9 ! ,c#e regi/]4 ,s1 fir/1 we note ! fact t ! ,c#d-b relay mu/ n be en]giz$1 s9ce x conta9s #j1 & t ! ,c#d-a relay mu/ be en]giz$1 s9ce x conta9s #a4 ,n[ ! table = negation1 ) c -a1 is3 a c ---------------- #j #j #a #c #b #b #c #a ,negation 9 ma*9e language w be3 a c ---------------- #jj #jj #ja #aa #aj #aj #aa #ja ,n[ if a is 9 ! ,c#a regi/] & if c is 9 ! ,c#e regi/]1 !n negation w be3 ,c#a ,c#e -------------------- #jj #jj #ja #aa #aj #aj #aa #ja ,b ea* ( ^! regi/]s ,c#a1 ,c#e w be made up ( two relays1 ! left-h& or #b relay & ! "r-h& or #a relay4 ,s1 9 t]ms ( ^! relays1 negation w be3 ,c#a-b ,c#a-a ,c#e-b ,c#e-a ---------------------------------------- ---------------- #j #j #j #j #j #a #a #a #a #j #a #j #a #a #j #a ,n[1 on exam9+ ! table1 we see t ! ,c#e-a relay is en]giz$ if & only if ! ,c#a-a relay is en]giz$4 ,s1 9 ord] to en]gize ! ,c#e-a relay1 all we h to d is transf] ! in=mation f ,c#a-a to ,c#e-a4 ,?is we c d by ! circuit %[n 9 ,fig4 #f4 7,9 ?is & lat] diagrams1 we h tak5 "o m /ep 9 /reaml9+ ! draw+ ( relay contacts3 ! contacts are drawn1 b ! coils t en]gize !m are repres5t$ only by _! names47 ,illu/ration3 ,,fig4 #f4 ,negation--"r-h& digit4 ,illu/ration3 ,,fig4 #g4 ,negation--left-h& digit4 ,tak+ ano!r look at ! table1 we see also t ! ,c#e-b relay mu/ be en]giz$ if & only if3 ,c#a-b ,,& ,c#a-a ,,holds3 ,,holds3 #j #a #a #j ,a circuit t w d ?is is ! "o %[n 9 ,fig4 #g4 ,9 ,fig4 #h is a circuit t w d all ! desir$ ?+s toge!r3 give ! "r in=mation to ! ,c#e relay coils if & only if ! ,c#d relays hold #ja4 ,illu/ration3 ,,fig4 #h4 ,negation circuit4 ,let u *eck ?is circuit4 ,fir/1 if !re is any op]ation o!r ?an #ja /or$ 9 ! ,c#d relays1 !n no curr5t w be able to get ?r\gh ! ,c#d contacts %[n & into ! ,c#e relay coils1 & ! result is blank4 ,second1 if we h ! op]ation #ja /or$ 9 ! ,c#d relays1 !n ! ,c#d-b contacts w n be en]giz$--a condition :i* passes curr5t--& ! ,c#d-a contacts w be en]giz$--ano!r condition :i* passes curr5t--&3 ,,if ,,! ,,numb] ,,& ,,! ,c#e ,,relays ,,9 ,c#a ,,is3 ,,!n ,c#a-a3 ,,& ,c#a-b3 ,,en]giz$ ,,are3 #j does n close does n close nei!r #a closes does n close ,c#e-b1 ,c#e-a #b does n close closes ,c#e-b only #c closes closes ,c#e-a only ,?us we h %[n t ?is circuit is correct4 ,we see t ?is circuit uses m ?an "o set ( contacts = sev]al relays 7,c#a-b1 ,c#d-a1 ,c#d-b72 relays are regul>ly made ) #d1 #f1 or #ab sets ( contacts arrang$ side by side1 all controll$ by ! same pickup coil4 ,^! are call$ #d-1 #f-1 or #ab-pole relays4 ,illu/ration3 ,,fig4 #i4 ,addition circuit4 ,illu/ration3 ,,fig4 #aj4 ,great]-?an circuit4 ,circuits = addition1 great] ?an1 & selection c also be det]m9$ r easily 7see ,figs4 #i1 #aj1 #aa74 7,note3 ,by means ( ! algebra ( logic1 ref]r$ to 9 ,*apt] #i & ,supplem5t #b1 ! conditions = _m relay circuits1 z well z ! circuit itself1 may be express$ algebraically1 & ! two expressions may be *eck$ by a ma!matical process47 ,= example1 let u *eck t ! addition circuit 9 ,fig4 #i w enable u to add #a & #b & obta9 #c4 ,we take a color$ p5cil & draw clos$ ! contacts = ,c#a-a 7s9ce ,c#a holds #ja7 & = ,c#b-b 7s9ce ,c#b holds #aj74 ,!n1 :5 we trace ?r\gh ! circuit1 rememb]+ t addition is /or$ z #jj 9 ! ,c#d relays1 we f9d t bo? ! ,c#e relays are en]giz$4 ,h5ce ,c#e holds #aa1 :i* is #c4 ,?us ,simon c add #a & #b & make #c6 ,illu/ration3 ,,fig4 #aa4 ,selection ,circuit4 ,,putt+ ,,simon ,,toge!r ,9 ord] to put ,simon toge!r & make him "w1 n v mu* is ne$$4 ,on ! outside ( ,simon we %all ne$ two small me*anisms = read+ pun*$ pap] tape4 ,inside ,simon1 !re w be ab\t #ej relays & p]haps #ajj feet ( wire = connect+ !m4 ,9 addition to ! #ae regi/]s 7,i1 ,s#a to ,s#h1 ,c#a to ,c#e1 & ,o71 we %all ne$ a regi/] ( #d relays1 :i* we %all call ! program regi/]4 ,?is regi/] w /ore ! successive in/ructions read (f ! program tape4 ,we c call ! #d relays ( ?is regi/] ,p#h1 ,p#d1 ,p#b1 ,p#a4 ,= example1 if ! ,p#h & ,p#b relays are en]giz$1 ! regi/] holds #ajaj1 & ?is is ! program in/ruction t calls = ! #h? plus #bnd1 or #aj?1 regi/]1 :i* is ,c#a4 ,= connect+ receiv+ regi/]s to ! bus1 we %all ne$ a relay ) #b poles1 "o = ! #b-l9e & "o = ! #a-l9e1 = ea* regi/] t c receive a numb] f ! bus4 ,= example1 = ent]+ ! output regi/]1 we actually ne$ only "o #b-pole relay in/ead ( ! two #a-pole relays drawn = simplicity 9 ,fig4 #e4 ,!re w be #ac #b-pole relays = ?is purpose1 s9ce only #ac regi/]s receive numb]s f ! bus2 regi/]s ,i & ,c#e d n receive numb]s f ! bus4 ,we call ^! #ac relays ! entrance relays or ,e relays1 s9ce ,e is ! initial lett] ( ! ^w entrance4 ,illu/ration3 ,,fig4 #ab4 ,select-,receiv+-,regi/] circuit4 ,! circuit = select+ & en]giz+ ! ,e relays is %[n 9 ,fig4 #ab4 ,we call ?is circuit ! ,select-,receiv+-,regi/] circuit4 ,= example1 suppose t ! ,p#h & ,p#b relays are en]giz$4 ,!n ?is circuit en]gizes ! ,e#aj relay4 ,! ,e#aj relay closes ! contacts betwe5 ! ,c#a relay coils & ! bus2 & s x connects ! ,c#a regi/] to receive ! next numb] t is s5t into ! bus4 ,?is k9d ( circuit expresses a classification & is sometimes call$ a pyramid circuit s9ce x spreads out l a pyramid4 ,a simil> pyramid circuit is us$ to select ! s5d+ regi/]4 ,we %all ne$ a relay = mov+ ! input tape a /ep at a "t4 ,we %all call ?is relay ! ,,mi relay1 = mov+ input tape4 ,we also ne$ a relay = mov+ ! program tape a /ep at a "t4 ,we %all call ?is relay ! ,,mp relay = mov+ program tape4 ,"h !n is approximately ! total numb] ( relays requir$3 ,,relays ,,"n ,,numb] ,i1 ,s1 ,c1 ,o ,input1 ,/orage1 ,comput]1 ,output #cj ,p ,program #d ,e ,entrance #ac ,,mi ,move ,input ,tape #a ,,mp ,move ,program ,tape #a -------- ,total #di ,a few m relays may be ne$$ to provide m contacts or poles4 ,= example1 a s+le ,p#a relay w probably n h en\gh poles to meet all ! ne$ = its contacts4 ,illu/ration3 ,,fig4 #ac4 ,lat* relay4 ,ea* cycle ( ! ma*9e w be divid$ into #e equal "t int]vals or times #a to #e4 ,! tim+ ( ! ma*9e w be ab\t z foll[s3 ,,"t ,,action #a ,move program tape4 ,move input tape if read out ( 9 la/ cycle4 #b ,read program tape1 det]m9+ ! receiv+ regi/]4 ,read ?r\gh ! comput+ circuit sett+ up ! ,c#e regi/]4 #c ,move program tape4 ,en]gize ! ,e relay belong+ to ! receiv+ regi/]4 #d ,read program tape aga91 det]m9+ ! s5d+ regi/]4 #e ,transf] in=mation by read+ ?r\gh ! ,select-,s5d+-,regi/] circuit & ! ,select-,receiv+-,regi/] circuit4 ,9 ord] t in=mation may rema9 9 /orage until want$1 regi/] relays %\ld hold _! in=mation until j be=e ! next in=mation is receiv$4 ,?is c be accompli%$ by keep+ curr5t 9 _! coils or 9 o!r ways4 ,!re is a type ( relay call$ a lat* relay1 :i* is made ) two coils & a lat*4 ,?is type ( relay has ! prop]ty ( /ay+ or lat*+ 9 ei!r position until ! opposite coil is impuls$ 7see ,fig4 #ac74 ,?is type ( relay w\ld be especially good = ! regi/]s ( ,simon4 ,if any read] sets to "w to con/ruct ,simon1 & if que/ions arise1 ! au?or w be glad to try to answ] !m4 ,*apt] #d ,,c\nt+ ,,holes3 ,,pun*-,,c>d ,,calculat+ ,,ma*9es ,:5 we ?9k ( c\nt+1 we usually ?9k ( say+ s(tly to ourselves 8"o1 two1 ?ree1 f\r1 40 ,?is is a good way to f9d ! total ( a small gr\p ( objects4 ,b :5 we h a l>ge gr\p ( objects or a great _m gr\ps ( objects to be c\nt$1 a mu* fa/] way ( c\nt+ is ne$$4 ,a v fa/ way ( sort+ & c\nt+ is pun*-c>d calculat+ ma*9]y4 ,?is is ma*9]y :i* h&les in=mation express$ z holes 9 c>ds4 ,pun*-c>d ma*9es c3 ,sort1 c\nt1 file1 select1 & copy in=mation1 ,make comp>isons1 & *oose accord+ to in/ructions1 ,add1 subtract1 multiply1 & divide1 ,li/ in=mation1 & pr9t totals4 ,= example1 9 a life insurance company1 mu* r\t9e h&l+ ( in=mation ab\t insurance policies is necess>y3 ,writ+ in=mation on newly issu$ policies4 ,sett+ up policy-hi/ory c>ds4 ,mak+ out notices ( premiums due4 ,mak+ regi/]s ( policies 9 =ce1 laps$1 di$1 etc41 = purposes ( valuation z requir$ by law or good managem5t4 ,calculat+ & tabulat+ premium rates1 divid5d rates1 res]ve factors1 etc4 ,comput+ & tabulat+ expect$ & actual dea? rates2 & mu* m4 ,all ^! op]ations c be done almo/ automatically by pun*-c>d ma*9es4 ,,orig9 ,,& ,,developm5t ,:5 a c5sus ( ! p ( a c\ntry is tak51 a great quantity ( sort+ & c\nt+ is ne$$3 by village1 c\nty1 city1 & /ate2 by sex2 by age2 by occupation2 etc4 ,9 #ahhf1 ! c5sus ( ! p ( ! ,unit$ ,/ates :i* _h be5 tak5 9 #ahhj 0 /ill be+ sort$ & c\nt$4 ,among ! m5 !n /udy+ c5sus problems 0 a /ati/ician & inv5tor1 ,h]man ,holl]i?4 ,he saw t exi/+ me?ods 7 s sl[ t ! next c5sus 7#ahij7 w\ld n be f9i%$ be=e ! foll[+ c5sus 7#aijj7 w\ld h to be begun4 ,he knew t c>ds ) patt]ns ( holes _h be5 us$ 9 weav+ patt]ns 9 clo?4 ,he realiz$ t ! pres5ce or abs5ce ( a prop]ty1 = example employ$ or unemploy$1 c\ld be repres5t$ by ! pres5ce or abs5ce ( a hole 9 a piece ( pap]4 ,an electrical device c\ld detect ! hole1 he believ$1 s9ce x w\ld all[ curr5t to fl[ ?r\gh1 :]eas ! abs5ce ( ! hole w\ld /op ! curr5t4 ,he exp]im5t$ ) sort+ & c\nt+1 us+ pun*$ holes 9 c>ds1 & ) electrical devices to detect ! holes & c\nt !m4 ,a def9ite mean+ 0 giv5 to ea* place 9 ! c>d :]e a hole might be pun*$4 ,!n electrical devices h&l$ ! p>ticul> in=mation t ! pun*es repres5t$4 ,^! devices ei!r c\nt$ or add$1 s+ly or 9 v>i\s comb9ations1 z might be desir$4 ,m ?an #ej ye>s ( developm5t ( pun*-c>d calculat+ ma*9]y h s9ce !n tak5 place4 ,sev]al l>ge companies h made quantities ( pun*-c>d ma*9es4 ,a great degree ( developm5t has tak5 place 9 ! pun*-c>d ma*9es ( ,int]national ,bus9ess ,ma*9es ,corporation 7,,ibm71 & = ?is reason ^! ma*9es w be ! ones describ$ 9 ?is *apt]4 ,:at is said "h1 h[ev]1 may also 9 _m ways apply to pun*-c>d ma*9es made by o!r manufactur]s--,rem+ton-,r&1 ,p[]s1 ,control ,in/rum5t1 etc4 ,,g5]al ,,pr9ciples ,to use pun*-c>d ma*9es1 we fir/ conv]t ! orig9al in=mation into patt]ns ( holes 9 c>ds4 ,!n we fe$ ! c>ds into ! ma*9es4 ,electrical impulses read ! patt]n ( holes & conv]t !m into a patt]n ( tim$ electrical curr5ts4 ,actually1 ! read+ ( a hole 9 a column ( a pun* c>d is done by a bru% ( sev]al /r&s ( copp] wire press$ aga9/ a metal roll] 7,fig4 #a74 ,! ma*9e fe$s ! c>d 7! bottom edge fir/1 :]e ! #i's are pr9t$7 ) v c>eful tim+ ov] ! roll]2 &1 :5 ! pun*$ hole is betwe5 ! bru% & ! roll]1 an electrical circuit belong+ to t column ( ! c>d is complet$4 ,! ma*9e responds accord+ to its g5]al design & its wir+ = ! p>ticul> problem3 x pun*es new c>ds1 or x pr9ts new m>ks1 or x puts in=mation into new /orage places4 ,cl]ks1 h[ev]1 move ! c>ds f "o ma*9e to ano!r4 ,!y wait on ! ma*9es1 keep ! c>d fe$s full1 & empty ! c>d hopp]s z !y fill up4 ,a human error ( putt+ ! wrong block ( c>ds into a ma*9e may f "t to "t cause a little tr\ble1 especially 9 sort+4 ,actually1 9 a ye>1 billions ( pun* c>ds are h&l$ precisely4 ,illu/ration3 ,,fig4 #a4 ,read+ ( pun* c>ds4 ,! pun* c>d is a ma/]piece ( eng9e]+ & /&>dization4 ,its exact ?ickness mat*es ! knife-blade edges t fe$ ! c>ds into slots 9 ! ma*9es1 & mat*es ! *annels :]eby ^! c>ds travel ?r\gh ! ma*9es4 ,! /&>d c>d is #g in*es long & #c in*es wide1 & x has a /&>d ?ickness ( #j4jjfe in* & o!r /&>d prop]ties ) respect to /iffness1 f9i%1 etc4 ,illu/ration3 ,,fig4 #b4 ,s*eme ( /&>d pun* c>d4 7,note3 ,positions #aa & #ab are n usually m>k$ by pr9t$ numb]s or lett]s47 ,! /&>d ,,ibm pun* c>d ( today has #hj columns & #ab positions = pun*+ 9 ea* column 7,fig4 #b74 ,a s+le pun*$ hole 9 ea* ( ! positions kn[n z #j to #i /&s = ea* ( ! digits #j to #i respectively4 ,! rema9+ #b s+le pun* positions available 9 any column are usually call$ ! #aa position & #ab position 7?\gh sometimes call$ ! num]ical ,x position & ,y position74 ,^! two positions d n behave ari?metically z #aa & #ab4 ,actually1 9 ! space betwe5 "o c>d & ! next c>d z !y are f$ ?r\gh ! ma*9es1 m positions occur4 ,= example1 !re may be #d m3 a #aj position prec$+ ! #i1 & a #ac1 a #ad1 & a #ae position foll[+ ! #ab4 ,! #af positions 9 total correspond to a full turn1 #cfj1 ( ! roll] "u ! bru%1 & to a complete cycle 9 ! ma*9e2 & a s+le position corresponds to _/ ( #cfj1 or #bb4 ,9 "s ma*9es1 ! total numb] ( positions may be #bj4 ,a pair ( pun*es /&s = ea* ( ! lett]s ( ! alphabet1 accord+ to ! s*eme %[n4 ,a #ab-a ,j #aa-a ,unus$ #j-a ,b #ab-b ,k #aa-b ,s #j-b ,c #ab-c ,l #aa-c ,t #j-c ,d #ab-d ,m #aa-d ,u #j-d ,e #ab-e ,n #aa-e ,v #j-e ,f #ab-f ,o #aa-f ,w #j-f ,g #ab-g ,p #aa-g ,x #j-g ,h #ab-h ,q #aa-h ,y #j-h ,i #ab-i ,r #aa-i ,z #j-i ,= example1 ! ^w ,,mason is %[n pun*$ 9 ,fig4 #c4 ,illu/ration3 ,,fig4 #c4 ,alphabetic pun*+4 ,illu/ration3 ,,fig4 #d4 ,s+le-panel plugbo>d4 ,to increase ! v]satility ( ! ma*9es & provide !m ) in/ructions1 _m ( !m h plugbo>ds 7,fig4 #d74 ,^! are /&>d int]*angeable bo>ds fill$ ) prongs on "o side & holes or t]m9als call$ hubs on ! o!r side4 ,! side ) ! prongs connects to ! ends ( electrical circuits 9 ! pun*-c>d ma*9e1 :i* are br\ght toge!r 9 "o place = ! purpose4 ,on ! o!r side ( ! bo>d1 us+ plugwires1 we c connect ! hubs to ea* o!r 9 diff]5t ways to produce diff]5t results4 ,! s+le-panel plugbo>d is #aj in*es long & #e in*es wide4 ,x conta9s #ffj hubs 9 front & #ffj correspond+ prongs 9 ! back4 ,a d\ble-panel plugbo>d or a triple-panel plugbo>d applies to "s ma*9es4 ,9 less "t ?an x takes to describe x1 we c take "o wir$-up plugbo>d out ( a ma*9e & put 9 a new wir$-up plugbo>d & ?us *ange completely ! in/ructions "u :i* ! ma*9e op]ates4 ,_m ( ! ma*9es h a numb] ( diff]5t swit*es t we mu/ also *ange1 :5 go+ f "o k9d ( problem to ano!r4 ,! numb]s t are /or$ or sort$ 9 pun*-c>d ma*9es may be ( any size up to #hj digits1 "o 9 ea* column ( ! pun* c>d4 ,9 do+ ari?metic 7add+1 subtract+1 multiply+1 & divid+71 h[ev]1 ! l>ge/ numb] ( digits is usually #aj4 ,beyond #aj digits1 we c "w out tricks 9 _m cases4 ,,types ,,( ,,pun*-,,c>d ,,ma*9es ,! *ief ,,ibm pun*-c>d ma*9es are3 ! key pun*1 ! v]ifi]1 ! sort]1 ! int]pret]1 ! reproduc]1 ! collator1 ! multiply+ pun*1 ! calculat+ pun*1 & ! tabulator4 ,( ^! #i ma*9es1 ! la/ #f h plugbo>ds & c d _m diff]5t op]ations z a result4 ,!re is a fl[ ( pun* c>ds ?r\gh ea* ( ^! ma*9es4 ,! ma*9es diff] f ea* o!r 9 ! numb] & relation ( ! pa?s ( fl[1 or c>d *annels1 & 9 ! numb] & relation ( ! mom5t>y /opp+ places1 or c>d /ations1 at :i* c>ds are read1 pun*$1 or o!rwise act$ on4 ,we c get a good idea ( :at a ma*9e is f a picture ( ^! c>d *annels4 ,key ,pun* ,we use a key pun* 7,fig4 #e7 to pun* orig9al in=mation into blank c>ds4 ,9 ! key pun* !re is "o c>d *annel2 x has "o entrance1 "o /ation1 & "o exit4 ,at ! c>d /ation1 !re are #ab pun*+ dies1 "o = ea* position 9 ! c>d column1 & ea* c>d column is pres5t$ "o by "o = pun*+4 ,! num]ic keybo>d 7,fig4 #f7 = ! key pun* has #ad keys3 ,"o key = ea* ( ! pun*es #j to #i1 #aa1 & #ab1 ,a space key1 :i* all[s a column ( ! pun* c>d to g by ) no pun* 9 x1 ,a release key1 :i* ejects ! c>d & fe$s ano!r c>d4 ,illu/ration3 ,,fig4 #e4 ,key pun*4 ,illu/ration3 ,,fig4 #f4 ,keybo>d ( key pun*4 ,( c\rse1 9 us+ a key pun*1 we mu/ pun* ! same k9d ( in=mation 9 ! same gr\p ( columns4 ,= example1 if ^! c>ds are to conta9 employees' social security numb]s1 we mu/ pun* t numb] always 9 ! same c>d columns1 numb]$1 say1 #ae to #bc1 or #gj to #gh1 etc4 ,v]ifi] ,! v]ifi] is really ! same ma*9e z ! key pun*1 b x has dull pun*+ dies mov+ g5tly in/ead ( %>p ones mov+ ) =ce4 ,x turns on a r$ light & /ops :5 !re is no pun*$ hole 9 ! "r spot to mat* ) a press$ key4 ,sort] ,! sort] is a ma*9e = sort+ c>ds1 "o column at a "t 7,fig4 #g74 ,! sort] has a c>d *annel t =ks2 x has "o entrance1 "o /ation1 & #ac exits4 ,ea* exit corresponds to3 "o ( ! #ab pun* positions #j to #i1 #aa1 & #ab2 or reject1 :i* applies :5 ! column is n[h]e pun*$4 ,x has "o c>d /ation :]e a bru% reads a s+le column ( ! c>d4 ,we c turn a h&le & move ! bru% to any column4 ,illu/ration3 ,,fig4 #g4 ,sort]4 ,int]pret] ,! int]pret] takes 9 a c>d1 reads its pun*es1 pr9ts on ! c>d ! m>ks indicat$ by ! pun*es1 & /acks ! c>d4 ,we call ?is process int]pret+ ! c>d1 s9ce x translates ! pun*$ holes into pr9t$ m>ks4 ,! int]pret] 7,fig4 #h7 has "o c>d *annel1 ) "o entrance1 #b c>d /ations1 & "o exit4 ,:at ! ma*9e does at ! second c>d /ation dep5ds on :at ! ma*9e reads at ! fir/ c>d /ation & on :at we h told ! ma*9e by swit*es & plugbo>d wir+ to d4 ,illu/ration3 ,,fig4 #h4 ,int]pret]4 ,reproduc] ,! reproduc] or reproduc+ pun* c3 ,reproduce1 or copy ! pun*es 9 "o gr\p ( c>ds into ano!r gr\p ( c>ds 79 ! same or diff]5t columns74 ,comp>e1 or make sure t ! pun*es 9 two gr\ps ( c>ds agree 7& %9e a r$ light if !y d n74 ,gang pun*1 or copy ! pun*es 9 a ma/] c>d into a gr\p ( detail c>ds4 ,summ>y pun*1 or copy totals or summ>ies obta9$ 9 ! tabulator into blank c>ds 9 ! reproduc]4 ,illu/ration3 ,,fig4 #i4 ,reproduc]4 ,! reproduc] 7,fig4 #i7 has #b indep5d5t c>d *annels1 ! c>ds n m+l+ 9 any way1 call$ ! read+ *annel & ! pun*+ *annel4 ,we c run ! ma*9e ) only ! pun*+ *annel work+2 9 fact1 ,,ibm equips "s models only ) ! pun*+ *annel1 p>ticul>ly = 8summ>y pun*0 op]ation4 ,! ma*9e is tim$ s t1 :5 any c>d is at ! middle /ation 9 ei!r *annel1 !n ! next prec$+ c>d is at ! late/ /ation1 & ! next foll[+ c>d is at ! e>lie/ /ation4 ,at #e /ations1 ! ma*9e reads a c>d4 ,at ! middle /ation ( ! pun*+ *annel1 ! ma*9e pun*es a c>d4 ,us+ a _m-wire cable1 we c connect ! tabulator to ! reproduc] & s cause ! tabulator to give in=mation electrically to ! reproduc]4 ,?is connection makes possible ! 8summ>y pun*0 op]ation4 ,"h is an in/ance ) pun*-c>d ma*9es :]e1 9 ord] to transf] in=mation f "o ma*9e to ano!r1 we are n requir$ to move c>ds physically f "o ma*9e to ano!r4 ,collator ,! collator is a ma*9e t arranges or collates c>ds4 ,x is p>ticul>ly useful 9 select+1 mat*+1 & m]g+ c>ds4 ,! collator 7,fig4 #aj7 has #b c>d *annels :i* jo9 & !n =k into #d *annels end+ 9 pockets call$ ,hopp]s #a1 #b1 #c1 & #d4 ,! #b c>d fe$s are call$ ! ,prim>y ,fe$ & ! ,second>y ,fe$4 ,c>ds f ! ,prim>y ,fe$ may fall only into ! fir/ & second hopp]s4 ,c>ds f ! ,second>y ,fe$ may fall only into ! second1 ?ird1 & f\r? hopp]s4 ,! collator has #c /ations at :i* c>ds may be read4 ,illu/ration3 ,no4#a--,select$ prim>ies ,no4#b--,m]g$ c>ds & unselect$ prim>ies ,no4#c--,sep>ate second>ies n select$ ,no4#d--,select$ second>ies ,,fig4 #aj4 ,collator4 ,,ibm c supply additional wir+ call$ ! collator c\nt+ device4 ,) ?is we c make ! collator c\nt c>ds z well z comp>e !m4 ,= example1 we c\ld put #ab blank c>ds f ! ,second>y ,fe$ beh9d ea* pun*$-c>d f ! ,prim>y ,fe$ 9 ord] to prep>e = "s o!r op]ation4 ,calculat+ ,pun* ,! calculat+ pun* 0 introduc$ 9 #aidf4 ,x is a v]satile ma*9e ( consid]able capacity4 ,x adds1 subtracts1 multiplies1 & divides4 ,x also has a control ov] a sequ5ce ( op]ations1 9 "s cases up to half a doz5 /eps4 ,?is ma*9e 7,fig4 #aa7 has "o c>d *annel ) #d /ations call$1 respectively1 control bru%es1 read+ bru%es1 pun* fe$1 & pun*+ dies4 ,at /ation #a1 !re are #bj bru%es2 we c set ^! by h& to read any #bj ( ! #hj c>d columns4 ,at /ation #b !re are #hj regul> read+ bru%es4 ,at /ation #c ! c>d waits = a "p ( a second :ile ! ma*9e calculates1 &1 :5 t is done1 ! c>d is f$ into /ation #d1 :]e x is pun*$ or v]ifi$4 ,! multiply+ pun* is an e>li] model ( ! calculat+ pun*1 )\t ! capacity = division4 ,illu/ration3 ,,fig4 #aa4 ,calculat+ pun*4 ,tabulator ,! tabulator c select & li/ in=mation f c>ds4 ,also1 x c total in=mation f gr\ps ( c>ds 9 c\nt]s ( ! tabulator & c pr9t ! totals4 ,illu/ration3 ,,fig4 #ab4 ,tabulator4 ,! tabulator 7,fig4 #ab7 has "o c>d *annel ) two /ations :]e c>ds may be read1 call$ ! ,upp] ,bru%es & ,l[] ,bru%es4 ,:5 ! ,l[] ,bru% /ation is read+ "o c>d1 ! ,upp] ,bru% /ation is read+ ! next c>d4 ,! tabulator also has ano!r *annel1 :i* is = endless pap] 7& sometimes sep>ate %eets or c>ds74 ,?is *annel has "o /ation2 "h pr9t+ takes place4 ,unlike ! typewrit]1 ! tabulator pr9ts a :ole r[ at a "t4 ,x c pr9t up to #hh num]als or lett]s across ! %eet 9 "o /roke4 ,! c>ds fl[+ ?r\gh ! c>d *annel & ! pap] fl[+ ?r\gh ! pap] *annel d n h to move 9 /ep2 9 fact1 we ne$ _m diff]5t "t relations betwe5 !m1 & ! numb] ( r[s pr9t$ on ! pap] may h almo/ any relation to ! numb] ( pun* c>ds fl[+ ?r\gh ! c>d *annel4 ,at ! /ation :]e pap] is pr9t$1 we c put on ! ma*9e a me*anism call$ ! automatic c>riage4 ,?is is l a typewrit] c>riage1 :i* holds ! pap] = a typewrit]1 b we c control ! movem5t ( pap] ?r\gh ! automatic c>riage by plugbo>d wir+1 swit* sett+s1 & holes 9 pun* c>ds4 ,?us we c arrange = head+s1 spac+1 & fe$+ ( new %eets to be controll$ by ! in=mation & ! in/ructions1 ) a great deal ( v]satility4 ,,h&l+ ,,in=mation ,we h n[ describ$ briefly ! *ief available pun*-c>d ma*9es z ( ! middle ( #aidh4 ,! next "q is3 ,h[ d we actually get some?+ done by means ( pun* c>ds8 ,let u g back to ! c5sus example1 ev5 ?\gh x may n be a v typical example1 & see :at w\ld be done if we wi%$ to compile a c5sus by pun* c>ds4 ,! fir/ ?+ we d is plan :i* columns ( ! pun* c>d w conta9 :at in=mation ab\t ! p be+ c\nt$4 ,= example1 ! foll[+ might be "p ( ! plan3 ,,no4 ,,( ,,in=mation ,,possibilities ,,columns ,/ate #fj #a- #b ,c\nty #a1jjj #c- #e ,t[n%ip #aj1jjj #f- #i ,city or village #aj1jjj #aj-ac ,sex #b #ad ,age la/ bir?day #ajj #ae-af ,occupation #ajj1jjj #ag-ba 444 444 444 ,"u ! head+ /ate1 we "k t !re are #dh /ates1 ! ,di/rict ( ,columbia1 & sev]al t]ritories & possessions--all told1 p]haps #fj possibilities4 ,s1 #b pun*-c>d columns are en\gh3 !y w all[ #ajj diff]5t sets ( pun*es f #jj to #ii to be put 9 !m4 ,we !n assign ! code #jj to ,ma9e1 #ja to ,new ,hamp%ire1 #jb to ,v]mont1 etc41 or we might assign ! code #jj to ,alabama1 #ja to ,arizona1 #jb to ,arkansas1 etc4--:i*ev] w\ld be m useful4 ,"u ! o!r head+s1 we d ! same ?+3 c\nt ! possibilities2 assign codes4 ,9 ?is case1 x w be reasonable to use num]ic codes #j to #i 9 ea* column 9 all places because we %all h millions ( c>ds to deal ) & num]ic codes c be sort$ fa/] ?an alphabetic codes4 ,alphabetic codes require #b pun*$ holes 9 ea* column1 & sort+ any column takes #b op]ations4 ,! pun* c>ds are pr9t$ ) ! *os5 head+s4 ,we set up ! codes 9 *>ts & give !m to cl]ks4 ,us+ key pun*es & v]ifi]s1 !y pun* up ! c>ds & *eck !m4 ,!y "w f ! orig9al in=mation collect$ by ! c5sus-tak] 9 ! field4 ,s9ce ! orig9al in=mation w come 9 geographically1 probably only "o geographic code at a "t w be ne$$1 & x w be simple to keep track (4 ,z to occupation1 h[ev]1 x may be useful to assign o!r cl]ks full-"t to exam9+ ! orig9al in=mation & specify+ ! "r code = ! occupation4 ,!n ! cl]ks :o d ! pun*+ w h only copy+ to d4 ,! great bulk ( ! "w ) ! c5sus w be sort+1 c\nt+1 & total+4 ,! orig9al pun* c>ds w be summ>iz$ into l>g] & l>g] gr\ps4 ,= example1 ! c>ds = all males age #bc la/ bir?day liv+ 9 ! /ate ( ,massa*usetts are sort$ toge!r4 ,?is gr\p ( c>ds may be put into a tabulator wir$ to a summ>y pun*4 ,:5 ! tabulator has c\nt$ ! la/ c>d ( ?is gr\p1 ! summ>y pun* pun*es "o c>d1 %[+ ! total numb] 9 ?is gr\p4 ,"s "t lat] a c>d l ?is w be ready = e /ate4 ,!n ! :ole gr\p ( /ate c>ds may be f$ into ! tabulator wir$ to ! reproduc] act+ z summ>y pun*4 ,:5 total$1 ! numb] ( males age #bc la/ bir?day 9 ! ,unit$ ,/ates w be pun*$ into a s+le c>d4 ,aft] m compil+1 a c>d l ?is w be ready = all males 9 ! ,unit$ ,/ates at ea* age4 ,!n ?is gr\p ( c>ds may be f$ into ! tabulator wir$ to ! summ>y pun*4 ,ea* c>d may be li/$ by ! tabulator on ! pap] fl[+ ?r\gh x1 %[+ ! age & ! numb] ( males liv+ at t age4 ,at ! end ( ! li/+1 ! tabulator w pr9t ! total numb] ( all males 9 ! li/1 & ! summ>y pun* w pun* a c>d conta9+ ?is total4 ,,ari?metical ,,op]ations ,pun*-c>d ma*9es c p]=m ! ari?metical op]ations ( c\nt+1 add+1 subtract+1 multiply+1 divid+1 & r\nd+ (f4 ,c\nt+ ,c\nt+ c be done by ! sort]1 ! tabulator1 & ! collator4 ,! tabulator c pr9t ! total c\nt4 ,! tabulator & summ>y pun* wir$ toge!r c put ! total c\nt automatically into ano!r pun* c>d4 ,! sort] %[s ! c\nt 9 dials4 ,add+ & ,subtract+ ,add+ & subtract+ c be done by ! tabulator1 ! calculat+ pun*1 & ! multiply+ pun*4 ,9 ! calculat+ & multiply+ pun*es1 ! sum or diff]5ce is usually pun*$ into ! same c>d f :i* ! numb]s 7 fir/ obta9$4 ,! tabulator1 h[ev]1 obta9s ! result fir/ 9 a c\nt]2 f ! c\nt]1 x c be pr9t$ on pap] or pun*$ into a blank c>d ) ! aid ( ! summ>y pun*4 ,numb]s are h&l$ z gr\ps ( decimal digits1 & ! ma*9es mirror ! prop]ties ( digits 9 ! decimal sy/em4 ,negative numb]s are usually h&l$ z complem5ts 7see ,supplem5t #b74 ,= example1 if we h 9 ! tabulator a c\nt] ) a capacity ( six digits1 ! numb]-#jjjjac is /or$ 9 ! c\nt] z ! complem5t #iiiihg4 ,we _c /ore 9 ! c\nt] ! numb] #iiiihg1 s9ce we _c di/+ui% x f-#jjjjac4 ,9 o!r words1 if a c\nt] is to be us$ = bo? positive & negative numb]s1 its capacity is actually "o digit less1 s9ce 9 ! la/ decimal place on ! left #j w mean positive & #i w mean negative4 ,multiply+ & ,divid+ ,multiply+ is done 9 ! calculat+ & multiply+ pun*es4 ,9 bo? cases1 ! multiplication table is built into ! circuits ( ! ma*9e1 & ! sy/em ( left-h& compon5ts & "r-h& compon5ts is us$ 7see ,supplem5t #b74 ,divid+ is done 9 ! calculat+ pun* & is c>ri$ out 9 t ma*9e mu* z 9 ord9>y ari?metic4 ,by means ( an e/imat+ circuit ! calculat+ pun* guesses :at multiple ( ! divisor w g into ! divid5d4 ,!n x det]m9es t multiple & tries x4 ,r\nd+ ,(f ,r\nd+ (f may be done 9 #c pun*-c>d ma*9es1 ! calculat+ & multiply+ pun*es1 & ! tabulator4 ,= example1 suppose we h ! numb]s #di4adgf1 #fh4ecbg1 & we wi% to r\nd !m (f to #b decimal places4 ,! results w be #di4ae & #fh4ec4 ,= ! fir/ numb]1 we raise ! 4#jjgf1 turn+ 4#adgf into 4#ae1 s9ce 4#jjgf is m ?an 4#jje4 ,= ! second numb]1 we drop ! 4#jjbg s9ce x is less ?an 4#jje4 ,ea* ( ^! pun*-c>d ma*9es provides :at is call$ a #e impulse 9 ea* ma*9e cycle4 ,:5 ! numb] is to be r\nd$ (f1 ! #e impulse is plugg$ into ! fir/ decimal place t is to be dropp$1 & x is !re add$4 ,if ! figure 9 ! decimal place to be dropp$ is #j to #d1 ! add$ #e makes no diff]5ce 9 ! la/ decimal place t is to be kept4 ,b1 if ! figure 9 ! decimal place to be dropp$ is #e to #i1 !n ! add$ #e makes a c>ry into ! la/ decimal place t is to be kept1 increas+ x by #a1 & ?is is j :at is want$ = r\nd+ (f4 ,,logical ,,op]ations ,pun*-c>d ma*9es d _m op]ations ( reason+ or logic t d n involve addition1 subtraction1 multiplication1 or division4 ,j z we c write equations = ari?metical op]ations1 s we c write equations = ^! logical op]ations us+ ma!matical logic 7see ,*apt] #i & ,supplem5t #b74 ,if any read]1 h[ev]1 is n int]e/$ 9 ^! logical equations1 he %\ld skip ea* p>agraph t beg9s ) 89 ! language ( logic10 or a simil> phrase4 ,translat+ ,read+ & writ+ are op]ations p]haps n /rictly ( reason+ b ( translat+ f "o language to ano!r4 ,basically ^! op]ations take 9 a m>k 9 "o language & give out a m>k ) ! same mean+ 9 ano!r language4 ,= example1 ! int]pret] takes 9 pun*$ holes & gives out pr9t$ m>ks1 b ! holes & ! m>ks h ! same mean+4 ,! major "p ( sort+ is done by a pun*-c>d sort+ ma*9e & c be consid]$ an op]ation ( translat+4 ,9 sort+ a c>d1 ! ma*9e takes 9 a m>k 9 ! =m ( a pun*$ hole on a pun* c>d & specifies a place be>+ ! same m>k :]e ! c>d is put4 ,! rema9+ "p ( sort+ is done by human be+s4 ,?is "p consi/s ( pick+ up blocks ( c>ds f ! pockets ( ! sort] & putt+ ! blocks toge!r 9 ! "r sequ5ce4 ,comp>+ ,illu/ration3 ,,fig4 #ac4 ,comp>]4 ,! fir/ op]ation ( reason+ done by pun*-c>d ma*9es is comp>+4 ,= an example ( comp>+ 9 ! op]ation ( ! tabulator1 let u take in/ruct+ ! ma*9e :5 to pick up a total & pr9t x4 ,z an illu/ration1 suppose t we are mak+ a table by /ate1 c\nty1 & t[n%ip ( ! numb] ( p]sons c\nt$ 9 a c5sus4 ,suppose t = ea* t[n%ip we h "o pun* c>d tell+ ! total numb] ( p]sons4 ,if all ! c>ds are 9 sequ5ce1 !n1 :5ev] ! c\nty *anges1 we want a m9or total1 &1 :5ev] ! /ate *anges1 we want a major total4 ,:at does ! ma*9e d8 ,! tabulator has a me*anism t we %all call a comp>] 7,fig4 #ac74 ,a comp>] has #b inputs t may be call$ ,previ\s & ,curr5t & "o output t may be call$ ,unequal4 ,! comp>] has ! prop]ty ( giv+ out an impulse if & only if !re is a diff]5ce betwe5 ! #b inputs4 ,9 ! language ( ! algebra ( logic 7see ,supplem5t #b & ,*apt] #i71 let ! pieces ( in=mation com+ into ! comp>] be a & b1 & let ! in=mation com+ out ( ! comp>] be p4 ,!n ! equation ( ! comp>] is3 p ,t7a b7 :]e 8,t 770 is 8! tru? value ( 0 & 80 is a /atem5t1 & :]e ! tru? value is #a if true & #j if false4 ,9 wir+ ! tabulator s t x c tell :5 to total1 we use ! comp>]4 ,we fe$ into x ! c\nty f ! curr5t c>d & ! c\nty f ! previ\s c>d4 ,out ( ! comp>] we get an impulse if & only if ^! two pieces ( in=mation are diff]5t4 ,?is is j :at happ5s :5 ! c\nty *anges4 ,! impulse f ! comp>] is !n us$ 9 fur!r wir+ ( ! tabulator3 x makes ! c\nt] t is busy total+ ! numb] ( p]sons 9 ! c\nty pr9t its total & !n cle>4 ,9 ! same way1 ano!r comp>]1 :i* wat*es /ate in/ead ( c\nty1 takes c>e ( major totals :5 ! /ate *anges4 ,select+ ,! next op]ation ( reason+ :i* pun*-c>d ma*9es c d is select+4 ,! tabulator1 collator1 int]pret]1 reproduc]1 & calculat+ pun* all may conta9 me*anisms t c select in=mation4 ,^! me*anisms are call$ selectors4 ,= example1 suppose t we are us+ ! tabulator to make a table %[+ = ea* city ! numb] ( males & ! numb] ( females4 ,9 ! table we %all h ?ree columns3 fir/1 city2 second1 males2 ?ird1 females4 ,suppose t ea* pun* c>d 9 columns #cj to #cf %[s ! total ( males or females 9 a city4 ,suppose t1 if & only if ! c>d is = females1 x has an ,x pun* 7or #aa pun*7 9 column #gi4 ,:at d we want to h happ58 ,we want ! numb] 9 columns #cj to #cf to g into ! second column ( ! table if !re is no ,x 9 column #gi1 & we want x to g into ! ?ird column ( ! table if !re is an ,x 9 column #gi4 ,?is is j ano!r way ( say+ t we want ! numb] to g into ! males column if x is a numb] ( males1 & into ! females column if x is a numb] ( females4 ,we make ?is happ5 by us+ a selector4 ,a selector 7,fig4 #ad7 is a me*anism ) #b inputs & #b outputs4 ,! #b inputs are call$ ,x ,pickup & ,common4 ,! #b outputs are call$ ,x & ,no ,x4 ,! ,x ,pickup1 z its "n implies1 wat*es = ,x's4 ,! ,common takes 9 in=mation4 ,:at comes out ( ,x is :at goes into ,common if & only if an ,x pun* is pick$ up2 o!rwise no?+ comes out4 ,:at comes out ( ,no ,x is :at goes into ,common if & only if an ,x pun* is n pick$ up2 o!rwise no?+ comes out4 ,f ! po9t ( view ( ord]+ pun*-c>d equipm5t1 we %\ld note t !re are two types ( selectors3 ,x selectors or ,x di/ributors1 :i* h a select+ capacity ( "o column--t is1 "o decimal digit--& class selectors1 :i* ord9>ily h a select+ capacity ( #aj columns or #aj decimal digits4 ,b we %all disreg>d ?is diff]5ce "h1 z we h disreg>d$ mo/ o!r que/ions ( capacity 9 multiplication1 division1 etc4 ,illu/ration3 ,,fig4 #ad4 ,selector4 ,9 ! language ( logic 7see ,*apt] #i & ,supplem5t #b71 if p1 a1 b1 c are ! in=mation 9 ,x ,pickup1 ,common1 ,x1 & ,no ,x1 respectively1 !n ! equations = a selector are3 b ap c a7#a - p7 ,return+ n[ to ! table we wi% to make1 we connect columns #cj to #cf ( ! pun* c>d to ,common4 ,we connect column #gi ( ! pun* c>d to ! ,x ,pickup4 ,we connect ! output ,no ,x to ! males column ( ! table4 ,we connect ! output ,x to ! females column ( ! table4 ,9 ?is way we make ! numb] 9 ! pun* c>d appe> 9 ei!r "o ( two places 9 ! table accord+ to :e!r ! numb] c\nts males or females4 ,we might m5tion sev]al m prop]ties ( selectors4 ,a selector c be us$ 9 ! rev]se way1 ) ,x ,pickup1 ,x1 & ,no ,x z inputs & ,common z output 7,fig4 #ae74 ,:at w come out ( ,common is 7#a7 :at goes into input ,no ,x if !re is no ,x pun* 9 ! column to :i* input ,x ,pickup is wir$1 & 7#b7 :at goes into input ,x if !re is an ,x pun* 9 ! column to :i* input ,x ,pickup is wir$4 ,9 ?is case ! logical equation = ! selector is3 a bp c7#a - p7 ,also1 selectors c be us$ "o aft] ano!r1 s t select+ bas$ on #b or #c ,x pun*es c be made4 ,illu/ration3 ,,fig4 #ae4 ,selector4 ,9 ! language ( logic1 if p1 q1 r are ! tru? values ( 8!re is an ,x pun* 9 column i1 j1 k10 respectively1 !n by means ( selectors we c get su* a function z3 c apq b7#a - q77#a - r7 ,also1 a selector may (t5 be en]giz$ n only by an ,x pun* b also by a pun* #j1 #a1 #b1 1 #i & #ab4 ,9 ?is case1 ! selector is equipp$ ) an additional input t c respond to any digit4 ,?is input is call$ ! ,digit ,pickup4 ,digit ,selector ,some?+ l an ord9>y selector is ano!r me*anism call$ a digit selector 7,fig4 #af74 ,?is has "o input1 ,common1 & #ab outputs1 #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i1 #aa1 #ab4 ,?is me*anism is (t5 includ$ 9 ! tabulator & may be includ$ 9 o!r pun*-c>d ma*9es4 ,= example1 suppose t we want to d some?+ if & only if column #fb ( a pun* c>d conta9s a #c or a #d or a #i4 ,!n we connect a bru% t reads column #fb ( ! pun* c>d to ! ,common input ( ! digit selector4 ,& we connect out f ! digit selector jo9tly f outputs #c1 #d1 & #i4 ,illu/ration3 ,,fig4 #af4 ,digit selector4 ,9 ! language ( logic1 if a is ! digit go+ into ,common1 & if p is ! impulse com+ out ( ! digit selector1 !n ! equation ( ! me*anism 9 ?is case is3 p ,t7a #c1 #d1 #i7 ,sequ5c] ,a f\r? op]ation ( reason+ done by pun*-c>d ma*9es is f9d+ t "o numb] is great] ?an1 or equal to1 or less ?an ano!r4 ,?is op]ation is done 9 ! collator & may be call$ sequ5c+4 ,= example1 suppose t we h a file ( pun* c>ds = cities1 %[+ 9 columns #da to #dh ! numb] ( p4 ,suppose t we wi% to pick out ! c>ds = cities ov] #abe1jjj 9 population4 ,n[ ! collator has a me*anism t has #b inputs & #c outputs 7,fig4 #ag74 ,we may call ?is me*anism a sequ5c]1 s9ce x c tell ! sequ5ce ( two numb]s4 ,:at goes into ! ,prim>y input is a numb]3 let u call x a4 ,:at goes into ,second>y is ano!r numb]3 let u call x b4 ,an impulse comes out ( ,l[ ,prim>y if a is less ?an b4 ,an impulse comes out ( ,equal if a equals b4 ,an impulse comes out ( ,l[ ,second>y if a is great] ?an b4 ,illu/ration3 ,,fig4 #ag4 ,sequ5c]4 ,9 ! language ( logic1 if p1 q1 r are ! ?ree indications 9 ,l[ ,prim>y1 ,equal1 & ,l[ ,second>y1 !n3 p ,t7a b7 q ,t7a b7 r ,t7a b7 ,return+ to our example1 we pun* up a c>d ) #abe1jjj 9 columns #dc to #dh1 & we put ?is c>d into ! ,second>y ,fe$4 ,we take ! pun* c>ds = cities & put !m into ! ,prim>y ,fe$4 ,9 ! plugbo>d1 we connect ! hubs ( ! ,second>y ,bru%es 7t read ! c>d 9 ! ,second>y ,fe$71 columns #dc to #dh1 to ! ,second>y input ( ! ,sequ5c]4 ,we connect ! hubs ( ! ,prim>y ,bru%es 7t read ! c>d 9 ! ,prim>y ,fe$71 columns #da to #dh1 to ! ,prim>y input ( ! ,sequ5c]4 ,!n we connect ! ,l[ ,prim>y output ( ! ,sequ5c] to a device t causes ! city c>d be+ exam9$ to fall into pocket #a4 ,we connect ,equal output & ,l[ ,second>y output to a device t causes ! city c>d be+ exam9$ to fall into pocket #b4 ,!n1 :5 ! c>d = any city comes along1 ! ma*9e comp>es ! numb] ( p 9 ! city ) #abe1jjj4 ,if ! numb] is great] ?an #abe1jjj1 ! c>d w fall into pocket #a2 o!rwise ! c>d w fall into pocket #b4 ,at ! end ( ! run1 we %all f9d 9 pocket #a all ! c>ds we want4 ,,new ,,developm5ts ,we may expect to see ov] ! next few ye>s major developm5ts 9 pun*-c>d ma*9]y4 ,x w\ld seem likely t types ( pun*-c>d ma*9es l ! foll[+ might be con/ruct$3 ,a pun*-c>d ma*9e t p]=ms any ari?metical or logical op]ation at high spe$ & may p]=m a doz5 su* op]ations 9 sequ5ce dur+ ! "t t a pun* c>d passes ?r\gh ! ma*9e4 ,a pun*-c>d ma*9e t uses loops ( pun*$ pap] tape1 :i* express ei!r a sequ5ce ( values 9 a table t ! ma*9e c consult or a sequ5ce ( in/ructions t gov]n ! op]ations ( ! ma*9e4 ,pun*-c>d ma*9]y t uses a l>g] c>d ?an ! #hj-;column c>d4 ,a pun*-c>d ma*9e t may h a fairly l>ge am\nt ( int]nal memory1 p]haps #cj or #dj regi/]s :]e numb]s or words may be /or$ & ref]r$ to4 ,,spe$ ,! spe$ ( v>i\s op]ations ) pres5t ,,ibm pun*-c>d ma*9es is ab\t z %[n 9 ! table4 ,,ma*9e ,,op]ation ,,"t ,,9 ,,seconds ,key pun* ,pun* #hj columns ,ab\t #bj to #dj ,v]ifi] ,*eck #hj columns ,ab\t #bj to #dj ,sort] ,sort #a c>d on #a column #j4ae ,int]pret] ,pr9t #a l9e #j4h ,reproduc] ,reproduce a c>d1 all #hj columns #j4f ,collator ,m]ge #b c>ds #j4be ,multiply+ pun* ,multiply by #h digits #e4f ,calculat+ pun* ,add #j4c ,calculat+ pun* ,multiply by #h digits #c4f ,calculat+ pun* ,divide1 obta9+ #h quoti5t digits #i4j ,tabulator ,pr9t #a l9e1 numb]s only #j4d ,tabulator ,pr9t #a l9e1 lett]s includ$ #j4ge ,tabulator ,add numb]s f #a c>d #j4d ,,co/ ,pun*-c>d ma*9es may be ei!r r5t$ or pur*as$ f "s manufactur]s b only r5t$ f o!rs4 ,if we take ! co/ ( a cl]k z #abj to #aej a mon?1 ! mon?ly r5t ( mo/ pun*-c>d ma*9es ranges f ( ! co/ ( a cl]k = ! simple/ type ( ma*9e1 su* z a key pun*1 to #c times ! co/ ( a cl]k = a complicat$ & v]satile type ( ma*9e1 su* z a tabulator ) _m atta*m5ts4 ,! r5tal basis is naturally conv5i5t = _m k9ds ( jobs4 ,,reliability ,! reliability ( "w ) pun* c>ds & pun*-c>d ma*9es is (t5 mu* bett] ?an #ii p] c5t3 9 #aj1jjj op]ations1 failures %\ld be less ?an #b or #c4 ,?is is1 ( c\rse1 mu* bett] ?an ) cl]ical op]ations4 ,!re are a numb] ( causes = ma*9e or c>d failures4 ,sometimes c>ds may be w>p$ & may n fe$ into ! ma*9es prop]ly4 ,or1 ! air 9 ! room may be v dry1 & /atic electricity may make ! c>ds /ick toge!r4 ,or1 ! air may be too humid2 ! c>ds may swell slightly & may jam 9 ! ma*9e4 ,a pun* may get slightly out ( true alignm5t1 & pun*es 9 ! c>ds may be slightly (f4 ,a relay may get du/ on its contact po9ts &1 f "t to "t1 fail to p]=m 9 ! "r way4 ,consid]able eng9e]+ ef=t has be5 put into rem$y+ ^! & o!r tr\bles1 ) mu* success4 ,to make sure t we h correct results f human be+s work+ ) pun*-c>d ma*9es1 we may v]ify ea* process4 ,in=mation t is pun*$ on ! key pun* may be v]ifi$ on ! v]ifi]4 ,multiplications done ) multiplic& a & multipli] b may be repeat$ & comp>$ ) multiplications done ) multiplic& b & multipli] a4 ,c>ds t are sort$ on ! sort] may be put ?r\gh ! collator to make sure t _! sequ5ce is correct4 ,x is (t5 good to plan e op]ation s t we h a pro( t ! result is "r4 ,x is /&>d practice to h ! ma*9es inspect$ regul>ly 9 ord] to keep !m op]at+ prop]ly4 ,on ! av]age1 = e #ej to #ge ma*9es1 !re w be "o full-"t s]vice man ma9ta9+ !m & tak+ c>e ( calls = repairs4 ,( c\rse1 z ) any ma*9]y1 "s s]vice calls w be a result ( ! human elem5t2 = example1 a problem may h be5 set up wrongly on a ma*9e4 ,,g5]al ,,usefulness ,pun*-c>d calculations are mu* fa/] & m accurate ?an h& calculations4 ,) pun* c>ds1 "w is organiz$ s t all cases are h&l$ at ! same "t 9 ! same way4 ,?is process is v diff]5t f h&l+ ea* case sep>ately f />t to f9i%4 ,z soon z ! numb] ( cases to be h&l$ is m ?an a hundr$ & ea* item ( in=mation is to be us$ five or m times1 pun* c>ds are likely to be advantage\s1 provid$ o!r factors are favorable4 ,va/ quantities ( in=mation h be5 h&l$ v successfully by pun*-c>d ma*9es4 ,ov] #cj sci5tific & eng9e]+ laboratories 9 ! ,unit$ ,/ates are do+ computation by pun* c>ds4 ,ov] a billion pun* c>ds1 9 fact1 are us$ annually 9 ?is c\ntry4 ,*apt] #e ,,measur+3 ,,massa*usetts ,,in/itute ,,( ,,te*nology',s ,,diff]5tial ,,analyz] ,,no4 #b ,9 ! previ\s *apt] we talk$ ab\t ma*9es t move in=mation express$ z holes 9 c>ds4 ,9 ?is *apt] we %all talk ab\t ma*9es t move in=mation express$ z measurem5ts4 ,,analogue ,,ma*9es ,a simple example ( a device t uses a measurem5t to h&le in=mation is a doorpo/4 ,"h ! height ( a *ild may be m>k$ f ye> to ye> z he gr[s 7,fig4 #a74 ,or1 suppose t we h a globe ( ! _w & wi% to f9d ! %orte/ pa? betwe5 ,*icago & ,mosc[4 ,we may lay a piece ( /r+ on ! globe1 pull x tight betwe5 ^? po9ts1 & !n measure ! /r+ on a scale to see ab\t :at di/ance x %[s 7,fig4 #b74 ,ma*9es t h&le in=mation z measurem5ts ( physical quantities are call$ analogue ma*9es1 because ! measurem5t is analog\s to1 or l1 ! in=mation4 ,a common example ( analogue ma*9e is ! slide rule4 ,) ?is we calculate by not+ ! positions ( rul$ l9es on /rips t slide by ea* o!r4 ,^! /rips are made ( f9e wood1 or ( pla/ic1 or ( /eel1 9 su* fa%ion t ! rul$ l9es w hold true positions & n w>p4 ,if we space ! rul+s s t #a1 #b1 #c1 #d1 #e1 #f are equally spac$1 !n ! slide rule is useful = addition 7,fig4 #c74 ,b if we space ! rul+s s t p[]s 7= example1 p[]s ( two--#a1 #b1 #d1 #h1 #af1 #cb 7 7,fig4 #d7 are equally spac$1 we c d multiplication4 ,! spac+s are !n accord+ to ! log>i?ms ( numb]s 7see ,supplem5t #b74 ,multiplication is m tr\blesome ?an addition1 & s m slide rules are made = multiplication ?an = addition4 ,illu/ration3 ,,fig4 #a4 ,measurem5t by doorpo/4 ,illu/ration3 ,,fig4 #b4 ,measurem5t by /r+4 ,illu/ration3 ,,fig4 #c4 ,slide ,rule = add+4 ,illu/ration3 ,,fig4 #d4 ,slide ,rule = multiply+4 ,dur+ ,_w ,w> ,,ii1 ! aim+ & fir+ ( guns aga9/ ho/ile planes 0 done by ma*9e4 ,aft] sight+ a plane1 ^! ma*9es automatically calculat$ h[ to direct fire aga9/ x4 ,!y 7 mu* bett] & fa/] ?an any man4 ,^! fire-control in/rum5ts 7 analogue ma*9es ) /eel & electrical p>ts built to f9e tol]ances4 ,) c>e we c get accuracy ( #a "p 9 #aj1jjj ) analogue ma*9es1 b great] accuracy is v h>d to get4 ,,physical ,,quantities ,suppose t we wi% to make an analogue ma*9e4 ,we ne$ to repres5t in=mation by a measurem5t ( some?+4 ,:at %\ld we select8 ,:at physical ?+ to be measur$ %\ld we *oose to put into ! ma*9e8 ,diff]5t am\nts ( ?is physical quantity w mat* ) diff]5t am\nts ( ! measurem5t be+ express$4 ,9 ! case ( ! doorpo/1 ! /r+1 & ! slide rule1 ! physical quantity is di/ance4 ,9 _m fire-control in/rum5ts1 ! physical quantity is ! am\nt ( turn+ ( a %aft 7,fig4 #e74 ,_m o!r physical quantities h f "t to "t be5 us$ 9 analogue ma*9es1 su* z electrical measurem5ts4 ,! spe$omet] ( an automobile tells di/ance travel$ & spe$4 ,x is an analogue ma*9e4 ,x uses ! am\nt ( turn+ ( a :eel1 & "s electrical prop]ties4 ,x h&les in=mation by means ( measurem5ts4 ,! basic physical quantity t x measures is ! am\nt ( turn+ ( a %aft4 ,illu/ration3 ,,fig4 #e4 ,measurem5t by am\nt ( turn+ ( a %aft4 ,,diff]5tial ,,analyz] ,! bigge/ & clev]e/ me*anical bra9 ( ! analogue type :i* has yet be5 built is ! diff]5tial analyz] f9i%$ 9 #aidb at ,massa*usetts ,in/itute ( ,te*nology 9 ,cambridge1 ,mass4 ,! fundam5tal physical quantity us$ 9 ?is ma*9e is ! am\nt ( turn+ ( a %aft4 ,! "n analyz] means an app>atus or ma*9e = analyz+ or solv+ problems4 ,x happ5s t ! ^w 8analyz]0 has be5 us$ r m (t5 9 connection ) analogue ma*9es1 & s 9 _m cases ! ^w 8analyz]0 c>ries ! mean+ 8analogue0 z well4 ,! ^w 8diff]5tial0 9 ! phrase 8diff]5tial analyz]0 ref]s to ! ma9 purpose ( ! ma*9e3 x is specially adapt$ = solv+ problems involv+ diff]5tial equations4 ,n[ :at is a diff]5tial equation8 ,,diff]5tial ,,equations ,9 ord] to expla9 :at a diff]5tial equation is1 we ne$ to use c]ta9 ideas4 ,^! ideas are3 equation2 =mula2 function2 rate ( *ange2 int]val2 d]ivative2 & integral4 ,9 ! next few p>agraphs1 we %all introduce ^! ideas briefly1 ) "s explanation & examples4 ,x is entirely possible = anyone to und]/& ^! ideas r easily1 by collect+ true /atem5ts ab\t !m2 no "o %\ld feel t because ^! ideas may be new !y _c be und]/ood readily4 ,,physical ,,problems ,9 physics1 *emi/ry1 me*anics1 & o!r sci5ces !re are _m problems 9 :i* ! behavior ( di/ance1 ( "t1 ( spe$1 heat1 volume1 electrical curr5t1 weight1 accel]ation1 pressure1 & _m o!r physical quantities are relat$ to ea* o!r4 ,examples ( su* problems are3 ,illu/ration3 ,,fig4 #f4 ,pa?s ( a %ot f a gun1 trajectories4 ,:at are ! v>i\s angles to :i* a gun %\ld be rais$ 9 ord] t x may %oot v>i\s di/ances8 7,see ,fig4 #f47 7,! pa?s ( a %ot f a gun are call$ trajectories47 ,if a plane flies 9 a direction always at ! same angle f ! nor?1 h[ mu* f>!r w x travel ?an if x flew along ! %orte/ pa?8 7,see ,fig4 #g47 7,a pa? always at ! same angle f ! nor? is call$ a loxodrome1 & a %orte/ pa? on a globe is call$ a great circle47 ,h[ %\ld an eng9e be design$ s t x w h ! lea/ vibration :5 x moves fa/8 ,9 physical problems l ^!1 ! answ] is n a s+le numb] b a =mula4 ,:at we want to d 9 any "o ( ^! problems is f9d a =mula s t any "o ( ! quantities may be calculat$1 giv5 ! behavior ( ! o!rs4 ,= example1 "h is a famili> problem 9 :i* ! answ] is a =mula & n a numb]3 ,illu/ration3 ,,fig4 #g4 ,pa?s ( a flight4 ,illu/ration3 ,,fig4 #h4 ,room =mulas4 ,h[ are ! floor area ( a room1 its l5g?1 & its wid? relat$ to ea* o!r8 7,see ,fig4 #h47 ,! answ] is told 9 any "o ( ?ree equations3 7floor area7 ,,equals 7l5g?7 ,,times 7wid?7 7l5g?7 ,,equals 7floor area7 ,,divid$ ,,by 7wid?7 7wid?7 ,,equals 7floor area7 ,,divid$ ,,by 7l5g?7 ,! fir/ equation %[s t ! floor area dep5ds on ! l5g? ( ! room & also on ! wid? ( ! room4 ,s we say floor area is a function ( l5g? & wid?4 ,?is p>ticul> function happ5s to be product1 ! result ( multiplication4 ,9 o!r words1 floor area is equal to ! product ( l5g? & wid?4 ,n[ !re is ano!r k9d ( function call$ a diff]5tial function or d]ivative4 ,a diff]5tial function or d]ivative is an in/antane\s rate ( *ange4 ,an in/antane\s rate ( *ange is ! result ( two /eps3 7#a7 f9d+ a rate ( *ange ov] an int]val & !n 7#b7 lett+ ! int]val become small] & small] indef9itely4 ,= example1 suppose t we h ! problem3 ,h[ are spe$1 di/ance1 & "t relat$ to ea* o!r8 ,"o ( ! answ]s is3 7spe$7 ,,equals ,,! ,,in/antane\s ,,rate ,,( ,,*ange ,,( 7di/ance7 ,,) ,,respect ,,to 7"t7 ,or we c say1 & x is j ! same ?+ 9 o!r words3 7spe$7 ,,equals ,,! ,,d]ivative ,,( 7di/ance7 ,,) ,,respect ,,to 7"t7 ,n[ we c tell :at a diff]5tial equation is4 ,x is simply an equation 9 :i* a d]ivative occurs1 su* z ! la/ example4 ,p]haps ! commone/ k9d ( equation 9 physical problems is ! diff]5tial equation4 ,,solv+ ,,physical ,,problems ,n[ we 7 able to *ange ! equation ab\t floor area into o!r =ms1 if we want$ to f9d l5g? or wid? in/ead ( floor area4 ,:5 we did ?is1 we ran into ! inv]se or opposite ( multiplication3 division4 ,9 ! same way1 we c *ange ! equation ab\t spe$ into o!r =ms1 if we want to f9d di/ance or "t in/ead ( spe$4 ,if we d ?is1 we run into a new idea1 ! inv]se or opposite ( ! d]ivative1 call$ integral4 ,! two new equations are3 7di/ance7 ,,equals ,,! ,,integral ,,( 7spe$7 ,,) ,,respect ,,to 7"t7 7"t7 ,,equals ,,! ,,integral ,,( ,,"o ,,divid$ ,,by 7spe$7 ,,) ,,respect ,,to 7di/ance7 ,^! equations may also be call$ diff]5tial equations4 ,an integral is ! result ( a process call$ integrat+4 ,to integrate spe$ & get di/ance is ! result ( ?ree /eps3 7#a7 break+ up an int]val ( "t into a l>ge numb] ( small bits1 7#b7 add+ up all ! small di/ances t we get by tak+ ea* bit ( "t & multiply+ by ! spe$ :i* appli$ 9 t bit ( "t1 & 7#c7 lett+ ! bits ( "t get small] & small]1 & lett+ ! numb] ( !m get l>g] & l>g]1 indef9itely4 ,9 o!r words1 7total di/ance7 ,,equals ,,! ,,sum ,,( ,,all ,,! ,,small 7di/ances71 ,,ea* ,,equal ,,to3 ,a ,,bit ,,( 7"t7 ,,multipli$ ,,by ,,! 7spe$7 ,,apply+ ,,to ,,t ,,bit ,?is is ano!r way ( say+ z be=e1 7di/ance7 ,,equals ,,! ,,integral ,,( 7spe$7 ,,) ,,respect ,,to 7"t7 ,to solve a diff]5tial equation1 we almo/ always ne$ to integrate "o or m quantities4 ,,orig9 ,,& ,,developm5t ,,( ,,! ,,diff]5tial ,,analyz] ,= at lea/ two c5turies1 solv+ diff]5tial equations to answ] physical problems has be5 a ma9 job = ma!maticians4 ,ma!matics is suppos$ to be logical1 & p]haps y w\ld ?9k ?is w\ld be easy4 ,b ma!maticians h be5 unable to solve a great _m diff]5tial equations2 only "h & !re1 z if by accid5t1 c\ld !y solve "o4 ,s !y (t5 wi%$ = bett] me?ods 9 ord] to make ! job easi]4 ,a ,briti% ma!matician & physici/1 ,william ,?omson 7,"l ,kelv971 9 #ahgi sugge/$ solv+ diff]5tial equations by a ma*9e4 ,he w5t fur!r3 he describ$ me*anisms = integrat+ & o!r ma!matical processes1 & h[ ^! me*anisms c\ld be connect$ toge!r 9 a ma*9e4 ,no su* ma*9e 0 !n built2 eng9e]+ 9 ^? ye>s 0 n equal to x4 ,9 #aibc1 a ma*9e ( ?is type = solv+ ! diff]5tial equations ( trajectories 0 propos$ by ,l4 ,wa9wright4 ,9 #aibe1 at ,massa*usetts ,in/itute ( ,te*nology1 ! problem ( a ma*9e to solve diff]5tial equations 0 aga9 be+ /udi$ by ,dr4 ,vannev> ,bu% & 8 associates4 ,dr4 ,bu% exp]im5t$ ) me*anisms t w\ld integrate1 add1 multiply1 etc41 & me?ods ( connect+ !m toge!r 9 a ma*9e4 ,a major "p ( ! success ( ! ma*9e dep5d$ on a device :]eby a v small turn+ =ce w\ld d a r l>ge am\nt ( "w4 ,he develop$ a way 9 :i* ! small turn+ =ce1 ab\t z small z a puff ( brea?1 c\ld be us$ to tight5 a /r+ ar\nd a drum already turn+ ) a consid]able =ce1 & ?us clut* ! drum1 br+ 9 t =ce1 & d ! "w t ne$$ to be done4 ,y may h wat*$ a %ip be+ load$1 se5 a man coil a rope ar\nd a w9*1 & wat*$ him sw+ a heavy load into ! air by a slight pull on ! rope 7,fig4 #i74 ,if s1 y h se5 ?is same pr9ciple at "w4 ,! turn+ =ce 7or torque7 t pulls on ! rope is greatly increas$ 7or amplifi$7 by su* a me*anism1 & s we call x a torque amplifi]4 ,illu/ration3 ,,fig4 #i4 ,increas+ turn+ =ce2 w9*1 or torque amplifi]4 ,by #aicj1 ,dr4 ,bu% & 8 gr\p _h f9i%$ ! fir/ diff]5tial analyz]4 ,x 0 entirely me*anical1 hav+ no electrical p>ts except ! motors4 ,x 0 s successful t a numb] ( eng9e]+ s*ools & manufactur+ bus9esses h s9ce !n built o!r ma*9es ( ! ,bu% type4 ,ea* "t1 "s improvem5ts 7 made 9 accuracy & capacity = solv+ problems4 ,b1 if y *ang$ f "o problem to ano!r on ?is type ( ma*9e1 y _h to d a lot ( "w ) screwdriv]s & wr5*es4 ,y _h to undo old me*anical connections betwe5 %afts & set up new ones4 ,accord+ly1 9 #aice1 ! m5 at ,,mit />t$ design+ a second diff]5tial analyz]4 ,9 ?is "o y c\ld make all ! connections electrically4 ,,mit f9i%$ its second diff]5tial analyz] 9 #aidb1 b ! fact 0 n publi%$ dur+ ,_w ,w> ,,ii1 = ! ma*9e 0 put to "w on important milit>y problems4 ,9 fact1 a rumor spread & 0 nev] d5i$ t ! ma*9e 0 a :ite elephant & w\ld n "w4 ,! ma*9e 0 (ficially ann\nc$ 9 ,octob] #aide4 ,x 0 ! mo/ advanc$ & effici5t diff]5tial analyz] ev] built4 ,we %all talk *iefly ab\t x = ! re/ ( ?is *apt]4 ,a good te*nical description ( ?is ma*9e is 9 a pap]1 8,a ,new ,type ( ,diff]5tial ,analyz]10 by ,vannev> ,bu% & ,samuel ,h4 ,caldwell1 publi%$ 9 ! ,j\rnal ( ! ,frankl9 ,in/itute = ,octob] #aide4 ,,g5]al ,,organization ,,( ,,mit ,,diff]5tial ,,analyz] ,,no4 #b ,a diff]5tial analyz] is basically made up ( %afts t turn4 ,:5 we set up ! ma*9e to solve a diff]5tial equation1 we assign "o %aft 9 ! ma*9e to ea* quantity ref]r$ to 9 ! equation4 ,x is ! job ( t %aft to keep track ( t quantity4 ,! total am\nt ( turn+ ( t %aft at any "t :ile ! problem is runn+ measures ! size ( t quantity at t "t4 ,if ! quantity decreases1 ! %aft turns 9 ! opposite direction4 ,= example1 if we h spe$1 "t1 & di/ance 9 a diff]5tial equation1 we label "o %aft 8spe$10 ano!r %aft 8"t10 & ano!r %aft 8di/ance40 ,if we wi%1 we may assign #aj turns ( ! 8"t0 %aft to mean 8"o second10 #b turns ( ! 8di/ance0 %aft to mean 8"o foot10 & #d turns ( ! 8spe$0 %aft to mean 8"o foot p] second40 ,^! are call$ scale factors4 ,we c\ld1 h[ev]1 use any o!r conv5i5t units t we wi%$4 ,by j look+ at a %aft or a :eel1 we c tell :at "p ( a full turn x has made--a half1 or a qu>t]1 or "s o!r "p--b we _c tell by look+ h[ _m full turns x has made4 ,9 ! ma*9e1 !re=e1 !re are me*anisms t record n only full turns b also t5?s ( turns4 ,^! are call$ c\nt]s4 ,we c connect a c\nt] to any %aft4 ,:5 we want to "k "s quantity t a %aft & c\nt] are keep+ track (1 we read ! c\nt+ me*anism4 ,! second diff]5tial analyz]1 :i* ,,mit f9i%$ 9 #aidb1 w5t a /ep fur!r ?an any previ\s "o4 ,9 ?is ma*9e1 a v>y+ numb] c be express$ ei!r 7#a7 me*anically z ! am\nt ( turn+ ( a %aft1 or 7#b7 electrically z ! am\nt ( two voltages 9 a pair ( wires4 ,! ,,mit m5 did ?is by means ( a me*anism call$ an angle-indicator4 ,angle indicators h ess5tially ?ree p>ts3 a transmitt]1 a receiv]1 & swit*es4 ,! transmitt] 7,fig4 #aj7 c s5se ! exact am\nt t a %aft has turn$ & give out a voltage 9 ea* ( two wires :i* tells exactly h[ mu* ! %aft has turn$ 7,fig4 #aa74 ,! receiv+ device 7,fig4 #ab71 :i* has a motor1 c take 9 ! voltages 9 ! two wires & drive a second %aft1 mak+ x turn 9 /ep ) ! fir/ %aft4 ,by means ( ! swit*bo>d 7,fig4 #ac71 ! two wires f ! transmitt] ( any angle-indicator c lead any:]e 9 ! ma*9e & be connect$ to ! receiv] ( any o!r angle indicator4 ,illu/ration3 ,,fig4 #aj4 ,s*eme ( angle-indicator transmitt]4 ,illu/ration3 ,,fig4 #aa4 ,indication ( angle4 ,illu/ration3 ,,fig4 #ab4 ,s*eme ( angle-indicator receiv]4 ,9 a diff]5tial analyz]1 we c connect ! %afts toge!r 9 _m diff]5t ways4 ,= example1 suppose t we want "o %aft b to turn twice z mu* z ano!r %aft a4 ,= ?is to happ5 we mu/ h a me*anism t w connect %aft a to %aft b & make %aft b turn twice z mu* z %aft a4 ,we c draw ! s*eme ( ?is me*anism 9 ,fig4 #ad3 a box1 /&+ = any k9d ( simple or complicat$ me*anism2 a l9e go+ into x1 /&+ = input ( ! quantity a2 a l9e go+ out ( x1 /&+ = output ( ! quantity b2 & a /atem5t say+ t b equals #b;a4 ,illu/ration3 ,,fig4 #ac4 ,swit*bo>d4 ,"o me*anism t w make %aft b turn twice z mu* z %aft a is a pair ( ge>s su* t3 7#a7 !y me% toge!r & 7#b7 ! ge> on %aft a has twice z _m tee? z ! ge> on %aft b 7,fig4 #ae74 ,on ! me*anical diff]5tial analyz] t ,,mit f9i%$ 9 #aicj1 a pair ( ge>s 0 ! me*anism actually us$ = d\bl+4 ,to make "o %aft turn twice z mu* z ano!r by ?is device1 we w\ld3 g ov] to ! ma*9e ) a screwdriv]2 pick out f a box two ge>s1 "o ) twice z _m tee? z ! o!r2 slide !m onto ! %afts t are to be connect$2 make ! ge>s me% toge!r2 & screw !m tight on _! %afts4 ,illu/ration3 ,,fig4 #ad4 ,s*eme ( a d\bl+ me*anism4 ,illu/ration3 ,,fig4 #ae4 ,example ( a d\bl+ me*anism4 ,on ! ,,mit diff]5tial analyz] ,no4 #b1 h[ev]1 we are bett] (f4 ,a mu* m conv5i5t device = d\bl+ is us$4 ,we make use (3 a ge>box 9 :i*!re are two %afts t may be ge>$ s t "o turns twice z mu* z ! o!r1 & two angle-indicator transmitt]s & receiv]s4 ,look+ at ! draw+ 7,fig4 #af71 we c see t3 %aft a drives %aft c to turn 9 /ep1 %aft c drives %aft d to turn twice z mu*1 & %aft d drives %aft b to turn 9 /ep4 ,"h we c accompli% d\bl+ by clos+ ! pairs ( swit*es t connect to ! ge>box %afts4 ,illu/ration3 ,angle indicators3 ,t1 transmitt]s1 & ,r1 receiv]s ,,fig4 #af4 ,ano!r example ( a d\bl+ me*anism4 ,above1 we h talk$ ab\t a me*anism ) ge>s t w\ld multiply ! am\nt ( turn+ by ! con/ant ratio #b4 ,b1 ( c\rse1 9 a calculation1 any ratio1 say #g4fe1 #c4adb1 1 might be ne$$1 n only #b4 ,9 ord] to h&le v>i\s con/ant ratios1 ge>boxes ( two k9ds are 9 diff]5tial analyz] ,no4 #b4 ,! fir/ k9d is a "o-digit ge>box4 ,x c be set to give any ( #aj ratios1 #j4a1 #j4b1 #j4c1 1 #a4j4 ,! second k9d is a f\r-digit ge>box4 ,x c be set to give any "o ( m ?an #aa ?\s& ratios1 #j4jjjj1 #j4jjja1 #j4jjjb1 1 #a4aaji1 #a4aaaj4 ,we c ?us multiply by con/ant ratios4 ,add]s ,we come n[ to a new me*anism1 ^: purpose is to add or subtract ! am\nt ( turn+ ( two %afts4 ,x is call$ an add]4 ,! s*eme ( x is %[n 9 ,fig4 #ag3 an input %aft ) am\nt ( turn+ a1 ano!r input %aft ) am\nt ( turn+ b1 & an output %aft ) am\nt ( turn+ a b4 ,! add] ess5tially is ano!r k9d ( ge>box1 call$ a diff]5tial ge> assembly4 ,?is "n is confus+3 ! ^w 8diff]5tial0 "h has no?+ to d ) ! ^w 8diff]5tial0 9 8diff]5tial analyz]40 ,?is me*anism is v closely relat$ to ! 8diff]5tial0 9 ! re> axle ( a motor c>1 :i* di/ributes a driv+ ?ru/ f ! motor to ! two re> :eels ( ! c>4 ,illu/ration3 ,,fig4 #ag4 ,s*eme ( an add] me*anism4 ,illu/ration3 ,,fig4 #ah4 ,example ( an add+ me*anism 7diff]5tial ge> assembly74 ,a type ( diff]5tial ge> assembly t w add is %[n 9 ,fig4 #ah4 ,?is is a set ( #e ge>s ,a to ,e4 ,! #b ge>s ,a & ,b are input ge>s4 ,! am\nt ( _! turn+ is a & b1 respectively4 ,!y bo? me% ) a ?ird ge>1 ,c1 free to turn1 b ! axis ( ,c is fa/5$ to ! inside rim ( a f\r?1 l>g] ge>1 ,d4 ,?us ,d is driv51 & ! am\nt ( its turn+ is 7a b7_/#b4 ,?is ge> me%es ) a ge> ,e ) half ! numb] ( tee?1 & s ! am\nt ( turn+ ( ,e is a b4 ,we c subtract ! turn+ ( "o %aft f ! turn+ ( ano!r simply by turn+ "o ( ! input %afts 9 ! opposite direction4 ,integrators ,ano!r me*anism 9 a diff]5tial analyz]1 & ! "o t makes x wor? :ile to build ! ma*9e1 is call$ an integrator4 ,?is me*anism c>ries out ! process ( integrat+1 ( add+ up a v l>ge numb] ( small *ang+ quantities4 ,figure #ai %[s :at an integrator is4 ,x has ?ree *ief p>ts3 a disc1 a little :eel1 & a screw4 ,! r\nd disc turns horizontally on its v]tical %aft4 ,! :eel re/s on ! disc & turns v]tically on its horizontal %aft4 ,! screw goes ?r\gh ! support ( ! disc2 :5 ! screw turns1 x *anges ! di/ance betwe5 ! edge ( ! :eel & ! c5t] ( ! disc4 ,illu/ration3 ,,fig4 #ai4 ,me*anism ( integrator4 ,n[ let u wat* ?is me*anism move4 ,if ! disc turns a little bit1 ! :eel press+ on x mu/ turn a little bit4 ,if ! screw turns a small am\nt1 ! di/ance betwe5 ! edge ( ! :eel & ! c5t] ( ! disc *anges4 ,! am\nt t ! :eel turns is d\bl$ if its di/ance f ! c5t] ( ! disc is d\bl$1 & halv$ if t di/ance is halv$4 ,s we see t3 7! total am\nt t ! :eel turns7 ,,equals ,,! ,,sum ,,( ,,all ,,! ,,small 7am\nts ( turn+71 ,,ea* ,,equal ,,to3 ,a ,,bit ,,( 7disc turn+7 ,,multipli$ ,,by ,,! 7di/ance f ! c5t] ( ! disc to ! edge ( ! :eel7 ,,apply+ ,,to ,,t ,,bit ,if we look back at our discussion ( integrat+ 7p4 #gb71 we see t ! capital words "h are j ! same z ^? us$ !re4 ,?us we h a me*anism t expresses integration3 7! total am\nt t ! :eel turns7 ,,equals ,,! ,,integral ,,( 7! di/ance f ! c5t] ( ! disc to ! :eel7 ,,) ,,respect ,,to 7! am\nt t ! disc turns7 ,! s*eme ( ?is me*anism is %[n 9 ,fig4 #bj4 ,= example1 suppose t ! screw measures ! spe$ at :i* a c> travels & t ! disc measures "t4 ,! :eel1 consequ5tly1 w measure di/ance travel$ by ! c>4 ,! me*anism ,,integrates spe$ ) respect to "t & gives di/ance4 ,illu/ration3 ,,fig4 #bj4 ,s*eme ( integrator4 ,?is me*anism is ! device t ,"l ,kelv9 talk$ ab\t 9 #ahgi & t ,dr4 ,bu% made practical 9 #aibe4 ,! me*anical difficulty is to make ! friction betwe5 ! disc & ! :eel turn ! :eel ) en\gh =ce to d o!r "w4 ,9 ! second diff]5tial analyz]1 ! angle indicator set on ! %aft ( ! :eel solves ! problem v neatly4 ,illu/ration3 ,,fig4 #ba4 ,graph ( air resi/ance coeffici5t4 ,function ,tables ,! behavior ( "s physical quantities c be describ$ only by a s]ies ( numb]s or a graphic curve4 ,= example1 ! resi/ance or drag ( ! air aga9/ a pass+ object is relat$ to ! spe$ ( ! object 9 a r complicat$ way4 ,"p ( ! relation is call$ ! drag coeffici5t or resi/ance coeffici5t2 a r\gh graph ( ?is is %[n 9 ,fig4 #ba4 ,?is graph %[s sev]al int]e/+ facts3 7#a7 :5 ! object is /ill1 !re is no air resi/ance2 7#b7 z x travels fa/] & fa/]1 air resi/ance rapidly increases2 7#c7 :5 ! object travels ) ! spe$ ( s\nd1 resi/ance is v great & increases enorm\sly2 7#d7 b1 :5 ! object />ts travel+ ) a spe$ ab\t #bj p] c5t fa/] ?an s\nd1 ! drag coeffici5t beg9s to decrease4 ,?is draw+ or graph %[s 9 "p h[ air resi/ance dep5ds on spe$ ( object2 9 o!r words1 x %[s ! drag coeffici5t z a function ( spe$ 7see ,supplem5t #b74 ,illu/ration3 ,,fig4 #bb4 ,po9t] foll[+ graph4 ,n[ we ne$ a way ( putt+ any function we wi% into a diff]5tial analyz]4 ,to d ?is1 we use a me*anism call$ a function table4 ,we draw a c>eful graph ( ! function accord+ to ! scale we wi% to use1 & we set ! graph on ! outside ( a l>ge drum 7,fig4 #bb74 ,= example1 we c put ! resi/ance coeffici5t graph on ! drum2 ! spe$ 7or indep5d5t v>iable7 goes ar\nd ! drum1 & ! resi/ance coeffici5t 7or dep5d5t v>iable7 goes along ! drum4 ,! ma*9e sl[ly turns ! drum1 z may be call$ = by ! problem4 ,a girl sits at ! function table & wat*es1 turn+ a h&:eel t keeps ! sight+ circle ( a po9t] "r ov] ! graph4 ,! turn+ ( ! h&:eel puts ! graph$ function into ! ma*9e4 ,in/ead ( employ+ a p]son1 we c make "o side ( ! graph black1 leav+ ! o!r side :ite1 & put 9 a phototube 7an electronic tube s5sitive to am\nt ( light7 t w /e] f pure black or pure :ite to half & half 7see ,fig4 #bc74 ,we d n ne$ _m function tables to put 9 in=mation1 because we c (t5 use integrators 9 neat comb9ations to avoid !m4 ,we %all say m ab\t ?is possibility lat]4 ,we c also use a function table to put out in=mation & to draw a graph4 ,to d s1 we disconnect ! h&:eel2 we connect ! %aft ( ! h&:eel to ! %aft t records ! function we are int]e/$ 92 we take out ! po9t] & put 9 a p52 & we put a blank %eet ( graph pap] ar\nd ! drum4 ,illu/ration3 ,,fig4 #bc4 ,phototube foll[+ graph4 ,we h n[ describ$ ! ma9 p>ts ( ! second ,,mit diff]5tial analyz]4 ,!y are ! p>ts t h&le numb]s4 ,we c n[ tell ! capacity ( ! diff]5tial analyz] by tell+ ! numb] ( ma9 p>ts t x holds3 ,%afts ,ab\t #acj ,"o-digit ge>boxes #ab ,f\r-digit ge>boxes #af ,add]s ,ab\t #af ,integrators #ah ,function tables #c ,on a simpl] level1 we c say t ! ma*9e holds ^! physical p>ts3 ,miles ( wire ,ab\t #bjj ,relays ,ab\t #cjjj ,motors ,ab\t #aej ,electronic tubes ,ab\t #bjjj ,,in/ruct+ ,,! ,,mit ,,diff]5tial ,,analyz] ,,no4 #b ,besides ! function tables = putt+ in=mation into ! ma*9e1 !re are ?ree me*anisms t read pun*$ pap] tape4 ,! ?ree tapes are call$ ! ,a tape1 ! ,b tape1 & ! ,c tape4 ,f ^! tapes ! ma*9e is set up to solve a problem4 ,suppose t we h decid$ h[ ! ma*9e is to solve a problem4 ,suppose t we "k ! numb] ( integrators1 add]s1 ge>boxes1 etc41 t mu/ be us$1 & "k h[ _! inputs & outputs are to be connect$4 ,to c>ry out ! solution1 we n[ h to put ! in/ructions & numb]s into ! ma*9e4 ,! ,a tape conta9s in/ructions = connect+ %afts 9 ! ma*9e4 ,ea* in/ruction connects a c]ta9 output ( "o type ( me*anism 7add]1 etc47 to a c]ta9 input ( ano!r type ( me*anism4 ,:5 ! ma*9e reads an in/ruction on ?is tape1 x connects electrically ! transmitt+ angle-indicator ( an output %aft to ! receiv+ angle-indicator ( ano!r input %aft4 ,n[ ! connect+ "p ( ! diff]5tial analyz] behaves z if x 7 v intellig5t3 x assigns an add] or an integrator or a ge>box1 etc41 to a new problem only if t me*anism is n busy4 ,= example1 if a problem tape calls = add] #c 79 ! li/ belong+ to ! problem71 ! ma*9e w assign ! fir/ add] t is n busy1 p]haps add] #ad 79 ! ma*9e71 to d ! "w4 ,ea* "t t add] #c 79 ! problem li/7 is call$ = 9 ! ,a tape1 ! ma*9e rememb]s t add] #ad 0 *os5 & assigns x ov] aga94 ,?is ability1 ( c\rse1 is v useful4 ,! ,b tape conta9s ! ratios at :i* ! ge>boxes are to be set4 ,= example1 suppose t we want ge>box #d 79 ! problem li/7 to *ange its input by ! ratio ( #j4begc4 ,! ma*9e1 aft] read+ ! ,a tape1 has assign$ ge>box #aa 79 ! ma*9e li/74 ,!n1 :5 ! ma*9e reads ! ,b tape1 x sets ! ratio 9 ge>box #aa to #j4begc4 ,! answ] to a diff]5tial equation is diff]5t = diff]5t />t+ conditions4 ,= example1 :5 we "k spe$ & "t & wi% to f9d di/ance travel$ & :]e we h arriv$1 we mu/ "k ! po9t at :i* we />t$4 ,we !re=e ne$ to arrange ! ma*9e s t we c put 9 diff]5t />t+ conditions 7or diff]5t initial conditions1 z ! ma!matician calls !m74 ,! ,c tape puts ! initial conditions into ! ma*9e4 ,= example1 read+ ! ,c tape = ! problem1 ! ma*9e f9ds t #cjjj %\ld1 at ! />t ( ! problem1 /& 9 c\nt] #d4 ,! ma*9e !n reads ! numb] at :i* c\nt] #d actually /&s1 say #fgbh4c4 ,x subtracts ! two numb]s & rememb]s ! diff]5ce1 -#cgbh4c4 ,& :5ev] ! ma*9e reads t c\nt] lat]1 f9d+1 say1 #idfh4d 9 x1 fir/ ! #cgbh4c is subtract$1 & !n ! answ] #egdj4a is pr9t$4 ,,answ]s ,in=mation may come out ( ! ma*9e 9 ei!r "o ( two ways3 9 pr9t$ numb]s or 9 a graph4 ,9 fact1 ! same quantity may come out ( ! ma*9e 9 bo? ways at ! same "t4 ,to obta9 a graph1 we *ange a function table f input to output1 put a p5 on x1 & h x draw ! graph4 ,! ma*9e has #c electric typewrit]s4 ,! ma*9e w take num]ical in=mation out ( ! c\nt]s at high spe$ ev5 :ile !y are turn+1 & x w put ! in=mation into relays4 ,!n x w read f ! relays into ! typewrit] keys "o by "o :ile !y type f left to "r across ! page4 ,,h[ ,,! ,,diff]5tial ,,analyz] ,,calculates ,up to ?is po9t 9 ?is *apt]1 ! au?or has tri$ to tell ! /ory ( ! diff]5tial analyz] 9 pla9 words4 ,b = read+ ?is section1 a little k ( calculus is necess>y4 7,see also ,supplem5t #b47 ,if y wi%1 skip ?is section1 & g on to ! next "o4 ,we h describ$ h[ v>y+ quantities1 or v>iables1 are op]at$ on 9 ! ma*9e 9 "o way or ano!r3 add+1 subtract+1 multiply+ by a con/ant1 ref]r+ to a table1 & integrat+4 ,:at d we d if we wi% to multiply #b v>iables toge!r8 ,a neat trick is to use ! =mula3 xy x dy y dx ,to multiply 9 ?is way requires #b integrators & #a add]4 ,! connections t are made betwe5 !m are z foll[s3 ,%aft x ,to ,integrator #a1 ,screw ,%aft x ,to ,integrator #b1 ,disc ,%aft y ,to ,integrator #a1 ,disc ,%aft y ,to ,integrator #b1 ,screw ,integrator #a1 ,:eel ,to ,add] #a1 ,input #a ,integrator #b1 ,:eel ,to ,add] #a1 ,input #b ,add] #a1 ,output ,to ,%aft express+ xy ,a product ( #b v>iables "u ! integral sign c be obta9$ a little m easily1 because ( ! curi\s p[]s ( ! diff]5tial analyz]4 ,?us1 if x is desir$ to obta9 xy dt1 we c use ! =mula3 xy dt x d y dt & ?is op]ation does n require an add]4 ,! connections are z foll[s3 ,%aft t ,to ,integrator #a1 ,disc ,%aft y ,to ,integrator #a1 ,screw ,integrator #a1 ,:eel ,to ,integrator #b1 ,disc ,%aft x ,to ,integrator #b1 ,screw ,integrator #b1 ,:eel ,to ,%aft express+ xy dt ,9 ord] to get ! quoti5t ( #b v>iables1 x_/y1 we c use "s m tricks4 ,fir/1 ! reciprocal #a_/y c be obta9$ by us+ ! two simultane\s equations3 #a #a -------- dy log y1 - -------- d7log y7 y y y ,! connections are z foll[s3 ,%aft y ,to ,integrator #a1 ,disc ,,& ,,to ,integrator #b1 ,:eel ,%aft log y ,to ,integrator #a1 ,:eel ,,& ,,to ,integrator #b1 ,disc ,%aft #a_/y ,to ,integrator #a1 ,screw1 ,,& ,,negatively ,,to ,integrator #b1 ,screw ,9 ord] to get x_/y1 we c !n multiply x by #a_/y4 ,we see t ?is setup gives u log y = no?+1 t is1 )\t ne$+ m integrators or o!r equipm5t4 ,cle>ly1 o!r tricks l ?is w give s9 x1 cos x1 e1 x1 & o!r functions t satisfy simple diff]5tial equations4 ,an integral ( a reciprocal c be obta9$ ev5 m directly4 ,suppose t #a y ---------- dt x #a ,!n ,dy ----------1 ,dy t x1 x & t x dy ,! connections !re=e are3 ,%aft t ,to ,integrator1 ,:eel ,%aft x ,to ,integrator1 ,screw ,%aft y ,to ,integrator1 ,disc ,! light :eel !n drives ! heavy disc4 ,cle>ly only ! angle-indicator device makes ?is possible at all4 ,naturally1 ! clos] ! :eel gets to ! c5t] ( ! disc1 t is1 x approa*+ z]o1 ! great] ! /ra9 on ! me*anism1 & ! m likely ! result is to be (f4 ,ma!matically1 ( c\rse1 ! limit ( #a_/x z x approa*es z]o equals inf9ity1 & ?is gives tr\ble 9 ! ma*9e4 ,!re is no /&>d ma!matical me?od = solv+ any diff]5tial equation4 ,b ! ma*9e provides a /&>d direct me?od = solv+ all diff]5tial equations ) only "o indep5d5t v>iable4 ,fir/3 assign a %aft = ea* t]m t appe>s 9 ! equation4 ,= example1 ! highe/ d]ivative t appe>s & ! indep5d5t v>iable are bo? assign$ %afts4 ,! integral ( ! highe/ d]ivative is easily obta9$1 & ! integral ( t integral1 etc4 ,second3 connect ! %afts s t all ! ma!matical relations are express$4 ,bo? explicit & implicit equations may be express$4 ,?ird3 = any %aft !re mu/ be j "o drive1 or s\rce ( torque4 ,a %aft may1 h[ev]1 drive m ?an "o o!r %aft4 ,f\r?3 *oose scale factors s t ! limits ( ! ma*9e are n exce$$ yet at ! same "t are well us$4 ,= example1 ! mo/ t an integrator or a function table c move is #a or #b feet4 ,also1 ! numb] ( full turns made by a %aft 9 repres5t+ its v>iable %\ld be l>ge1 (t5 betwe5 #ajjj & #aj1jjj4 ,( c\rse1 z ) all ^! l>ge ma*9es1 anyone w\ld ne$ "s mon?s ( actual practice be=e he c\ld put on a problem & get an answ] effici5tly4 ,,an ,,appraisal ,,( ,,! ,,ma*9e ,! second ,,mit diff]5tial analyz] is probably ! be/ ma*9e ev] built = solv+ mo/ diff]5tial equations4 ,x regul>ly has an accuracy ( #a "p 9 #aj1jjj4 ,?is is en\gh = mo/ eng9e]+ problems4 ,if great] accuracy is ne$$1 ! second diff]5tial analyz] _c provide x4 ,once 9 a :ile ! ma*9e c rea* an accuracy ( #a "p 9 #ej1jjj2 b1 to balance ?is1 x is sometimes less accurate ?an #a "p 9 #aj1jjj4 ,! ,,mit diff]5tial analyz] ,no4 #b c f9d answ]s to problems v quickly4 ,! "t = sett+ up a problem to be run on ! ma*9e ranges f #e to #ae m9utes4 ,! "t = prep>+ ! tapes t set up ! problem is1 ( c\rse1 long]2 b ! pun* = prep>+ ! tape is a sep>ate ma*9e & does n delay ! diff]5tial analyz]4 ,! "t = ! ma*9e to produce a s+le solution to a problem ranges usually f #c m9utes to a half-h\r4 ,x is easy to put on a problem1 run a few solutions1 take ! problem (f1 /udy ! results1 *ange a few numb]s1 & !n put ! problem back on aga94 ,?is virtue is a great help 9 a se>* 9 a new field4 ,:ile ! /udy is go+ on1 "t is n wa/$1 = ! ma*9e c be busy ) a diff]5t problem4 ,runn+ a problem a second "t is a good *eck on ! reliability ( an answ]4 ,=1 :5 ! problem is run ! second "t1 we c arrange t ! ma*9e w r\te ! problem to o!r me*anisms4 ,! ma*9e has a control panel4 ,"h ! op]ator wat*+ ! ma*9e c tell :at units are do+ :at p>ts ( :at problems4 ,if a unit gives tr\ble or ne$s to be inspect$1 ! cl]k c ?r[ a 8busy0 swit*4 ,!n ! ma*9e _c *oose t unit = "w to be done4 ,! ma*9e conta9s _m protect+ signals & al>ms4 ,x is idle = repairs less ?an #e p] c5t ( ! "t4 ,x is n easy to det]m9e ! total co/ ( ! ma*9e1 = x 0 p>tially f9anc$ by sev]al l>ge gifts4 ,also1 mu* ( ! labor 0 done by graduate /ud5ts 9 return = ! in/ruction t !y ga9$4 ,! actual out-(-pocket co/ 0 ab\t #abe1jjj4 ,if ! ma*9e 7 to be built by indu/ry1 ! co/ w\ld likely be m ?an #d times z mu*4 ,a simple diff]5tial analyz]1 h[ev]1 c be *eap4 ,small scale diff]5tial analyz]s h be5 built = less ?an #ajjj2 _! accuracy has be5 ab\t #a "p 9 #ajj4 ,!re are _m ?+s t ?is ma*9e _c d2 x 0 n built to d !m4 7#a7 ,x _c *oose me?ods ( solution4 7#b7 ,x _c p]=m /eps 9 solv+ a problem t dep5d on results z !y are f\nd4 7#c7 ,x _c solve diff]5tial equations conta9+ two or m indep5d5t v>iables4 ,su* equations are call$ p>tial diff]5tial equations2 !y appe> 9 connection ) ! fl[ ( heat or air or electricity 9 #b or #c dim5sions1 & else:]e4 7#d7 ,x _c solve problems requir+ #f or m digits ( accuracy4 7#e7 ,! ma*9e1 :ile runn+1 c /ore numb]s only = an in/ant1 s9ce x op]ates on ! pr9ciple ( smoo?ly *ang+ quantities2 h[ev]1 :5 ! ma*9e /ops1 ! numb] la/ held by ea* device is p]man5tly /or$4 ,none ( ^! comm5ts1 h[ev]1 are criticisms ( ! ma*9e4 ,in/ead !y %[ av5ues ( developm5t = future ma*9es4 ,z 0 said be=e1 = solv+ mo/ diff]5tial equations1 ?is ma*9e has no equal to date4 ,! range ( problems :i* any diff]5tial analyz] c d dep5ds mo/ly on ! numb] ( its integrators4 ,! second diff]5tial analyz] has #ah & provides = expansion to #cj4 ,! ma*9e is con/ruct$1 also1 s t x c be op]at$ 9 #c indep5d5t sections1 ea* work+ to solve a diff]5t problem4 ,! diff]5tial analyz] c op]ate unatt5d$4 ,aft] x has be5 set up & ! fir/ few results exam9$1 x c be left alone to gr9d out l>ge blocks ( answ]s4 ,an int]e/+ example ( ! exp]im5tal use ( a diff]5tial analyz] 9 a comm]cial bus9ess is ! foll[+3 ,9 ,great ,brita91 ,r4 ,e4 ,be>d ( ! ,pe>l ,assurance ,company built a diff]5tial analyz] ) #f integrators4 ,he appli$ ?is ma*9e to compute to #c figures c]ta9 insurance values kn[n z cont9u\s annuities & cont9u\s cont+5t insurances4 ,he has describ$ ! ma*9e & ! application he made 9 a pap] publi%$ 9 ! ,j\rnal ( ! ,in/itute ( ,actu>ies1 ,vol4 #ga1 #aidb1 pp4 #aic-bbg4 ,*apt] #f ,,accuracy ,,to #bc ,,digits3 ,,h>v>d',s ,,ibm ,,automatic ,,sequ5ce-,,controll$ ,,calculator ,"o ( ! fir/ giant bra9s to be f9i%$ 0 ! ma*9e 9 ! ,computation ,laboratory at ,h>v>d ,univ]sity call$ ! ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator4 ,?is great me*anical bra9 />t$ "w 9 ,april #aidd & has be5 runn+ #bd h\rs a day almo/ all ! "t ev] s9ce4 ,x has produc$ quantities ( in=mation = ! ,unit$ ,/ates ,navy4 ,al?\gh _m problems t h be5 plac$ on x h be5 classifi$ by ! ,navy z confid5tial1 ! ma*9e itself is fully public4 ,! way x 0 work+ on ,sept4 #a1 #aide1 has be5 ?or\ghly describ$ 9 a #edj-page book publi%$ 9 #aidf1 ,volume ,i ( ! ,annals ( ! ,h>v>d ,computation ,laboratory1 entitl$ ,manual ( ,op]ation ( ! ,automatic ,sequ5ce-,controll$ ,calculator4 ,s9ce !n ! ma*9e has be5 improv$ 9 _m ways4 ,?is ma*9e does ?\s&s ( calculat+ /eps1 "o aft] ano!r1 accord+ to a s*eme fix$ ahead ( "t4 ,?is prop]ty is :at gives ! ma*9e its "n3 automatic1 s9ce ! individual op]ations are automatic1 once ! pun*$ tape fix+ ! *a9 ( op]ations has be5 put on ! ma*9e1 & sequ5ce-controll$1 s9ce control ov] ! sequ5ce ( its op]ations has be5 built into ! ma*9e4 ,,orig9 ,,& ,,developm5t ,m ?an a hundr$ ye>s ago1 an ,engli% ma!matician & actu>y1 ,*>les ,babbage 7#agib-ahga71 design$ a ma*9e--or eng9e z he call$ x--t w\ld c>ry out ! sequ5ces ( ma!matical op]ations4 ,9 ! #ahcj's he receiv$ a gov]nm5t grant to build an analytical eng9e :]eby long *a9s ( calculations c\ld be p]=m$4 ,b he 0 unsuccessful1 because ! ref9$ physical devices necess>y = quantities ( digital calculation 7 n yet develop$4 ,only 9 ! #aicj's did ^! physical devices become suffici5tly v]satile & reliable = a calculator ( hundr$s ( ?\s&s ( p>ts to be successful4 ,! ,automatic ,sequ5ce-,controll$ ,calculator at ,h>v>d 0 l>gely ! concept ( ,pr(essor ,h[>d ,h4 ,aik5 ( ,h>v>d4 ,x 0 built ?r\gh a p>tn]%ip ( ef=ts1 ideas1 & eng9e]+ betwe5 him & ! ,int]national ,bus9ess ,ma*9es ,corporation1 9 ! ye>s #aicg to #aidd4 ,! calculator 0 a gift f ,,ibm to ,h>v>d ,univ]sity4 ,"s v useful additional control units1 nam$ ! ,subsidi>y ,sequ5ce ,me*anism1 7 built at ! ,h>v>d ,computation ,laboratory 9 #aidg & jo9$ to ! ma*9e4 ,illu/ration3 ,,fig4 #a4 ,s*eme ( ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator4 ,,g5]al ,,organization ,! ma*9e 7see ,fig4 #a7 is ab\t #ej feet long1 #h feet high1 & ab\t #b feet wide4 ,x consi/s ( #bb panels2 #ag ( !m are set 9 a /raight l9e1 & ! la/ #e are at ! re> ( ! ma*9e4 ,9 ! s*eme ( ! ma*9e %[n 9 ,fig4 #a1 ! details y w\ld see 9 a photograph h be5 left out4 ,in/ead y see ! sections ( ! ma*9e t are important because ( :at !y d3 input1 memory1 control1 & output4 ,:y d we n see a section label$ 8comput]08 ,because 9 ?is me*anical bra9 ! comput+ "p ( ! ma*9e is closely jo9$ to ! memory3 e /orage regi/] c add & subtract4 ,we %all soon discuss ^! sections ( ! ma*9e m fully4 ,,physical ,,devices ,n[ 9 ord] = any bra9 to "w1 physical devices mu/ be us$4 ,= example1 9 ! human body1 a n]ve is ! physical device t c>ries in=mation f "o "p ( ! body to ano!r4 ,9 ! ,h>v>d ma*9e1 an insulat$ wire is ! physical device t c>ries in=mation f "o "p ( ! ma*9e to ano!r4 ,"o side ( e panel 9 ! ,h>v>d ma*9e is heavily lad5 ) a great network ( wires4 ,betwe5 ! panels1 y c see 9 _m places cables z ?ick z y\r arm & conta9+ hundr$s ( wires4 ,m ?an #ejj miles ( wire are us$4 ,! physical devices 9 ! ,h>v>d ma*9e are num]\s1 z we w\ld expect4 ,x is p]haps n surpris+ t ?is ma*9e has m ?an #gfj1jjj p>ts4 ,b1 curi\sly en\gh1 !re are only #g ma9 k9ds ( physical devices 9 ! major "p ( ! ma*9e4 ,!y are3 wire1 two-position swit*es1 two-position relays 7see ,*apt] #b71 t5-position swit*es1 t5-position relays1 buttons1 & cam contacts 7see bel[74 ,^! are ! devices t h&le in=mation 9 ! =m ( electrical impulses4 ,!y c be comb9$ by electrical circuits 9 a great v>iety ( ways4 ,!re are1 ( c\rse1 o!r k9ds ( physical devices t are important1 b !y are n num]\s1 & !y h r simple duties4 ,look+ at ! ma*9e1 y c see ?ree examples easily4 ,physical devices ( ! fir/ k9d conv]t pun*$ holes into electrical impulses3 #b c>d fe$s1 #d tape fe$s4 ,^? ( ! second k9d conv]t electrical impulses into pun*$ holes3 #a c>d pun*1 #a tape pun*4 ,^? ( ! ?ird k9d conv]t electrical impulses into pr9t$ *>act]s3 #b electric typewrit]s4 ,we c ?9k ( a f\r? k9d ( physical device t w\ld be a help1 b1 at pres5t writ+1 x does n yet exi/3 a device t conv]ts pr9t$ *>act]s into electrical impulses4 ,! ,h>v>d ma*9e1 ( c\rse1 is complicat$4 ,b x is complicat$ because ( ! v>iety ( ways 9 :i* relatively simple devices h be5 connect$ toge!r to make a ma*9e t ?9ks4 ,swit*es ,a two-position swit* 7see ,fig4 #b7 turn$ by h& connects a wire to ei!r "o ( #b o!rs4 ,^! #b positions may /& = 8yes0 & 8no10 #j & #a1 etc4 ,!re are _m two-position swit*es 9 ! ma*9e4 ,a t5-position swit* or dial swit* 7see ,fig4 #c7 turn$ by h& connects ! wire runn+ into ! c5t] ( ! swit* ) a wire at any "o ( t5 positions #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i ar\nd ! edge4 ,!re are ov] #adjj dial swit*es 9 ! ma*9e4 ,h[ does turn+ ! po9t] on ! top ( ! dial make connection betwe5 ! c5t] wire & ! edge wire8 ,"u ! face ( ! dial is ! "p t works1 a %ort rod ( metal fa/5$ to ! po9t] 7%[n ) da%es 9 ,fig4 #c74 ,:5 ! po9t] turns1 ?is rod also turns1 mak+ ! desir$ connection4 ,illu/ration3 ,,fig4 #b4 ,two-position swit*4 ,illu/ration3 ,,fig4 #c4 ,dial swit*4 ,relays ,two-position relays--m (t5 call$ j relays 7see ,*apt] #b7--;d ! automatic r\t+ ( ! electrical impulses t cause comput+ to take place4 ,ea* relay may take #b positions1 op5 or clos$1 & ^! positions may /& = #j & #a4 ,!re are m ?an #cjjj relays 9 ! ,h>v>d ma*9e4 ,a magnet pull+ "o way & a spr+ pull+ ! o!r way are suffici5t 9 an ord9>y relay to give #b positions1 8on0 & 8(f10 8yes0 & 8no10 #j & #a4 ,b h[ d we make a relay t c hold any "o ( #aj positions8 ,figure #d %[s "o s*eme = a t5-position relay4 ,! arm c take any "o ( #aj positions1 connect+ ! contact ,common to any "o ( ! contacts ,o1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 & #i s t curr5t c fl[4 ,! ge> turns all ! "t4 ,:5 an impulse comes 9 on ! ,pickup l9e1 ! clut* connects ! arm to ! ge>4 ,:5 an impulse comes 9 on ! ,drop-out l9e1 ! clut* disconnects ! arm f ! ge>4 ,= example1 suppose t ! t5-position relay is /opp$ at contact #b1 z %[n4 ,suppose t we n[ pick up ! relay1 hold x j long en\gh to turn #c /eps1 & !n drop x out4 ,! relay w n[ re/ at contact #e4 ,illu/ration3 ,,fig4 #d4 ,s*eme ( a t5-position relay1 or c\nt] position4 ,illu/ration3 ,,fig4 #e4 ,s*eme ( a c\nt] :eel4 ,9 ! ,h>v>d ma*9e1 ! t5-position relays1 mu* l ! s*eme %[n1 d ! same "w z c\nt] :eels 7,fig4 #e7 9 an ord9>y desk calculat+ ma*9e1 & s !y are (t5 spok5 ( z c\nt] positions 9 ! ,h>v>d ma*9e4 ,!y are v useful 9 ! ma*9e n only because !y express ! #aj decimal digits #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i b also because add+ & subtract+ numb]s is accompli%$ by turn+ !m ?r\gh ! prop] numb] ( /eps4 ,9 fact1 an additional impulse is provid$ :5 ! c\nt] position turns f #i to #j1 = purposes ( c>ry4 ,a gr\p ( #bd c\nt] positions makes up ea* /orage c\nt]--or /orage regi/]--9 ! ma*9e4 ,!re are #bbjj ( ^! c\nt] positions4 ,ea* is connect$ to a cont9u\sly runn+ ge> on a small %aft 7,fig4 #f74 ,all ^! %afts are connect$ by o!r ge>s & %afts to a ma9 drive %aft1 & !y are driv5 by a #e-;horsep[] motor at ! back ( ! ma*9e4 ,:5 a c\nt] position is suppos$ to /ep1 a clut* connects ! drive to ! runn+ ge>1 & ! c\nt] position /eps4 ,:5 ! c\nt] position is suppos$ to /ay un*ang$1 ! clut* is disconnect$ & ! driv+ ge> runs free4 ,9 fact1 :5 y fir/ approa* ! ,h>v>d ma*9e1 ab\t ! fir/ ?+ y are aw>e ( is ! runn+ ( ^! ge>s & ! int]mitt5t :irr+ & click+ ( ! c\nt] positions z !y /ep4 ,! ma*9e gives a f9e impression ( be+ busy6 ,illu/ration3 ,,fig4 #f4 ,s*eme ( c\nt] #af4 ,tim+ ,contacts ,a button 7see ,fig4 #g7 is a device = clos+ an electric circuit :5 & only :5 y pu% x4 ,a simple example is ! button = r++ a bell3 y pu% ! button1 a circuit is clos$1 & some?+ happ5s4 ,:5 y let g1 ! circuit is op5$4 ,! ,h>v>d ma*9e has a button = />t+1 a button = /opp+1 & _m o!rs4 ,illu/ration3 ,,fig4 #g4 ,button4 ,illu/ration3 ,,fig4 #h4 ,cam1 ) #e lobes & contact4 ,a cam contact 7see ,fig4 #h7 is an automatic device = clos+ an electric circuit = j a %ort int]val ( "t4 ,:5 ! lobes on ! cam /rike ! contact1 x closes & curr5t fl[s4 ,:5 ! lobes h gone by1 ! spr+ pu%es op5 ! contact1 & no curr5t fl[s4 ,j z a two-position relay is ! automatic equival5t ( a two-position swit*1 & a t5-position relay is ! automatic equival5t ( a t5-position swit*1 s a cam contact is ! automatic equival5t ( a button4 ,all ! cams 9 ! ma*9e h #bj pockets :]e small r\nd metal lobes may or may n be ins]t$4 ,ea* cam makes a full turn once 9 _/ ( a second & is 9 "t ) all ! o!rs4 ,?us we c "t all ! electrical circuits 9 ! ma*9e 9 units ( _/ ( a second4 ,,numb]s ,numb]s 9 ! ma*9e regul>ly consi/ ( #bc decimal digits4 ,! #bd? num]ical position at ! left 9 any regi/] conta9s only #j = a positive numb] & only #i = a negative numb]4 ,n9es complem5ts 7see ,supplem5t #b7 are us$ = negative numb]s4 ,= example1-#jjbhd is repres5t$ z #iiigae1 suppos+ t we _h #e-;digit numb]s in/ead ( #bc-;digit numb]s4 ,! sum ( two n9es complem5ts is automatically correct$ s t x is /ill a correct n9es complem5t4 ,! device t accompli%es ?is is call$ end-ar\nd-c>ry 7see ,supplem5t #b74 ,! decimal po9t is fix$ = ea* problem2 9 o!r words1 9 any problem1 ! decimal po9t is consi/5tly kept 9 "o place1 usually betwe5 ! #ae? & #af? decimal columns f ! "r4 ,,h[ ,,in=mation ,,goes ,,into ,,! ,,ma*9e ,num]ical in=mation may g into ! ma*9e 9 any "o ( #c ways3 7#a7 by regul> ,,ibm pun* c>ds1 us+ /&>d ,,ibm c>d fe$s 7panel #af72 7#b7 by h&-set dial swit*es 7panels #a1 #b72 & 7#c7 by long loops ( pun*$ tape plac$ on ! value tape fe$s 7panels #ab to #ad74 ,?ree sets ( #bd columns ea* pun*$ on a regul> ,,ibm pun* c>d c be us$ to s5d #c numb]s & _! signs into ! ma*9e 9 "o ma*9e cycle4 ,?is is ! fa/e/ way = giv+ numb]s to ! ma*9e1 b ! mo/ limit$2 = ! c>ds mu/ be ref]r$ to 9 ord] & c be ref]r$ to automatically only once4 ,also1 !re is ! risk t !y may be out ( ord]4 ,a c>d may be pass$ ?r\gh ! ma*9e )\t read+2 ?is saves "s sort+ 9 prep>+ c>ds = ! ma*9e4 ,ma*9es = prep>+ ! c>ds are regul> ,,ibm key pun*es1 & ma*9es = sort+ !m aft] prep>ation are regul> ,,ibm c>d sort]s4 ,9 panels #a & #b !re are #fj regi/]s by :i* un*ang+ numb]s l #a1 or #c4adaeibfe1 or #g4fe may be put into ! ma*9e4 ,^! are call$ ! con/ant regi/]s4 ,ea* con/ant regi/] consi/s ( #bd dial swit*es & conta9s #bc digits & a sign1 #j if positive & #i if negative4 ,:5ev] ! ma!matician says a c]ta9 con/ant is ne$$ = a problem1 ! op]ator ( ! ma*9e walks ov] to ^! panels1 &1 :ile ! ma*9e is turn$ (f1 sets ! dial swit*es = ! numb]1 "o by "o1 by h&4 ,if we ne$ #dj con/ants ( #aj digits ea* = a problem1 !n ! op]ator sets #djj dial swit*es by h& & makes c]ta9 t ! rema9+ #ad swit*es 9 ea* ( ! #dj con/ant regi/]s us$ are ei!r at #j or #i1 dep5d+ on ! sign ( ! numb]4 ,only !n c he return to />t ! ma*9e4 ,illu/ration3 ,,fig4 #i4 ,value tape code4 ,! ?ird means by :i* num]ical in=mation c be put into ! ma*9e is ! value tape fe$s1 9 panels #ab1 #ac1 & #ad4 ,"h ! ma*9e c consult tables ( numb]s4 ,! numb]s are pun*$ on pap] tape #bd holes wide1 made ( pun*-c>d /ock4 ,tapes = ! value tape fe$s may be prep>$ by h& or by ! ma*9e itself us+ pun* c>ds or ma*9e calculation4 ,! tapes use equally spac$ argum5ts 7see ,supplem5t #b74 ,! tape pun* *anges ! decimal digits 9 its keybo>d into ! foll[+ pun*+ code 7see ,fig4 #i73 #j #jjjj #e #aajj #a #ajjj #f #ajaj #b #jajj #g #ajja #c #jjaj #h #jaaj #d #jjja #i #jaja ,"h ! #a d5otes a pun*$ hole & #j no pun*$ hole1 & ! #d columns f left to "r ( ! code correspond to #d r[s ( ! pap] tape f bottom to top4 ,to make sure ! value tape is correct1 ! ma*9e itself c read ! value tape & *eck x ma!matically or comp>e x ) pun*-c>d values4 ,,h[ ,,in=mation ,,comes ,,out ,,( ,,! ,,ma*9e ,in=mation comes out ( ! ma*9e 9 any "o ( ?ree ways3 7#a7 by pun*+ on ,,ibm c>ds ) a regul> ,,ibm c>d pun* t is built into ! ma*9e 7panel #ag71 7#b7 by typ+ on pap] %eets ) electric typewrit]s 7panels #af & #ag71 & 7#c7 by pun*+ pap] tape #bd holes wide ( ! same k9d z is f$ into ! ma*9e4 ,usually1 "o ( ! electric typewrit]s is us$ to pr9t a result = a visual *eck & to pr9t x be=e ! ma*9e makes a specifi$ *eck ( ! value4 ,!n1 ab\t #aj seconds lat]1 aft] ! result has be5 *eck$ z specifi$ 9 ! ma*9e1 ! *eck$ result is pr9t$ by ! second typewrit]4 ,9 ! second typewrit]1 a special "o-use c>bon ribbon ( pap] is us$ to produce copy = publication by a photographic process4 ,! c>d pun* writes a numb] m rapidly ?an an electric typewrit]4 ,?is extra spe$ is sometimes v useful4 ,h[ev]1 ! pun*'s *ief purpose is to record int]m$iate results on pun* c>ds4 ,!n1 if !re is a ma*9e failure1 & if ! problem has be5 well organiz$1 ! problem may be run ov] f ^! int]m$iate results1 in/ead ( requir+ a return to ! orig9al />t+ in=mation4 ,! tape pun* us$ = prep>+ tape by h& c also be op]at$ by cable f ! ma*9e4 ,,h[ ,,in=mation ,,is ,,h&l$ ,,9 ,,! ,,ma*9e ,! ma*9e is a me*anical bra94 ,s1 betwe5 tak+ 9 in=mation & putt+ out in=mation1 ! ma*9e does "s 8?9k+40 ,x does ?is ?9k+ accord+ to in/ructions4 ,! in/ructions g into ! ma*9e z3 7#a7 ! sett+ ( swit*es1 or 7#b7 ! press+ ( buttons1 or 7#c7 ! wir+ ( plugbo>ds1 or 7#d7 fe$+ 9 tape pun*$ ) holes4 ,! in/ructions are rememb]$ 9 ! ma*9e 9 ^! #d ways1 & we c call ^! sets ( devices ! control ( ! ma*9e4 ,to illu/rate3 ,"o ( ! buttons press$ = e problem is ! ,/>t ,key3 :5 y press x1 ! ma*9e />ts to "w on ! problem4 ,"o ( ! swit*es ) :i* y give in/ructions is a swit* t turns electric typewrit] #a on or (f4 ,"o ( ! plugbo>ds conta9s "s hubs by :i* y c tell ! ma*9e h[ _m figures to *oose 9 ! quoti5t :5 divid+1 = cle>ly y d n ne$ a quoti5t ( #bc figures e "t ! ma*9e divides4 ,y c h #e *oices 9 any "o problem2 y c specify !m by plugg+1 & y c call = any "o ( #e *oices ( quoti5t size f "t to "t dur+ ! problem4 ,9 _m cases1 :5 we wi% ! ma*9e to d ! same ?+ = all ( a s+le problem & d x :5ev] ! occasion arises1 we c put ! in/ruction into ! wir+ ( a plugbo>d4 ,we use plugbo>d wir+1 = example1 9 fix+ ! decimal po9t 9 multiplication1 s t ! product w read out prop]ly1 & 9 guid+ ! op]ation ( ! typewrit]s1 s t pr9t+ w take place 9 ! columns :]e we want x4 ,sequ5ce ( ,/eps ,! mo/ important "p ( ! control ( ! ma*9e is ! sequ5ce-tape fe$ & its sequ5ce-control tape4 ,^! tell ! ma*9e a great "p ( :at op]ations are to be p]=m$4 ,illu/ration3 ,,fig4 #aj4 ,sequ5ce-control tape code4 ,at ! end ( ! room :]e ! ma*9e is1 !re is ! special tape pun* m5tion$ above4 ,x holds a big spool ( c>d /ock t is ?91 flexible1 smoo?1 & t\gh4 ,) "o keybo>d we may prep>e value tape4 ,) ano!r keybo>d we prep>e ! sequ5ce-control tape4 ,! tape 7see ,fig4 #aj7 conta9s places = #bd r\nd pun*$ holes 9 ea* r[4 ,"s & only "s ( ^! holes are pun*$4 ,ea* r[ ( pun*$ holes is equival5t to an in/ruction to ! ma*9e & is call$ a l9e ( cod+ or cod+ l9e4 ,9 g5]al1 ! in/ruction has ! =m3 ,take a numb] out ( ,regi/] ,a2 put ! numb] into ,regi/] ,b2 & p]=m op]ation ,c4 ,! fir/ gr\p ( #h holes at ! left is call$ ! ,a field or ! out-field4 ,"h we tell ! ma*9e :]e a numb] is to be tak5 f4 ,! middle gr\p ( #h holes is call$ ! ,b field or ! 9-field4 ,"h we tell ! ma*9e :]e a numb] is to be put4 ,! la/ gr\p ( #h holes is call$ ! ,c field or ! miscellane\s field4 ,"h we tell ! ma*9e "p or all ( ! op]ation t is to be p]=m$4 ,to illu/rate 7see ,fig4 #aj71 we h holes #c1 #b1 #a pun*$ 9 ! ,a field1 holes #c1 #b pun*$ 9 ! ,b field1 & hole #g pun*$ 9 ! ,c field4 ,n[ #cba is ! code--or ma*9e language1 or ma*9e call numb]--= /orage c\nt] #g2 #cb is ! code = /orage c\nt] #f2 & #g 9 ! ,c field is ! code 79 ?is case1 & g5]ally7 = 8,add1 & read ! next l9e ( cod+40 ,s1 if we pun* out ?is l9e ( cod+ & put ! tape on ! ma*9e1 we tell ! ma*9e to read ! numb] 9 c\nt] #g1 add x into c\nt] #f1 & proce$ to ! next l9e ( cod+ & read t4 ,! holes 9 ea* gr\p ( #h holes f left to "r are numb]$3 #h1 #g1 #f1 #e1 #d1 #c1 #b1 #a4 ,! code #fca1 = example1 means t holes #f1 #c1 #a are pun*$ & t no holes are pun*$ at #h1 #g1 #e1 #d1 #b4 ,s9ce x is m natural1 ! code is read f left to "r1 or #fca1 in/ead ( f "r to left 9 ! sequ5ce #acf4 ,! devices 9 ! ma*9e h 9-codes1 us$ 9 ! 9-field1 & out-codes1 us$ 9 ! out-field4 ,= ea* ( ! #gb regul> /orage c\nt]s1 ! 9-code & ! out-code are ! same4 ,! fir/ #h /orage c\nt]s h ! codes #a1 #b1 #ba1 #c1 #ca1 #cb1 #cba1 #d1 #da2 ! la/ #b /orage c\nt]s1 ! #ga/ & ! #gbnd1 h ! codes #gcba1 #gd4 ,! con/ant regi/]s--(t5 call$ con/ant swit*es1 or j swit*es--naturally h only out-codes1 s9ce numb]s c be ent]$ into ! con/ant regi/]s only by sett+ dial swit*es by h&4 ,! fir/ #h con/ant regi/]s h ! out-codes #gda1 #gdb1 #gdba1 #gdc1 #gdca1 #gdcb1 #gdcba1 #ge1 & ! #ei? & #fj? con/ant regi/]s h ! out-codes #hba1 #hc4 ,transf]r+1 ,add+1 & ,cle>+ ,ea* /orage c\nt] has ! prop]ty t any numb] transf]r$ into x is add$ into x4 ,= example1 ! in/ruction ,take ! numb] 9 swit* #gda2 transf] x into /orage regi/] #cba is cod$3 #gda1 #cba1 #g ,! #g 9 ! ?ird column is an in/ruction to ! sequ5ce-tape fe$ to turn up to ! next cod+ l9e & read x4 ,if any numb] is already /or$ 9 regi/] #cba1 ! cont5t ( #gda w be add$ to x1 & ! total w !n be /or$ 9 #cba4 ,resett+ or cle>+ a regul> /orage regi/] is accompli%$ by a cod+ t is a dep>ture f ! usual s*eme ( 8out0 & 8940 ,! in/ruction ,cle> regi/] #cba2 read ! next cod+ l9e is cod$3 #cba1 #cba1 #g ,simil>ly1 y c cle> any o!r regul> /orage regi/] if y repeat its code 9 ! out-& 9-fields4 ,h[ev]1 a few ( ! /orage regi/]s 9 ! ma*9e h special reset codes1 & ^! may occur 9 any ( ! ?ree fields ,a1 ,b1 ,c4 ,z ! result ( a rec5t modification ( ! ma*9e1 y c easily d\ble ! numb] 9 any /orage regi/]4 ,= example1 ! in/ruction ,d\ble ! numb] 9 regi/] #cba2 read ! next cod+ l9e is cod$3 #cba1 #cba1 #gdc ,subtract+ ,if ! numb] 9 swit* #gda is to be subtract$ f ! numb] 9 /orage c\nt] #cba1 ! in/ruction is *ang$ into3 ,take ! negative ( ! numb] 9 swit* #gda2 transf] x into /orage regi/] #cba2 read ! next l9e ( cod+ ,! cod+ l9e becomes3 #gda1 #cba1 #gcb ,by putt+ #cb 9 ! ,c field1 we cause ! numb] 9 swit* #gda to be subtract$ f :atev] numb] is 9 regi/] #cba4 ,we h #b m *oices 9 add+ & subtract+4 ,! value ( ! numb] )\t reg>d to sign--9 o!r words1 its absolute value 7see ,supplem5t #b7--may be add$ or subtract$4 ,! in/ruction ,add ! absolute value ( is express$ by a ,c field code #b1 & ! in/ruction ,add ! negative ( ! absolute value ( is express$ by a ,c field code #a4 ,multiply+ ,:5 we wi% to multiply "o numb] by ano!r & get a product1 we h #c numb]s4 ,we tell ! ma*9e ab\t ea* ( ^! numb]s on a sep>ate l9e ( cod+4 ,multiplication is signal$ by s5d+ a numb] into ! multiplic& c\nt]4 ,! multiplic& c\nt] has an 9-code #gfa4 ,if ! multiplic& is 9 #cba1 ! in/ruction is3 ,take ! numb] 9 #cba2 ent] x z multiplic&2 read ! next cod+ l9e ,! cod+ is3 #cba1 #gfa1 #g ,on ! ?ird foll[+ cod+ l9e1 ! multipli] is s5t into ! multipli] c\nt]4 ,if ! multipli] is 9 swit* #gda1 ! in/ruction is3 ,take ! numb] 9 #gda2 ent] x z multipli]2 read ! next cod+ l9e ,! cod+ is3 #gda1 ----1 #g ,we d n pun* any?+ 9 ! middle field3 ! ma*9e is 8educat$0 & 8kn[s0 t x has />t$ a multiplication & ne$s a multipli]1 & x expects ?is multipli] 9 ! ?ird cod+ l9e4 ,to h no code = ! multipli] c\nt] is1 ( c\rse1 a dep>ture f ! g5]al rule1 b x saves "s pun*+ & p]mits ! use ( ?is space = c]ta9 o!r codes1 ?us sav+ "s op]at+ "t4 ,we ne$ n confuse ! #gfa 9-code = ! multiplic& c\nt] ) ! #gfa out-code1 :i* happ5s to be ! out-code ( ! #be? con/ant regi/]1 because nei!r c occur 9 ! o!r's field4 ,we may1 ( c\rse1 use o!r regi/]s besides #cba & #gda = supply+ ! multiplic& & multipli]4 ,to get ! product & put x into any /orage c\nt] ,d1 we use two l9es ( cod+ "o "r aft] ! o!r3 ---- ---- #fdba #hgfa ,d ---- ,! product c\nt] has ! out-code #hgfa4 ,:5 ! product is desir$1 x is call$ =1 transf]r$ into c\nt] ,d1 & ! multiplication unit is automatically cle>$4 ,x takes "t1 h[ev]1 = ! ma*9e to p]=m a multiplication4 ,t is ! reason = ! prec$+ cod+ l9e & ! #fdba 9 ! ,c field4 ,:ile ! multiplication is go+ on1 we c in/ruct ! ma*9e to d o!r ?+s t we want done4 ,we c ins]t or int]pose cod+ l9es 9 betwe5 ! multipli] l9e & ! product l9e4 ,= example1 if we h a multipli] ( #aj digits1 we c ins]t #h cod+ l9es & maybe m4 ,! #fdba code ess5tially tells ! ma*9e to f9i% bo? ! multiplication & ! int]pos$ in/ructions1 &1 z soon z ! lat] "o ( ^! two tasks is f9i%$1 to transf] out ! product to c\nt] ,d4 ,up to ! middle ( #aidf1 ! wir+ ( ! ma*9e 0 a little diff]5t & less conv5i5t4 ,:5 ! product 0 obta9$ by ! multiplication unit1 x _h to be accept$ & transf]r$ at once into "o ( ! #gb /orage regi/]s4 ,divid+ ,division is call$ = by fir/ s5d+ ! divisor into ! divisor c\nt]1 & ?is has a code #gf 9 ! ,b field4 ,if ! divisor is 9 c\nt] #cba1 ! in/ruction may be3 ,take ! numb] 9 #cba2 ent] x z divisor2 read ! next cod+ l9e ,! cod+ w !n be3 #cba1 #gf1 #g ,?ree cod+ l9es lat]1 ! divid5d is call$ =1 & ! cod+1 if ! divid5d is 9 swit* #gdca1 is3 #gdca1 ----1 #g ,we c s5d ! quoti5t1 :5 ready1 into any desir$ c\nt] ,q by ! foll[+ two l9es ( cod+3 ---- ---- #fdb #hgf ,q ---- ,9 ! same way z ) multiplication1 we c ins]t a numb] ( cod+ l9es 9 betwe5 ! divid5d l9e & ! fir/ quoti5t l9e4 ,bo? multiplication & division are c>ri$ out 9 ! same unit ( ! ma*9e1 ! multiply-divide unit4 ,! ma*9e fir/ con/ructs a table ( ! multiples ( ! multiplic& or divisor3 #a times1 #b times1 #c times1 1 #i times4 ,9 multiplication ?is table is !n us$ by select+ multiples accord+ to ! digits ( ! multipli] "o aft] ano!r4 ,9 division ! table is us$ by comp>+ multiples ( ! divisor aga9/ ! divid5d & successive rema9d]s1 f9d+ :i* w g & :i* w n4 ,s9ce ! numb]s 9 ! ma*9e are normally ( #ae to #bc digits1 any p>ticul> multiple w be us$1 on ! av]age1 sev]al times1 & s ?is process is relatively effici5t4 ,actually ! multiplic& & ! divisor g into ! same c\nt]4 ,division1 h[ev]1 has ! code #gf & multiplication ! code #gfa1 & s ! diff]5ce is ess5tially an op]ation code n 9 ! ?ird or ,c field4 ,consult+ a ,table ,:5 we desire ! ma*9e to consult a table ( values 7i4e41 a function--see ,supplem5t #b71 we pun* ! table ) its argum5ts & function values on a tape1 & we put ! tape on a value tape fe$ me*anism4 ,! in/ruction to ! ma*9e may be3 ,take ! numb] 9 regi/] ,a2 f9d ! value ( ! function = ?is numb]1 & ent] x 9 regi/] ,b4 ,! cod+ is3 ---- ---- #gc ,a #gfed #fa ---- ---- #gfb ---- ---- #edc ---- ---- #gedca #hda #gfed ---- ,a #gfc #fdba #hgfb ,b #gc ---- #hgfc #g ,)\t expla9+ ?is cod+ l9e by l9e1 we c say t ?is is :at happ5s3 ,! ma*9e reads ! argum5t 9 regi/] ,a4 ,! ma*9e reads ! argum5t 9 ! table at :i* ! value tape fe$ is re/+4 ,x subtracts !m1 & !reby det]m9es h[ f> away ! desir$ argum5t is4 ,! ma*9e !n turns ! tape t requir$ di/ance4 ,x *ecks t ! new argum5t is ! want$ argum5t4 ,x reads ! value ( ! function ent]$ at t po9t on ! function tape4 ,select+ ,!re is a /orage c\nt] 9 ! ma*9e t is call$ ! selection c\nt]4 ,! selection c\nt] is c\nt] #gj & has ! code #gcb4 ,x has all ! prop]ties ( an ord9>y /orage c\nt] &1 9 addition1 "o extra prop]ty3 dep5d+ on ! sign ( ! numb] /or$ 9 ! selection c\nt]1 x is possible to select :e!r "s o!r numb] %all be treat$ positively or negatively4 ,9 o!r words1 addition ( a numb] any:]e 9 ! ma*9e may take place ei!r positively or negatively1 if ! numb] /or$ 9 ! selection c\nt] is positive or negative1 respectively4 ,= example1 suppose t x is ! numb] 9 ! selection c\nt]4 ,suppose t y is ! numb] 9 "s o!r c\nt] ,a4 ,suppose t z is ! numb] 9 c\nt] ,b4 ,suppose t we use ! cod+3 ,a1 ,b1 #gdcb ,:at we get 9 ,b1 because ( ! #gdcb 9 ! ?ird or ,c field1 is z plus y if x is positive or z]o1 & z m9us y if x is negative4 ,9 ! language ( ! algebra ( logic 7see ,*apt] #i & ,supplem5t #b71 :]e ,t7 4447 is 8! tru? value ( 44410 ! numb] 9 b equals3 z y,t7x #j7 - y,t7x #j7 7,! n9es complem5t ( #j1 namely #iiii to #bd digits1 is treat$ by ! ma*9e z negative47 ,:y d we ne$ an op]ation l ?is 9 a me*anical bra98 ,among o!r reasons1 :at we want to d ) a numb]1 9 ma!matics1 (t5 dep5ds on its sign4 ,x may happ5 t a table is1 = negative argum5ts1 ! negative ( :at x is = positive argum5ts2 9 o!r words1 ,f7-x7 -,f7x74 ,?is is true1 = in/ance1 = a table ( cubes ,f7x7 x or = a table ( trigonometric tang5ts 7see ,supplem5t #b74 ,if s1 we c]ta9ly d n want to take ! "t & tr\ble to li/ ! :ole table4 ,we put d[n only half ! table & !n1 if x is negative1 use ! negative ( ! value 9 ! table4 ,9 ord] to apply su* a "t-sav+ rule :5 us+ ! ma*9e1 we ne$ ! selection c\nt] or its equival5t4 ,*eck+ ,!re is ano!r special c\nt] 9 ! ma*9e t is call$ ! *eck c\nt]4 ,x also has all ! prop]ties ( an ord9>y /orage c\nt] &1 9 addition1 "o extra prop]ty3 ,if ! sign ( ! numb] /or$ 9 ! *eck c\nt] on a c]ta9 cod+ l9e is negative1 !n on ! next cod+ l9e ! ma*9e may be /opp$4 ,9 o!r words1 suppose t ! *eck c\nt] /ores a c]ta9 tol]ance t4 ,suppose1 "u ! in/ructions we give ! ma*9e1 t x calculates a positive numb] x t ought to be less ?an ?is tol]ance4 ,suppose t some?+ may g wrong & t x actually may be great] ?an t4 ,!n we put a *eck into our in/ructions4 ,we tell ! ma*9e3 ,:5 y h f\nd x1 subtract x f t4 ,if ! result is positive1 g ahead4 ,if ! result is negative or z]o1 /op6 ,"h is ! cod+4 ,suppose t ! tol]ance t is 9 swit* #gea4 ,suppose t ! numb] x to be *eck$ is 9 c\nt] #dcba4 ,!n ! in/ructions & cod+ are3 ,cle> ! *eck c\nt] -- -- #g ,put 9 ! tol]ance1 f swit* #gea #gea #gd #g ,subtract ! absolute value ( ! numb] to be *eck$ #dcba #gd #ga ,/op1 ,o ,me*anical ,bra91 if y\r result be negative6 -- -- #fd ,an op]ation l ?is is v useful 9 a me*anical bra94 ,x enables ! calculation to be int]rupt$ if some?+ has gone wrong4 ,( c\rse1 o!r op]ations ( *eck+ besides ?is "o are us$--= example1 inspect+ = reasonabl5ess ! results pr9t$ on typewrit] #a4 ,o!r ,op]ations ,!re are o!r op]ations 9 ! ma*9e4 ,!re are two pairs ( /orage regi/]s t c be c\pl$ toge!r s t we c h&le problems requir+ numb]s ( #df digits in/ead ( #bc4 ,regi/]s #fd & #fe c be c\pl$1 & regi/]s #fh & #fi c be c\pl$4 ,!re is ano!r /orage c\nt]1 ,no4 #ga1 t has an extra prop]ty4 ,we c read out ! numb] x holds times #a1 or times #aj1 or times #aj1 z may be call$ =4 ,z a result ( ?is c\nt]1 we c d problems requir+ #add regi/]s /or+ numb]s ( #aa digits ea*1 in/ead ( #gb regi/]s /or+ #bc digits ea*4 ,bigg] /ati/ical problems c be h&l$1 = example4 ,!re are "s m9or sequ5ces ( op]ations1 or subr\t9es1 t c be call$ = by a s+le code4 ,! subr\t9e may be a :ole set ( additions1 subtractions1 multiplications1 divisions1 & *oices1 hav+ a s+le purpose3 to compute "s numb] by a process ( rapid approximation 7see ,supplem5t #b74 ,!re are built-9 subr\t9es = "s special ma!matical functions3 ! log>i?m ( a numb] to ! base #aj1 ! expon5tial ( a numb] to ! base #aj1 & ! s9e ( a numb]4 7,see ,supplem5t #b47 ,!re are also #aj *angeable subr\t9es1 ea* ( #bb cod+ l9es1 :i* c be call$ 91 :5 want$1 by ! ma9 sequ5ce-control tape or by ea* o!r4 ,^! subr\t9es con/itute ! ,subsidi>y ,sequ5ce ,me*anism1 & are extremely useful4 ,!y h ,a1 ,b1 & ,c fields j l ! ma9 sequ5ce-control1 b !y are giv5 in=mation by plugg+ ) %ort l5g?s ( wire in/ead ( by fe$+ pun*$ pap] tape4 ,,rapid ,,approximation ,,= ,a ,,log>i?m ,up to ?is po9t 9 ?is *apt] ! au?or has tri$ to tell ! facts ab\t ! ,h>v>d ma*9e 9 pla9 words4 ,b = read+ ?is section1 a little k ( calculus is necess>y4 7,see also ,supplem5t #b47 ,if y wi%1 skip ?is section & g on to ! next "o4 ,:at is ! process t ! ma*9e uses to compute any desir$ log>i?m to #bc digits8 ,suppose t we take = an example ! process by :i* ! ma*9e computes log#aj #di4cgbd4 ,we *oose a #f-;digit numb] = simplicity2 ! ma*9e w\ld h&le a #bc-;digit numb] 9 ! same way4 ,! process uses #b fundam5tal equations involv+ ! log>i?m3 ! sum relation log 7abc7 log a log b log c & ! s]ies relation h h h log7#a h7 h - -------- -------- - -------- 1 h #a #b #c #d ,! error 9 ?is s]ies is less ?an ! fir/ neglect$ t]m4 ,n[1 ! ma*9e /ores ! base #aj log>i?ms 7to #bc decimal places7 ( ! foll[+ #cf numb]s3 #a #a4a #a4ja #a4jja #b #a4b #a4jb #a4jjb 444 444 444 444 #i #a4i #a4ji #a4jji ,fir/1 ! numb] #di4cgbd is exam9$ 9 a c\nt] call$ ! ,log>i?m-,9-,out c\nt]1 & ! position ( ! decimal po9t is det]m9$1 giv+ ! *>act]i/ic ( ! log>i?m4 ,! numb] #di4cgbd has ! *>act]i/ic #a4 ,next1 #d successive divisions are p]=m$1 9 :i* ! #d divisors are 7#a7 ! fir/ digit ( ! numb]1 7#b7 ! fir/ #b digits ( ! quoti5t1 7#c7 ! fir/ #c digits ( ! next quoti5t1 & 7#d7 ! fir/ #d digits ( ! subsequ5t quoti5t2 ?us1 #d4icgbd_/d #a4bcdca #a4bcdca_/a4b #a4jbhfj #a4jbhfj_/a4jb #a4jjhdc #a4jjhdc_/a4jjh #a4jjjdc ,= simplicity we h kept only #f digits1 al?\gh ! ma*9e1 ( c\rse1 w\ld keep #bc4 ,x is int]e/+ to note t ! ma*9e is able to s5se digits & ?us det]m9e ! #d divisors2 ?is is an ari?metical & num]ical process & "o t _c be done 9 ord9>y algebra4 ,we n[ h3 log #di4cgbd #a log #d log #a4b log #a4jb log #a4jjh log #a4jjjdc ,to compute log #a4jjjdc to #ba decimals we use 7 h h h h h 7 loge 7h - ---------- ---------- - -------- ---------- - ----------7 7 #b #c #d #e #f 7 ) h #j4jjjdc4 ,only #f t]ms ( ! s]ies relation are ne$$4 ,=1 ! error is less ?an h_/#g1 :i* is less ?an #aj_/g1 s9ce h _/4 ,! ma*9e uses ! s]ies relation 9 ! =m log 7#a h7 77ch c7h ch ch c7h ch :]e c ,m1 c -,m_/#b1 c ,m_/#c1 1 & ,m loge #j4dcdbid4 ,! #f values ( ! c's are also /or$ 9 ! ma*9e4 ,:5 any log>i?m is to be comput$1 ! sum ( ! *>act]i/ic1 ( ! #d log>i?ms ( ! successive divisors1 & ( ! fir/ #f t]ms ( ! s]ies relation gives ! log>i?m4 ,! maximum "t requir$ is #ij seconds4 ,,an ,,appraisal ,,( ,,! ,,calculator ,! ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator at ,h>v>d is a l&m>k 9 ! developm5t ( ma*9es t ?9k4 ,its capacity = _m problems = :i* x is suit$ is f> beyond ! capacity ( a hundr$ human comput]s4 ,spe$ ,! "t requir$ 9 ! ma*9e = add+1 subtract+1 transf]r+1 or cle>+ numb]s is _/ ( a second4 ,?is is ! "t ( "o ma*9e cycle or ( read+ "o cod+ l9e4 ,multiplication takes at ! mo/ #f seconds1 & an av]age ( #d seconds4 ,division takes at ! mo/ #af seconds1 & an av]age ( #aa seconds4 ,ea*1 h[ev]1 requires only #c l9es ( cod+1 or _/ ( a second's att5tion f ! sequ5ce me*anism2 int]pos$ op]ations fill ! re/ ( ! "t4 ,to calculate a log>i?m1 an expon5tial1 or a s9e to ! full numb] ( digits obta9able by means ( ! automatic subr\t9e takes at ! mo/ #ij1 #ff1 & #fj seconds1 respectively4 ,to get ?ree #bd-;digit numb]s f fe$+ a pun* c>d takes second4 ,to pun* a numb] takes f second up to #c seconds4 ,to pr9t a numb] takes f #a seconds up to #g seconds4 ,co/ & ,value ,! co/ ( ! ma*9e 0 some:]e ne> #c or #d hundr$ ?\s& doll>s1 if we leave out "s ( ! co/ ( rese>* & developm5t1 :i* w\ld h be5 done :e!r or n ?is p>ticul> ma*9e _h ev] be5 built4 ,a /aff ( #aj m51 consi/+ ( #d ma!maticians1 #d op]ators1 & #b ma9t5ance m51 are ne$$ to keep ! ma*9e runn+ #bd h\rs a day4 ,?is might repres5t1 if capitaliz$1 ano!r #a or #b hundr$ ?\s& doll>s4 ,if a capital value ( #ejj1jjj is tak5 z equival5t to #ej1jjj a ye>1 !n ! co/ ( ! ma*9e 9 op]ation #bd h\rs a day is 9 ! neighborhood ( #aej a day or #f an h\r4 ,! value ( ! ma*9e1 h[ev]1 is v mu* great]4 ,if #ajj human be+s ) desk calculators 7 set to "w #h h\rs a day at #a4ej an h\r1 ! co/ w\ld be #abjj a day1 or #h times z mu*4 ,yet x is v d\btful t ! "w !y c\ld produce w\ld equal t turn$ out by ! ma*9e1 ei!r 9 quality or quantity1 :5 ! ma*9e is well suit$ to ! problem4 ,reliability ,by reliability we mean ! ext5t to :i* ! results produc$ by ! ma*9e c be reli$ on to be "r4 ,! ma*9e conta9s no built-9 device = mak+ its op]ations reliable4 ,s1 if we wi% to *eck a multiplication1 = example1 we c d ! multiplication a second "t1 int]*ang+ ! multipli] & ! multiplic&4 ,b if1 say1 digit #af ( ! product 7 n transf]r+ correctly1 we w\ld get ! same wrong result bo? ways & we w\ld n h a suffici5t *eck4 ,?us1 :5 we set up a problem = ! ma*9e to d1 "o ( ! big tasks we h is *eck+4 ,we h to "w out ways ( mak+ sure t ! result1 :5 we get x1 is "r & ways ( in/ruct+ ! ma*9e to make ! te/s we want4 ,?is is n a new task4 ,:5ev] y or ,i set out to solve a problem1 we h to make sure--usually by do+ ! problem twice1 & pref]ably by do+ x a diff]5t way ! second "t--t our answ]1 :5 we get x1 is correct4 ,"o ( ! *ief tasks = ! ma!matician1 9 mak+ a sequ5ce-control tape = ! ma*9e1 is to put into x suffici5t *ecks to make sure t ! results are correct4 ,we c use a numb] ( diff]5t k9ds ( p>tial *ecks3 ! *eck c\nt]2 diff]5ces1 & smoo?ness 7see ,supplem5t #b72 wat*+ ! results pr9t$ on typewrit] #a2 ma!matical *ecks2 comp>ison ) kn[n specific values2 etc4 ,9 actual exp]i5ce on ! ma*9e1 human failures1 su* z failure to /ate ! problem exactly or failure to put x on ! ma*9e correctly1 h giv5 ab\t z mu* tr\ble z me*anical failures4 ,! ma*9e op]ates )\t me*anical failure ab\t #ij to #ie p] c5t ( ! "t4 ,! balance ( ! "t ! ma*9e is idle :ile be+ s]vic$ or repair$4 ,! ma*9e is s]vic$ by me*anics tra9$ & sup]vis$ at ,h>v>d4 ,(t5 :5 we *ange ! ma*9e f "o problem to ano!r problem1 we f9d "s k9d ( tr\ble4 ,consequ5tly1 we ne$ to "w out 9 detail ! fir/ "p ( any calculation plac$ on ! ma*9e4 ,we !n comp>e ! results /ep by /ep ) ! results produc$ by ! ma*9e4 ,any ma!matician work+ ) ! ma*9e ne$s consid]able tra9+ 9 ord] to diagnose tr\ble quickly & guide ! ma9t5ance m5 to ! place :]e repair or replacem5t is ne$$4 ,once y f9d ! tr\ble1 y c fix x easily4 ,)\t di/urb+ ! sold]$ connections1 y c easily pull out f its socket a relay t is misbehav+ & plug 9 a new relay4 ,) a screwdriv] y c *ange a c\nt] position--deta* x f its socket & replace x by ano!r "o t is work+ correctly4 ,"o 8bug0 t w long be rememb]$ ar\nd ! ,laboratory 0 a case involv+ a #e t w\ld incorrectly come 9 to a numb] e n[ & !n4 ,x did n happ5 (t5--only once 9 a :ile4 ,aft] a week ( se>* ! bug 0 f9ally locat$3 ! insulation on a wire t c>ri$ a #e _h worn ?r\gh 9 "o spot1 & once 9 a :ile ?is wire w\ld %ake aga9/ a po/ t c\ld c>ry curr5t & took 9 ! #e6 ,effici5cy ,9 _m respects1 ?is ma*9e is effici5t & well-balanc$4 ,its read+ & writ+ spe$ is close to its calculat+ spe$4 ,we c pun* or pr9t a result on ! av]age = e #aj additions or #a multiplications4 ,! memory ( #gb numb]s 9 ! ma*9e is extremely useful2 a small] memory is a s]i\s limitation on ! a*ievem5ts ( a comput+ ma*9e4 ,! ma*9e c d _m k9ds ( ari?metic & logic4 ,x is well educat$ & c compute automatically "s r complicat$ ma!matical functions1 l log>i?m or s9e4 ,x has done difficult & important problems4 ,x has comput$ & tabulat$ 7see ,supplem5t #b7 ,bessel functions1 def9ite integrals1 etc4 ,x c solve diff]5tial equations 7see ,*apt] #e7 & _m o!r problems 9 ma!matics1 physics1 & eng9e]+4 ,on ! o!r h&1 no calculator w ev] aga9 be built j l ?is "o1 useful ?\gh x is4 ,electronic comput+ is easily #ajj times z fa/ z relay comput+2 ne>ly e future calculator w d its comput+ electronically4 ,_m o!r improvem5ts w be made4 ,= example1 9 ?is calculator1 !re are #gb addition-subtraction me*anisms1 yet only "o ( ^! c be us$ at a "t4 ,also1 ! ma*9e has only "o comb9$ multiply-divide unit4 ,s we h to organize any computation ) few multiplications1 & ) /ill few] divisions1 = !y take long] /ill4 ,until #aidg1 we _h to organize any computation 9 ?is calculator into "o s+le fix$ sequ5ce ( op]ations4 ,9 o!r words1 !re 0 no way to move f "o subr\t9e to ano!r subr\t9e dep5d+ on "s indication t turn$ up 9 our computation4 ,rec5tly1 ! ,h>v>d ,computation ,laboratory decid$ to rem$y ?is condition & provid$ ! ,subsidi>y ,sequ5ce ,me*anism equival5t to #aj subr\t9es ( #bb l9es ( cod+ ea*4 ,^! are on relays & plug wires & may be call$ = by ! sequ5ce-control tape or by ea* o!r4 ,?is provision has add$ greatly to ! effici5cy ( ! calculator4 ,:atev] else c be said ab\t ! ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator1 x mu/ be said t ?is 0 ! fir/ g5]al-purpose me*anical bra9 us+ numb]s 9 digit =m & able to d ari?metic & logic 9 hundr$s ( ?\s&s ( /eps "o aft] ano!r4 ,& great cr$it mu/ g to ,pr(essor ,h[>d ,h4 ,aik5 ( ,h>v>d & ! m5 ( ,int]national ,bus9ess ,ma*9es ,corporation :o made ?is great me*anical bra9 come into exi/5ce4 ,*apt] #g ,,spe$--#ejjj ,,additions ,a ,,second3 ,,moore ,,s*ool',s ,,eniac 7,,electronic ,,num]ical ,,integrator ,,& ,,calculator7 ,ano!r ( ! giant bra9s t has begun to "w is nam$ ,,eniac4 ,?is "n comes f ! initial lett]s ( ! full "n1 ,electronic ,num]ical ,integrator & ,calculator4 ,eniac 0 born 9 #aidb at ! ,moore ,s*ool ( ,electrical ,eng9e]+1 ( ! ,univ]sity ( ,p5nsylvania1 9 ,philadelphia4 ,eniac's fa!r 0 ! ,ordnance ,dep>tm5t ( ! ,u4 ,s4 ,army1 :i* provid$ ! funds to fe$ & re> ! prodigy4 ,9 ! %ort space ( f\r ye>s1 ,eniac grew to maturity1 & 9 ,febru>y #aidf he began to e>n 8 own liv+ by electronic ?9k+4 ,eniac promptly set sev]al _w's records4 ,he 0 ! fir/ giant bra9 to use electronic tubes = calculat+4 ,he 0 ! fir/ "o to rea* ! spe$ ( #ejjj additions a second4 ,he 0 ! fir/ piece ( electronic app>atus conta9+ z _m z #ah1jjj electronic tubes all function+ toge!r successfully4 ,z soon z ,eniac />t$ ?9k+1 he promptly made relay calculators obsolete f ! sci5tific po9t ( view1 = !y h a top spe$ ( p]haps #aj additions a second4 ,at ! age ( #e1 he mov$ to ,m>yl& at a co/ ( ab\t #ij1jjj1 & 8 p]man5t home is n[ ! ,balli/ic ,rese>* ,laboratories at ! ,u4 ,s4 ,army's ,prov+ ,gr\nd at ,ab]de51 ,md4 ,,orig9 ,,& ,,developm5t ,9 ! ,dep>tm5t ( ,t]re/rial ,magnetism 9 ! ,c>negie ,in/itution ( ,wa%+ton1 a great deal ( in=mation ab\t ! e>? is /udi$4 ,_m k9ds ( physical obs]vations are !re ga!r$ & analyz$3 electricity 9 ! atmosph]e1 magnetism 9 ! e>?1 & ! wea!r1 = example4 ,9 #aida1 a physici/1 ,dr4 ,john ,w4 ,mau*ly1 0 ?9k+ ab\t ! great mass ( num]ical in=mation !y _h to h&le4 ,he became conv9c$ t mu* swift] ways ( h&l+ ^! numb]s 7 ne$$4 ,he 0 c]ta9 electronic devices c\ld be us$ = comput+ at v high spe$s1 yet he f\nd no "o busy apply+ electronics 9 ?is field4 ,) hopes ( f9d+ "s way ( develop+ electronic comput+1 he jo9$ ! /aff ( ! ,moore ,s*ool ( ,electrical ,eng9e]+ 9 ! autumn ( #aida4 ,! ,moore ,s*ool 9 #aicd & #aice _h built a diff]5tial analyz]2 &1 f t "t on1 ! s*ool _h made a numb] ( improvem5ts 9 x4 ,9 #aida1 ) w> imm95t1 ! diff]5tial analyz] 0 put h>d at "w calculat+ tables = ! ,army's ,balli/ic ,rese>* ,laboratories4 ,^! tables 7 mo/ly fir+ tables1 tables ( ! pa?s along :i* projectiles travel :5 fir$--trajectories2 obvi\sly1 y _c fire a gun usefully1 unless y "k h[ to aim x4 ,! am\nt ( calculation ( trajectories 0 s huge t ,dr4 ,mau*ly sugge/$ t a ma*9e us+ electronic tubes be con/ruct$ to calculate !m4 ,a good deal ( discussion took place betwe5 m5 at ! ,moore ,s*ool1 m5 at ! ,balli/ic ,rese>* ,laboratories1 & m5 f ! ,ordnance ,dep>tm5t 9 ,wa%+ton4 ,a contract = rese>* into an electronic trajectory comput] 0 conclud$ ) ! ,ordnance ,dep>tm5t ( ! ,u4 ,s4 ,army4 ,mau*ly & "o ( ! "y electronics eng9e]s /udy+ at ,moore ,s*ool1 ,j4 ,presp] ,eck]t1 ,jr41 set to "w on ! design4 ,gradually ! design ( a ma*9e took =m1 & ! crucial exp]im5ts on equipm5t 7 complet$4 ,9 #aidc1 ! design 0 settl$ z a special-purpose ma*9e to calculate trajectories4 ,lat] on1 ! gr\p modifi$ ! plans "h & !re to enable ! ma*9e to calculate a v wide class ( problems4 ,a gr\p ( ,moore ,s*ool electronics eng9e]s & te*nicians dur+ #aidd & #aide built ! ma*9e1 us+ z mu* z possible /&>d radio tubes & p>ts4 ,"h1 aga91 9 spite ( ! successful progress ( ! electronic ma*9e1 ! rumor t x 0 a 8:ite elephant0 0 all[$ to spread 9 ord] to protect ! "w f pry+ enemy e>s4 ,,g5]al ,,organization ,! ma9 "p ( ,eniac consi/s ( #db panels1 :i* are plac$ along ! sides ( a squ>e ,u4 ,ea* ( ^! panels is #i feet high1 #b feet wide1 & #a foot ?ick4 ,!y are ( %eet /eel1 pa9t$ black1 ) swit*es1 lights1 etc41 m\nt$ on !m4 ,at ! tops ( all ! panels are air ducts = draw+ (f ! hot air ar\nd ! tubes4 ,l>ge motors & fans above ! ma*9e suck ! heat$ air away ?r\gh ! ducts4 ,!re are also #e pieces ( equipm5t :i* c be roll$ f place to place & are call$ portable1 b !re is no *oice z to :]e !y c be plugg$ 94 ,we %all call ?is equipm5t panels #dc to #dg4 ,panels ,n[ :at are ^! panels1 & :at d !y d8 ,ea* panel is an assembly ( "s equipm5t4 ,! names ( ! panels are %[n 9 ! accompany+ table4 ,! arrangem5t ( ,eniac at ! ,balli/ic ,rese>* ,laboratories z %[n 9 ! table is slightly diff]5t f ! arrangem5t ( ,eniac at ,moore ,s*ool4 ,,names ,,( ,,panels ,,( ,,eniac ,,panel ,,no4 ,,"n 7,,& ,,additional ,,names ,,9 ,,"s ,,cases7 #a ,initiat+ ,unit #b ,cycl+ ,unit #c1 #d ,ma/] ,programm]1 panels #a1 #b #e ,accumulator #a #f ,accumulator #b #g ,accumulator #c #h ,accumulator #d 7,quoti5t7 #i ,divid]-,squ>e-,root] #aj ,accumulator #e 7,num]ator ,i7 #aa ,accumulator #f 7,num]ator ,,ii7 #ab ,accumulator #g 7,d5om9ator--,squ>e ,root ,i7 #ac ,accumulator #h 7,d5om9ator--,squ>e ,root ,,ii7 #ad ,accumulator #i 7,%ift ,i7 #ae ,accumulator #aj 7,%ift ,,ii7 #af ,blank panel = new unit 7,conv]t]7 #ag ,accumulator #aa 7,multipli]7 #ah ,accumulator #ab 7,multiplic&7 #ai-ba ,multipli]1 panels #a1 #b1 #c #bb ,accumulator #ac 7,left-,h& ,p>tial ,products ,i7 #bc ,accumulator #ad 7,left-,h& ,p>tial ,products ,,ii7 #bd ,accumulator #ae 7,"r-,h& ,products ,i7 #be ,accumulator #af 7,"r-,h& ,products ,,ii7 #bf ,blank panel = new unit 7#ajj ,regi/]s7 #bg ,accumulator #ag #bh ,accumulator #ah #bi ,accumulator #ai #cj ,accumulator #bj #ca1 #cb ,function ,table #a1 panels #a1 #b #cc1 #cd ,function ,table #b1 panels #a1 #b #ce1 #cf ,function ,table #c1 panels #a1 #b #cg-ci ,con/ant ,transmitt]1 panels #a1 #b1 #c #dj-db ,pr9t]1 panels #a1 #b1 #c #dc-de ,portable ,function ,tables ,a1 ,b1 & ,c #df ,,ibm ,c>d ,read] #dg ,,ibm ,summ>y ,pun* ,note3 ,! accumulators f :i* a numb] c be s5t to ! pr9t] are n[ accumulators #a1 #b1 & #ae to #bj4 ,9 read+ ov] ! table1 we f9d a numb] ( words t ne$ expla9+4 ,"s ( ! explanation we c give 9 ! summ>y ( ! units ( ,eniac3 ,,summ>y ,,( ,,units ,,( ,,eniac ,,quantity ,,device ,,significance #bj ,accumulators ,/ore1 add1 & subtract numb]s #a ,multipli] ,multiplies #a ,divid]-,squ>e-,root] ,divides1 & obta9s twice ! squ>e root ( a numb] 7see ,supplem5t #b7 #c ,function ,tables ,"p ( ! memory1 = ref]r+ to tables ( numb]s #a ,con/ant ,transmitt] ,/ores numb]s f ! c>d read] & f h&-set swit*es #a ,pr9t] ,pun*es ma*9e results into c>ds #a ,cycl+ ,unit ,controls ! tim+ ( ! v>i\s p>ts ( ! ma*9e #a ,initiat+ ,unit ,has controls = />t+ a calculation1 = cle>+1 etc4 #a ,ma/] ,programm] ,holds ! *ief controls = coord9at+ ! v>i\s p>ts ( ! ma*9e ,an accumulator is a /orage c\nt]4 ,x c hold a numb]2 x c cle> a numb]2 x c transmit a numb] ei!r positively or negatively2 & x c receive a numb] by add+ ! numb] 9 & ?us hold+ ! sum ( :at x held be=e & ! numb] receiv$4 ,eniac :5 fir/ built _h only #bj accumulators1 & s x c\ld rememb] only #bj numb]s at "o "t 7except = con/ant numb]s set 9 swit*es74 ,?is small memory 0 ! mo/ s]i\s drawback ( ,eniac2 panel #bf 0 design$1 !re=e1 to provide a great additional memory capacity4 ,! divid]-squ>e-root]1 z its "n tells1 is a me*anism t c divide & t c f9d twice ! squ>e root ( a numb]4 ,eniac is "o ( ! sev]al giant bra9s t h _h squ>e root capacity built into !m1 p>ticul>ly s9ce squ>e root is ne$$ = solv+ trajectories4 ,_m panels ( ,eniac h d\ble duty & "s h triple duty4 ,= example1 panel #bd is an accumulator1 b x also 7#a7 /ores ! "r-h& p>tial products 7see ,supplem5t #b7 ( ! multipli] & 7#b7 0 a regi/]1 :5 ,eniac 0 at ,moore ,s*ool1 f :i* in=mation to be pun*$ 9 ! pr9t] c\ld be obta9$4 ,cle>ly1 if we h a multiplication to d1 we _c also use ?is accumulator = /or+ a numb] t is to rema9 un*ang$ dur+ ! multiplication4 ,p>ts ,! total numb] ( p>ts 9 ,eniac is ne> half a million1 ev5 if we c\nt electronic tubes z s+le p>ts4 ,!re are ov] #ah1hjj electronic tubes 9 ! ma*9e4 ,x is int]e/+ to note t only #aj k9ds ( electronic tubes are us$ 9 ! calculat+ circuits & only ab\t #fj k9ds ( resi/ors & #cj k9ds ( capacitors4 ,a resi/or is a device t opposes ! /eady fl[ ( electric curr5t ?r\gh x to a c]ta9 ext5t 7call$ resi/ance & measur$ 9 ohms74 ,a capacitor is a device t c /ore electrical en]gy up to a c]ta9 ext5t 7call$ capacitance & measur$ 9 f>ads74 ,all ^! tubes & p>ts are /&>d p>ts 9 radios4 ,all types are id5tifi$ by ! color labels e/abli%$ 9 /&>d radio manufactur+4 ,x is ! comb9ations ( ^! p>ts1 l ! comb9ations ( pieces 9 a *ess game1 t give rise to ! m>vel\s p[]s ( ,eniac4 ,! comb9ations ( p>ts at ! fir/ level are call$ plug-9 units4 ,a plug-9 unit is a /&>d box or tray or *assis made ( %eet /eel conta9+ a /&>d assembly ( tubes1 wires1 & o!r p>ts4 ,x c be pu%$ 9 or pull$ out ( a /&>d socket ) _m connections4 ,an example ( a plug-9 unit is a decade1 or1 m exactly1 an accumulator decade4 ,?is is j a c\nt] :eel or decimal position express$ 9 ,eniac language3 x c express successively all ! digits f #j to #i & !n pass f #i to #j1 giv+ rise to a c>ry impulse4 ,x is /rik+ t a me*anical c\nt] to hold #aj digits c be made up ( #aj little :eels1 in* wide & an in* high4 ,b an accumulator 9 ,eniac1 to hold #aj digits1 is a set ( #aj decades ea* #b in*es wide & #b feet high4 ,!re are only ab\t #bj k9ds ( plug-9 units altoge!r4 ,ea* plug-9 unit is int]*angeable ) any o!r ( ! same k9d4 ,s1 if a decade1 = example1 %[s tr\ble1 y c pull x out ( its socket & plug 9 a sp>e decade in/ead4 ,numb]s ,numb]s 9 ,eniac are ( #aj decimal digits ) a sign t may be plus or m9us4 ,! decimal po9t is fix$4 ,h[ev]1 :5 y are connect+ "o accumulator ) ano!r1 y c %ift ! decimal po9t if y want to4 ,also1 #b accumulators may be c\pl$ toge!r s z to h&le numb]s ( #bj digits4 ,,h[ ,,in=mation ,,goes ,,into ,,! ,,ma*9e ,!re are ?ree ways by :i* in=mation--numb]s or in/ructions--c g into ! ,eniac4 ,numb]s c be put into ! ma*9e by means ( pun* c>ds f$ into ! ,c>d ,read]1 panel #df1 or swit*es on ! ,con/ant ,transmitt]1 panels #cg to #ci4 ,numb]s or in/ructions c also g into ! ma*9e by means ( ! ,function ,tables1 panels #dc to #de4 ,"h !re are dial swit*es1 :i* are set by h&4 ,in/ructions c also g into ! ma*9e by sett+ ! swit*es1 plugg+ ! inputs & outputs1 etc41 ( ! wires or l9es along :i* numb]s & in/ructions travel4 ,,h[ ,,in=mation ,,comes ,,out ,,( ,,! ,,ma*9e ,!re are two ways by :i* num]ical in=mation c come out ( ! ma*9e4 ,numb]s c come out ( ! ma*9e pun*$ on c>ds by ! ,summ>y ,pun*1 panel #dg4 ,!y are !n pr9t$ 9 ano!r room by means ( a sep>ate ,,ibm tabulator4 ,also1 numb]s c be read out ( ! ma*9e by means ( ! lights 9 ! neon bulbs m\nt$ on ea* accumulator4 ,y c read 9 ! lights ( a panel ! numb] held by ! accumulator1 if ! panel is n comput+4 ,,h[ ,,in=mation ,,is ,,manipulat$ ,,9 ,,! ,,ma*9e ,eniac h&les in=mation r diff]5tly f any o!r ( ! big bra9s4 ,in/ead ( hav+ only "o bus or 8railroad l9e0 along :i* numb]s c be s5t1 ,eniac has m ?an #aj su* l9es4 ,!y are call$ digit trays & label$ ,a1 ,b1 ,c1 4 ,ea* conta9s #aa digit trunk l9es or digit trunks--#aj to c>ry ! digits ( a numb]1 & ! #aa? to c>ry ! sign4 ,in/ead ( hav+ only "o telegraph l9e along :i* in/ructions c be s5t1 ,eniac has m ?an #ajj su* l9es4 ,!y are call$ program trunk l9es or program trunks & label$ ,a#a1 ,a#b1 1 ,a#aa1 ,b#a1 ,b#b1 1 ,b#aa1 1 etc4 ,!y are assembl$ 9 gr\ps ( #aa to a tray2 ! program trays1 9 fact1 look j l ! digit trays1 except = _! connectors & _! purpose1 :i* are diff]5t4 ,bel[1 we %all make cle> h[ ! program trays c>ry control in=mation4 ,n[1 actually1 ,eniac has _m m trunk l9es ?an we h j /at$1 = ea* ( ! l9es we h m5tion$ c be divid$ into num]\s sep>ate sections by ! removal ( plug connections4 ,h[ we *oose to d ?is dep5ds on ! ne$s ( ! problem1 ! space betwe5 ! panels1 ! "t :5 ! l9e is us$1 etc4 ,transf]r+ ,numb]s1 ,add+1 & ,subtract+ ,basically1 a numb] is repres5t$ 9 ,eniac by an arrangem5t ( on & (f electronic tube elem5ts 9 pairs1 call$ flip-flops4 ,!re is "o flip-flop enclos$ 9 a s+le tube 7type #f,,sn#g7 = ea* value #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i = ea* ( ! #aj digits /or$ 9 an accumulator4 ,s we h at lea/ #ajj flip-flops = ea* accumulator1 & ?us at lea/ #ajj electronic tubes are requir$ to /ore #aj digits4 ,actually1 an accumulator ne$s #eej electronic tubes4 ,s we see t !re is n v mu* ( a future 9 ?is type ( arrangem5t4 ,! new] electronic bra9s use diff]5t devices = /orage ( numb]s4 ,9 ord] to %[ :at numb] is /or$ 9 an accumulator1 !re are #ajj little neon bulbs m\nt$ on ! face ( ea* accumulator panel4 ,ea* bulb gl[s :5 ! flip-flop t belongs to x is on4 ,= example1 suppose t ! #d? decade 9 ,accumulator #aa holds ! digit #g4 ,!n ! #g? flip-flop 9 t decade w be on1 & all ! o!rs w be (f4 ,! #g? neon bulb = t decade w gl[4 ,n[ suppose t ! numb] #g is 9 ! #d? decade 9 ,accumulator #aa & is to be add$ into1 say1 ! #d? decade 9 ,accumulator #ac4 ,& suppose t x is to be subtract$ f ! #d? decade 9 ,accumulator #af4 ,:at d we d1 & :at w ,eniac d8 ,fir/1 we pick out #b digit trays1 say ,b & ,d4 ,accumulator #aa has #b outputs1 call$ ! add output & ! subtract output4 ,we plug ,b into ! add output & ,d into ! subtract output4 ,!n we g ov] to ,accumulators #ac & #af4 ,!y h #e inputs1 t is1 #e ways ( be+ plugg$ to receive numb]s f digit trunks4 ,^! inputs are nam$ ) ,greek lett]s1 1 1 1 1 4 ,we *oose "o input1 say 1 = ,accumulator #ac1 & we plug ,b into t input4 ,we *oose "o input1 say 1 = ,accumulator #af1 & we plug ,d into t input4 ,n[ we h ! 8railroad0 swit*+ = numb]s accompli%$4 ,we h set up a *annel :]eby ! numb] 9 ,accumulator #aa w be r\t$ positively into ,accumulator #ac & negatively into ,accumulator #af4 ,n[ let u suppose t1 at "s def9ite "t fix$ by ! control1 ,accumulator #aa is /imulat$ to transmit & ,accumulators #ac & #af are condition$ to receive4 ,:5 ?is happ5s1 a gr\p ( #aj pulses comes along a direct trunk f ! cycl+ unit1 & a gr\p ( #i pulses comes along ano!r trunk4 ,we c ?9k ( ea* pulse z a little surge ( electricity la/+ ab\t #b million?s ( a second4 ,! t5-pulses1 z ! fir/ gr\p is call$1 are #aj million?s ( a second ap>t4 ,! n9e-pulses1 z ! second gr\p is call$1 are also #aj million?s ( a second ap>t b are s&wi*$ betwe5 ! t5-pulses4 ,:5 ! #a/ t5-pulse comes along1 ! #g? flip-flop 9 ,accumulator #aa goes (f1 ! #h? flip-flop goes on1 ! foll[+ n9e-pulse goes ?r\gh & goes out on ! subtract l9e to ,accumulator #af4 ,!n ! #bnd t5-pulse comes along1 ! #h? flip-flop goes (f1 ! #i? flip-flop goes on1 & ! next n9e-pulse goes out on ! subtract l9e to ,accumulator #af4 ,n[ ! decade sits at #i1 & = ?is reason ! next t5-pulse *anges an electronic swit* 7actually ano!r flip-flop7 s t all lat] n9e-pulses w g out on ! add l9e4 ,?is t5-pulse also turns (f ! #i? flip-flop & turns on ! #j? flip-flop )\t caus+ any c>ry4 ,n[ ! #d? ( ! t5-pulses comes along1 turns ! #j? flip-flop (f1 & turns ! #a/ flip-flop on1 & ! next n9e-pulse goes out on ! add l9e to ,accumulator #ac4 ,! next #f ( ! t5-pulses !n come along & *ange ,accumulator #aa back to ! digit #g z be=e1 & ! next #f ( ! n9e-pulses g out to ,accumulator #ac4 ,?us ,eniac has add$ #g into ,accumulator #ac1 has add$ #b1 ! n9es complem5t ( #g 7see ,supplem5t #b71 into ,accumulator #af1 & has left ,accumulator #aa hold+ ! same numb] z be=e4 ,?is is j ! result t we want$4 ,9 ?is way1 ! n9es complem5t ( any digit 9 a decade is transf]r$ out along ! subtract l9e1 & ! digit un*ang$ is transmitt$ out along ! add l9e4 ,z ! pulses arrive at any o!r accumulator1 !y add into t accumulator4 ,multiply+ & ,divid+ ,eniac p]=ms multiplication by a built-9 table ( ! products 9 ! #aj-;by-#aj multiplication table1 us+ ! me?od ( left-h& compon5ts & "r-h& compon5ts 7see ,supplem5t #b74 ,= example1 suppose t ! #crd digit ( ! multipli] is #g & t ! #e? digit ( ! multiplic& is #f4 ,!n1 :5 ,eniac att5ds to ! #crd digit ( ! multipli]1 ! "r-h& digit ( ! #db #f #g is ga!r$ 9 "o accumulator1 & ! left-h& digit #d is ga!r$ 9 ano!r accumulator4 ,aft] ,eniac has att5d$ to all ! digits ( ! multipli]1 !n ,eniac p]=ms "o m addition & transf]s ! sum ( ! left-h& digits into ! "r-h& digits accumulator4 ,eniac does division 9 r a novel way4 ,fir/1 ! divisor is subtract$ ov] & ov] until ! result becomes negative or #j4 ,!n ! ma*9e %ifts to ! next column & adds ! divisor until ! result becomes positive or #j4 ,x cont9ues ?is process1 alt]nat+ f column to column4 ,= example1 suppose t we divide #c into #hd 9 ?is way4 ,we h3 #c 7 #hd 7 #cb -#c ---- #ed -#c ---- #bd -#c ---- -#f #c ---- -#c #c ---- #j ,aft] we subtract #c ! ?ird "t1 ! result becomes negative1-#f2 9 ! next column1 aft] we add #c twice1 ! result becomes #j4 ,! quoti5t is #cb1 :i* is ! same z #cj - #b1 or #bh2 & #c #bh is #hd4 ,?us ! process *ecks4 ,consult+ a ,table ,eniac has ?ree ,function ,tables4 ,"h y c /ore numb]s or in/ructions = ! ma*9e to ref] to4 ,ea* ,function ,table has #ajd argum5ts 7see ,supplem5t #b74 ,= ea* argum5t1 y c /ore #ab digits & #b signs t may be plus or m9us4 ,?is capacity c be devot$ to "o #ab-;digit numb] ) a sign1 or to two #f-;digit numb]s ea* ) a sign1 or to six #b-;digit in/ructions4 ,! ?ree ,function ,tables are panels #dc1 #dd1 & #de4 ,to put 9 ! numb]s or in/ructions1 y h to g ov] to ^! panels & set ! numb]s or in/ructions1 digit by digit1 turn+ dial swit*es by h&4 ,x is sl[ & h>d to d ?is "r1 b once x is done1 ,eniac c ref] to any numb] or in/ruction 9 any table 9 _/ ( a second4 ,?is is mu* fa/] ?an ! table ref]5ce "t 9 any o!r ( ! giant bra9s built up to #aidh4 ,programm+ ,we said above t ,eniac has ov] #ajj control l9es or program trunks along :i* in/ructions c be s5t4 ,^! in/ructions are express$ z pulses call$ program pulses4 ,n[ h[ d we make ^! pulses d :at we want !m to d8 ,= example1 h[ c we in/ruct ,accumulator #aa to add :at x holds into ,accumulator #ac8 ,on ea* unit ( ,eniac !re are plug hubs or sockets 7call$ program-pulse input t]m9als7 to :i* a program trunk may be connect$4 ,a program pulse receiv$ "h c make ! unit act 9 "s desir$ way4 ,on ea* accumulator ( ,eniac1 we f9d #ab program-pulse input hubs4 ,correspond+ to ea* ( ^! hubs1 !re is a n9e-way swit*1 call$ a program-control swit*4 ,! sett+ ( ?is swit* det]m9es :at ! accumulator w d :5 ! program-pulse input hub belong+ to ! swit* receives a program pulse4 ,= in/ance1 !re are swit* sett+s =3 receive input on ! l9e1 receive input on ! l9e1 etc42 & transmit output on ! add l9e1 etc4 ,!re is ev5 a swit* sett+ t in/ructs ! accumulator to d no?+1 & ?is in/ruction may be bo? useful & important4 ,n[1 9 ord] t ,accumulator #aa may transf] a numb] to ,accumulator #ac1 we ne$3 7#a7 a digit tray1 say ,b1 = ! numb] to travel along2 7#b7 a program trunk l9e1 say ,g#c1 to tell ,accumulator #aa :5 to s5d ! numb] & ,accumulator #ac :5 to receive x2 & 7#c7 c]ta9 plugg+ z foll[s3 #a4 ,we plug f program trunk ,g#c into a program-pulse input hub1 say ,no4 #e1 ( ,accumulator #aa2 #b4 ,we plug f ! same program trunk ,g#c into a program-pulse input hub1 say ,no4 #g1 ( ,accumulator #ac2 #c4 ,we set program-control swit* ,no4 #e ( ,accumulator #aa to 8add02 #d4 ,we set program-control swit* ,no4 #g ( ,accumulator #ac to "s input1 say 4 #e4 ,we plug f digit tray ,b into ! add output ( ,accumulator #aa4 #f4 ,we plug f digit tray ,b into ! input ( ,accumulator #ac4 ,n[1 :5 ! program pulse comes along l9e ,g#c1 x makes ,accumulator #ac transmit additively along digit tray ,b into ,accumulator #ac4 ,& t is ! result t we want$4 ,z ea* me*anism ( ,eniac f9i%es :at x is in/ruct$ to d1 x may or may n put out a program pulse4 ,?is pulse 9 turn may be plugg$ into any o!r program trunk l9e & may /imulate ano!r me*anism to act4 ,!n1 :5 ?is me*anism f9i%es1 x too may or may n put out a program pulse1 & s on4 ,9 g5]al1 !re are two diff]5t ways to in/ruct ,eniac to d a problem4 ,"o way is to set all ! swit*es1 plug all ! connections1 etc41 = ! specific problem4 ,?is is a long & h>d task4 ,v (t51 ev5 ) great c>e1 x is done n q correctly1 & !n ! sett+s mu/ be c>efully *eck$ all ov] aga94 ,a second me?od 7call$ ! von ,neumann programm+ me?od7 is to /ore all ! in/ructions = a problem 9 "o or two function tables ( ,eniac & !n tell ,eniac to read ! function tables 9 sequ5ce & to d :at !y say4 ,! re/ ( ! ma*9e is !n wir$ up 9 a /&>d fa%ion4 ,?is me?od ( in/ruct+ ,eniac 0 propos$ by ,dr4 ,john von ,neumann ( ! ,in/itute ( ,advanc$ ,/udy at ,pr9ceton1 ,n4 ,j4 ,eniac has be5 modifi$ to ! slight ext5t ne$$ s t ?is me?od c be us$ :5 desir$4 ,9 ?is me?od1 ea* in/ruction is a select$ "o ( #fj diff]5t /&>d in/ructions or ord]s--"o ( !m1 = example1 be+ 8multiplication40 ,ea* /&>d ord] is express$ by #b decimal digits4 ,! #fj /&>d ord]s are suffici5t s t ,eniac c d any ma!matical problem t does n ov]/ra9 its capacity4 ,s9ce ea* ( ! #c ,function ,tables c hold #fjj #b-;digit in/ructions1 ! ma*9e c hold a program ( #ahjj in/ructions "u ! von ,neumann programm+ me?od4 ,,an ,,appraisal ,,( ,,eniac ,,z ,a ,,comput] ,z a g5]al-purpose calculat+ ma*9e1 ,eniac suff]s f unbalance4 ,t is to say1 ,eniac op]ates rapidly & successfully 9 "s respects1 & sl[ly & tr\blesomely 9 o!r respects4 ,?is is altoge!r to be expect$1 h[ev]1 9 a calculator z novel z ,eniac & made to s l>ge an ext5t out ( /&>d radio p>ts4 ,x 0 c]ta9ly bett] to f9i% a calculator l ?is "o & !n />t on a new "o1 z ! ,moore ,s*ool ( ,electrical ,eng9e]+ did1 ?an to prolong design & con/ruction indef9itely 9 ord] to make improvem5ts4 ,spe$ ,eniac adds or subtracts v swiftly at ! rate ( #ejjj a second4 ,eniac multiplies at ! rate ( #cfj to #ejj a second4 ,division1 h[ev]1 is sl[1 relatively2 ! rate is ab\t #ej a second4 ,read+ numb]s f pun*$ c>ds1 #ab a second = #aj-;digit numb]s1 is ev5 sl[]4 ,z a result ( ^! rates1 y f9d1 :5 y put a problem on ,eniac1 t "o division delays y z long z #ajj additions or #h multiplications4 ,division might h be5 spe$$ some:at by 7#a7 rapidly conv]g5t approximation 7see ,supplem5t #b7 to ! reciprocal ( ! divisor & 7#b7 multiply+ by ! divid5d2 ?is might h tak5 #e or #f multiplication times in/ead ( #h4 ,also1 ! use ( a /&>d ,,ibm pun*-c>d fe$ & c>d pun* sl[s ! ma*9e greatly4 ,"o way to ov]come ?is drawback might be to in/all "o or two additional sets ( su* equipm5t1 :i* might increase input & output spe$4 ,ease ( ,programm+ ,eniac has a v rapid & flexible automatic control ov] ! programm+ ( op]ations4 ,eniac has m ?an #aj *annels along :i* numb]s c be transf]r$ & m ?an #ajj *annels along :i* program-control pulses c be transf]r$4 ,!re are _m ways = provid+ subr\t9es4 ,eniac has ! additional advantage t !re is no delay 9 giv+ ! ma*9e successive in/ructions3 all ! in/ructions ! ma*9e may ne$ at any "t are ready at ! />t ( ! problem1 & indications occurr+ 9 ! calculation c *ange ! r\t9e completely4 ,all ^! advantages1 h[ev]1 are paid = r heavily by ! sl[ me?ods = *ang+ programm+4 ,y h to plug l>ge numb]s ( program trunk l9es & digit trunk l9es1 or y h to set l>ge numb]s ( swit*es1 or bo?4 ,also1 :5 y wi% to return to a previ\s problem1 y mu/ d all ! plugg+ & swit* sett+ ov] aga94 ,_m delays 9 ! op]ation ( ! ma*9e are due to human errors 9 sett+ ! ma*9e = a new problem4 ,"h aga91 we mu/ rememb] t ,eniac 0 orig9ally design$ z a special-purpose ma*9e = solv+ trajectories4 ,to calculate a l>ge family ( trajectories v little *ang+ ( wires & swit*es w\ld be ne$$4 ,memory ,! mo/ sev]e limitation on ! usefulness ( ,eniac 01 at ! outset1 ! fact t x _h only #bj regi/]s = /or+ numb]s4 ,!re are l>ge numb]s ( problems t _c be simply h&l$ ) s small an int]nal memory4 ,ev5 ! ,h>v>d ,,ibm calculator 7see ,*apt] #f7 is (t5 /ra9$ dur+ a problem because ( ! numb] ( int]m$iate results t mu/ be /or$ = a "t be=e comb9+4 ,! ,balli/ic ,rese>* ,laboratories1 h[ev]1 contract$ = ext5sions to ,eniac to provide m memory & easi] *ang+ ( in/ructions4 ,reliability ,*eck+ results ) ,eniac is n easy4 ,!re is no built-9 gu>antee t ,eniac's results are correct4 ,a l>ge calculator c & does make bo? con/ant & int]mitt5t errors4 ,ways = *eck+ ) ,eniac are3 ,ma!matical1 if & :5 available1 & ?is w be seldom4 ,runn+ ! problem a second "t1 & ?is w1 at mo/1 prove consi/5cy4 ,delib]ate te/+ ( small p>ts ( ! problem1 :i* is v useful & is /&>d practice b leads only to a probability t ! f9al result is correct4 ,y c op]ate ,eniac "o addition at a "t1 & ev5 "o pulse at a "t1 & see :at ! ma*9e %[s 9 its little neon bulbs4 ,?is is a v useful p>tial *eck4 ,co/ ,! co/ ( ,eniac is high] ?an t ( "s ( ! o!r l>ge me*anical bra9s--ov] half a million doll>s4 ,because "s ( ! "w 0 done at ! ,moore ,s*ool by /ud5ts1 ! co/ 0 probably less ?an x o!rwise w\ld h be54 ,! l>ge/ "p ( ! co/ 0 ! design+ ( ! ma*9e & ! con/ruction ( ! panels2 ! tubes 7 only a small portion ( ! co/4 ,! tubes us$ 9 ! calculat+ circuits co/ only #bj to #ij c5ts4 ,h[ev]1 no lat] electronic calculator ne$ co/ z mu*1 = _m improvem5ts c n[ be se54 ,! p[] requir$ = ,eniac is ab\t #aej kil[atts or ab\t #bjj horsep[]1 mo/ ( :i* is us$ = ! heat]s ( ! electronic tubes4 ,! l>ge/ numb] ( electronic tubes m5tion$ = future electronic calculators is ab\t #cjjj1 s we c see t !y are likely to use less ?an a qu>t] ( ! p[] ne$$ = ,eniac4 ,eniac w d\btless give a numb] ( ye>s ( successful op]ation & be extremely useful = problems t employ its assets & are n exclud$ by its limitations4 ,9 fact1 at ! ,balli/ic ,rese>* ,laboratories1 = a typical week ( actual "w1 ,eniac has already prov$ to be equal to #ejj human comput]s work+ #dj h\rs ) desk calculat+ ma*9es1 & x appe>s t soon two or ?ree times z mu* "w may be obta9$ f ,eniac4 ,*apt] #h ,,reliability--,,no ,,wrong ,,results3 ,,bell ,,laboratories' ,,g5]al-,,purpose ,,relay ,,calculator ,9 #aidf1 ,bell ,telephone ,laboratories 9 ,new ,york f9i%$ two g5]al-purpose relay calculators--me*anical bra9s4 ,!y 7 tw9s4 ,"o 0 %ipp$ 9 ,july #aidf to ! ,national ,advisory ,committee = ,a]onautics at ,langley ,field1 ,virg9ia4 ,! o!r1 aft] "s mon?s ( trial op]ation1 0 %ipp$ 9 ,febru>y #aidg to ! ,balli/ic ,rese>* ,laboratories at ! ,u4 ,s4 ,army's ,prov+ ,gr\nd1 ,ab]de51 ,md4 ,ea* ma*9e is rem>kably reliable & v]satile4 ,x c d a wide v>iety ( calculations 9 a great _m diff]5t ways4 ,yet ! ma*9e nev] takes a new /ep )\t a *eck t ! old /ep 0 correctly p]=m$4 ,!re is1 !re=e1 a *ance ( bett] ?an #ii4iii1iii1iii p] c5t t ! ma*9e w n let a wrong result come out4 ,! automatic *eck+1 ( c\rse1 does n prev5t 7#a7 human mi/akes--= example1 in/ruct+ ! ma*9e incorrectly--or 7#b7 me*anical failures1 9 :i* ! ma*9e /ops dead 9 its tracks1 lett+ no result at all come out4 ,,orig9 ,,& ,,developm5t ,9 ,bell ,telephone ,laboratories ! telephone sy/em ( ! c\ntry is cont9ually /udi$4 ,_! rese>* produc$ ! common type ( dial telephone sy/em3 a ma/]ly ma*9e = select+ in=mation4 ,n[ :5 a telephone eng9e] /udies an electric circuit1 he (t5 f9ds x v conv5i5t to use numb]s 9 pairs3 l #b1 #e or-#d1-a4 ,"h ! comma is a sep>ation sign to keep ! two numb]s 9 ! pair sep>ate & 9 sequ5ce4 ,ma!maticians call numb]s ( ?is k9d1 = no v good reason1 complex numb]s2 ( c\rse1 !y are f> less complex ?an :y ! sun %9es or :y plants gr[4 ,:5 ,bell ,laboratories te/ ! design ( new circuits1 girl comput]s d ari?metic ) complex numb]s4 ,addition & subtraction are easy3 ea* means two op]ations ( addition or subtraction ( ord9>y numb]s4 ,= example1 #b1 #e1 plus-#d1-a equals #b-d1 #e-a1 :i* equals-#b1 #d4 ,& #b1 #e m9us-#d1-a is ! same z #b1 #e plus #d1 #a2 & ?is equals #b #d1 #e #a1 :i* equals #f1 #f4 ,multiplication ( two complex numb]s1 h[ev]1 is m "w4 ,if a1 b & c1 d are two complex numb]s1 !n ! =mula = _! product is 7a c7-7b d71 7a d7 7b c74 ,to get ! answ]1 we ne$ #d multiplications1 #a subtraction1 & #a addition4 ,division ( two complex numb]s requires ev5 m "w4 ,if a1 b & c1 d are two complex numb]s1 ! =mula = ! quoti5t ( a1 b divid$ by c1 d is3 7a c7 7b d7 7c c7 7d d71 7b c7 - 7a d7 7c c7 7d d7 ,= example1 7#b1 #e7 7-#d1 -#a7 7#b -#d -#h7 7#e -#a -#e7 7-#d -#d #af7 7-#a -#a #a71 7#e -#d -#bj7 - 7#b -#a -#b7 #af #a -7_/71 -7_/7 ,?us1 division ( "o complex numb] by ano!r ne$s #f multiplications1 #b additions1 #a subtraction1 & #b divisions ( ord9>y numb]s--& always 9 ! same patt]n or sequ5ce4 ,! ,complex ,comput] ,ab\t #aici1 an eng9e] at ,bell ,telephone ,laboratories 9 ,new ,york1 ,dr4 ,george ,r4 ,/ibitz1 notic$ ! great volume ( ?is patt]n ari?metic4 ,he began to wond] :y telephone swit*+ equipm5t c\ld n be us$ to d ! multiplications & divisions automatically4 ,he decid$ x c\ld4 ,all t 0 necess>y 0 t ! relays 7see ,*apt] #b7 us$ 9 regul> telephone equipm5t %\ld h a way ( rememb]+ & calculat+ ) numb]s4 ,regul> telephone equipm5t w\ld take c>e ( ! prop] sequ5ce ( op]ations4 ,regul> equipm5t kn[n z teletypewrit]s w\ld pr9t ! numb]s ( ! answ] :5 x 0 obta9$4 ,a teletypewrit] consi/s ess5tially ( a typewrit] t may be op]at$ by electrical impulses4 ,x has a keybo>d t may produce electrical impulses 9 sets correspond+ to lett]s2 & x c receive or transmit ov] wires4 ,dr4 ,/ibitz cod$ ! numb]s3 ea* decimal digit 0 mat*$ up ) a gr\p ( f\r relays 9 sequ5ce1 & ea* ( ^! relays c\ld be op5 or clos$4 ,if #j means op5 & #a means clos$1 "h is ! patt]n or code t he us$3 ,,decimal ,,digit ,,relay ,,code #j #j #j #a #a #a #j #a #j #j #b #j #a #j #a #c #j #a #a #j #d #j #a #a #a #e #a #j #j #j #f #a #j #j #a #g #a #j #a #j #h #a #j #a #a #i #a #a #j #j ,) regul> telephone relays & regul> telephone company te*niques1 ,dr4 ,/ibitz & ,bell ,telephone ,laboratories design$ & con/ruct$ ! ma*9e4 ,x 0 call$ ! ,complex ,comput] & 0 built j = multiply+ & divid+ complex numb]s4 ,six or eight panels ( relays & wires 7 9 "o room4 ,two floors away1 "s ( ! girl comput]s sat 9 ano!r room1 :]e "o ( ! teletypewrit]s ( ! ma*9e 0 locat$4 ,:5 !y wi%$1 !y c\ld type into ! ma*9e's teletypewrit] ! numb]s to be multipli$ or divid$4 ,9 a few seconds back w\ld come ! answ]4 ,9 fact1 !re 7 two m comput+ rooms :]e teletypewrit]s ( ! ma*9e 7 /ation$4 ,to prev5t conflicts betwe5 /ations1 ! ma*9e _h a circuit l ! busy signal f a telephone4 ,9 #aidj1 a demon/ration ( ! ,complex ,comput] took place3 ! comput+ panels rema9$ 9 ,new ,york1 b ! teletypewrit] input-output /ation 0 set up at ,d>tm\? ,college 9 ,hanov]1 ,n4 ,h4 ,ma!maticians gave problems to ! ma*9e 9 ,d>tm\?1 x solv$ !m 9 ,new ,york1 & x report$ ! answ]s 9 ,d>tm\?4 ,special-,purpose ,comput]s ,) ?is z a beg9n+1 ,bell ,laboratories develop$ ano!r ma*9e = a wide v>iety ( ma!matical processes call$ int]polat+ 7see ,supplem5t #b74 ,!n1 dur+ ,_w ,w> ,,ii1 ,bell ,laboratories made m special-purpose comput+ ma*9es4 ,!y 7 us$ 9 milit>y laboratories *>g$ ) te/+ ! accuracy ( in/rum5ts = controll+ ! fire ( guns4 ,^! comput]s took 9 a set ( gun-aim+ directions put out by ! fire-control in/rum5t 9 "s te/4 ,!y also took 9 ! set ( obs]vations t w5t into ! fire-control in/rum5t on t te/4 ,!n !y comput$ ! diff]5ces betwe5 ! gun-aim+ produc$ by ! fire-control in/rum5t & ! gun-aim+ really requir$ by ! obs]vations4 ,us+ ^! diff]5ces1 ! fire-control in/rum5t c\ld be adju/$ & correct$4 ,^! special-purpose comput]s 7 also useful 9 *eck+ ! design ( new fire-control in/rum5ts & 9 *eck+ *anges due to new types ( guns or explosives4 ,regul>ly1 aft] ea* ( ^! special-purpose comput]s 0 f9i%$1 p began to put o!r problems on x4 ,x seem$ to be fat$ t1 z soon z y _h made a ma*9e = "o purpose1 y want$ to use x = some?+ else4 ,accord+ly1 9 #aidd1 two ag5cies ( ! ,u4 ,s4 ,gov]nm5t toge!r made a contract ) ,bell ,telephone ,laboratories = two g5]al-purpose relay comput]s4 ,^! two ma*9es 7 f9i%$ 9 #aidf & are tw9s4 ,,organization ,,( ,,! ,,g5]al-,,purpose ,,comput] ,:5 a man sits d[n at a desk to "w on a computation1 he has six ?+s on 8 desk to "w )3 a "w %eet2 a desk calculator1 to add1 subtract1 multiply1 & divide2 "s rules to be foll[$2 ! tables ( numb]s he w ne$2 ! data = ! problem2 & an answ] %eet4 ,9 8 head1 he has ! capacity to make decisions & to d 8 "w 9 a c]ta9 sequ5ce ( /eps4 ,^! sev5 subdivisions ( calculation are all f\nd 9 ! ,bell ,laboratories' g5]al-purpose relay comput]4 ,! g5]al-purpose comput] is a comput+ sy/em1 9 fact1 m ?an x is a s+le ma*9e4 ,! "p ( ! sy/em :i* does ! actual calculat+ is call$1 9 ! foll[+ p>agraphs1 ! comput]1 or else1 s9ce x is 9 two halves1 ,comput] #a & ,comput] #b4 ,physical ,units ,! comput+ sy/em deliv]$ to ! ,balli/ic ,rese>* ,laboratories fills a room ab\t #cj by #dj feet & consi/s ( ! foll[+3 #b comput]s3 panels ( relays1 wir+1 etc41 :i* add1 subtract1 multiply1 divide1 select1 decide1 control1 etc4 #d problem positions3 tables ea* hold+ #ab me*anisms = fe$+ pap] tape1 :i* read numb]s & in/ructions pun*$ on tape & conv]t !m into electrical impulses4 #b h& p]=ators3 keybo>d devices = pun*+ in/ructions & numb]s on pap] tape4 #a processor3 a table hold+ me*anisms = fe$+ #b pap] tapes & pun*+ a ?ird pap] tape1 us$ = *eck+ numb]s & in/ructions pun*$ on tape4 #b record]s3 ea* a table hold+ a teletypewrit]1 a tape pun*1 & a tape fe$1 us$ = record+ answ]s &1 if necess>y1 consult+ !m aga94 ,! #b comput]s correspond to ! "w %eet1 ! desk calculator1 & ! man's capacity to make decisions & to c>ry out a sequ5ce ( /eps4 ,! #d problem positions correspond to ! problem data1 ! rules1 & ! tables ( numb]s4 ,! #b record]s correspond to ! answ] %eet4 ,! #b h& p]=ators & ! processor are auxili>y ma*9es3 !y translate ! ord9>y language ( ari?metic into ! ma*9e language ( pun*$ holes 9 pap] tape4 ,?is is ! comput+ sy/em z organiz$ = ! ,balli/ic ,rese>* ,laboratories at ,ab]de54 ,! "o = ! ,national ,advisory ,committee = ,a]onautics has only #c problem positions4 ,! comput] sy/em may1 9 fact1 be organiz$ ) #a to #aj comput]s & ) #a to #bj problem positions4 ,! great bulk ( ?is comput+ sy/em1 l ! me*anical bra9s describ$ 9 previ\s *apt]s1 is made up ( l>ge numb]s ( id5tical p>ts ( only a few k9ds4 ,^! are3 /&>d telephone relays2 wire2 & /&>d teletype transmitt]s1 me*anisms t read pun*$ pap] tape & produce electrical impulses4 ,numb]s ,! numb]s t ! ,bell ma*9e conta9s range f #j4ajjjjjj to #j4iiiiiii times a p[] ( #aj v>y+ f #aj1jjj1jjj1jjj1jjj1jjj1jjj to #j4jjj1jjj1jjj1jjj1jjj1jjj1a1 or1 9 o!r words1 f #aj to #aj4 ,! ma*9e also conta9s z]o & inf9ity3 z]o arises :5 ! numb] is small] ?an #aj1 & inf9ity arises :5 ! numb] is equal to or great] ?an #i1iii1iii1jjj1jjj1jjj1jjj4 7,see ,supplem5t #b47 ,! sy/em us$ 9 ! ma*9e to repres5t numb]s on relays is call$ biqu9>y--! bi-1 because x is p>tly tw(old l ! h&s1 & ! -qu9>y because x is p>tly fivefold l ! f+]s4 ,?is sy/em is us$ 9 ! abacus 7see ,*apt] #b & ,supplem5t #b74 ,9 ! ma*9e1 = ea* decimal digit1 #g relays are us$4 ,^! relays are call$ ! #jj & #e relays1 & ! #j1 #a1 #b1 #c1 & #d relays4 ,if1 z be=e1 #j indicates a relay t is n en]giz$ & #a indicates a relay t is en]giz$1 !n ea* decimal digit is repres5t$ by ! position+ ( ! #g relays z foll[s3 ,,decimal ,,digit ,,relays #jj #e #j #a #b #c #d #j #a #j #a #j #j #j #j #a #a #j #j #a #j #j #j #b #a #j #j #j #a #j #j #c #a #j #j #j #j #a #j #d #a #j #j #j #j #j #a #e #j #a #a #j #j #j #j #f #j #a #j #a #j #j #j #g #j #a #j #j #a #j #j #h #j #a #j #j #j #a #j #i #j #a #j #j #j #j #a ,!n1 = any decimal digit1 "o & only "o ( ! #jj & #e relays is en]giz$1 & "o & only "o ( ! #j1 #a1 #b1 #c1 & #d relays is en]giz$4 ,if m or less ?an exactly "o relay 9 ea* set is en]giz$1 !n ! ma*9e kn[s t x has made a mi/ake1 & x /ops dead 9 its tracks4 ,?us any accid5tal failure ( a relay is at once caught1 & ! *ance ( two comp5sat+ failures occurr+ at ! same "t is extremely small4 ,,h[ ,,in=mation ,,goes ,,into ,,! ,,ma*9e ,9 ord] to put a problem into ?is ma*9e--j z ) ! o!r ma*9es--fir/ a ma!matician :o kn[s h[ ! problem is to be solv$1 & :o kn[s h[ to organize x = ! ma*9e1 lays out ! s*eme ( calculation4 ,!n1 a girl goes to "o ( ! h& p]=ators4 ,sitt+ at ! keybo>d1 %e presses keys & pun*es out feet or y>ds ( pap] tape express+ ! in/ructions & numb]s = ! calculation4 ,ea* "* pun*$--digit1 lett]1 or sign--has "o or m ( a maximum ( #f holes across ! tape4 ,ano!r girl1 us+ ! o!r h& p]=ator1 also pun*es out ! in/ructions & numb]s = ! calculation4 ,if %e wi%es to erase a wrong "*1 %e c press an erase key t pun*es all #f holes1 & !n ! ma*9e w pass by ?is r[ z if x 7 n !re4 ,?ree k9ds ( tapes are produc$ = ! ma*9e3 ,problem tapes1 :i* conta9 in=mation belong+ to ! p>ticul> problem4 ,table tapes1 :i* conta9 tables ( numb]s to be ref]r$ to f "t to "t4 ,r\t9e tapes1 :i* conta9 ! program1 or r\t9e1 or sequ5ce ( /eps t ! ma*9e is to c>ry out4 ,9 ea* ( ^! tapes "o "* takes up ( an in* along ! tape4 ,9 ! case ( a table tape1 h[ev]1 an ord9>y #a-;digit numb] requires #d *>act]s on ! tape1 & a #g-;digit numb] requires #aa *>act]s on ! tape4 ,on a table tape !re w be on ! av]age ab\t #a in* ( tape p] numb]4 ,! ,processor ,! two pap] tapes prep>$ on ! p]=ator %\ld agree4 ,b :e!r or n !y agree1 a girl takes !m ov] to ! processor & puts !m bo? 94 ,! processor has two tape fe$s1 & %e puts "o tape on ea* & />ts ! ma*9e4 ,! processor comp>es !m r[ by r[1 mak+ sure t !y agree1 & pun*es a new tape r[ by r[4 ,if ! two input tapes disagree1 ! processor /ops4 ,y c look to see :i* tape is "r1 & !n y c put ! correct pun* into ! new tape ) a keybo>d m\nt$ on ! processor4 ,z ! processor comp>es ! two input tapes1 x also conv]ts any numb] writt5 9 ! usual way into ma*9e language4 ,= example1 ! processor w automatically translate #bc1ahh into 4#bca #hhjj #aj4 ,! processor also puts 9 c]ta9 safegu>ds4 ,if y want x to1 ! processor w also make a pr9t$ record ( a tape4 ,also1 :5 a tape becomes worn f use 9 ! ma*9e1 y c put x into ! processor & make a fre% copy4 ,! ,problem ,positions ,next1 ! girl takes ! pun*$ tape made by ! processor ov] to a problem position t is idle4 ,two ( ! problem positions are always busy guid+ ! two comput]s4 ,! o!r two problem positions /& by1 ready to be load$ ) problems4 ,a problem position looks l a l>ge cov]$-ov] table4 ,"u ! cov]s are #ab tape fe$s1 or tape transmitt]s4 ,all ^! transmitt]s look exactly alike except = _! labels & consi/ ( regul> teletype transmitt]s4 ,six-hole pap] tape c be f$ into any transmitt]4 ,six metal f+]s s5se ! holes 9 ! pap] tape & give out electrical impulses at prop] times4 ,at ! front ( ! problem position is a small gr\p ( swit*es t provide complete control ov] ! problem :ile x is on ! ma*9e4 ,^! are swit*es = />t+1 disconnect+1 mom5t>y /op1 etc4 ,"o tape transmitt] is ! problem tape transmitt]4 ,x takes 9 all ! data = ! problem su* z ! />t+ numb]s4 ,! fir/ ?+ x does at ! />t ( a problem is to *eck 7by comp>+ tape numb]s7 t ! "r tapes are 9 ! "r fe$s4 ,five transmitt]s are r\t9e tape transmitt]s4 ,ea* ( ^! takes 9 ! sequ5ce ( comput+ /eps4 ,! r\t9e tapes also conta9 in=mation = ref]r+ to table tapes & in/ructions = pr9t+ & pun*+ tape4 ,! ma*9e c *oose accord+ to in/ructions betwe5 ! five r\t9e tapes & c *oose betwe5 _m diff]5t sections on ea* tape4 ,!re=e1 we c use a l>ge numb] ( diff]5t r\t9es 9 a calculation1 & ?is capacity makes ! ma*9e v]satile & p[]ful4 ,six transmitt]s are table tape transmitt]s4 ,!y read tables ( numb]s :5 direct$ to4 ,a table tape c be z long z #ajj feet & w hold numb]s at ! rate ( #a in* p] numb]1 s t ab\t #abjj numb]s ( sev5 decimal digits c be /or$ on a table tape4 ,:5 we look up a numb] 9 a table1 su* z ! foll[+1 #b #c #c ---------------------------------------- ---------------- #a #a4jbejj #a4jcjjj #a4jcejj #b #a4jejfc #a4jfjij #a4jgabc #c #a4jgfhi #a4jibgc #d #a4ajcha #e #a4acada #f #a4aeifi #g #h #i #aj we look along ! top & d[n ! side until we f9d ! column & r[ ( ! numb] we are look+ =4 ,^! are call$ ! argum5ts ( ! tabul> value t we are look+ = 7see ,supplem5t #b74 ,n[ :5 we put ?is table on a tape to g into ! ,bell ,laboratories ma*9e1 we write x all on "o l9e1 "o figure aft] ano!r1 & we pun* x z foll[s3 #b- #a-e #a4jbejj #a4jejfc #a4jgfhi #a4ajcha #a4acada #f-aj #a4aeifi #aa-ae #c #a-e #a4jcjjj #a4jfjij #c #a-e #a4jcejj ,y w notice t ! column labels #b1 #c1 #c h be5 put on ! tape1 ea* 9 front ( ! gr\p ( numb]s !y apply to4 ,! r[ labels #a to #e1 #f to #aj1 h also be5 put on ! tape1 ea* 9 front ( ! gr\p ( numb]s !y apply to4 ,! appropriate column & r[ numb]s1 or argum5ts1 mu/ be put (t5 on e table tape1 s t x is easy = ! ma*9e to tell :at "p ( ! table tape x is read+4 ,9 ! ,bell ,laboratories ma*9e1 we d n ne$ to put equal blocks ( argum5ts l #a-e1 #f-aj on ! table tape4 ,in/ead we c put individual argum5ts l #a1 #b1 #c1 #d 1 or1 if we wi%1 we c use blocks ( diff]5t sizes1 l #a-c1 #d-ae1 #af-cj4 ,= "s tables1 su* z income tax tables1 x is v useful to h v>y+-siz$ blocks ( argum5ts4 ,! ma*9e1 :5 hunt+ = a c]ta9 value 9 ! table1 makes a comp>ison at ea* block ( argum5ts4 ,! ma*9e ne$s ab\t #f seconds to se>* a foot ( tape4 ,if we want to set up a table economically1 !re=e1 we ne$ to consid] ! av]age l5g? ( "t ne$$ = se>*+4 ,illu/ration3 ,,fig4 #a4 ,s*eme ( a record]4 ,,h[ ,,in=mation ,,comes ,,out ,,( ,,! ,,ma*9e ,at ei!r "o ( ! two record]s 7,fig4 #a71 in=mation comes out ( ! ma*9e1 ei!r 9 ! =m ( pr9t$ *>act]s or z pun*$ tape4 ,! record] consi/s ( a pr9t]1 a rep]=ator1 & a tape transmitt]4 ,"o record] table belongs to ea* comput] & records ! results x computes4 ,! pr9t] is a regul> teletypewrit] connect$ to ! ma*9e4 ,x translates in=mation produc$ by ! ma*9e z electrical impulses & pr9ts ! in=mation 9 lett]s & digits on pap]4 ,! rep]=ator is an automatic tape pun*4 ,x translates in=mation produc$ by ! ma*9e 9 ! =m ( electrical impulses & pun*es ! in=mation on pap] tape4 ,next to ! tape pun* is a tape transmitt]4 ,aft] ! tape comes ?r\gh ! pun*1 x is f$ into ! transmitt]4 ,"h ! ma*9e c hunt = a previ\s result pun*$ 9 ! tape1 read t result1 & use x aga94 ,,h[ ,,in=mation ,,is ,,manipulat$ ,,9 ,,! ,,ma*9e ,! ma9 "p ( ! comput+ sy/em consi/s ( #bg l>ge frames load$ ) relays & wir+1 call$ ! comput]1 or ,comput] #a & ,comput] #b4 ,9 ?is 8telephone c5tral /ation10 all ! 8phone calls0 f "o numb] to ano!r are att5d$ to4 ,!re are #h types ( ^! frames 9 ! comput]3 ,,frames ,,numb] ,/or+ regi/] frames #f ,pr9t] frames #b ,problem frames #b ,position frames #b ,calculator frames #f ,control frames #b ,r\t9e frames #d ,,btl 7,block-,trig-,log7 frames #b ,p]man5t table frames #a ---- ,total #bg ,9 mo/ b n q all respects1 ! two halves1 ,comput] #a & ,comput] #b1 c compute indep5d5tly4 ,! /or+ regi/] frames hold en\gh relays to /ore #cj numb]s4 ,! regi/]s = ^! numb]s are nam$ ,a1 ,b1 ,c1 ,d1 1 ,m1 ,n1 ,o 9 two gr\ps ( #ae ea*4 ,"o gr\p belongs to ,comput] #a & ! o!r to ,comput] #b4 ,9 ea* ,comput]1 ! calculator frames hold en\gh relays = /or+ two numb]s 7held 9 ! ,x & ,y regi/]s7 & = p]=m+ addition1 subtraction1 multiplication1 division1 & squ>e root4 ,9 ea* ,comput]1 ! problem frame /ores ! numb]s t are read (f ! problem tape & ! table tapes1 & ! pr9t] frame /ores ! numb]s t are read into ! pr9t]4 ,! pr9t] frame also /ores indications1 = example1 ! signs ( numb]s1 plus or m9us1 = purposes ( comb9+ !m4 ,^! frames also hold ! relays t control ! pr9t]1 ! problem tape1 & ! table tapes4 ,jo9tly = bo? ,comput]s1 ! position frames connect a problem 9 "s problem position to a ,comput] t becomes idle4 ,= example1 "o problem may f9i% 9 ! middle ( ! night2 ! ma*9e automatically & unatt5d$ swit*es to ano!r problem position & proce$s ) ! in/ructions !re conta9$4 ,a backlog ( comput+ on h& c be /or$ 9 two ( ! problem positions1 :ile ! o!r two control ! two ,comput]s4 ,9 ea* ,comput]1 ! r\t9e frames hold ! relays t make ! ,comput] foll[ ! r\t9e in/ructions4 ,jo9tly = bo? ,comput]s1 ! rema9+ frames--! control frames1 ! ,,btl frames1 & ! p]man5t table frames--hold ! relays t control3 ! al>ms & lights = indicat+ failures2 "s circuits call$ ! ,,btl controls2 ! tape processor2 & ! ma!matical tables t are p]man5tly wir$ into ! ma*9e4 ,! p]man5t table frames hold ! foll[+ ma!matical functions 7see ,supplem5t #b73 s9e1 cos9e1 antitang5t1 log>i?m1 & antilog>i?m4 ,/or+ ,numb]s c be /or$ 9 ! ma*9e 9 ! #cj regul> /or+ regi/]s ( bo? ,comput]s toge!r4 ,!y c also be /or$1 at ! co/ ( ty+ up "s ma*9e capacity1 9 ! o!r regi/]s3 ! #d calculator regi/]s1 ! #b problem regi/]s1 ! #b table regi/]s1 & ! #b pr9t] regi/]s4 ,numb]s c also be pun*$ out on tape1 9 ei!r ( ! two pr9t]s1 & lat] read aga9 f ! tape4 ,labels id5tify+ ! numb]s c also be pun*$ & read aga9 f ! tape4 ,ea* regi/] 9 ! ma*9e /ores a numb] 9 ! biqu9>y notation1 z expla9$ above4 ,9 programm+ ! ma*9e1 aft] m5tion+ a regi/] x is necess>y--z a "p ( ! s*eme = *eck+--to tell ! ma*9e specifically :e!r to hold ! numb] 9 ! regi/] or to cle> x4 ,addition & ,subtraction ,! calculator frames c add two numb]s toge!r1 if s in/ruct$ 9 ! r\t9e tape4 ,suppose t ! two numb]s are 9 ! regi/]s ,b & ,d & t we wi% to put ! sum 9 regi/] ,f4 ,suppose t we wi% to cle> ! ,d numb] b hold ! ,b numb] aft] us+ !m4 ,! code on ! r\t9e tape is ,b ,h ,d ,c ,f4 ,h & ,c com+ "r aft] ! names ( ! regi/]s always designate 8hold0 & 8cle>10 respectively4 ,! calculator frames c1 likewise1 subtract a numb]4 ,! r\t9e in/ruction ,b ,h-,d ,c ,f means3 ,take ! numb] 9 regi/] ,b 7hold x72 subtract ! numb] 9 ,d 7cle> x72 put ! result 9 ,f ,multiplication & ,division ,! calculator frames p]=m multiplication by /or+ ! digits ( ! multipli]1 add+ ! multiplic& ov] & ov]1 & %ift+1 until ! product is obta9$4 ,h[ev]1 if ! multipli] is #aihi1 = example1 ! calculator treats x z #bjjj-aa4 ,?is %ort-cut applies to digits #f1 #g1 #h1 #i & cuts ! "t requir$ = multiply+4 ,! r\t9e in/ruction is ,b ,h ,d ,c ,f4 ,! calculator p]=ms division by repeat$ subtraction4 ,! r\t9e in/ruction is ,b ,h ,d ,c ,f4 ,! op]ation signs 1-1 1 actually appe> on ! keybo>d ( ! p]=ator & on ! pr9t$ tape produc$ by ! pr9t]4 ,discrim9ation ,discrim9ation is ! t]m us$ 9 ! ,bell ,laboratories comput] = :at we h previ\sly call$ selection1 or comp>ison1 or sequ5c+4 ,! discrim9ator is a "p ( ! calculator t comp>es or selects or decides--8discrim9ates40 ,! discrim9ator c decide :e!r a numb] is z]o or n z]o4 ,9 ! language ( ! algebra ( logic 7see ,*apt] #i & ,supplem5t #b71 if a is a numb]1 ! discrim9ator c f9d ,t7a #j74 ,! discrim9ator c also decide :e!r a numb] is positive or negative4 ,9 ! language ( logic1 x c f9d ,t7a #j7 or ,t7a #j74 ,! actions t a discrim9ator c cause to be tak5 are3 ,/op ! ma*9e4 ,/op ! problem1 & proce$ to ano!r problem4 ,/op ! r\t9e go+ on1 & proce$ ) a new r\t9e4 ,p]mit pr9t+1 or prev5t pr9t+2 etc4 ,9 ?is way ! discrim9ator c3 ,di/+ui% betwe5 "r & wrong results4 ,tell t a c]ta9 result is impossible4 ,recognize a c]ta9 result to be ! answ]4 ,control ! numb] ( repetitions ( a =mula4 ,*ange f "o =mula to ano!r =mula4 ,*eck a numb] aga9/ a tol]ance2 etc4 ,,problems ,among ! problems t h be5 plac$ on ! ma*9e successfully are3 solv+ ! diff]5tial equation ( a trajectory 7see ,*apt] #e7 & solv+ #cb l9e> simultane\s equations 9 #cb unkn[ns 7see ,supplem5t #b74 ,9 ! second case1 ! r\t9e tapes 7 design$ to apply equally well to #aa to #ajj l9e> equations 9 #aa to #ajj unkn[ns4 ,h[ev]1 ! ma*9e c d a v broad class ( problems1 includ+1 = example1 comput+ a p]sonal income tax4 ,?is calculation ) all its complexity ( *oices _c be plac$ on any ( ! me*anical bra9s describ$ 9 previ\s *apt]s4 ,! ma*9e c1 ( c\rse1 be us$ to calculate any tables t we may wi% to ref] to4 ,,an ,,appraisal ,,( ,,! ,,calculator ,! ,bell ,telephone ,laboratories g5]al-purpose relay comput] is probably ! be/ me*anical bra9 made up to ! end ( #aidg1 9 reg>d to ! two important factors ( reliability & v]satility4 ,reliability ,! ma*9e produces results t are practically #ajj p] c5t reliable1 = ! ma*9e *ecks ea* /ep be=e tak+ ! next "o4 ,! *eck+ pr9ciple is t exactly a c]ta9 numb] ( relays mu/ be en]giz$4 ,= example1 z we said be=e1 = ea* decimal digit !re are #g relays4 ,exactly #b ( ^! relays mu/ be en]giz$--no m1 no less4 ,if ?is does n happ51 ! ma*9e /ops at once )\t los+ any numb]s4 ,lights %9e = _m circuits 9 ! control panel1 &1 if y comp>e :at !y ought to %[ ) :at !y d %[1 y c usually f9d at once ! location ( ! mi/ake4 ,! tr\ble may be a speck ( dirt betwe5 two contact po9ts on a relay1 &1 :5 x is bru%$ away1 ! ma*9e c g "r ahead f :]e x /opp$4 ,accord+ to a /atem5t by ,franz ,l4 ,alt1 director ( ! comput+ laboratory at ! ,balli/ic ,rese>* ,laboratories1 9 ,decemb] #aidg1 8! ,bell ma*9e _h n giv5 a s+le wrong result 9 eight mon?s ( op]ation1 except :5 op]ators int]f]$ ) its normal runn+40 ,to gu>d aga9/ ! risk ( putt+ tapes 9 ! wrong transmitt]s1 ! ma*9e w *eck by ! in/ructions conta9$ 9 ! tapes t ! "r tapes are 9 ! "r places4 ,"t ,requir$ ,! "t requir$ to d problems on ?is me*anical bra9 is p]haps long] ?an on ! o!rs4 ,! numb]s are h&l$ digit by digit on ! input tapes1 & ! typewrit] 9 ! record] moves space by space 9 ord] to get to ! prop] writ+ po9t4 ,^! are sl[ proc$ures4 ,! spe$s ( num]ical op]ation are3 addition1 _/ second2 multiplication1 #a second on ! av]age2 division1 #b4g seconds on ! av]age2 squ>e root1 #d4e seconds on ! av]age2 log>i?m1 ab\t #ae seconds4 ,/aff ,9 ord] to op]ate ! ma*9e1 ! /aff requir$ is3 "o ma9t5ance man2 "o ma!matical eng9e]2 ab\t six girls = pun*+ tape1 etc41 dep5d+ on ! numb] ( problems to be h&l$ at ! rate ( ab\t "o problem p] week p] girl4 ,unlike any ( ! o!r me*anical bra9s built by ! end ( #aidg1 ?is ma*9e w run unatt5d$4 ,ma9t5ance ,! relays 9 ! ma*9e w op]ate = ye>s ) no failure2 !y h ! exp]i5ce ( /&>d telephone te*niques built into !m4 ,"u laboratory conditions ?is type ( relay _h by #aidf op]at$ successfully mu* m ?an #ajj million times4 ,! tape fe$+ & read+ equipm5t 9 ! ma*9e may be ma9ta9$ by p]iodic inspection & s]vice4 ,! total numb] ( teletype transmitt]s 9 ! ma*9e is #ch4 ,if "o fails1 x is easy to plug 9 a sp>e4 ,! total p[] requir$ = ! ma*9e is ab\t #bh horsep[]4 ,batt]ies are furni%$ s t1 if ! p[] supply %\ld be int]rupt$1 ! ma*9e c /ill op]ate = z long z a half-h\r4 ,co/ ,! co/ ( production ( ?is ma*9e 9 ! size ( #d problem positions & #b comput]s has be5 r\ghly e/imat$ z half a million doll>s4 ,?is co/ includes mat]ial1 manufacture1 in/allation1 & te/+4 ,no developm5t co/ is includ$ 9 ?is figure4 ,in/ead1 ! co/ ( developm5t has be5 reckon$ z squ>+ ) pat5ts & o!r contributions ( ! "w to ! telephone swit*+ art4 ,x is unlikely t ! g5]al-purpose relay comput] w be manufactur$ g5]ally4 ,! pressure ( ord]s = telephones1 ! ne$ to cat* up ) ! backlog ( dem&1 & ! developm5t ( electronic comput]s--all indicate t ! ,bell sy/em w h>dly g fur!r ) ?is type ( comput]4 ,9 an em]g5cy1 h[ev]1 ! ,bell sy/em w\ld probably con/ruct su* ma*9es = ! gov]nm5t1 if reque/$4 ,9 ! meantime1 _m pr9ciples fir/ us$ 9 ! g5]al-purpose relay comput] are likely to f9d applications 9 telephone sy/em "w4 ,9 fact1 a pres5t major developm5t be+ pursu$ 9 ! telephone sections ( ,bell ,laboratories is ! application ( ! comput] pr9ciples to ! automatic computation ( telephone bills4 ,*apt] #i ,,reason+3 ,,! ,,kal9-,,burkh>t ,,logical-,,tru? ,,calculator ,s f> we h talk$ ab\t me*anical bra9s t are ma!maticians4 ,!y are fond ( numb]s2 _! ma9 "w is ) numb]s2 & ! o!r k9ds ( ?9k+ !y d are second>y4 ,we n[ come to a me*anical bra9 t is a logician4 ,x is fond ( reason+--logic2 its ma9 "w is ) :at is logically true & :at is logically false2 & x does n h&le numb]s4 ,?is me*anical bra9 0 f9i%$ 9 ,june #aidg4 ,x is call$ ! ,kal9-,burkh>t ,logical-,tru? ,calculator4 ,z its "n tells1 x calculates logical tru?4 ,n[ :at d we mean by t8 ,,tru? ,to be true or false is a prop]ty ( a /atem5t4 ,usually we say t a /atem5t is true :5 x expresses a fact4 ,= example1 take ! /atem5t 8,salt dissolves 9 wat]40 ,we consid] ?is /atem5t to be true because x expresses a fact4 ,actually1 9 ?is case we c r\ghly prove ! fact ourselves4 ,we take a b[l1 put "s wat] 9 x1 & put 9 a little salt4 ,aft] a :ile we look into ! wat] & notice t no salt :atev] is to be se54 ,( c\rse1 ?is /atem5t1 l _m ano!r1 occurs 9 a context :]e c]ta9 ?+s are und]/ood4 ,"o ( ! und]/&+s "h1 = example1 is 8a small am\nt ( salt 9 a mu* l>g] am\nt ( wat]40 ,= if we put a :ole bag full ( salt 9 j a little wat]1 n all ! salt w dissolve4 ,ne>ly e /atem5t occurs 9 a context t we mu/ "k if we are to decide :e!r ! /atem5t is true or false4 ,,logical ,,tru? ,logical tru? is diff]5t f ord9>y tru?4 ,) logical tru? we appeal n to facts b to suppositions4 ,usually we say t a /atem5t is logically true :5 x foll[s logically f c]ta9 suppositions4 ,9 o!r words1 we play a game t has useful1 ev5 wond]ful1 results4 ,! game />ts ) 8if0 or 8suppose0 or 8let u assume40 ,:ile ! game la/s1 any /atem5t is logically true if x foll[s logically f ! suppositions4 ,= example1 let u take five /atem5ts3 #a4 8,! e>? is flat l a %eet ( pap]40 #b4 8,! e>? is r\nd l a ball40 #c4 8,john ,doe travels z fa/ z he c1 )\t turn+ to left or to "r1 = _m days40 #d4 8,john ,doe w fall (f ! e>?40 #e4 8,john ,doe w arrive back at 8 />t+ po9t40 ,let u also take a c]ta9 context 9 :i*3 ,we "k :at we mean by su* words z 8e>?10 8flat10 8fall+10 etc42 we h o!r /atem5ts & und]/&+s su* z 8if ,john ,doe walks (f ! edge ( a cliff1 he w fall10 8a flat %eet ( pap] has an edge10 etc4 ,9 ?is context1 if /atem5ts #a & #c are suppos$1 !n /atem5t #d is logically true4 ,on ! o!r h&1 if /atem5ts #b & #c are suppos$1 !n /atem5t #e is logically true4 ,( c\rse1 = _m c5turies1 ne>ly all m5 believ$ /atem5t #a2 & ! importance ( ! ye>s #adib to #aeba 7,columbus to ,magellan7 is l9k$ ) ! f9al pro( t /atem5t #b expresses a fact4 ,s1 dep5d+ on ! game1 or ! context1 :i*ev] we wi% to call x1 almo/ any /atem5t c be logically true4 ,:at we become int]e/$ 91 !re=e1 is ! connections betwe5 /atem5ts :i* make !m foll[ logically4 ,,logical ,,patt]ns ,p]haps ! mo/ famili> example ( 8foll[+ logically0 is a patt]n ( words l ! foll[+3 #a4 ,all igs are ows4 #b4 ,all ows are umphs4 #c4 ,!re=e1 all igs are umphs4 ,if /atem5ts #a & #b are suppos$1 !n /atem5t #c is logically true4 ,9 o!r words1 /atem5t #c logically foll[s f /atem5ts #a & #b4 ,?is ^w patt]n is logically true1 no matt] :at sub/itutions we make = igs1 ows1 & umphs4 ,= example1 we c replace igs by m51 ows by animals1 & umphs by mortals1 & obta93 #d4 ,all m5 are animals4 #e4 ,all animals are mortals4 #f4 ,!re=e1 all m5 are mortals4 ,! inv5t$ words 8igs10 8ows10 8umphs0 m>k places 9 ! logical patt]n :]e we c ins]t any names we are int]e/$ 94 ,! words 8all10 8are10 8!re=e0 & ! end+ s m>k ! logical patt]n4 ,( c\rse1 in/ead ( us+ inv5t$ words l 8igs10 8ows10 8umphs0 we w\ld usually put ,a's1 ,b's1 ,c's4 ,?is logical patt]n is call$ a syllogism & is "o ( ! mo/ famili>4 ,b !re are ev5 simpl] logical patt]ns t are also famili>4 ,,! ,,simple/ ,,logical ,,patt]ns ,_m simple logical patt]ns are s famili> t we (t5 use !m )\t be+ consci\s ( do+ s4 ,! simple logical patt]ns are m>k$ by words l 8&10 8or10 8else10 8n10 8if10 8!n10 8only40 ,9 ! same way1 simple ari?metical patt]ns are m>k$ by words l 8plus10 8m9us10 8times10 8divid$ by40 ,let u see :at "s ( ^! simple logical patt]ns are4 ,suppose t we take two /atem5ts ab\t :i* we h no factual in=mation t might int]f]e ) logical suppos+3 #a4 ,john ,doe is eligible = insurance4 #b4 ,john ,doe requires a m$ical exam9ation4 ,9 practice1 we might be conc]n$ ) su* /atem5ts :5 writ+ ! rules gov]n+ a plan ( insurance = a gr\p ( employees4 ,"h1 we %all play a game3 7#a7 ,we %all make up "s new /atem5ts f /atem5ts #a & #b1 us+ ! words 8&10 8or10 8else10 8n10 8if10 8!n10 8only40 7#b7 ,we %all exam9e ! logical patt]ns t we c make4 7#c7 ,we %all see :at we c f9d out ab\t _! logical tru?4 ,suppose we make up ! foll[+ /atem5ts3 #c4 ,john ,doe is n eligible = insurance4 #d4 ,john ,doe does n require a m$ical exam9ation4 #e4 ,john ,doe is eligible = insurance & requires a m$ical exam9ation4 #f4 ,john ,doe is eligible = insurance1 & ,john ,doe is eligible = insurance4 #g4 ,john ,doe is eligible = insurance1 or ,john ,doe requires a m$ical exam9ation4 #h4 ,if ,john ,doe is eligible = insurance1 !n he requires a m$ical exam9ation4 #i4 ,john ,doe requires a m$ical exam9ation if & only if he is eligible = insurance4 #aj4 ,john ,doe is eligible = insurance or else he requires a m$ical exam9ation4 ,n[ cle>ly x is tr\blesome to repeat quantities ( words :5 we are int]e/$ only 9 ! way t 8&10 8or10 8else10 8n10 8if10 8!n10 8only0 occur4 ,s1 let u use j #a & #b = ! two orig9al /atem5ts1 rememb]+ t 8#a ,,& #b0 means "h 8/atem5t #a ,,& /atem5t #b0 & does n mean #a plus #b4 ,!n we h3 #c3 ,,n-#a #d3 ,,n-#b #e3 #a ,,& #b #f3 #a ,,& #a #g3 #a ,,or #b #h3 ,,if #a1 ,,!n #b #i3 #a ,,if ,,& ,,only ,,if #b #aj3 #a ,,or ,,else #b ,"h !n are "s simple logical patt]ns t we c make4 ,,calculation ,,( ,,logical ,,tru? ,n[ :at c we f9d out ab\t ! logical tru? ( /atem5ts #c to #aj8 ,if we "k some?+ ab\t ! tru? or falsity ( /atem5ts #a & #b1 :at w logically foll[ ab\t ! tru? or falsity ( /atem5ts #c to #aj8 ,9 o!r words1 h[ c we calculate ! logical tru? ( /atem5ts #c to #aj1 giv5 ! tru? or falsity ( /atem5ts #a & #b8 ,= example1 #c is ,,n-#a2 t is1 /atem5t #c is ! negative or ! d5ial ( /atem5t #a4 ,x foll[s logically t1 if #a is true1 #c is false2 if #a is false1 #c is true4 ,suppose t we use ,t = logically true & ,f = logically false4 ,!n we c %[ our calculation ( ! logical tru? ( /atem5t #c 9 ,table #a4 ,table #a ,table #b #a ,,n-#a #c #b ,,n-#b #d ,t ,f ,t ,f ,f ,t ,f ,t ,our rule = calculation is3 ,= ,t put ,f2 = ,f put ,t4 ,( c\rse1 exactly ! same rule applies to /atem5ts #b & #d 7see ,table #b74 ,! ,t & ,f are call$ tru? values4 ,any mean+ful /atem5t c h tru? values4 ,?is type ( table is call$ a tru? table4 ,= any logical patt]n1 we c make up a tru? table4 ,let u take ano!r example1 8,,&40 ,/atem5t #e is ! same z /atem5t #a ,,& /atem5t #b4 ,h[ c we calculate ! logical tru? ( /atem5t #e8 ,we c make up ! same sort ( a table z be=e4 ,on ! left-h& side ( ?is table1 !re w be #d cases3 #a4 ,/atem5t #a true1 /atem5t #b true4 #b4 ,/atem5t #a false1 /atem5t #b true4 #c4 ,/atem5t #a true1 /atem5t #b false4 #d4 ,/atem5t #a false1 /atem5t #b false4 ,on ! "r-h& side ( ?is table1 we %all put d[n ! tru? value ( /atem5t #e4 ,/atem5t #e is true if bo? /atem5ts #a & #b are true2 /atem5t #e is false 9 ! o!r cases4 ,we "k ?is f our common ev]yday exp]i5ce ) ! mean+ ( 8,,&0 betwe5 /atem5ts4 ,s we c set up ! tru? table1 & our rule = calculation ( logical tru?1 9 ! case ( ,,&1 is %[n on ,table #c4 ,table #c #a #b #a ,,& #b #e ,t ,t ,t ,f ,t ,f ,t ,f ,f ,f ,f ,f 8,,&0 & ! o!r words & phrases jo9+ toge!r ! orig9al two /atem5ts to make new /atem5ts are call$ connectives1 or logical connectives4 ,! connectives t we h illu/rat$ 9 /atem5ts #g to #aj are3 ,,or1 ,,if ,,!n1 ,,if ,,& ,,only ,,if1 ,,or ,,else4 ,table #d %[s ! tru? table t applies to /atem5ts #g1 #h1 #i1 & #aj4 ,?is tru? table expresses ! calculation ( ! logical tru? or falsity ( ^! /atem5ts4 ,table #d #a ,,if ,,& #a ,,or #b ,,if #a1 ,,!n #b ,,only ,,if #b #a ,,or ,,else #b #a #b #g #h #i #aj ,t ,t ,t ,t ,t ,f ,f ,t ,t ,t ,f ,t ,t ,f ,t ,f ,f ,t ,f ,f ,f ,t ,t ,f ,! 8,,or0 7z 9 /atem5t #g7 t is def9$ 9 ! tru? table is (t5 call$ ! inclusive 8or0 & means 8,,&_/,,or40 ,/atem5t #g1 8#a ,,or #b10 is consid]$ to be ! same z 8#a ,,or #b ,,or ,,bo?40 ,!re is ano!r 8,,or0 9 common use1 (t5 call$ ! exclusive 8or10 mean+ 8,,or ,,else0 7z 9 /atem5t #aj74 ,/atem5t #aj1 8#a ,,or ,,else #b10 is ! same z 8#a ,,or #b ,,b ,,n ,,bo?0 or 8,,ei!r #a ,,or #b40 ,9 ord9>y ,engli%1 !re is "s confusion ov] ^! two 8,,or's40 ,usually we rely on ! context to tell :i* "o is int5d$4 ,( c\rse1 su* reliance is n safe4 ,sometimes we rely on a necess>y conflict betwe5 ! two /atem5ts connect$ by 8,,or0 :i* prev5ts ! 8bo?0 case f be+ possible4 ,9 ,lat9 ! two k9ds ( 8,,or0 7 di/+ui%$ by diff]5t words1 vel mean+ 8,,&_/,,or10 & aut mean+ 8,,or ,,else40 ,! 8,,if ,,!n0 t is def9$ 9 ! tru? table agrees ) our usual und]/&+ t 7#a7 :5 ! 8,,if clause0 is true1 ! 8,,!n clause0 mu/ be true2 & 7#b7 :5 ! 8,,if clause0 is false1 ! 8,,!n clause0 may be ei!r true or false4 ,! 8,,if ,,& ,,only ,,if0 t is def9$ 9 ! tru? table agrees ) our usual und]/&+ t 7#a7 if ei!r clause is true1 ! o!r is true2 & 7#b7 if ei!r clause is false1 ! o!r is false4 ,9 /atem5t #f1 !re are only two possible cases1 & ! tru? table is %[n 9 ,table #e4 ,table #e #a #a ,,& #a #f ,t ,t ,f ,f ,we "k t #f is true if & only if #a is true4 ,9 o!r words1 ! /atem5t 8#a ,,& #a ,,if ,,& ,,only ,,if #a0 is true1 no matt] :at /atem5t #a may ref] to4 ,x is because ( ?is fact t we nev] use a /atem5t 9 ! =m 8#a & #a03 x c always be replac$ by ! pla9 /atem5t 8#a40 ,,logical-,,tru? ,,calculation ,,by ,,exam9+ ,,cases ,,& ,,reason+ ,n[ y may say t ?is is all v well1 b :at good is x8 ,almo/ anybody c use ^! connectives correctly & c]ta9ly has _h a great deal ( practice us+ !m4 ,:y d we ne$ to g into tru? values & tru? tables8 ,:5 we draft a contract or a set ( rules1 we (t5 h to consid] sev]al conditions t give rise to a numb] ( cases4 ,we mu/ avoid3 #a4 ,all conflicts1 9 :i* two /atem5ts t disagree apply to ! same case4 #b4 ,all loopholes1 9 :i* !re is a case n cov]$ by any /atem5t4 ,if we h "o /atem5t or condition only1 we h to consid] #b possible cases3 ! condition satisfi$ or ! /atem5t true2 ! condition n satisfi$ or ! /atem5t false4 ,if we h #b conditions1 we h to consid] #d possible cases3 true1 true2 false1 true2 true1 false2 false1 false4 ,if we h #c conditions1 we h to consid] #h possible cases "o aft] ! o!r 7see ,table #f74 ,table #f ,,case #a,,/ ,,condition #b,,nd ,,condition #c,,rd ,,condition #a ,t ,t ,t #b ,f ,t ,t #c ,t ,f ,t #d ,f ,f ,t #e ,t ,t ,f #f ,f ,t ,f #g ,t ,f ,f #h ,f ,f ,f ,in/ead ( ,t's & ,f's1 we w\ld ord9>ily use *eck-m>ks 77 & crosses 771 :i*1 ( c\rse1 h ! same mean+4 ,we may consid] & /udy ea* case individually4 ,9 any ev5t1 we mu/ make sure t ! propos$ contract or set ( rules cov]s all ! cases )\t conflicts or loopholes4 ,! numb] ( possible cases t we h to consid] d\bles :5ev] "o m condition is add$4 ,cle>ly1 x soon becomes too mu* "w to consid] ea* case individually1 & s we mu/ turn to a second me?od1 ?\ghtful classify+ & reason+ ab\t classes ( cases4 ,n[ suppose t ! numb] ( conditions increases3 #d conditions give rise to #af possible cases2 #e1 #f1 #g1 #h1 #i1 #aj1 conditions give rise to #cb1 #fd1 #abh1 #bef1 #eab1 #ajbd1 cases respectively4 ,because ( ! l>ge numb] ( cases1 we soon beg9 to make mi/akes :ile reason+ ab\t classes ( cases4 ,we ne$ a m effici5t way ( kn[+ :e!r all cases are cov]$ prop]ly4 ,,logical-,,tru? ,,calculation ,,by ,,algebra ,"o ( ! m effici5t ways ( reason+ is (t5 call$ ! algebra ( logic4 ,?is algebra is a "p ( a new sci5ce call$ ma!matical logic4 ,ma!matical logic is a sci5ce t has ! foll[+ *>act]i/ics3 ,x /udies *iefly nonnum]ical reason+4 ,x seeks accurate mean+s & necess>y consequ5ces4 ,its *ief in/rum5ts are effici5t symbols4 ,ma!matical logic /udies especially ! logical relations express$ 9 su* words z 8or10 8&10 8n10 8else10 8if10 8!n10 8only10 8!10 8(10 8is10 8e10 8all10 8none10 8"s10 8same10 8diff]5t10 etc4 ,! algebra ( logic /udies especially only ! fir/ sev5 ( ^! words4 ,! great ?9k]s ( anci5t ,greece fir/ /udi$ ! problems ( logical reason+ z ^! problems turn$ up 9 philosophy1 psy*ology1 & debate4 ,ari/otle orig9at$ :at 0 call$ =mal logic4 ,?is 0 devot$ ma9ly to v>iations ( ! logical patt]n %[n above call$ ! syllogism4 ,9 ! la/ #aej ye>s1 ! f9e symbolic te*niques develop$ by ma!maticians 7 appli$ to ! problems ( ! calculation ( logical tru?1 & ! result 0 ma!matical logic1 mu* broad] & mu* m p[]ful ?an =mal logic4 ,a mile/one 9 ! developm5t ( ma!matical logic 0 ,! ,laws ( ,?\ght1 writt5 by ,george ,boole1 a great ,engli% ma!matician1 & publi%$ 9 #ahed4 ,boole introduc$ ! bran* ( ma!matical logic call$ ! algebra ( logic1 also call$ ,boolean algebra4 ,9 late ye>s1 all ! bran*es ( ma!matical logic h be5 improv$ & made easi] to use4 ,we c give a simple num]ical example ( ,boolean algebra & h[ x c calculate logical tru?4 ,suppose t we take ! tru? value ( a /atem5t z #a if x is true & #j if x is false4 ,n[ we h numb]s #a & #j in/ead ( lett]s ,t & ,f4 ,s9ce !y are numb]s1 we c add !m1 subtract !m1 & multiply !m4 ,we c also make up simple num]ical =mulas t w let u calculate logical tru?4 ,if ,p & ,q are /atem5ts1 & if p & q are _! tru? values1 respectively1 we h ,table #g4 ,table #g ,,/atem5t ,,tru? ,,value ,,n-,p #a - p ,p ,,& ,q pq ,p ,,or ,q p q - pq ,,if ,p1 ,,!n ,q #a - p pq ,p ,,if ,,& ,,only ,,if ,q #a - p - q #bpq ,p ,,or ,,else ,q p q - #bpq ,= example1 suppose t we h two /atem5ts ,p & ,q3 ,p3 ,john ,doe is eligible = insurance4 ,q3 ,john ,doe requires a m$ical exam9ation4 ,to te/ t ! tru? value ( 8,p ,,or ,q0 is p q-pq1 let u put d[n ! f\r cases1 & calculate ! result 7see ,table #h74 ,table #h p q p q - pq #a #a #a #a - #a #a #j #a #j #a - #j #a #a #j #a #j - #j #a #j #j #j #j - #j #j ,n[ we "k t ,p or ,q is true if & only if ei!r "o or bo? ( ,p & ,q are true1 & ?us we see t ! calculation is correct4 ,! algebra ( logic 7see also ,supplem5t #b7 is a m effici5t way ( calculat+ logical tru?4 ,b x is /ill a good deal ( "w to use ! algebra4 ,= example1 if we h #aj conditions1 we %all h #aj lett]s l p1 q to h&le 9 calculations4 ,?us we ne$ a /ill m effici5t way4 ,,calculation ,,( ,,circuits ,,by ,,! ,,algebra ,,( ,,logic ,9 #aicg a rese>* assi/ant at ,massa*usetts ,in/itute ( ,te*nology1 ,claude ,e4 ,%annon1 0 /udy+ = 8 degree ( ma/] ( sci5ce4 ,he 0 enroll$ 9 ! ,dep>tm5t ( ,electrical ,eng9e]+4 ,he 0 int]e/$ 9 automatic swit*+ circuits & wond]$ :y an algebra %\ld n apply to !m4 ,he wrote 8 !sis on ! answ] to ?is "q & %[$ t3 7#a7 ,!re is an algebra t applies to swit*+ circuits4 7#b7 ,x is ! algebra ( logic4 ,a pap]1 bas$ on 8 !sis1 0 publi%$ 9 #aich 9 ! ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s ) ! title 8,a ,symbolic ,analysis ( ,relay & ,swit*+ ,circuits40 ,illu/ration3 ,,fig4 #a4 ,swit*es 9 s]ies4 ,= a simple example ( :at ,%annon f\nd out1 suppose t we h two swit*es1 #a1 #b1 9 s]ies 7see ,fig4 #a74 ,:5 d we get curr5t fl[+ f ! s\rce to ! s9k8 ,!re are #d possible cases & results 7see ,table #i74 ,table #i ,,swit* #a ,,is ,,clos$ ,,swit* #b ,,is ,,clos$ ,,curr5t ,,fl[s ,yes ,yes ,yes ,no ,yes ,no ,yes ,no ,no ,no ,no ,no ,n[ :at does ?is table rem9d u (8 ,x is precisely ! tru? table = 8,,&40 ,x is j :at we w\ld h if we wrote d[n ! tru? table ( ! /atem5t 8,swit* #a is clos$ ,,& swit* #b is clos$40 ,illu/ration3 ,,fig4 #b4 ,swit*es 9 p>allel4 ,illu/ration3 ,,fig4 #c4 ,swit* op5--curr5t fl[+4 ,suppose t we h two swit*es #a1 #b 9 p>allel 7see ,fig4 #b74 ,:5 d we get curr5t fl[+ f ! s\rce to ! s9k8 ,answ]3 :5 ei!r "o or bo? ( ! swit*es are clos$4 ,!re=e1 ?is circuit is an exact repres5tation ( ! /atem5t 8,swit* #a is clos$ or swit* #b is clos$40 ,suppose t we h a swit* t has two positions1 & at any "t mu/ be at "o & only "o ( ^! two positions 7see ,fig4 #c74 ,suppose t curr5t fl[s only :5 ! swit* is op54 ,!re are two possible cases & results 7see ,table #aj74 ,table #aj ,,swit* #a ,,is ,,clos$ ,,curr5t ,,fl[s ,yes ,no ,no ,yes ,?is is l ! tru? table = 8,,n02 & ?is circuit is an exact repres5tation ( ! /atem5t 8,swit* #a is ,,n clos$40 7,note3 ,^! examples are 9 sub/antial agreem5t ) ,%annon's pap]1 al?\gh ,%annon uses diff]5t conv5tions47 ,we see1 !re=e1 t !re is a v neat correspond5ce betwe5 ! algebra ( logic & automatic swit*+ circuits4 ,?us x happ5s t3 #a4 ,! algebra ( logic c be us$ 9 ! calculation ( "s electrical circuits4 #b4 ,"s electrical circuits c be us$ 9 ! calculations ( ! algebra ( logic4 ,?is fact is :at l$ to ! next /ep4 ,,logical-,,tru? ,,calculation ,,by ,,ma*9e ,9 #aidf two und]graduates at ,h>v>d ,univ]sity1 ,!odore ,a4 ,kal9 & ,william ,burkh>t1 7 tak+ a c\rse 9 ma!matical logic4 ,!y notic$ t !re 7 a l>ge numb] ( tru? tables to be work$ out4 ,to "w !m out took "t & ef=t & yet 0 a r tiresome automatic process n requir+ mu* ?9k+4 ,!y _h _h "s exp]i5ce ) electrical circuits4 ,kn[+ ( ,%annon's "w1 !y said to ea* o!r1 8,:y n build an electrical ma*9e to calculate tru? tables80 ,!y took ab\t two mon?s to decide on ! ess5tial design ( ! ma*9e3 #a4 ,! ma*9e w\ld h dial swit*es 9 :i* logical connectives w\ld be ent]$4 #b4 ,x w\ld h dial swit*es 9 :i* ! numb]s ( /atem5ts l #a1 #b1 #c w\ld be ent]$4 #c4 ,x w\ld scan ! prop] tru? table l9e by l9e by s5d+ electrical pulses ?r\gh ! dial swit*es4 #d4 ,x w\ld compute ! tru? or falsehood ( ! :ole expression4 ,,con/ruction ,,& ,,completion ,,( ,,! ,,kal9-,,burkh>t ,,logical-,,tru? ,,calculator ,) ! designs 9 m9d1 ,kal9 & ,burkh>t b\ght "s w> surplus mat]ials1 includ+ relays1 swit*es1 wires1 lights1 & a metal box ab\t #cj in*es long by #af in*es tall1 & #ac in*es deep4 ,f ,m>* to ,june1 #aidg1 !y con/ruct$ a ma*9e 9 _! sp>e "t1 assembl+ & m\nt+ ! p>ts inside ! box4 ,! total co/ ( mat]ials 0 ab\t #aej4 ,9 ,june ! ma*9e 0 demon/rat$ 9 ,cambridge1 ,mass41 be=e sev]al logicians & eng9e]s1 & 9 ,augu/ x 0 mov$ = "s mon?s to ! (fice ( a life insurance company4 ,!re "s /udy 0 made ( ! possible application ( ! ma*9e 9 draft+ contracts & rules4 ,,g5]al ,,organization ,,( ,,! ,,ma*9e ,! logical-tru? calculator built by ,kal9 & ,burkh>t is n giant 9 size1 al?\gh giant 9 capacity4 ,l o!r me*anical bra9s1 ! ma*9e is made up ( _m pieces ( a r small numb] ( diff]5t k9ds ( p>ts4 ,! ma*9e conta9s ab\t #de dial swit*es1 #bc snap swit*es 7or two-position swit*es71 #he relays1 #f pu% buttons1 less ?an a mile ( wire1 etc4 ,! lid ( ! metal box is ! front1 v]tical panel ( ! ma*9e4 ,,units ,,( ,,! ,,ma*9e ,! ma*9e conta9s #af units4 ,^! units are li/$ 9 ,table #aa1 9 approximately ! ord] 9 :i* !y appe> on ! front panel ( ! ma*9e--r[ by r[ f top to bottom1 & f left to "r 9 ea* r[4 ,table #aa ,,units1 ,,_! ,,names1 ,,& ,,significance ,,unit ,,r[ ,,"p ,,no4 ,,m>k ,,"n ,,significance #a #a ,small r$ #ab -- ,/atem5t tru?- ,output3 gl[s if lights value lights /atem5t is assum$ true 9 ! case #b #a #b-position #ab ,/atem5t d5ial ,input3 if up1 snap swit*es swit*es /atem5t is d5i$ #c #b #ad-position #ab ,v ,/atem5t ,input ( dial swit*es swit*es /atem5ts #d #c #d-position #aa k ,connective ,input ( dial swit*es swit*es connectives3 7&71 7or71 7if-!n71 7if & only if7 #e #d #aa-position #aa ,a ,antec$5t ,input ( dial swit*es swit*es antec$5ts #f #e #aa-position #aa ,c ,consequ5t ,input ( dial swit*es swit*es consequ5ts #g #f #b-position #aa ,s ,/op swit*es ,input3 if up1 snap swit*es associates connective to ma9 tru?-value light #h #f #b-position #aa ,connective d5ial ,input3 if up1 snap swit*es swit*es /atem5t produc$ by connective is d5i$ #i #g ,r$ light & #a ,/>t ,automatic />t ,input3 causes ! l>ge button calc4 to />t d[n a tru? table automatically #aj #g ,r$ light & #a ,/>t ,p[] swit* ,input3 turns ! #b buttons ,/op p[] on or (f #aa #g #b-position #a ,/op 8,/op-on-true-or- ,input3 causes ! snap swit* false0 swit* calc4to /op & r$ ei!r on true button cases or on false cases #ab #g ,yell[ light #a -- ,ma9 tru?-value ,output3 gl[s if light ! /atem5t produc$ by ! ma9 connective is true = ! case #ac #g ,l>ge button #a ,man4 ,manual pulse ,input3 causes ! ,pulse button calc4 to g to ! next l9e ( a tru? table #ad #g #aa-position #a k ,connective *eck ,output3 gl[s :5 dial swit* swit* & light any specifi$ connective is true #ae #g #ac-position #a ,,tt 8,tru?-table-r[- ,input3 causes ! dial swit* ,r[ /op0 swit* calc4 to /op on ,/op la/ r[ ( ! ! tru? table #af ,be- ,cont9u\s #a -- ,tim+ control ,input3 controls ! twe5 dial knob knob spe$ at :i* #f #g & button ! calculator scans r[s ( ! tru? table ,"s ( ! words appe>+ 9 ?is table ne$ to be def9$4 ,connective "h means 8,,&10 8,,or10 8,,if ,,!n10 8,,if ,,& ,,only ,,if40 ,only ^! f\r connectives appe> on ! ma*9e2 o!rs :5 ne$$ c be con/ruct$ f ^!4 ,! symbols us$ = ^! connectives 9 ma!matical logic are 1 1 1 4 ,^! signs s]ve z labels = ! connective swit* po9ts4 ,9 ?is ma*9e1 :5 !re is a connective betwe5 two /atem5ts1 ! /atem5t t comes be=e is call$ ! antec$5t & ! /atem5t t comes aft] is call$ ! consequ5t4 ,,h[ ,,in=mation ,,goes ,,into ,,! ,,ma*9e ,( ! #af units #ac are input units4 ,!y control ! setup ( ! ma*9e s t x c solve a problem4 ,( ! #ac input units1 ^? t h ! mo/ to d ) tak+ 9 ! problem are %[n 9 ,table #ab4 ,table #ab ,"n ( ,,k9d ,,( ,,unit ,,swit*es ,,m>k ,,swit* ,,swit* ,,sett+s #c ,/atem5t ,v to ,dial ,/atem5ts #a to #ab or con/ant ,v ,t or ,f #b ,/atem5t ,snap ,affirmative 7d[n7 or negative d5ial 7up7 #d ,connective k to ,dial 7,,&71 k 7,,or71 7,,if-,,!n71 7,,if ,,& ,,only ,,if7 #h ,connective ,snap ,affirmative 7d[n7 or negative d5ial 7up7 #e ,antec$5t ,a to ,dial ,v or v>i\s k's ,a #f ,consequ5t ,c to ,dial ,v or v>i\s k's ,c #g ,/op ,s to ,snap ,n connect$ 7d[n7 or ,s connect$ 7up7 ,! fir/ /ep 9 putt+ a problem on ! ma*9e is to express ! :ole problem z a s+le comp\nd /atem5t t we want to "k ! tru? or falsity (4 ,we express ! s+le comp\nd /atem5t 9 a =m su* z ! foll[+3 ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v k ,v :]e ea* ,v repres5ts a /atem5t1 ea* k repres5ts a connective1 & we "k ! gr\p+1 or 9 o!r words1 we "k ! antec$5t & consequ5t ( ea* connective4 ,= example1 let u *oose a problem ) an obvi\s answ]3 ,,problem4 ,giv53 /atem5t #a is true2 & if /atem5t #a is true1 !n /atem5t #b is true2 & if /atem5t #b is true1 !n /atem5t #c is true2 & if /atem5t #c is true1 !n /atem5t #d is true4 ,is /atem5t #d true8 ,h[ d we express ?is :ole problem 9 a =m t w g on ! ma*9e8 ,we express ! :ole problem z a s+le comp\nd /atem5t t we want to "k ! tru? or falsity (3 ,if #a & 7if #a !n #b7 & 7if #b !n #c7 & 7if #c !n #d71 !n #d ,! #h /atem5ts occurr+ 9 ?is problem are1 respectively3 #a #a #b #b #c #c #d #d4 ,^! are ! values at :i* ! ,v swit*es 7! /atem5t dial swit*es1 ,unit #b7 f ,v to ,v are set4 ,! #g connectives occurr+ 9 ?is problem are1 respectively3 ,,&1 ,,if-,,!n1 ,,&1 ,,if-,,!n1 ,,&1 ,,if-,,!n1 ,,if-,,!n4 ,^! are ! values at :i* ! k swit*es 7! connective dial swit*es1 ,unit #d7 f k to k are set4 ,a gr\p+ 7"o ( sev]al possible gr\p+s7 t specifies ! antec$5t & consequ5t ( ea* connective is ! foll[+3 #a ,,& #a ,,if-,,!n #b ,,& #b ,,if-,,!n #c ,,& #c ,,if-,,!n #d ,,if-,,!n #d ------------------ ------------------ ------------------ k k k ------------------------------ ---------------------------------------- ---------- k k ---------------------------------------- ---------------------------------------- -------------- k ---------------------------------------- ---------------------------------------- ---------------------------------- k ,! gr\p+ has "h be5 express$ graphically ) l9es b may be express$ 9 ! normal ma!matical way ) p>5!ses & brackets z foll[s3 #a ,,& 7#a ,,if-,,!n #b7 ,,& 7#b ,,if-,,!n #c7 ,,& 7#c ,,if-,,!n #d7 ,,if-,,!n #d4 ,s ! values at :i* ! antec$5t & consequ5t dial swit*es are set are z %[n 9 ,table #ac4 ,table #ac ,,antec$5t ,,consequ5t ,,connective ,,swit* ,,set ,,at ,,swit* ,,set ,,at k ,a ,v ,c k k ,a ,v ,c ,v k ,a k ,c k k ,a ,v ,c ,v k ,a k ,c k k ,a ,v ,c ,v k ,a k ,c ,v ,9 any problem1 /atem5ts t are diff]5t are numb]$ "o aft] ano!r #a1 #b1 #c1 #d 4 ,a /atem5t t is repeat$ be>s always ! same numb]4 ,9 ne>ly all cases t are int]e/+1 !re w be repetitions ( ! /atem5ts4 ,if any /atem5t appe>$ ) a 8,,n0 9 x1 we w\ld turn up ! d5ial swit* = t /atem5t 7,unit #b74 ,! diff]5t connectives available on ! ma*9e are 8,,&10 8,,or10 8,,if ,,!n10 8,,if ,,& ,,only ,,if40 ,if a 8,,n0 affect$ ! comp\nd /atem5t produc$ by any connective1 we w\ld turn up ! d5ial swit* = t connective 7,unit #h74 ,! la/ /ep 9 putt+ ! problem on ! ma*9e is to connect ! ma9 connective ( ! :ole comp\nd /atem5t to ! yell[ light output 7,unit #ab74 ,9 ?is problem ! la/ 8,,if-,,!n10 k1 is ! ma9 connective1 ! "o t produces ! :ole comp\nd /atem5t4 ,s we turn ,/op ,swit* #g 79 ,unit #g7 t belongs to k into ! up position4 ,!re are a few m ?+s to d1 naturally1 b ! ess5tial "p ( putt+ ! in=mation ( ! problem into ! ma*9e has n[ be5 describ$4 ,,h[ ,,in=mation ,,comes ,,out ,,( ,,! ,,ma*9e ,( ! #af units li/$ 9 ,table #aa1 #c are output units1 & only #b ( ^! are really important1 z %[n 9 ,table #ad4 ,table #ad ,,unit ,,"n ,,( ,,light ,,m>k ,,k9d ,,( ,,light #a ,/atem5t tru? value ,v to ,v ,small1 r$ #ac ,ma9 tru? value ,l>ge1 yell[ ,! answ] to a problem is %[n by a patt]n ( ! lights ( ,units #a & #ac4 ,! patt]n ( lights is equival5t to a r[ ( ! tru? table4 ,ea* little r$ light 7,unit #a7 gl[s :5 its /atem5t is assum$ to be true1 & x is d>k :5 its /atem5t is assum$ to be false4 ,! yell[ light 7,unit #ac7 gl[s :5 ! :ole comp\nd /atem5t is calculat$ to be logically true1 & x is d>k :5 ! :ole comp\nd /atem5t is calculat$ to be logically false4 ,! ma*9e turns its 8att5tion0 automatically to ea* l9e ( ! tru? table "o aft] ! o!r1 & pulses are f$ 9 accord+ to ! patt]n ( assum$ true /atem5ts4 ,we c set ! ma*9e to /op on true cases or on false cases or on e case1 s z to give u "t to copy d[n :i*ev] k9d ( results we are int]e/$ 94 ,:5 we h not$ ! case1 we c press a button & ! ma*9e w !n g ahead se>*+ = m cases4 ,a ,,complete ,,& ,,concrete ,,example ,! read] may /ill be wond]+ :5 he w see a complete & concrete example ( ! application ( ! logical-tru? calculator4 ,s f> we h giv5 only pieces ( examples 9 ord] to illu/rate "s explanation4 ,!re=e1 let u consid] n[ ! foll[+ problem3 ,,problem4 ,! ,a4 ,a4 ,adams ,co41 ,inc41 has ab\t #ajjj employees4 ,ab\t #fjj ( !m are insur$ "u a contract = gr\p insurance ) ! ,i4 ,i4 ,insurance ,co4 ,mr4 ,adams decides t m ( 8 employees ought to be insur$4 ,z a "p ( 8 /udy ( ! *ange1 he asks 8 manag] 9 *>ge ( ! gr\p insurance plan1 8,:at are ! possible /atuses ( my employees :o are n insur$80 ,! manag] replies1 8,i c tell y ! names ( ! m5 :o are n insur$1 & all ! data y may want to "k ab\t !m40 ,mr4 ,adams says1 8,no1 ,john1 t won't be en\gh1 = ,i ne$ to "k :e!r !re are any gr\ps or classes t = "s basic reason ,i %\ld exclude f ! *ange ,i am consid]+40 ,s ! manag] goes to "w ) ! foll[+ #e /atuses & ! foll[+ #e rules1 & he produces ! foll[+ answ]4 ,our "q is1 8,is he "r1 or has he made a mi/ake80 ,/atuses4 ,a /atus = any employee is a report ab\t t employee1 answ]+ all ! foll[+ #e que/ions ) 8yes0 or 8no40 #a4 ,is ! employee eligible = insurance8 #b4 ,has ! employee appli$ = insurance8 #c4 ,has ! employee's application = insurance be5 approv$8 #d4 ,does ! employee require a m$ical exam9ation = insurance8 #e4 ,is ! employee insur$8 ,rules4 ,! rules apply+ to employees are3 ,a4 ,any employee1 to be insur$1 mu/ be eligible = insurance1 mu/ make application = insurance1 & mu/ h su* application = insurance approv$4 ,b4 ,only eligible employees may apply = insurance4 ,c4 ,! application ( any p]son eligible = insurance )\t m$ical exam9ation is automatically approv$4 ,d4 7,naturally7 an application c be approv$ only if ! application is made4 ,e4 7,naturally7 a m$ical exam9ation w n be requir$ f any p]son n eligible = insurance4 ,answ] by ! ,manag]4 ,!re are #e possible comb9ations ( /atuses = employees :o are n insur$1 z %[n 9 ,table #ae4 ,table #ae ,,possible ,,/atus #c1 ,,/atus #d1 ,,comb9ation ,,/atus #a1 ,,/atus #b1 ,,application ,,exam9ation ,,/atus #e1 ,,( ,,/atuses ,,eligible ,,appli$ ,,approv$ ,,requir$ ,,insur$ #a ,yes ,yes ,yes ,yes ,no #b ,yes ,yes ,yes ,no ,no #c ,yes ,yes ,no ,yes ,no #d ,yes ,no ,yes ,no ,no #e ,no ,no ,no ,no ,no ,! "q may be ask$ :y employees :o are eligible1 :o h appli$ = insurance1 :o h _h _! applications approv$1 & :o require no m$ical exam9ation 7comb9ation #b7 are yet n insur$4 ,! answ] is t ! rules giv5 d n logically lead to ?is conclusion4 ,z a matt] ( fact1 !re might be additional rules1 su* z3 any sick employee mu/ fir/ return to "w2 or any p]iod f date ( approval ( application to ! fir/ ( ! foll[+ mon? mu/ fir/ pass4 ,! fir/ /ep 9 putt+ ?is problem on ! ,kal9-,burkh>t ,logical-,tru? ,calculator is to rephrase ! rules1 us+ ! language ( ! connectives t we h on ! ma*9e4 ,! rules rephras$ are3 ,a4 ,if an employee is insur$1 !n he is eligible1 he has appli$ = insurance1 & 8 application has be5 approv$4 ,,if #e1 ,,!n #a ,,& #b ,,& #c ,b4 ,if an employee has appli$ 7"u ^! rules7 = insurance1 !n he is eligible4 ,,if #b1 ,,!n #a ,c4 ,if an employee is eligible = insurance1 has appli$1 & requires no m$ical exam9ation1 8 application is automatically approv$4 ,,if #a ,,& #b ,,& ,,n-#d1 ,,!n #c ,d4 ,if an employee's application has be5 approv$1 !n he has appli$4 ,,if #c1 ,,!n #b ,e4 ,if an employee is n eligible1 !n he does n require a m$ical exam9ation 7"u ^! rules74 ,,if ,,n-#a1 ,,!n ,,n-#d ,to get ! answ] we seek1 we mu/ add "o m rule = ?is answ] only3 ,f4 ,! employee is n insur$4 ,,n-#e ,we n[ h a total ( #d #b #d #b #b #a occurr5ces ( /atem5ts1 or #ae occurr5ces4 ,?is is beyond ! capacity ( ! exi/+ ma*9e4 ,b =tunately ,rule ,f & ,rule ,a cancel ea* o!r2 !y may bo? be omitt$2 & ?is gives u #aj occurr5ces in/ead ( #ae4 ,9 o!r words1 all ! possible /atuses "u 8,rule ,b ,,& ,rule ,c ,,& ,rule ,d ,,& ,rule ,e0 w give u ! answ] we seek4 ,! rephras+ & reason+ we h done "h is p]haps n easy4 ,= example1 go+ f ! logical patt]n ,only igs may be ows to ! logical patt]n ,if x is an ow1 !n x is an ig z we did 9 rephras+ ,rule ,b1 des]ves r m ?\ght & discussion ?an we c give to ! subject "h4 ,a p]son :o is responsible = prep>+ problems = ! ,logical-,tru? ,calculator %\ld "k ! algebra ( logic4 ,*oos+ an appropriate gr\p+1 we n[ set on ! ma*9e3 7,,if #b1 ,,!n #a7 ,,& ,,if 7#a ,,& #b7 ,,& ,,n-#d1 ,,!n #c ,,& 7,,if #c1 ,,!n #b7 ,,& 7,,if ,,n-#a1 ,,!n ,,n-#d7 ,! sett+ is z %[n 9 ,table #af4 ,aft] ?is sett+1 ! ma*9e is turn$ on & set to /op on ! 8true0 cases4 ,! ,table #af ,,sett+ ,,( ,,! ,,problem ,,on ,,! ,,logical-,,tru? ,,calculator ,,unit #c ,/atem5t ,dial ,no4 ,v ,v ,v ,v ,v ,v #c ,/atem5t ,dial ,sett+ #b #a #a #b #d #c #b ,/atem5t ,d5ial ,swit* ,sett+ -- -- -- -- up -- #d ,connective ,dial ,no4 k k k k k k #d ,connective ,dial ,sett+ #h ,connective ,d5ial ,swit* ,sett+ -- -- -- -- -- -- #e ,antec$5t ,dial ,no4 ,a ,a ,a ,a ,a ,a #e ,antec$5t ,dial ,sett+ ,v k ,v k k k #f ,consequ5t ,dial ,no4 ,c ,c ,c ,c ,c ,c #f ,consequ5t ,dial ,sett+ ,v k ,v ,v ,v k #g ,/op ,swit*es1 associat+ connective to ,ma9 ,tru?-,value ,light -- -- -- -- -- up ---------------------------------------- ------------------------- #c ,/atem5t ,dial ,no4 ,v ,v ,v ,v ,v ,v #c ,/atem5t ,dial ,sett+ #c #b #a #d ,f ,f #b ,/atem5t ,d5ial ,swit* ,sett+ -- -- up up -- -- #d ,connective ,dial ,no4 k k k k k #d ,connective ,dial ,sett+ (f (f #h ,connective ,d5ial ,swit* ,sett+ -- -- -- -- -- #e ,antec$5t ,dial ,no4 ,a ,a ,a ,a ,a #e ,antec$5t ,dial ,sett+ ,v k ,v (f (f #f ,consequ5t ,dial ,no4 ,c ,c ,c ,c ,c #f ,consequ5t ,dial ,sett+ ,v k ,v (f (f #g ,/op ,swit*es1 associat+ connective to ,ma9 ,tru?-,value ,light -- -- -- -- -- possible /atuses ( employees :o are n insur$ are %[n 9 ,table #ag4 ,z we look d[n ! la/ column 9 ,table #ag1 we obs]ve #f occurr5ces ( ,t1 in/ead ( #e z ! manag] det]m9$ 7see ,table #ae74 ,?us1 :5 we comp>e ! manag]'s result ) ! ma*9e result1 we f9d an additional possible comb9ation to be report$ to ,mr4 ,adams1 comb9ation #g3 ,employee eligible1 employee has n appli$1 employee's application n approv$1 employee requires a m$ical exam9ation1 employee n insur$4 ,table #ag ,,solution ,,( ,,! ,,problem ,,by ,,! ,,calculator ,,leg5d3 ,a ,,! ,,employee ,,is ,,eligible ,,= ,,insurance ,b ,,! ,,employee ,,has ,,appli$ ,,= ,,insurance ,c ,,! ,,employee',s ,,application ,,= ,,insurance ,,has ,,be5 ,,approv$ ,d ,,! ,,employee ,,requires ,a ,,m$ical ,,exam9ation ,e ,,! ,,employee ,,is ,,insur$ ,f ,,case1 ,,or ,,comb9ation ,,no4 ,g ,,! ,,comb9ation ,,does ,,n ,,contradict ,,! ,,rules1 ,i4,e41 ,,! ,,yell[ ,,light ,,is ,,on ,a ,b ,c ,d ,e ,f ,g ,/atus3 #a #b #c #d #e ,t ,t ,t ,t ,f #a ,t ,f ,t ,t ,t ,f #b ,f ,t ,f ,t ,t ,f #c ,f ,f ,f ,t ,t ,f #d ,f ,t ,t ,f ,t ,f #e ,t ,f ,t ,f ,t ,f #f ,f ,t ,f ,f ,t ,f #g ,t ,f ,f ,f ,t ,f #h ,f ,t ,t ,t ,f ,f #i ,t ,f ,t ,t ,f ,f #aj ,f ,t ,f ,t ,f ,f #aa ,f ,f ,f ,t ,f ,f #ab ,f ,t ,t ,f ,f ,f #ac ,f ,f ,t ,f ,f ,f #ad ,f ,t ,f ,f ,f ,f #ae ,t ,f ,f ,f ,f ,f #af ,t ,because ( ! m$ical exam9ation1 ?is additional class ( employee w\ld ne$ to be consid]$ r c>efully 9 any *ange ( ! gr\p insurance plan4 ,,an ,,appraisal ,,( ,,! ,,calculator ,9 apprais+ ! ,kal9-,burkh>t ,logical-,tru? ,calculator1 we mu/ rememb] t ?is is a fir/ model4 ,x 0 ! only ma*9e ( its k9d up to ! end ( #aidh2 & x work$4 ,! co/ ( ! ma*9e1 z /at$ be=e1 0 ab\t #aej ( p>ts & p]haps #ajjj ( labor4 ,?is is less ?an _/ ( ! co/ ( ! o!r giant bra9s describ$ 9 previ\s *apt]s4 ,yet we c prop]ly call ?is ma*9e a me*anical bra9 because x transf]s in=mation automatically f "o "p to ano!r ( ! ma*9e1 has automatic control ov] ! sequ5ce ( op]ations1 & does c]ta9 k9ds ( reason+4 ,! ma*9e is swift4 ,x c *eck up to a #ajj cases aga9/ a set ( rules 9 less ?an #a m9ute4 ,x c *eck3 #abh cases = #g conditions 9 #a m9utes1 #bef cases = #h conditions 9 #b m9utes1 & #djif cases = #ab conditions 9 #ch m9utes4 ,t is ! limit ( ! pres5t ma*9e4 ,( c\rse1 sett+ up ! ma*9e to d a problem takes "s m "t4 ,! programm+ ( ?is ma*9e to d a problem is less complicat$ ?an ! programm+ ( mo/ ( ! big ma*9es previ\sly describ$4 ,( c\rse1 9 ord] to prep>e a problem = ! ma*9e1 ! prep>] ne$s to "k a fair am\nt ( ! algebra ( logic4 ,?is1 h[ev]1 is n v h>d4 ,z to reliability1 ! ma*9e has 9 practice be5 out ( ord] less ?an #b p] c5t ( op]at+ "t4 ,! big b>ri] to wide use ( ! ma*9e1 ( c\rse1 is lack ( und]/&+ ( ! field ( problems 9 :i* x c be appli$4 ,ev5 9 ?is mod]n _w ( ours1 we are 9 r a primitive /age 9 reg>d to recogniz+ problems 9 logical tru? & kn[+ h[ to calculate x4 ,"h1 h[ev]1 is an electrical in/rum5t = logical reason+1 & x seems likely t its applications w multiply4 ,*apt] #aj ,,an ,,excursion3 ,,! ,,future ,,design ,,( ,,ma*9es ,,t ,,?9k ,9 ! previ\s *apt]s we h describ$ f\r giant me*anical bra9s f9i%$ by ! end ( #aidf3 ,massa*usetts ,in/itute ( ,te*nology's ,diff]5tial ,analyz] ,no4 #b1 ,h>v>d's ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator1 ,moore ,s*ool ( ,electrical ,eng9e]+'s ,electronic ,num]ical ,integrator & ,calculator 7,eniac71 & ,bell ,telephone ,laboratories' ,g5]al-,purpose ,relay ,comput]4 ,all ^! bra9s h actually work$ long en\gh to h demon/rat$ ?or\ghly "s facts ( great importance4 ,,:at ,,exi/+ ,,ma*9es ,,h ,,prov$ ,! exi/+ me*anical bra9s h prov$ t in=mation c be automatically transf]r$ betwe5 any two regi/]s ( a ma*9e4 ,no human be+ is ne$$ to pick up a physical piece ( in=mation produc$ 9 "o "p ( ! ma*9e1 p]sonally move x to ano!r "p ( ! ma*9e1 & !re put x 9 aga94 ,we c ?9k ( a me*anical bra9 z some?+ l a batt]y ( desk calculators or pun*-c>d ma*9es all cabl$ toge!r & communicat+ automatically4 ,! exi/+ me*anical bra9s h also prov$ t flexible1 automatic control ov] long sequ5ces ( op]ations is possible4 ,we c lay out ! :ole r\t9e to solve a problem1 translate x into ma*9e language1 & put x into ! ma*9e4 ,!n we press ! 8/>t0 button2 ! ma*9e />ts :irr+ & pr9ts out ! answ]s z x obta9s !m4 ,me*anical bra9s h remov$ ! limits on complexity ( r\t9e3 ! ma*9e c c>ry out a complicat$ r\t9e z easily z a simple "o4 ,! exi/+ giant bra9s h %[n t a ma*9e ) hundr$s ( ?\s&s ( p>ts w "w successfully4 ,x w op]ate accurately1 x w run unatt5d$1 & x w h rem>kably few me*anical tr\bles4 ,^! ma*9es h %[n t enorm\s spe$s c be realiz$3 #ejjj additions a second is ,eniac's record4 ,high spe$ is ne$$ = _m problems 9 sci5ce1 gov]nm5t1 & bus9ess4 ,9 fact1 !re are economic & /ati/ical problems1 n[ settl$ by arm*air me?ods1 = :i* high-spe$ me*anical bra9s may make x possible to compute answ]s r ?an guess !m4 ,also1 ^! ma*9es h be5 %[n to be reasonable 9 co/4 ,! co/ ( ea* ( ! l>ge calculators is 9 ! neighborhood ( #bej1jjj to #ejj1jjj4 ,if we assume a t5-ye> life1 :i* is cons]vative1 ! co/ is ab\t #c to #f an h\r = #bd-;h\r op]ation4 ,s9ce ea* me*anical bra9 c1 = problems = :i* x is suit$1 d ! "w ( a hundr$ human comput]s1 su* a ma*9e c save its co/ half a doz5 times4 ,& ^! ma*9es are only eng9e]s' models1 built )\t ! advantages ( production-l9e assembly4 ,! co/ ( giant me*anical bra9s "u design 9 #aidg & #aidh is 9 ! neighborhood ( #ajj1jjj to #bjj1jjj4 ,! ma9 reason = ! r$uction f ! previ\s co/ is ! use ( *eap] automatic memory4 ,z designs improve & *>ges = rese>* & developm5t are paid (f1 ! co/ %\ld cont9ue to g d[n4 ,,new ,,devices ,,= ,,h&l+ ,,in=mation ,9 ! laboratories work+ on new me*anical & electronic bra9s1 sci5ti/s are do+ a lot ( ?9k+ ab\t new devices = h&l+ in=mation4 ,rese>* into devices = /or+ in=mation %[s t magnetic wire z us$ 9 s\nd record+ is a r good /orage m$ium4 ,magnetic ,wire ,= example1 on a hundr$? ( an in* ( f9e /eel wire we c 8write0 a magnetiz$ spot by means ( a small 8writ+0 electromagnet4 ,! electromagnet is simply "s copp] wire coil$ ar\nd "s s(t iron %ap$ 9 a ,u4 ,:5 curr5t fl[s ?r\gh ! coil1 ! iron becomes a magnet1 & ! tips ( ! ,u magnetize ! little section ( ! wire betwe5 !m4 ,! magnetiz$ spot c be ( two k9ds1 say nor?-s\? or s\?-nor?1 dep5d+ on :i* way ! curr5t fl[s4 ,we c 8read0 ?is diff]5ce by means ( ano!r small 8read+0 electromagnet4 ,we c erase ! spot by means ( a /rong] 8eras+0 magnet t produces a uni=m magnetic /ate ?r\gh\t ! wire4 ,! diff]5ce betwe5 nor?-s\? & s\?-nor? corresponds to ! diff]5ce betwe5 #a & #j1 or 8yes0 & 8no10 etc41 & is a unit ( in=mation 7see ,*apt] #b74 ,_m o!r v>iations are possible4 ,= example1 ! pres5ce or abs5ce ( a magnetiz$ spot may be ! unit ( in=mation1 or ! 8writ+10 8read+10 & 8eras+0 electromagnets all may be ! same4 ,magnetic wire s\nd record+s made 9 ! #ahij's are /ill good4 ,?is fact %[s t magnetic wire may be a m p]man5t m$ium = /or+ in=mation ?an is pap]4 ,/ray magnetic =ces are likely to h no h>mful effect on in=mation /or$ on magnetic wire1 = ^! =ces w\ld n be /rong en\gh or detail$ en\gh to *ange greatly ! diff]5ce betwe5 ! magnetiz$ spot & its neighbor+ neutral area4 ,a reel ( magnetic wire a mile long & _/ ( an in* ?ick co/s ab\t #e4 ,at #hj magnetiz$ spots to ! in*1 a mile ( wire c /ore ab\t #e million units ( in=mation4 ,h5ce1 ! co/ ( /or+ "o unit ( in=mation is ab\t _/ ( a c5t4 ,! "t ne$$ = *ang+ a magnetiz$ spot f #a to #j or f #j to #a is ab\t _/ ( a second4 ,magnetic ,tape ,!re is1 h[ev]1 a /orage device t may be ev5 m useful1 & ?is is magnetic tape 7see ,fig4 #a74 ,! usual size ( su* tape is in* wide & #b or #c ?\s&?s ( an in* ?ick4 ,magnetic tape may be made ( pla/ic ) magnetic p[d] all ?r\gh x1 or x may be ( pap] coat$ ) magnetic p[d]1 or x may be ( /a9less /eel or a magnetic alloy1 or x may be ( brass or a nonmagnetic alloy coat$ ) a magnetic plat+4 ,magnetic tape has ! add$ advantage t f #d to #bj *annels across ! tape c be fill$ ) magnetiz$ spots1 & ! co/ !n becomes ab\t _/ ( a c5t p] spot4 ,x seems possible t #ajjj units ( in=mation c be /or$ 9 a qu>t] ( a squ>e in* ( magnetic tape4 ,?is means t m ?an #a million units ( in=mation c be /or$ 9 a cubic in* ( space fill$ ) magnetic tape1 & ab\t #b billion units ( in=mation 9 a cubic foot1 except t "s ( ! space %\ld be allott$ to ! reels & o!r equipm5t t hold ! tape 7see ,fig4 #b74 ,?is is clos] pack+ ?an pr9t$ in=mation 9 ! telephone book1 & yet ) magnetic tape we c get to ! in=mation automatically4 ,illu/ration3 ,,fig4 #a4 ,magnetic tape4 ,illu/ration3 ,,fig4 #b4 ,tape reels4 ,?9k ( ! enorm\s files 9 libr>ies1 gov]nm5t1 & bus9ess4 ,?9k ( ! problems ( space & co/ & access :i* ^! files imply4 ,we c !n see t ?is new developm5t may well be ( extraord9>y importance4 ,m]cury ,tanks ,illu/ration3 ,,fig4 #c4 ,m]cury tank4 ,sci5ti/s are inve/igat+ o!r /orage devices hav+ /ill m rem>kable prop]ties1 b ^! h ! disadvantage t1 :5 ! p[] goes (f1 ! in=mation vani%es4 ,"o ( ^! new /orage devices is call$ a m]cury tank 7see ,fig4 #c74 ,x consi/s ma9ly ( a section ( iron or /eel pipe fill$ ) m]cury4 ,at ea* end ( ?is pipe1 t\*+ ! m]cury1 is a ?9 slab ( a cry/al ( qu>tz4 ,qu>tz1 :i* is a common /one1 & :i* ne>ly all s& is made (1 *anges its %ape :5 puls$ ) electricity4 ,we put a patt]n ( electrical pulses into ! qu>tz slab at "o end ( ! m]cury tank2 = example1 we c\ld h ! patt]n #aaja mean+ 8pulse1 pulse1 no pulse1 pulse40 ,! electrical pulses go+ into ! qu>tz slab make ! qu>tz vibrate4 ,?us ripples are produc$ 9 ! m]cury1 & waves 9 ! patt]n #aaja mean+ 8wave1 wave1 no wave1 wave0 travel d[n ! tank & /rike ! qu>tz slab at ! f> end4 ,! qu>tz slab !re *anges its %ape 9 ! rhy?m #aaja1 & x conv]ts ! waves back into electrical pulses 9 ! same patt]n4 ,!n we take ! pulses out ( ! f> end along a wire1 make !m /rong] aga9 ) an amplifi]1 give !m ! "r =m aga91 & fe$ !m back into ! front end ( ! m]cury tank4 ,! m]cury tank is a clev] use ( ! pr9ciple ( an e*o1 z :5 y call across a valley & ! rocks answ] y back4 ,we c /ore a patt]n ( #djj pulses 7ea* a unit ( in=mation1 a #a or a #j1 & ea* a million? ( a second 9 duration71 9 a m]cury tank ab\t #bj in*es long4 ,a m]cury tank & an e*o are examples ( delay l9es--8l9es0 along :i* waves are 8delay$40 ,electro/atic ,/orage ,tube ,ano!r ( ! memory devices be+ develop$ is call$ an electro/atic /orage tube 7see ,fig4 #d74 ,?is is a big electronic tube ) a scre5 across "o end4 ,! scre5 may be ( two lay]s3 "o ( copp]1 :i* conducts electricity1 & "o ( mica1 a mat]ial t does n4 ,9 ! o!r end ( ! tube is a beam ( electrons1 :i* we c turn on & (f & %oot at any ( #b or #c ?\s& specific po9ts or spots on ! scre54 ,illu/ration3 ,,fig4 #d4 ,electro/atic /orage tube4 ,!re are two sizes ( electric *>ge or quantity ( electrons2 we c call ^! #a & #j4 ,9 ab\t a million? ( a second1 we c put ei!r size ( *>ge on "o ( ! spots ( ! scre54 ,) o!r circuits we c keep x !re z long z we want1 if ! p[] does n flick] (f4 ,we c 8rememb]0 p]haps #b or #c ?\s& units ( in=mation 9 "o ( ^! electronic tubes4 ,we c read1 write1 or erase any unit ( in=mation 9 a few million?s ( a second4 ,nei!r ! m]cury tank nor ! electro/atic /orage tube _h1 by ! end ( #aidg1 be5 put into a work+ me*anical bra94 ,b !re is good reason to believe t !y w be successful devices & w op5 up a new era ( spe$ 9 /or+ & ref]r+ to in=mation4 ,9 fact1 sev]al laboratories are develop+ electronic calculat+ circuits us+ ^! devices :i* w p]=m up to #ajj1jjj additions a second or #aj1jjj multiplications a second4 ,our m9ds c]ta9ly /agg] at ! ?\ght ( su* spe$s4 ,,new ,,op]ations ,_m k9ds ( comb9+ op]ations h already be5 built into "o or m me*anical bra9s4 ,! op]ations may be ari?metical3 addition1 subtraction1 multiplication1 division1 look+ up numb]s 9 tables1 etc4 ,or ! op]ations may be logical3 comp>+1 select+1 *eck+1 etc4 ,additional logical op]ations w be built into "s ( ! me*anical bra9s n[ be+ con/ruct$3 sort+1 collat+1 mat*+1 m]g+1 etc4 ,,new ,,ideas ,,9 ,,programm+ ,programm+--! way to give in/ructions to ma*9es--is also be+ /udi$ 9 ! laboratories4 ,sev]al new ideas ( importance h develop$ z a result4 ,"o idea is t ! ma*9e %\ld be able to /ore its in/ructions or program or r\t9e 9 its memory 9 j ! same physical ways z x /ores numb]s4 ,!re is basically no reason :y numb]s only %\ld be /or$ 9 "s regi/]s1 & in/ructions only /or$ 9 o!r regi/]s4 ,ano!r idea is t ! ma*9e %\ld h 9 its p]man5t memory any subr\t9e x may ne$4 ,= example1 a subr\t9e %\ld always be available 9 ! ma*9e = f9d+ squ>e root4 ,at any "t :5 a squ>e root 0 ne$$1 we w\ld only h to call on ! ma*9e = ! subr\t9e ( squ>e root4 ,! ma*9e w\ld !n consult ! "r "p ( its memory & c>ry out ! subr\t9e = squ>e root4 ,a ?ird idea1 & "o ( ! mo/ int]e/+1 is t ! ma*9e %\ld be able to compute its own in/ructions4 ,= example1 consid] a program = f9d+ ! product ( two matrices 7see ,supplem5t #b71 ea* ( #ajj t]ms 9 an array ( #aj columns & #aj r[s1 result+ 9 a new matrix ( #ajj t]ms4 ,! :ole program c be made to consi/ ( ab\t #ej ord]s4 ,only "o ( !m is 8multiply10 & only "o ( !m is 8add02 ! o!r ord]s consi/ ( h[ to *oose expressions to be multipli$ or add$1 etc4 ,su* problems z ^! are (t5 fasc9at+ to ma!maticians1 :o love to play ) ! intricate ideas ne$$4 ,,new ,,ideas ,,9 ,,reliability ,reliability has a numb] ( aspects3 #a4 ,no wrong results all[$ out ( ! ma*9e4 #b4 ,few failures4 #c4 ,rapid location ( failures4 #d4 ,quick repair or replacem5t ( p>ts t fail4 #e4 ,easy ma9t5ance4 #f4 ,unatt5d$ op]ation ov]night4 ,= example1 ,bell ,laboratories prov$ t me*anical bra9s c be built s t no wrong results are all[$ to come out4 ,9 o!r words1 ! ma*9e *ecks itself all ! "t z x goes along & /ops at once if ! *eck %[s t some?+ is wrong4 ,?is is likely to be a /&>d feature ( new automatic ?9k+ ma*9]y4 ,! frequ5cy ( failures 9 ! ma*9]y be+ design$ 9 ! laboratories may be ( ! ord] ( "o or two me*anical failures a week4 ,= any type ( failure an al>m circuit & tr\ble lights w %[ :at "p ( ! ma*9e ne$s att5tion4 ,plug-9 p>ts = replacem5t are already 9 use 9 at lea/ two ( ! f\r me*anical bra9s describ$ & %\ld be available 9 all ! new ma*9es4 ,x is possible to build a ma*9e t w automatically *ange f fail+ equipm5t to prop]ly function+ equipm5t4 ,= "s ye>s ?\gh1 ?is may be too exp5sive to be reasonable4 ,! use ( magnetic tape = /orage r$uces greatly ! numb] ( p>ts & s increases reliability4 ,= example1 in/ead ( #ah1jjj electronic tubes 9 an electronic bra91 !re may be less ?an #cjjj4 ,a f9al degree ( reliability is ga9$ :5 mo/ ( ! "t ! ma*9e op]ates unatt5d$4 ,!n1 !re is no human op]ator /&+ by :o may fail to d ! correct ?+ at ! mom5t :5 ! ma*9e ne$s "s att5tion4 ,9 fact1 ! motto = ! room h\s+ a me*anical bra9 %\ld become1 8,don't ?9k2 let ! ma*9e d x = y40 ,unatt5d$ op]ation f ! end ( "o work+ day to ! beg9n+ ( ! next1 ) ! ma*9e *ang+ itself f "o problem to ano!r problem1 has already be5 prov$ possible on ! ,bell ,laboratories ma*9e4 ,,auxili>y ,,devices ,9 ord] to use a me*anical bra91 we h to give x & take f x language t x und]/&s1 ma*9e language4 ,a me*anical bra9 t c d #aj1jjj additions a second c v easily f9i% almo/ all its "w at once4 ,h[ c we1 sl[ z we are1 keep our fri5d1 ! giant bra91 busy8 ,we h f\nd s f> sev]al answ]s to ?is "q1 none ( !m yet v good4 ,devices = prep>+ input w be v important4 ,= ea* bra91 we %all ne$ a great _m ( ^! devices4 ,=1 at be/1 we type at a rate1 say1 ( #d *>act]s a second1 select+ any "o ( "s #ch keys1 ea* ( :i* is equival5t to ab\t #f units ( in=mation4 ,?is is ab\t #hjj units ( in=mation p] second4 ,! ma*9e1 h[ev]1 is likely to be able to gulp in=mation f its input me*anism at ! amaz+ rate ( #fj1jjj units ( in=mation p] second1 equal to #ge p typ+ ) no mi/akes & no re/+4 ,=tunately1 at lea/ "s ( ! "t ! ma*9e w be busy comput+6 ,= an input-prep>ation device1 we may get some?+ t c be fa/5$ to an ord9>y typewrit] & t w produce magnetic tape agree+ ) :at is pr9t$ by ! typewrit]4 ,s9ce ! input in=mation mu/ be c>efully v]ifi$1 we %all ne$ a second magnetic tape device su* z exi/s = pap] tape on ! ,bell ,laboratories ma*9e3 ! processor4 ,! processor takes two h&-prep>$ tapes1 comp>es !m1 reports any diff]5ces1 & produces a ?ird tape4 ,! ?ird tape copies ! two orig9al tapes if !y agree1 & x receives correct$ in=mation z furni%$ by a girl at a keybo>d if ! two orig9al tapes disagree4 ,= in=mation already on pun* c>ds1 we ne$ an input device t w read pun* c>ds & write on magnetic tape4 ,:]e in=mation is on pun*$ pap] tape1 we ne$ a ma*9e t w read pun*$ pap] tape & write on magnetic tape4 ,problem data1 tables ( numb]s1 & r\t9e in/ructions w g into ! me*anical bra94 ,!y w all be prep>$ on regul> input devices4 ,! ma*9e w accept in=mation 9 ! =m 9 :i* x is mo/ conv5i5t = y & me to prep>e x4 ,!n1 ! ma*9e w be in/ruct$ to *ange ! in=mation into ! =m ) :i* x is mo/ conv5i5t = ! ma*9e to op]ate4 ,_m output devices w also be ne$$1 s9ce ! ma*9e w be able to produce in=mation v swiftly4 ,^! output devices might be cabl$ to ! ma*9e4 ,a k9d ( traffic control sy/em w\ld gov]n !m4 ,ea* w h a magnetic tape t w be load$ up swiftly ) in=mation4 ,!n ! output device w unload its in=mation m sl[ly1 9 any =m t we may desire3 pr9t+1 graphs1 film1 pun* c>ds1 or pun*$ pap] tape4 ,! ma*9e is likely to be able to put out in=mation on magnetic tape at ! same high spe$ ( #fj1jjj units ( in=mation p] second or #aj1jjj *>act]s p] second4 ,b ! be/ pr9t+ spe$ ( an electric typewrit] is ab\t #aj or #ab *>act]s a second4 ,c>d-pun*+ spe$ is ab\t #acj *>act]s a second4 ,pun*-c>d tabulator spe$ c rea* a maximum ( ab\t #bjj *>act]s a second4 ,?us we see t "h1 too1 we may be sn[$ "u ) ! in=mation t ! giant bra9 puts out1 if we fail to ask ! giant only = :at we really want4 ,,me*anical ,,bra9s ,,"u ,,con/ruction ,?is *apt] w\ld n be complete )\t m5tion ( ! great me*anical bra9s t 7 actually "u con/ruction at ! end ( #aidg4 ,9 p[] !y are int]m$iate betwe5 ! ma*9]y n[ be+ design$1 describ$ 9 ?is *apt]1 & ! e>li] ma*9es describ$ 9 ! previ\s *apt]s ( ?is book4 ,! me*anical bra9s "u con/ruction on ,decemb] #ca1 #aidg1 73 ,h>v>d's ,sequ5ce-,controll$ ,relay ,calculator ,m>k ,,ii1 con/ruct$ at ! ,h>v>d ,computation ,laboratory1 te/$ !re ,july #aidg to ,janu>y #aidh1 & deliv]$ to ! ,naval ,prov+ ,gr\nd1 ,dahlgr51 ,va41 9 #aidh4 ,! ,,ibm ,selective-,sequ5ce ,electronic ,calculator1 con/ruct$ 9 ! ,,ibm laboratories1 ,endicott1 ,n4 ,y41 & in/all$ 9 #aidg at ! (fice ( ,int]national ,bus9ess ,ma*9es1 #eij ,madison ,ave41 ,new ,york1 ,n4 ,y4 ,moore ,s*ool ( ,electrical ,eng9e]+'s ,,edvac 7,electronic ,digital ,v>iable ,automatic ,comput]7 be+ con/ruct$ p>tly at ,moore ,s*ool & p>tly else:]e1 & to be deliv]$ to ! ,balli/ic ,rese>* ,laboratories1 ,ab]de51 ,md4 ,h>v>d's ,sequ5ce-,controll$ ,electronic ,calculator ,m>k ,,iii1 be+ con/ruct$ at ! ,h>v>d ,computation ,laboratory1 & to be deliv]$ to ! ,naval ,prov+ ,gr\nd1 ,dahlgr51 ,va4 ,we %all cov] briefly 7& p]haps a little te*nically7 "s ( ! ma9 features ( ! fir/ two ( ^! ma*9es2 =1 dur+ #aidh1 !y began to d problems4 ,! o!r two _h n be5 f9i%$ by ! end ( #aidh & s w\ld be difficult to describe correctly1 = me*anical bra9s gr[1 & design *anges g on until !y are f9i%$--& ev5 aft]w>ds4 ,"s in=mation ab\t ^! ma*9es c be obta9$ f ! organizations ref]r$ to above & f reports t %\ld appe> f "t to "t 9 "s ( ! j\rnals m5tion$ 9 ,supplem5t #c4 ,!re is also a regul> section entitl$ 8,automatic ,comput+ ,ma*9]y0 9 ! qu>t]ly ,ma!matical ,tables & ,o!r ,aids to ,computation1 :]e x is likely t curr5t in=mation may be f\nd4 ,h>v>d's ,m>k ,,ii ,! ,h>v>d ,sequ5ce-,controll$ ,calculator ,m>k ,,ii began to d problems "u te/ dur+ ,july #aidg4 ,?is ma*9e is at lea/ twelve times z p[]ful z ,m>k ,i 7see ,*apt] #f7 & 0 con/ruct$ entirely by ! ,h>v>d ,computation ,laboratory4 ,! ma*9e conta9s ab\t #ac1jjj relays ( a new type t w op]ate reliably )9 _/ ( a second4 ,numb]s 9 ! ma*9e are regul>ly ( #aj decimal digits betwe5 #a4jjj1jjj1jjj & #i4iii1iii1iii1 inclusive1 multipli$ by a p[] ( #aj betwe5 #a1jjj1jjj1jjj1jjj1jjj & #j4jjj1jjj1jjj1jjj1jja1 inclusive4 ,= /orage ( numb]s1 ! ma*9e has #ajj relay regi/]s total+ ab\t #abjj decimal digits4 ,also1 x c consult any "o ( #h tape fe$s = numb]s & any "o ( #d tape fe$s = in/ructions4 ,effectively1 ! ma*9e c read "o numb] & "o in/ruction f pap] tape 9 _/ ( a second4 ,! ma*9e p]=ms all ari?metical & mo/ logical op]ations4 ,9 e second x c c>ry out #d multiplications1 #h additions 7or subtractions71 & #ab transf]s4 ,division is p]=m$ by rapid approximation us+ ! o!r op]ations4 ,9 ea* second ! ma*9e c p]=m #cj in/ructions4 ,an in/ruction is express$ by #f digits betwe5 #j & #g :i* y c select &1 9 effect1 by #c m digits fix$ by ! "t 7)9 ! second7 :5 ! ma*9e reads ! in/ruction4 ,= example1 9 ! #i? in/ruction ( ! #cj in/ructions 9 ea* second1 we c specify a multiplic&4 ,b1 if we d n want to multiply "r !n--a r>e ev5t if we are cod+ wisely--we leave ! #i? in/ruction empty4 ,! ma*9e may op]ate z a :ole1 att5d+ to "o problem2 or ! ma*9e may be sep>at$ into halves1 & ea* half w att5d to its own problem4 ,! ,,ibm ,selective-,sequ5ce ,electronic ,calculator ,! ,,ibm ,selective-,sequ5ce ,electronic ,calculator 0 ann\nc$ publicly on ,janu>y #bg1 #aidh1 aft] "s mon?s ( trial runn+4 ,x is a l>ge & p[]ful me*anical bra91 & x is ! int5tion ( ,int]national ,bus9ess ,ma*9es to devote x to solv+ sci5tific problems4 ,! /aff ( ! ,watson ,sci5tific ,comput+ ,laboratory 9 ,new ,york w be ma9ly 9 *>ge ( ! ma*9e4 ,! ma*9e conta9s ab\t #ab1ejj electronic tubes & ab\t #ba1ejj relays4 ,numb]s 9 ! ma*9e are regul>ly ( ei!r #ad or #ai decimal digits4 ,in/ructions are express$ z numb]s4 ,= /orage ( in=mation1 ! ma*9e has a capacity ( #h regi/]s total+ #afj decimal digits ( v rapid memory 9 electronic tubes4 ,also1 x has ab\t #aej regi/]s total+ #cjjj decimal digits ( less rapid memory 9 relays4 ,also1 x c consult any "o ( #ff pap] tape fe$s2 ea* r[ on a pap] tape c hold up to #gh pun*$ holes or #ai decimal digits1 & ! ma*9e c consult #be r[s on "o tape 9 "o second4 ,^! pap] tapes toge!r give ! ma*9e ab\t #djj1jjj decimal digits ( memory4 ,= ari?metical & logical op]ations1 ! ma*9e has an ari?metical unit us+ electronic tubes4 ,?is unit c c>ry out ab\t #ej multiplications or ab\t #bej additions p] second1 includ+ ! transf]s ( numb]s4 ,9 ea* second ! ma*9e c read & p]=m #ej in/ructions1 & ea* in/ruction consi/s1 usually1 ( gett+ two numb]s out ( two relay regi/]s1 p]=m+ an op]ation1 & putt+ ! result into a ?ird relay regi/]4 ,eck]t-,mau*ly's ,b9ac ,z ?is book w5t to press1 ano!r me*anical bra91 ! ,electronic ,b9>y ,automatic ,comput]1 or ,,b9ac1 0 ann\nc$ on ,augu/ #bb1 #aidi4 ,?is ma*9e 0 con/ruct$ by ! ,eck]t-,mau*ly ,comput] ,corporation1 ,philadelphia1 ,pa41 = ,nor?rop ,aircraft1 ,inc41 ,haw?orne1 ,calif4 ,?is ma*9e has "s rem>kable prop]ties4 ,x does addition or subtraction at ! rate ( #cejj p] second4 ,x does multiplication or division at ! rate ( #ajjj p] second4 ,! input is f a keybo>d or magnetic tape2 ! output is to magnetic tape or an electric typewrit]4 ,b9ac has #eab regi/]s ( v rapid memory 9 m]cury tanks1 & ea* regi/] holds #cj b9>y digits4 ,! ma*9e actually is a pair ( tw9s3 ! /orage1 ! comput+ elem5t1 & ! control are d\ble1 & ea* tw9 runs 9 /ep ) ! o!r & *ecks e op]ation ( ! o!r4 ,9 te/s 9 ,july ! ma*9e ran ov] #aj consecutive h\rs ) no error4 ,ea* tw9 has only #gjj electronic tubes4 ,b9ac h&les all numb]s 9 b9>y notation1 except t ! keybo>d & ! typewrit] express numb]s 9 octal notation 7see ,supplem5t #b74 ,f9ally1 ,b9ac is only #e feet high1 #d feet long1 & "o foot wide4 ,*apt] #aa ,,! ,,future3 ,,ma*9es ,,t ,,?9k1 ,,& ,,:at ,,!y ,,might ,,d ,,= ,,m5 ,! p5 is mighti] ?an ! sword1 x is (t5 said4 ,& if ?is is true1 !n ! p5 ) a motor may be mighti] ?an ! sword ) a motor4 ,9 ! ,middle ,ages1 !re 7 few k9ds ( weapons1 & x 0 easy = a man to protect himself aga9/ mo/ ( !m by we>+ armor4 ,z gunp[d] came into use1 a man c\ld no long] c>ry ! weight ( armor t w\ld protect him1 & s armor 0 giv5 up4 ,b 9 #aiag1 armor1 equipp$ ) a motor & c>ry+ ! man & 8 weapons1 came back into s]vice--z ! tank4 ,9 mu* ! same way1 9 ! ,middle ,ages1 !re 7 few books1 & x 0 easy = a man to h&le ne>ly all ! in=mation t 0 9 books4 ,z ! pr9t+ press came into use1 man's bra9 c\ld no long] h&le all record$ in=mation1 & ! ef=t to d s 0 giv5 up4 ,b 9 #aidd1 a bra9 to h&le in=mation1 equipp$ ) a motor & support+ ! man & 8 reason+1 came into exi/5ce--z ! sequ5ce-controll$ calculator4 ,9 previ\s *apt]s we h exam9$ "s ( ! giant me*anical bra9s t h be5 f9i%$2 we h also consid]$ ! design ( su* ma*9es4 ,n[ 9 ?is *apt] we %all discuss ! future significance ( ma*9es t ?9k1 ( motoriz$ in=mation4 ,we %all discuss :at we c =esee if we look ) imag9ation into ! future4 ,!re are two que/ions we ne$ to ask3 ,:at types ( ma*9es t ?9k c we =esee8 ,:at types ( problems to be solv$ by ^! ma*9es c we =esee8 ,,future ,,types ,,( ,,ma*9es ,,t ,,?9k ,! ma*9es t already exi/ %[ t "s processes ( ?9k+ c already be p]=m$ v quickly3 ,calculat+3 add+1 subtract+1444 ,reason+3 comp>+1 select+1444 ,ref]r+3 look+ up in=mation 9 li/s1444 ,we c expect o!r processes ( ?9k+ to come up to high spe$ ?r\gh ! fur!r developm5t ( ?9k+ ma*9es4 ,automatic ,address ,book ,n[adays :5 we wi% to s5d out ann\ncem5ts ( an ev5t1 l go+ to ,s\? ,am]ica = a ye>1 we may copy ! addresses ( our fri5ds onto ! envelopes by h&4 ,9 ! future1 we c see our address book z a spool ( magnetic tape4 ,:5 we wi% to s5d out ann\ncem5ts1 we put a /ack ( blank envelopes into ! ma*9e t w read ! magnetic tape1 & we press a button4 ,out w come ! envelopes address$4 ,if we wi% to select only ^? fri5ds ( ours ^: la/ names we put d[n on a li/1 we c write ! li/ on ano!r magnetic tape1 place x also 9 ! ma*9e1 & set a few swit*es4 ,!n ! ma*9e w read ! names on ! li/1 f9d _! addresses 9 ! address-book tape1 & prep>e only ! envelopes we want4 ,if a fri5d's address *anges1 we c notify ! ma*9e4 ,x w f9d 8 old address1 erase x1 & ent] ! new address4 ,automatic ,libr>y ,we c =esee ! developm5t ( ma*9]y t w make x possible to consult in=mation 9 a libr>y automatically4 ,suppose t y g into ! libr>y ( ! future & wi% to look up ways = mak+ biscuits4 ,y w be able to dial into ! catalogue ma*9e 8mak+ biscuits40 ,!re w be a flutt] ( movie film 9 ! ma*9e4 ,soon x w /op1 &1 9 front ( y on ! scre51 w be project$ ! "p ( ! catalogue :i* %[s ! names ( ?ree or f\r books conta9+ recipes = biscuits4 ,if y are satisfi$1 y w press a button2 a copy ( :at y saw w be made = y & come out ( ! ma*9e4 ,aft] fur!r developm5t1 all ! pages ( all books w be available by ma*9e4 ,!n1 :5 y press ! "r button1 y w be able to get f ! ma*9e a copy ( ! exact recipe = biscuits t y *oose4 ,we are n yet at ! end ( =eseeable developm5t4 ,!re w be a ?ird /age4 ,y w !n h 9 y\r home an automatic cook+ ma*9e op]at$ by program tapes4 ,y w /ock x ) v>i\s supplies1 & x w put toge!r & cook :atev] di%es y desire4 ,!n1 :at y w ne$ f ! libr>y w be a program or r\t9e on magnetic tape to control y\r automatic cook4 ,& ! libr>y1 in/ead ( produc+ a pictorial copy ( ! recipe = y to read & apply1 w produce a r\t9e on magnetic tape = controll+ y\r cook+ ma*9e s t y w actually get excell5t biscuits6 ,( c\rse1 y may h o!r k9ds ( automatic produc+ ma*9]y 9 y\r home or (fice4 ,! furni%+ ( r\t9es to control automatic ma*9]y w become a bus9ess ( importance4 ,automatic ,translator ,ano!r ma*9e t we c =esee w\ld be us$ = translat+ f "o language to any o!r4 ,we c call x an automatic translator4 ,suppose t y want to say 8,h[ mu*80 9 ,sw$i%4 ,y dial into ! ma*9e 8,h[ mu*80 & press ! button 8,sw$i%10 & ! ma*9e w promptly write out 8,hur mycket80 = y4 ,x also w pron\nce x1 if y wi%1 = !re w\ld be little difficulty 9 record+ on magnetic tape ! pronunciation ( ! ^w z spok5 by a good speak] ( ! language4 ,! ma*9e c\ld be set to repeat ! pronunciation sev]al times s t ! /ud5t c\ld really le>n ! s\nd4 ,he c\ld le>n x bett]1 probably1 by he>+ x & try+ to say x ?an he c\ld by us+ any set ( writt5 symbols4 ,automatic ,typi/ ,we n[ come to a possible ma*9e t uses a new pr9ciple4 ,?is pr9ciple is t ( be+ able to recognize signs4 ,?is ma*9e w\ld p]ceive writ+ on a piece ( pap] & recognize t all ! a's t appe> on ! pap] are cases ( a1 & t all ! b's t appe> on x are in/ances ( b1 & s =?4 ,! ma*9e c\ld !n control an electric typewrit] & copy ! m>ks t x sees4 ,! fir/ /age ( ?is ma*9e w\ld be "o 9 :i* only pr9t$ *>act]s ( a high degree ( lik5ess c\ld be recogniz$4 ,9 lat] /ages1 h&writ+1 ev5 r illegible h&writ+1 might be recognizable by ! ma*9e4 ,we c call x an automatic typi/4 ,! elem5ts ( ! automatic typi/ w\ld be ! foll[+3 #a4 ,phototubes 7electronic tubes s5sitive to ! brightness ( light71 :i* c\ld s5se ! diff]5ce betwe5 black & :ite 7^! already exi/74 #b4 ,a memory ( ! %apes ( #eb lett]s1 #aj digits1 & punctuation m>ks4 ,f9e di/9ctions w\ld be requir$ ( ?is memory 9 "s cases--l ! diff]5ce betwe5 ! num]al #e & ! capital lett] ,s4 #c4 ,a control t w\ld cause ! ma*9e to tune itself1 s t a good mat*+ betwe5 ! m>ks x obs]v$ & ! %apes x rememb]$ w\ld be rea*$4 #d4 ,a trigg]+ control s t1 :5 ! ma*9e _h rea*$ good en\gh mat*+ betwe5 its obs]vations & its memory1 ! ma*9e w\ld proce$ to id5tify ! m>ks1 read !m1 & transf] !m4 #e4 ,an electric typewrit]1 :i* w\ld respond to ! transf]r$ in/ructions4 7,?is also already exi/s47 ,?is ma*9e is p]haps n s f>fet*$ z x might seem4 ,dur+ ,_w ,w> ,,ii1 gun-aim+ equipm5t us+ ! new te*nique rad> rea*$ a high /age ( developm5t4 ,_m %ots t disabl$ & sank enemy %ips 7 fir$ 9 total d>kness by rad>-controll$ guns4 ,on ! gl[+ scre5 9 ! control room1 !re 7 two spots1 "o t m>k$ ! t>get & "o t report$ ! po9t at :i* ! gun 0 aim$4 ,^! two spots c\ld be br\ght almo/ automatically into agreem5t4 ,9 ! same way1 a report f a phototube tell+ ! %ape ( an obs]v$ m>k & a report f ! memory ( ! ma*9e tell+ ! %ape ( a simil> m>k c\ld be comp>$ by ! ma*9e = lik5ess &1 if judg$ en\gh alike1 c\ld be approv$ z id5tical4 ,ev5 ! phrase 8en\gh alike0 c be appli$ by a ma*9e4 ,dur+ ,_w ,w> ,,ii1 trem5d\s advances 7 made 9 ma*9]y = deciph]+ enemy messages4 ,ma*9es obs]v$ v>i\s features & patt]ns 9 enemy messages1 swiftly c\nt$ ! frequ5cy ( ^! features1 & c>ri$ out /ati/ical te/s4 ,!n ! ma*9es select$ ^? few cases 9 :i* ! patt]ns %[$ mean+ in/ead ( r&omness4 ,a ma*9e l ! automatic typi/1 if made flexible en\gh1 w\ld be1 ( c\rse1 extremely useful4 ,a great load ( dull (fice "w is n[ be+ ?r[n on cl]ks ^: task is to translate f writ+ & typ+ into languages t ma*9es c read1 su* z pun* c>ds4 ,at ! pres5t "t1 if pun*-c>d ma*9es are widely us$ 9 a big company1 ! company mu/ employ l>ge numb]s ( girls ^: sole duty is to read pap]s & pun* up c>ds4 ,a /ill bigg] *ore is ! "w ( typi/s 9 all k9ds ( bus9esses ^: ma9 duty is to read h&writ+1 etc41 & !n copy ! words on a typewrit]4 ,illu/ration3 ,ea* squ>e 9 ! grill is wat*$ by a phototube4 ,,fig4 #a4 ,s*eme = di/+ui%+ ,a & ,h by #ae phototubes4 ,rese>* has already begun on v>i\s features ( ! automatic typi/ because ( its obvi\s labor-sav+ value4 ,= example1 _m pat5ts h be5 issu$ on s*emes = divid+ ! area occupi$ by a lett] or a digit into an array ( spots1 ) a batt]y ( phototubes ea* wat*+ a spot4 ,! reports f ! phototubes toge!r w di/+ui% ! lett] or digit4 ,= example1 if we consid] ,a & ,h plac$ 9 a grill ( fifte5 spots1 #e long by #c wide 7see ,fig4 #a71 !n ! phototubes c di/+ui% betwe5 ,a & ,h by s5s+ black or :ite 9 ! spot 9 ! middle ( ! top r[4 ,:5 we consid] h[ easily & swiftly a human be+ does ?is1 we c once m m>vel at ! recogniz+ ma*9e we all c>ry ar\nd ) u 9 our heads4 ,automatic ,/5ograph] ,ano!r developm5t t we c =esee is "o t we c call ! automatic /5ograph]4 ,?is is a ma*9e t w li/5 to s\nds & write !m d[n 9 prop]ly spell$ ,engli% words4 ,! elem5ts ( ?is ma*9e c be outl9$3 #a4 ,microphones1 :i* c s5se spok5 s\nds 7^! already exi/74 #b4 ,a memory /or+ ! #dj 7m or less7 phonetic units or s\nds t make up ,engli%1 su* z ! #bc consonant s\nds1 p b l ng f v m ? t d n r s z h y k g w * j % zh 7he>d 9 8pleasure07 & ! #ag v[el s\nds1 ,,long ,,%ort ,,o!r ,a 78ate07 a 78cat07 ar 78are07 ,e 78eat07 e 78end07 aw 78awe07 ,i 78isle07 i 78907 er 78err07 ,o 78owe07 o 78on07 ow 78owl07 ,u 78cute07 u 78up07 oi 78oil07 ,,oo 78ro(07 oo 78book07 #c4 ,a collection ( ! rules ( spell+ 9 ,engli%1 conta9+ _m /atem5ts l ,! s\nd b is always spell$ b ,! s\nd % may be spell$ % 7%ip71 s 7sug>71 ti 7/ation71 ci 7physician71 ce 7ocean7 or tu 7picture7 & o!r /atem5ts bas$ on context1 ^w li/s1 d]ivation1 etc4 ,^! are ! /atem5ts by means ( :i* a good ,engli% spell] kn[s h[ to spell ev5 words t he he>s = ! fir/ "t4 #d4 ,a trigg]+ control s t1 :5 ! ma*9e rea*es good en\gh mat*+ betwe5 its obs]vations ( s\nds1 its memory ( s\nds1 & its k ( spell+ rules1 ! ma*9e w id5tify gr\ps ( s\nds z words1 det]m9e _! spell+1 & report ! lett]s det]m9$4 #e4 ,an electric typewrit]1 :i* w\ld type ! report$ lett]s4 ,) ?is type ( ma*9e1 y w\ld dictate y\r lett]s into a ma*9e 7n[ exi/+7 t w\ld record y\r voice4 ,!n ! record w\ld be plac$ on ! automatic /5ograph]1 & out w\ld come y\r lett]s writt5 & spac$ z !y %\ld be4 ,automatic ,recogniz] ,we c =esee a recogniz+ ma*9e ) v g5]al p[]s4 ,suppose t we call x an automatic recogniz] 7see ,fig4 #b74 ,x w h ! foll[+ elem5ts3 #a4 ,input4 ,?is elem5t w consi/ ( a set ( obs]v+ in/rum5ts1 capable ( p]ceiv+ sights1 s\nds1 etc4 ,!re w be ways ( position+ or tun+ ^! in/rum5ts4 #b4 ,memory4 ,?is elem5t w /ore k4 ,x may /ore ! patt]ns ( obs]vations t we are int]e/$ 92 or x may /ore g5]al rules on h[ to f9d patt]ns ( obs]vations t we w be int]e/$ 94 ,x w conta9 k ab\t acceptable gr\ps ( patt]ns1 ab\t actions to be p]=m$ 9 response to patt]ns1 etc4 #c4 ,program #a4 ,! elem5t 8,program #a0 p]=ms a set ( /&>d in/ructions4 ,"u ^! in/ructions1 ! ma*9e3 ,comp>es gr\p aft] gr\p ( obs]vations ) ! in=mation 9 ! memory4 ,comp>es ^! gr\ps ) patt]ns furni%$1 or seeks to organize ! obs]vations into patt]ns4 ,c\nts cases & te/s frequ5cies4 ,f9ds out h[ mu* mat*+ ) patt]ns !re is4 ,tunes ! obs]v+ in/rum5ts 9 ways to increase mat*+4 ,illu/ration3 ,,fig4 #b4 ,s*eme ( an automatic recogniz]4 #d4 ,program #b4 ,! elem5t 8,program #b0 p]=ms ano!r set ( /&>d in/ructions4 ,"u ^! in/ructions1 ! ma*9e1 if x is tun$ well1 mat*es sets ( obs]vations "o aft] ano!r ) ! patt]ns & s reads !m4 #e4 ,trigg]+ ,control4 ,?is elem5t %ifts ! control ( ! ma*9e f ,program #a to ,program #b4 ,x does ?is :5 ! ma*9e rea*es 8good mat*+40 ,we %all set ! mean+ ( ?is into ! ma*9e 9 mu* ! same way z we set 8w>m0 into a !rmo/at4 #f4 ,output4 ,?is elem5t p]=ms any action t we want1 dep5d+ on recogniz$ patt]ns read & any o!r k or in/ructions /or$ 9 ! memory4 ,! automatic recogniz] w be capable ( extraord9>y tasks4 ,) microphones & a l>ge memory1 ?is type ( ma*9e w\ld be able to he> a =eign language spok5 & translate x into spok5 or writt5 ,engli%4 ,) phototubes & ) an exp&$ filt]+ & decod+ capacity z 9 deciph]+ ma*9es1 ! automatic recogniz] %\ld be able to read a dead language1 ev5 ^? 7su* z ,m9oan or ,etruscan7 t h s f> resi/$ ef=ts to read x4 ,! ma*9e w\ld d]ive rules = ! translation ( ! language & translate any sample4 ,an automatic recogniz] c\ld p]haps be equipp$ ) _m s5sitive1 t9y obs]v+ in/rum5ts t c\ld be plac$ ar\nd or 9 ! bra9 & n]v\s sy/ems ( animals4 ,!n ! ma*9e might enable u to f9d out :at activity 9 ! n]v\s sy/em corresponds ) :at activity 9 ! animal4 ,,types ,,( ,,problems ,,t ,,ma*9es ,,w ,,solve ,,9 ,,! ,,future ,we turn n[ to ! second "q reg>d+ ! future ( ma*9es t ?9k3 ,:at types ( problems c we =esee z solv$ by ^! ma*9es8 ,problems ( ,control ,probably ! =emo/ problem :i* ma*9es t ?9k c solve is automatic control ov] all sorts ( o!r ma*9es4 ,?is involves controll+ a ma*9e t is runn+ s t x w d ! "r ?+ at ! "r "t 9 response to in=mation4 ,= example1 suppose t y are m[+ a lawn ) a m[+ ma*9e4 ,y wat* ! prec$+ /rip s z to /ay next to x4 ,y wat* ! ends ( ! /rips1 :]e y turn ar\nd4 ,if a /ick is caught 9 ! cutt+ blade1 y /op & take x out4 ,n[ x is entirely possible to put devices on ! m[+ ma*9e s t all ^! ?+s w be tak5 c>e ( automatically4 ,9 fact1 9 ! case ( pl[+ a l>ge field1 a tractor-pl[ c be equipp$ ) a device t guides x next to ! prec$+ furr[4 ,?us1 once ! fir/ furr[ ar\nd ! edge has be5 made1 rid]less tractors w pl[ a :ole field & /op 9 ! middle4 ,= ano!r example1 take a gas furnace = heat+ /eam to keep a h\se w>m4 ,su* a furnace has automatic controls1 :i* respond to ! foll[+ in=mation :5ev] report$3 ,h\se too w>m4 ,h\se n w>m en\gh4 ,too mu* /eam pressure4 ,n en\gh wat] 9 boil]4 ,gas flame n lit4 ,daytime4 ,nighttime4 ,9 fact1 y\r own mean+ ( 8w>m0 c be put into ! control sy/em3 y set ! dial on y\r !rmo/at at ! temp]ature t 8w>m0 is to be = y4 ,9 ! future _m k9ds ( automatic control w be common4 ,we %all h automatic pilots = fly+ & l&+ airplanes4 ,we %all h automatic missiles = de/ructive purposes1 su* z bomb+ & kill+1 & = con/ructive purposes1 su* z deliv]+ mail & fa/ freight4 ,an article 9 ! magaz9e ,=tune = ,novemb] #aidf describ$ ! automatic factory 7see ,supplem5t #c74 ,?is is a factory 9 :i* !re w\ld be automatic arms = hold+ /uff be+ manufactur$1 & automatic fe$ l9es = supply+ mat]ial j :]e x is ne$$4 ,all ?is factory w\ld be controll$ by ma*9es t h&le in=mation automatically & produce actions t respond to in=mation4 ,?is prospect fills u ) conc]n z well z ) amazem5t4 ,h[ %all we control ^! automatic ma*9es1 ^! robots1 ^! ,frank5/e9s8 ,:at w !re be left = u to d to e>n our liv+8 ,b m ( ?is 9 ! next *apt]4 ,problems ( ,sci5ce ,o!r problems = :i* we c =esee ! use ( ma*9es t ?9k are ! und]/&+1 & lat] ! controll+1 ( nature4 ,"o ( ^! problems is wea!r =eca/+ & wea!r control4 ,! ,wea!r ,bra9 ,we c imag9e ! foll[+ type ( ma*9e--a wea!r bra94 ,a ?\s& wea!r obs]vatories all ov] ! c\ntry obs]ve ! wea!r at #h ,a4,m4 ,! obs]vations are f$ automatically ?r\gh a c\ntrywide network ( communication l9es into a c5tral /ation4 ,"h a giant ma*9e1 conta9+ a great deal ( sci5tific k ab\t ! wea!r1 takes 9 all ! data report$ to x4 ,at #h3ae ! wea!r bra9 />ts to calculate2 9 half an h\r x has f9i%$1 hav+ produc$ an excell5t =eca/ ( ! wea!r = ! :ole c\ntry4 ,!n x proce$s to transmit its =eca/ all ov] ! c\ntry4 ,by #h3ej e wea!r /ation1 newspap]1 radio /ation1 & airport 9 ! c\ntry has ! details4 ,9 ,octob] #aide1 ,dr4 ,v4 ,k4 ,zworyk9 ( ! ,pr9ceton ,laboratories ( ! ,radio ,corporation ( ,am]ica propos$ solv+ ! problem ( wea!r =eca/+ 9 ?is way by a giant bra94 ,! wea!r bra9 w h a second /age ( application4 ,f "t to "t & "h & !re1 ! wea!r is un/able3 x c be trigg]$ to behave 9 "o way or ano!r4 ,= example1 rec5tly1 pellets ( froz5 c>bon dioxide--(t5 call$ ,dry ,ice--h be5 dropp$ f planes & h caus$ ra94 ,9 fact1 a few p\nds ( ,dry ,ice h app>5tly caus$ sev]al hundr$ tons ( ra9 or sn[4 ,9 simil> ways1 we may1 = example1 turn away a hail /orm s t hail w fall ov] a b>r5 m\nta9 in/ead ( ov] a f>m+ valley & ?us protect crops4 ,or we may dispel conditions t w\ld lead to a tornado1 ?us avoid+ its damage4 ,bo? ^! examples involve local wea!r di/urbances4 ,h[ev]1 ev5 ! greate/ wea!r di/urbances1 l hurricanes & blizz>ds1 may ev5tually be direct$ to "s ext5t4 ,?us ! wea!r may become to "s degree subject to man's control1 & ! wea!r bra9 w be able to tell m5 :]e & :5 to take action4 ,psy*ological ,te/+ ,ano!r sci5tific problem to :i* new ma*9]y = h&l+ in=mation applies is ! problem ( und]/&+ human be+s & _! behavior4 ,?is increas$ und]/&+ may lead to mu* wis] deal+ ) human behavior4 ,= example1 consid] te/s ( aptitudes4 ,if y take "o ( ^! te/s1 y may be ask$ to m>k :i* ^w out ( five sugge/$ ones is ne>e/ 9 mean+ to a giv5 ^w4 ,or y\r te/ may be #dj simple ari?metical problems to be solv$ 9 #be m9utes4 ,or y may be giv5 a %eet ) #bj circles1 & be ask$ to put #c dots 9 ! fir/1 #g dots 9 ! second1 #d dots 9 ! ?ird1 #aa dots 9 ! f\r?1 & s on1 irregul>ly2 y may be giv5 a total ( #de seconds to d ?is z well z y c4 ,n[1 if a vocational c\nselor gives y "o ( ^! te/s1 & if y get #hd out ( #ajj on x1 he ne$s to "k j :at he has measur$ ab\t y4 ,also1 he ne$s to "k :e!r he c reasonably =eca/ t1 z a result ( y\r grade ( #hd1 y w be good at writ+ articles1 or good at sup]vis+ ! "w ( o!r p1 or good at design+ 9 a ma*9e %op4 ,he ne$s to "k ! records ( p ) scores ( ab\t #hd on ?is te/ & to h evid5ce support+ 8 =eca/s4 ,if we wi% to make ! mo/ use ( ! te/s1 we ne$ to c>ry out a good deal ( /ati/ics1 ma!matics1 & logic4 ,= example1 x w turn out t answ]s to "s que/ions are mu* m significant ?an answ]s to o!rs1 & s we c greatly improve ! quality ( ! te/s by keep+ only ! m significant que/ions4 ,p[]ful ma*9]y = h&l+ calculations w be v useful 9 ! field ( aptitude te/+4 ,b1 y may ask1 :at if ! p]son analyz+ y\r answ]s has to use int]pretations & judgm5ts8 ,if ! judgm5ts & int]pretations c be express$ 9 words1 & if ! words c be translat$ into ma*9e language1 !n ! ma*9e c c>ry out ! analysis4 ,usually ! diff]5ce betwe5 a rule & a judgm5t is simply ?is3 a rule 9 a case 9 :i* x is h>d to express all ! factors be+ consid]$ is call$ a judgm5t4 ,psy*ological ,tra9] ,x is conceivable t ma*9es t ?9k c ev5tually be appli$ 9 ! actual treatm5t ( m5tal illness & maladju/m5t4 ,consid] :at a physician does4 ,9 treat+ a psy*iatric case1 su* z a neurosis1 a physician uses words almo/ entirely4 ,he asks que/ions4 ,he li/5s to ! pati5t's answ]s4 ,ea* answ] takes ! physician ne>] & ne>] to a diagnosis4 ,by & by ! physician kn[s :at mo/ ( ! difficulty is4 ,!n he mu/ pres5t 8 k sl[ly to ! pati5t1 gradually guid+ ! pati5t to und]/&+4 ,x is a psy*ological tru? t tell+ a man 9 t5 m9utes :at is wrong ) him does n cure him4 ,! physician seeks to free ! pati5t f ! torm5t+ circles ( habit & worry 9 :i* he has be5 trapp$4 ,(t5 ! diagnosis is %ort & ! treatm5t is long2 ! reasons = ! neurosis may soon be cle> to ! physician1 b !y may take mon?s to become cle> to ! pati5t4 ,n[ let u consid] ! foll[+ k9d ( ma*9e z an aid to ! physician4 ,we might call ?is k9d ( ma*9e a psy*ological tra9]1 = 9 _m ways x is l ! tra9+ ma*9es us$ 9 ,_w ,w> ,,ii = tra9+ a pilot to fly an airplane4 ,! psy*ological tra9] w\ld h ! foll[+ prop]ties3 #a4 ,! ma*9e is able to %[ s\nd movies--produce pictures & utt] words4 #b4 ,x is able to put be=e ! pati5t3 situations1 problems1 que/ions1 exp]i5ces1 etc4 #c4 ,x is able to take 9 responses f ! pati5t4 #d4 ,x is able to receive a program ( in/ructions f ! physician4 #e4 ,dep5d+ on ! responses ( ! pati5t & on ! program f ! physician1 ! tra9+ ma*9e c select m mat]ial to put be=e ! pati5t4 #f4 ,! tra9+ ma*9e produces a record ( :at x pres5t$ & ( h[ ! pati5t respond$1 s t ! physician & ! pati5t c /udy ! record lat]4 ,:at sort ( films w\ld ! ma*9e hold8 ,! ma*9e c\ld be load$ ) a numb] ( films :i* w\ld help 9 ! p>ticul> type ( neurosis f :i* ! pati5t 0 suff]+4 ,:at sort ( responses c\ld ! pati5t make8 ,! pati5t might h buttons 9 front ( him :i* he c\ld press to indicate su* answ]s z3 ,yes ,i don't "k ,repeat ,no ,x dep5ds ,g ahead ,also1 ! pati5t might hold a device--l a lie detector1 p]haps--:i* w\ld report 8 /ate ( t5s5ess1 etc41 & s report :at he really felt4 ,:]e w\ld ! ma*9e's que/ions come f8 ,f "o or m physicians v clev] 9 ! treatm5t ( m5tal illness4 ,suppose t ! pati5t is inconsi/5t 9 8 answ]s8 ,! ma*9e1 discov]+ ! inconsi/5cies1 c\ld return to ! subject & ask relat$ que/ions 9 a diff]5t way4 ,z soon z sev]al que/ions relat$ to ! same po9t are answ]$ consi/5tly1 ! ma*9e c\ld exclude gr\ps ( que/ions t no long] apply & c\ld proce$ to o!r que/ions t w\ld /ill apply4 ,pati5ts w\ld v>y 9 _! ability to g z fa/ z ! ma*9e c\ld4 ,s f "t to "t ! ma*9e w\ld ask que/ions to te/ ! effect ( :at x _h pres5t$2 &1 dep5d+ on ! answ]s1 ! ma*9e w\ld g fa/] or w\ld br+ 9 additional mat]ial to cl>ify "s po9t4 ,?is ma*9e might h a few advantages ov] ord9>y treatm5t4 ,= example1 ) ! ma*9e1 treatm5t does n dep5d on ! physician's mak+ ! "r answ] 9 a split second1 z x may 9 a p]sonal int]view4 ,also1 ! pati5t might be frank] ) ! ma*9e ?an ) ! physician1 = x might be arrang$ t ! pati5t c\ld review 8 record1 & !n decide :e!r to confess x to 8 physician4 ,su* a ma*9e w\ld enable physicians to treat _m m pati5ts ?an !y n[ c4 ,9 fact1 x is e/imat$ t ne>ly #ej p] c5t ( p]sons :o consult physicians are suff]+ only f m5tal illness4 ,su* a ma*9e w\ld !re=e be a great help4 ,problems ( ,bus9ess ,ano!r l>ge gr\p ( problems = :i* we c =esee ! use ( ma*9es t ?9k is f\nd 9 bus9ess & economics4 ,= example1 consid] production s*$ul+ 9 a bus9ess or a factory4 ,! ma*9e takes 9 a description ( ea* ord] receiv$ by ! bus9ess & a description ( its relative urg5cy4 ,! ma*9e kn[s 7t is1 has 9 its memory7 h[ mu* ( ea* k9d ( raw mat]ial is ne$$ to fill ! ord] & :at equipm5t & manp[] are ne$$ to produce x4 ,! ma*9e makes a s*$ule %[+ :at p>ticul> m5 & :at p>ticul> equipm5t are to be set to "w to produce ! ord]4 ,! ma*9e turns out ! be/ possible production s*$ule1 %[+ :o %\ld d :at :51 s t all ! ord]s w be fill$ 9 ! be/ sequ5ce4 ,:at is ! 8be/0 sequ5ce8 ,we c decide :at we ?9k is ! be/ sequ5ce1 & we c set ! ma*9e = mak+ t k9d ( selection1 9 ! same way z we decide :at is 8w>m0 & set ! !rmo/at to produce x6 ,on a mu* l>g] scale1 we c use me*anical bra9s to /udy economic relations 9 a society4 ,ev]y?+ produc$ 9 a society is made by consum+ "s mat]ials1 labor1 equipm5t1 & skill4 ,! output produc$ by "o man or factory or indu/ry becomes ! input = o!r m51 factories1 indu/ries4 ,9 ?is way all economic units are l9k$ toge!r by _m diff]5t k9ds & degrees ( dep5d5ce4 ,! situation is1 ( c\rse1 complicat$3 x *anges z "t goes on & z p want diff]5t ?+s produc$4 ,economi/s h already set up simple models ( economic societies & h /udi$ !m4 ,b ) ma*9es t ?9k1 x w be possible to set up & /udy f> m complicat$ models--models t are v mu* l ! society we live 94 ,we c !n answ] que/ions ( economics by calculation in/ead ( by argum5ts & c\nt+ noses4 ,we %all be able to solve def9itely su* problems z3 8,h[ w a rise 9 ! price ( /eel affect ! f>m+ indu/ry80 8,h[ mu* money mu/ be paid out z wages & sal>ies s t consum] pur*as+ p[] w buy back :at indu/ry produces80 ,ma*9es & ! ,individual ,:at ab\t ! ord9>y ev]yday effects ( ^! ma*9es ^u y & me z an individual8 ,we c see t ! new ma*9]y w apply on a small scale ev5 to u4 ,small ma*9es us+ a few electronic tubes--mu* l a radio set1 = example--& conta9+ spools ( magnetic wire or magnetic tape w d\btless be available to u4 ,we %all be able to use !m to keep addresses & telephone numb]s1 to figure out ! income tax we %\ld pay1 to help u keep acc\nts & make ends meet1 to rememb] _m ?+s we ne$ to "k1 & p]haps ev5 to give u m in=mation4 ,= !re are a great _m ?+s t all ( u c\ld d mu* bett] if we c\ld only apply :at ! wise/ ( u kn[s4 ,we c ev5 imag9e :at new ma*9]y = h&l+ in=mation may "s day become3 a small pocket in/rum5t t we c>ry ar\nd ) u1 talk+ to x :5ev] we ne$ to1 & ei!r /or+ in=mation 9 x or receiv+ in=mation f x4 ,?us ! bra9 ) a motor w guide & advise ! man j z ! armor ) a motor c>ries & protects him4 ,*apt] #ab ,,social ,,control3 ,,ma*9es ,,t ,,?9k ,,& ,,h[ ,,society ,,may ,,control ,,!m ,x is (t5 easi] = m5 to create a device ?an to guide x well aft]w>ds3 x is (t5 easi] = a sci5ti/ to /udy 8 sci5ce ?an to /udy ! results = good or evil t 8 discov]ies may lead to4 ,b x is n "r nor prop] = a sci5ti/1 a man :o is loyal to tru? z an ideal1 to h no reg>d = :at 8 discov]ies may lead to4 ,?is pr9ciple is n[ be+ widely recogniz$4 ,_m sci5ti/s today--bo? z individuals & z gr\ps1 & especially ! atomic sci5ti/s--are consid]+ ! results ( _! sci5tific discov]ies2 & !y are %>+ 9 ! ef=t to r5d] ^? results truly useful to humanity4 ,x w\ld be easy to leave out ( ?is book any discussion ( h[ ma*9es t ?9k may be controll$1 any consid]ation ( h[ !y may be made truly useful to humanity4 ,b t w\ld be h>dly "r or prop]4 ,9 conclud+ a book su* z ?is "o1 t t\*es on _m aspects ( ma*9es t ?9k1 we ne$ to consid] :at c & %\ld be done to make su* ma*9es ( true b5efit to all ( humanity4 ,s1 we come to ! mo/ important ( all our que/ions3 ,:at sort ( control ov] ma*9es t ?9k d we ne$ 9 human society8 ,,ma*9e ,,t ,,bo? ,,?9ks ,,& ,,acts ,f a n>r[ po9t ( view1 a ma*9e t only ?9ks produces only in=mation4 ,x takes 9 in=mation 9 "o /ate1 & x puts out in=mation 9 ano!r /ate4 ,f ?is viewpo9t1 in=mation 9 itself is h>mless2 x is j an arrangem5t ( m>ks2 & accord+ly1 a ma*9e t ?9ks is h>mless1 & no control is necess>y4 ,al?\gh x is true t ! in=mation produc$ only becomes good or evil aft] o!r ma*9]y or human be+s act on ! in=mation1 9 reality a ma*9e ) ! p[] to produce in=mation is con/ruct$ only = ! reason ( its use4 ,we want to "k :at su* ma*9es c tell u only because we c !n proce$ to act mu* m effici5tly ?an be=e4 ,= example1 a guid$ missile ne$s a me*anical bra9 only because !n x c rea* its t>get4 ,9 all cases me*anical bra9s are insep>able f _! uses4 ,= ! purposes ( ?is *apt]1 ! n>r[ view w be reject$ because x dodges ! issue4 ,we %all be mu* conc]n$ ) ! comb9ation ( a ma*9e t ?9ks ) ano!r ma*9e t acts2 & we %all (t5 call ?is comb9ation ! robot ma*9e4 ,,read+ ,,?is ,,*apt] ,n[1 be=e laun*+ fur!r into ! discussion1 we ne$ to say t ! conclusions sugge/$ 9 ?is *apt] are n f9al4 ,ev5 if !y are express$ a little positively 9 places1 !y are nev]!less subject to *ange z m in=mation is discov]$ & z ! appraisal ( in=mation *anges ) "t4 ,also1 almo/ any conclusions ab\t social control--includ+1 c]ta9ly1 ! conclusions 9 ?is *apt]--are subject to controv]sy4 ,b controv]sy is good3 x leads to ?\ght4 ,! m m9ds t g to "w on solv+ ! problem ( social control ov] robot ma*9es & o!r products ( ! new te*nology--:i* is ru%+ ^u u f ! discov]ies ( ! sci5ti/s--! bett] (f we all w be4 ,if1 :ile /imulat+ disagreem5t1 ! ideas express$ 9 ?is *apt] %\ld succe$ 9 /imulat+ ?\ght & delib]ation1 ! purpose ( ?is *apt] w be well fulfill$4 ,up to ?is po9t 9 ?is book1 ! emphasis has be5 on possibilities ( b5efits to humanity t may arise f ma*9es t ?9k4 ,9 ?is *apt]1 devot$ z x is to ! subject ( control1 ! emphasis is on possibilities = h>m4 ,bo? possibilities are valid1 & ! happ5+ ( ei!r dep5ds ^u ! actions ( m54 ,9 mu* ! same way1 atomic en]gy is a great possibility = b5efit & = h>m4 ,x is ! nature ( control to put a f5ce ar\nd dang]2 & s x is natural 9 ?is *apt] t ! weight ( att5tion %\ld %ift to ! dang]\s aspects ( ma*9es t ?9k4 ,p]haps a read] may feel t a *apt] ( ?is k9d is r out ( place 9 a book1 su* z ?is "o1 t seeks to be sci5tific4 ,if s1 he is rem9d$ t1 9 accordance ) ! g5]al sugge/ions = read+ ?is book /at$ 9 ! preface1 he %\ld omit ?is *apt]4 ,,frank5/e9 ,p]haps ! fir/ /udy ( ! consequ5ces ( a ma*9e t ?9ks is a prophetic novel call$ ,frank5/e91 writt5 m ?an a hundr$ ye>s ago1 9 #ahah4 ,! au?or1 !n only #ba ye>s old1 0 ,m>y ,w4 ,godw91 :o became ! wife ( ! poet ,p]cy ,bys%e ,%elley4 ,accord+ to ! /ory1 a "y ,swiss1 an ard5t /ud5t ( physiology & *emi/ry1 ,victor ,frank5/e91 f9ds ! secret ( life4 ,he makes an extremely ugly1 clev]1 & p[]ful mon/]1 ) human desires4 ,frank5/e9 promptly flees f 8 laboratory & h&iwork4 ,! mon/]1 aft] seek+ "u great h>d%ips = a ye> or two to e>n fair treatm5t among m51 f9ds himself cont9ually attack$ & h>m$ on acc\nt ( 8 ugl9ess1 & he becomes embitt]$4 ,he beg9s to se>* = 8 creator = ei!r rev5ge or a b>ga94 ,:5 !y meet3 8,i expect$ ?is reception10 said ! daemon4 8,all m5 hate ! wret*$2 h[ !n mu/ ,i be hat$ :o am mis]able beyond all liv+ ?+s6 ,yet y my creator dete/ & spurn me1 ?y creature1 to :om ?\ art b\nd by ties only dissoluble by ! annihilation ( "o ( u4 ,y purpose to kill me4 ,h[ d>e y sport ?us ) life8 ,d y\r duty t[>ds me1 & ,i w d m9e t[>ds y & ! re/ ( mank9d4 ,if y w comply ) my conditions1 ,i w leave !m & y at peace2 b if y refuse1 ,i w glut ! maw ( dea?1 until x be satiat$ ) ! blood ( y\r rema9+ fri5ds40 ,frank5/e9 />ts to comply ) ! ma9 condition1 :i* is to make a mate = ! mon/]2 b ,frank5/e9 _c br+ himself to d x4 ,s ! mon/] causes ! dea? "o aft] ano!r ( all ,frank5/e9's family & close/ fri5ds2 & ! tale f9ally ends ) ! dea? ( ,frank5/e9 & ! disappe>ance ( ! mon/]4 ,z ! diction>y says ab\t ,frank5/e91 8,! "n has become a synonym = "o de/roy$ by 8 own works40 ,,rossum',s ,,univ]sal ,,robots ,p]haps ! next /udy ( ! consequ5ces ( a ma*9e t ?9ks is a rem>kable play call$ ,r4,u4,r4 7= ,rossum's ,univ]sal ,robots71 fir/ produc$ 9 ,prague 9 #aiba4 ,k>el apek1 ! ,cze* dramati/ :o wrote x1 0 !n only #ca4 ,! ^w 8robot0 comes f ! ,cze* ^w 8robota10 mean+ compulsory s]vice4 ,accord+ to ! play1 ,rossum ! eld]1 a sci5ti/1 discov]$ a 8me?od ( organiz+ liv+ matt]0 t 0 8m simple1 flexible1 & rapid0 ?an ! me?od us$ by nature4 ,rossum ! y\ng]1 an eng9e]1 f\nd$ a factory = ! mass production ( artificial workm51 robots4 ,!y _h ! =m ( human be+s1 intellig5ce1 memory1 & /r5g?2 b !y 7 )\t feel+s4 ,9 ! fir/ act1 ! factory "u ,h>ry ,dom91 ,g5]al ,manag]1 is busy supply+ robots to pur*as]s all ov] ! _w--= "w1 = fight+1 = any purpose at all1 to anyone :o c\ld pay = !m4 ,dom9 decl>es3 8444 9 t5 ye>s1 ,rossum's ,univ]sal ,robots w produce s mu* corn1 s mu* clo?1 s mu* ev]y?+ t ?+s w be practically )\t price4 ,!re w be no pov]ty4 ,all "w w be done by liv+ ma*9es4 ,ev]ybody w be free f worry & lib]at$ f ! degradation ( labor4 ,ev]ybody w live only to p]fect himself4444 ,x's b\nd to happ540 ,9 ! second act1 t5 ye>s lat]1 x turns out t ,dom9 & ! o!rs 9 *>ge ( ! factory h be5 mak+ "s robots ) additional human *>act]i/ics1 su* z ! capacity to feel pa94 ,! new] types ( robots1 h[ev]1 h unit$ all ! robots aga9/ man1 = ! robots decl>e t !y are 8m highly develop$ ?an man1 /rong]1 & m intellig5t1 & man is _! p>asite40 ,9 ! la/ act1 ! robots conqu] & slay all m5 except "o--an ar*itect1 ,alqui/1 :o 9 ! epilogue provides a f9al quirk to ! plot4 ,,fact ,,& ,,fancy ,n[ :at is fact & :at is fancy 9 ^! two w>n+s giv5 to u a hundr$ ye>s ap>t8 ,( c\rse1 x is v d\btful t a ,frank5/e9 mon/] or a ,rossum robot w soon be con/ruct$ ) n]ves1 fle%1 & blood l an animal body4 ,b we "k t _m types ( robot ma*9es c ev5 n[ be con/ruct$ out ( h>dw>e--:eels1 motors1 wires1 electronic tubes1 etc4 ,!y c h&le _m k9ds ( in=mation & are able to p]=m _m k9ds ( actions1 & !y are /rong] & swift] ?an man4 ,( c\rse1 x is d\btful t ! robot ma*9es1 by !mselves & ( _! own 8free w10 w be dang]\s to human be+s4 ,b z soon z antisocial human be+s h access to ! controls ov] robot ma*9es1 ! dang] to society becomes great4 ,we want to escape t dang]4 ,escape f ,dang] ,a natural long+ ( _m ( u is to escape to an e>li]1 simpl] life on ?is e>?4 ,victor ,frank5/e9 long$ to undo ! pa/4 ,he said3 8,le>n f me1 if n by my precepts1 at lea/ by my example1 h[ dang]\s is ! acquirem5t ( k1 & h[ mu* happi] t man is :o believes 8 native t[n to be ! _w1 ?an he :o aspires to become great] ?an 8 nature w all[40 ,any sort ( return to ! pa/ is1 ( c\rse1 impossible4 ,x is d\btful t m5 c\ld1 ev5 if !y want$ to1 /op ! great flood ( te*nical k t sci5ce is n[ produc+4 ,we all mu/ n[ face ! fact t ! k9d ( _w we us$ to live 91 ev5 s rec5tly z #aici1 is gone4 ,!re n[ exi/ weapons & ma*9es s p[]ful & dang]\s 9 ! wrong h&s t 9 a day or two mo/ ( ! p ( ! e>? c\ld be put to dea?4 ,giant bra9s are closely relat$ to at lea/ two ( ^! weapons3 sci5ti/s h already us$ me*anical bra9s = solv+ problems ab\t atomic explosives & guid$ missiles4 ,9 addition1 ?9k+ me*anisms design$ = ! automatic control ( gunfire 7 an important "p ( ! w9n+ ( ,_w ,w> ,,ii4 ,!y w be a /ill m important "p ( ! fight+ ( any future w>4 ,nor c we escape to ano!r "p ( ! e>? :i* ! new weapons w n rea*4 ,at #cjj miles an h\r1 any spot on e>? c be rea*$ f any o!r 9 less ?an #dh h\rs4 ,a mod]n plane exce$s ?is spe$2 a rocket or guid$ missile d\bles or trebles x4 ,nor c we tru/ t "s k9d ( good luck w pull u ?r\gh & help m5 to escape ! consequ5ces ( :at m5 d4 ,bo? ,frank5/e9 & ,dom9 reap$ 9 full ! consequ5ces ( :at !y did4 ,! hi/ory ( life on ?is e>? t is record$ 9 ! rocks is full ( evid5ce ( races ( liv+ ?+s t h populat$ ! e>? = a "t & !n become ext9ct1 su* z ! d9osaurs4 ,9 t long hi/ory1 r>ely does a race survive4 ,9 our own day1 insects & fungi r ?an m5 h %[n fitness to survive & spread ov] ! e>?3 witness ! blight t de/roy$ ! *e/nut trees ( ,nor? ,am]ica1 9 spite ( ! be/ ef=ts ( sci5ti/s to /op x4 ,!re seems to be no k9d ( escape possible4 ,x is necess>y to grapple ) ! problem3 ,h[ c we be safe aga9/ ! ?reat ( physical h>m f robot ma*9es8 ,,unemploym5t ,! o!r *ief ?reat f robot ma*9es is aga9/ our economic life4 ,h>ry ,dom91 9 ,r4,u4,r41 y rememb]1 prophesi$3 8,all "w w be done by liv+ ma*9es40 ,z an example1 9 ! magaz9e ,mod]n ,indu/ry = ,feb4 #ae1 #aidg1 appe>$ a picture ( a ma*9e = sell+ books1 & "u ! picture 7 ! words3 ,ano!r new product 9 robot salesm5--,late/ 9 ! p>ade ( me*anical v5d+ ma*9es is ?is book salesman4444 ,x is design$ = use 9 hospitals1 rail t]m9als1 & /ores4 ,x (f]s #ae diff]5t titles1 select$ manually1 & obta9$ by dropp+ qu>t] 9 slot4 ,cab9et /ores #if books4 ,c y feel ! brea? ( ! robot salesman1 workman1 eng9e]1----1 on ! back ( y\r neck8 ,at ! mom5t :5 we comb9e automatic produc+ ma*9]y & automatic controll+ ma*9]y1 we get a va/ sav+ 9 labor & a great increase 9 te*nological unemploym5t4 ,9 extreme cases1 p]haps1 ! effect ( robot ma*9es w be ! disappe>ance ( m5 f a factory4 ,su* a factory w be l a mod]n p[] plant t turns a wat]fall into electricity3 once ! ma*9]y is in/all$1 only "o wat*man is ord9>ily ne$$4 ,b1 9 mo/ cases1 ?is w be ! effect3 9 a great numb] ( factories1 m9es1 f>ms1 etc41 ! labor =ce ne$$ w be cut by a great proportion4 ,! effect is n diff]5t 9 quality1 because ! new developm5t is robot ma*9]y2 b ! am\nt ( te*nological unemploym5t com+ f robot ma*9es is likely to be consid]ably great] ?an previ\sly4 ,! robot ma*9e raises ! two que/ions t hang l swords ov] a great _m ( u ^! days4 ,! fir/ "o is = any employee3 ,:at %all ,i d :5 a robot ma*9e r5d]s wor?less all ! skill ,i h sp5t ye>s 9 develop+8 ,! second "q is = any bus9essman3 ,h[ %all ,i sell :at ,i make if half ! p to :om ,i sell lose _! jobs to robot ma*9es8 ,,social ,,control ,,& ,,its ,,two ,,sides ,! two *ief h>mful effects ^u humanity :i* are to be expect$ f robot ma*9es are physical dang] & unemploym5t4 ,^! are s]i\s risks1 & "s degree ( social control is ne$$ to gu>d aga9/ !m4 ,!re w also be v great advantages f robot ma*9es4 ,! mon/] 9 ,frank5/e9 is "r :5 he says1 8,d y\r duty t[>ds me1 & ,i w d m9e t[>ds y & ! re/ ( mank9d40 ,& ,h>ry ,dom9 9 ,r4,u4,r4 is "r z to possibility :5 he says1 8,!re w be no pov]ty4444 ,ev]ybody w be free f worry40 ,social control mu/ also be conc]n$ ) h[ ! advantages f robot ma*9es are to be %>$4 ,! problem ( social control ov] m5 & _! devices has always _h two sides4 ,! fir/ side deals ) :at we might plan = control if m5 7 reasonable & tol]ant4 ,?is "p ( ! problem seems relatively easy4 ,! o!r side deals ) :at we mu/ ord9>ily arrange1 s9ce mo/ m5 are (t5 unreasonable & prejudic$ &1 z a result1 (t5 act 9 antisocial ways4 ,?is "p ( ! problem is h>d4 ,let u beg9 ) ! easi] side fir/4 ,,types ,,( ,,control--,,if ,,m5 ,,7 ,,reasonable ,9 seek+ to fulfill wants & a*ieve safety1 m5 h us$ hundr$s ( types ( control4 ,! ma9 types are usually call$ political & economic sy/ems1 b !re are always great quantities ( exceptions4 ,! m mature & fre] ! society1 ! great] ! v>iety ( types ( control t c be f\nd 9 x4 ,probably ! mo/ widely us$ type ( control 9 ?is c\ntry is private & public control work+ toge!r1 z private own]%ip & public regulation--= example1 railroads1 banks1 airl9es1 life insurance companies1 telephone sy/ems1 & _m o!rs4 ,x w\ld be reasonable to expect private own]%ip & public regulation ( a great _m classes ( robot ma*9es1 to ! end t !y w\ld nev] ?reat5 ! safety ( p4 ,ano!r common type ( control is public own]%ip & op]ation2 examples are toll bridges1 airports1 city transit sy/ems1 & wat]-supply sy/ems4 ,atomic en]gy 0 s cle>ly fraught ) s]i\s implications t 9 #aidf ! ,congress ( ! ,unit$ ,/ates plac$ x entirely "u public control express$ z ! ,atomic ,en]gy ,commission4 ,!re is a class ( robot ma*9]y :i* has already rea*$ ! /age ( acute public conc]n3 guid$ missiles & automatic fire-control4 ,x w\ld be reasonable t 9 ?is c\ntry all activity 9 ?is subdivision %\ld be "u close control by ! ,dep>tm5t ( ,def5se4 ,9 ! int]national ar5a1 aga91 ! problem becomes soluble if we assume m5 to be reasonable4 ,an int]national ag5cy1 su* z an organ ( ! ,unit$ ,nations1 w\ld take ov] inspection & control ( robot ma*9e activities closely affect+ ! public safety any:]e 9 ! _w4 ,p>ticul>ly1 ?is ag5cy w\ld conc]n itself ) guid$ missiles1 robot pilots = planes1 automatic gunfire control1 etc4 ,mu* manufactur+ skill is ne$$ to make su* products z ^!3 ! factories :]e !y c\ld be manufactur$ w\ld !reby be det]m9$4 ,also1 a giant bra9 is a useful device = solv+ sci5tific problems ab\t weapons ( mass de/ruction4 ,s ! ag5cy w\ld ne$ to inspect ! problems be+ solv$ on su* ma*9es4 ,?is ag5cy w\ld be responsible to a legislature or an executive body repres5t+ all ! p 9 ! _w--if m5 7 reasonable4 ,9 reg>d to ! effects ( robot ma*9es on unemploym5t1 aga91 if m5 7 reasonable1 ! problem w\ld be soluble4 ,! problem is equival5t to ! problem ( abundance3 h[ %\ld m5 di/ribute ! advantages ( a va/ increase 9 production among all ! memb]s ( society 9 a fair & s5sible way8 ,a va/ increase 9 production is n s impossible z x may seem4 ,= example1 9 #aici1 ) #de million employ$1 ! ,unit$ ,/ates index ( indu/rial production 0 at #aji1 &1 9 #aidc1 ) #eb million employ$1 ! index ( production 0 at #bci4 ,if m5 7 reasonable1 ! net pr(its f robot ma*9]y w\ld be divid$ among 7#a7 ^? :o _h mo/ to d ) devis+ ! new ma*9]y1 & 7#b7 all ( society4 ,a rule w\ld be adopt$ 7probably x c\ld be less complicat$ ?an "s exi/+ tax rules7 :i* w\ld take into acc\nt v>i\s factors su* z rew>ds to ! inv5tors1 inc5tives to cont9ue inv5t+1 adequate assi/ance to ^? made unemploy$ by ! robot ma*9es1 r$uction ( prices to b5efit consum]s1 & contributions to basic & appli$ sci5tific rese>*4 ,9 fact1 "u ! assumption 8if m5 7 reasonable10 x w\ld h>dly be necess>y to devote a *apt] to ! problem ( social control ov] robot ma*9es6 ,,ob/acles ,! discussion above ( h[ robot ma*9es c\ld be controll$ suppos+ t m5 7 reasonable1 seems1 ( c\rse1 to be gl>+ly impractical4 ,m5 are n reasonable on mo/ occasions mo/ ( ! "t4 ,if we /opp$ at ?is po9t1 aga9 we w\ld be dodg+ ! issue4 ,:at are ! ob/acles to reasonable control8 ,!re are1 x seems1 two big ob/acles & "o small] "o to reasonable types ( social control ov] robot ma*9es4 ,! small] "o is ignorance1 & ! two big ob/acles are prejudice & a n>r[ po9t ( view4 ,ignorance ,by ignorance we mean lack ( k & in=mation4 ,n[ me*anical bra9s are a new & intricate subject4 ,a great _m p w1 ?r\gh no fault ( _! own1 naturally rema9 un9=m$ ab\t me*anical bra9s & robot ma*9es = a long "t4 ,h[ev]1 !re is a widespread ?ir/ = k ^! days3 witness 9 magaz9es1 = example1 ! gr[? ( ! article & ! decl9e ( ! essay4 ,!re is also a fairly /eady surge ( k f ! au/]e sci5tific f\nta9 ( new te*nology4 ,we c ?us see bo? a dem& & a supply = in=mation 9 su* fields z me*anical bra9s & robot ma*9es4 ,we c expect1 !re=e1 a fairly /eady decl9e 9 ignorance4 ,prejudice ,prejudice is a mu* m s]i\s ob/acle to reasonable control ov] robot ma*9es4 ,x w be wor? our :ile to exam9e x at l5g?4 ,prejudice is frequ5t 9 human affairs4 ,= example1 9 "s c\ntries1 b n 9 all1 !re is conflict among m51 bas$ on _! religi\s diff]5ces4 ,aga91 9 o!r c\ntries1 b n 9 all1 !re is wide discrim9ation among m51 bas$ on ! color ( _! sk94 ,ov] ! :ole _w today1 !re is a %>p lack ( und]/&+ betwe5 cons]vatives1 grad+ ov] to reaction>ies1 on ! "o h&1 & lib]als1 grad+ ov] to radicals1 on ! o!r h&4 ,all ^! diff]5ces are bas$ on m5's attitudes1 on /rongly held sets ( beliefs4 ,^! attitudes are n affect$ by 8in=mation02 ! 8in=mation0 is n believ$4 ,! attitudes are n subject to 8judgm5t02 !y come 8be=e judgm5t03 !y are prejudices4 ,ev5 9 ! mid/ ( all ! sci5ce ( today1 prejudice is widespread4 ,9 ,g]many1 f #aicc to #aici1 we saw "o ( ! mo/ sci5tific ( c\ntries become "o ( ! mo/ prejudic$4 ,prejudice is (t5 difficult to detect4 ,we f9d x h>d to recognize ev5 9 ourselves4 ,= a prejudice always seems1 to ! p]son :o has x1 ! mo/ natural attitude 9 ! _w4 ,z we li/5 to o!r p1 we are (t5 unc]ta9 h[ to sep>ate in=mation1 guesses1 humor1 prejudice1 etc4 ,circum/ances compel u to accept provisionally quantities ( /atem5ts j on o!r p's say-s4 ,a good te/ ( a /atem5t = prejudice1 h[ev]1 is to comp>e x ) ! sci5tific view4 ,prejudice is mo/ dang]\s = society4 ,its m extreme manife/ations are aggressive w>1 intol]ance 7especially ( /range p & cu/oms71 viol5ce1 race hatr$1 etc4 ,9 ! consum+ hatr$ t a prejudic$ man has t[>ds ! object ( 8 prejudice1 he is likely to de/roy himself & de/roy _m m p besides4 ,9 =m] days1 ! h&y weapon 0 a sword or a pi/ol2 n too mu* damage c\ld be done :5 "o man ran amuck4 ,b n[adays a s+le use ( a s+le weapon has sla9 #gj1jjj p 7! atom bomb dropp$ at ,hiro%ima71 & s a great _m p live anxi\s & afraid4 ,:at is prejudice8 ,h[ does x arise8 ,h[ c x be cur$1 & ?us remov$ f ob/ruct+ reasonable control ov] robot ma*9es & ! re/ ( today's amaz+ sci5tific developm5ts8 ,prejudice is a disease ( m5's m9ds4 ,x is infecti\s4 ,! cause & developm5t ( ! disease are ab\t z foll[s3 ,deprive someone ( some?+ he deeply ne$s1 su* z affection1 food1 or opportunity4 ,9 ?is way hurt him1 make him res5tful1 ho/ile2 b prev5t him f express+ 8 res5tm5ts 9 a reasonable way1 giv+ him in/ead false outlets1 su* z o!r p to hurt1 my?s to believe1 ho/ile behavior patt]ns to imitate4 ,he w !n break out ) prejudices z if !y 7 measles4 ,! process ( cur+ ! disease ( prejudice is ab\t z foll[s3 ,make fri5ds ) ! pati5t2 w9 8 tru/4 ,enc\rage him to p\r out 8 half-=gott5 hates4 ,help him to talk !m ov] freely1 by means ( que/ions b n criticisms1 until f9ally ! pati5t a*ieves insight1 sees ?r\gh 8 =m] prejudices1 & drops !m4 ,9 ^! days prejudice is a c>d9al problem ( society4 ,x is p]haps cons]vative to say t a *ief pres5t requirem5t = ! survival ( human society--) ! atom bomb1 bact]ial w>f>e1 guid$ missiles1 etc41 ne> at h&--is cure ( prejudice & its consequ5ces1 irrational & unre/ra9$ hate4 ,n>r[ ,po9t ( ,view ,a n>r[ po9t ( view reg>d+ :at is desirable or good is ! ?ird ob/acle to rational control ov] robot ma*9es4 ,:at d we mean by ?is8 ,our po9t ( view z a two-ye>-old is bas$ on pure self-int]e/4 ,if we see a toy1 we grab x4 ,!re is no prejudice ab\t ?is2 x is entirely natural--= two-ye>-olds4 ,z we gr[ old]1 our po9t ( view conc]n+ :at is good or desirable rapidly broad5s3 we ?9k ( o!rs & _! advantage besides our own4 ,= example1 we may become int]e/$ 9 a cons]vation program to cons]ve birds1 or soil1 or =e/s1 & our po9t ( view exp&s1 embraces ^! objectives1 :i* become "p ( our p]sonality & loyalties4 ,un=tunately1 x seems to be true t ! exp&+ po9t ( view1 ! exp&+ loyalties1 ( mo/ p z !y gr[ up are arre/$ some:]e along ! l9e (3 self1 family1 neighborhood1 community1 section ( c\ntry1 nation4 ,an honorable exception is ! sci5ti/s' old & f9e tradition ( _w-wide unity & loyalty 9 ! se>* = objective tru?4 ,n[ ! problem ( rational control ov] robot ma*9es & o!r p>ts ( ! new te*nology is no respect] ( national b\nd>ies4 ,to be solv$ x requires a _w-wide po9t ( view1 a loyalty to human society & its be/ int]e/s1 a social po9t ( view4 ,almo/ all t y & ,i h & d & ?9k is ! result ( a long hi/ory ( human society on ?is e>?4 ,all m5 on ! e>? today are desc5dants ( o!r m5 :o liv$ #ajjj1 #bjjj1 #cjjj 444 ye>s ago1 :e!r !y 7 ,romans or ,*9ese or ,babylonians or ,mayas or memb]s ( any o!r race4 ,to ride 9 a subway or an airplane1 to talk on ! telephone1 to speak a language1 to calculate1 to survive smallpox or ! black dea?1 etc4--all ^! privileges are our inh]itance f c\ntless ?\s&s ( o!r human be+s1 ( _m c\ntries1 & ne>ly all ( :om are n[ dead4 ,dur+ our lives we pass on to our own *ildr5 an inh]itance 9 :i* our own contribution is rem>kably small4 ,s9ce ea* p]son is ! *ild ( two o!rs1 ! numb] ( our =efa!rs is huge1 & we are all und\bt$ly blood c\s9s4 ,because ( ?is relation%ip1 & because we owe to ! re/ ( society ne>ly all t we are1 we h a social responsibility--we ne$ to hold a social po9t ( view4 ,ea* ( u ne$s to accept & welcome a _w-wide social responsibility1 z a memb] ( human society1 z a b5efici>y & tru/ee ( our human inh]itance4 ,o!rwise we are drones1 "p ( ! hive )\t e>n+ our keep4 ,! social po9t ( view is equitable1 x is inspir+1 & x is probably requir$ n[ 9 ord] = human be+s to survive4 ,we ne$ to let g ( a n>r[ po9t ( view4 ,,conclusion ,we h n[ outl9$ ! problem ( social control ov] robot ma*9es1 suppos+ t human be+s 7 reasonable4 ,we h also discuss$ ! practical ob/acles t ob/ruct reasonable control4 ,x is n easy to ?9k ( any yet organiz$ gr\p ( p any:]e t w\ld h bo? ! /r5g? & ! vision ne$$ to solve ?is problem ?r\gh its own ef=ts4 ,= example1 a "p ( ! ,unit$ ,nations might h "s ( ! vision ne$$1 b x does n h ! p[]4 ,consequ5tly1 x is necess>y & desirable = individuals & gr\ps ev]y:]e to take ^u !mselves an add$ load ( social responsibility--j z !y t5d to d 9 "t ( w>4 ,p (t5 8want to d _! %>e40 ,?r\gh enc\ragem5t & education1 ! basic attitude ( a numb] ( p c conta9 m ( 8,?is is our bus9ess2 we h a responsibility = help+ to solve ?is problem40 ,we also ne$ public responsibility2 we ne$ a public body responsible = /udy1 education1 advice1 & "s measure ( control4 ,x might be some?+ l an ,atomic ,en]gy ,commission1 ,bact]ial ,def5se ,commission1 ,m5tal ,heal? ,commission1 & ,robot ,ma*9e ,commission1 all roll$ into "o4 ,:51 at la/1 !re is an effective gu>antee ( ! two elem5ts physical safety & adequate employm5t1 !n at la/ we %all all be free f ! ?reat ( ! robot ma*9e4 ,we c !n welcome ! robot ma*9e z our deliv]] f ! long h>d *ores ( _m c5turies4 ,supplem5t #a ,,words ,,& ,,ideas ,! purpose ( ?is book is to expla9 ma*9es t ?9k1 )\t us+ te*nical words any m ?an necess>y4 ,?is supplem5t is a digression4 ,its purposes are to consid] h[ to expla9 9 ?is way & to discuss ! attempt made 9 ?is book to a*ieve simple explanation4 ,,words ,,z ,,in/rum5ts ,,= ,,expla9+ ,words are ! *ief in/rum5ts we use = expla9+4 ,( c\rse1 _m o!r devices--pictures1 numb]s1 *>ts1 models1 etc4--are also us$2 b words are ! prime tools4 ,we d mo/ ( our expla9+ ) !m4 ,words1 h[ev]1 are n v good in/rum5ts4 ,l a /one arr[-head1 a ^w is a clumsy weapon4 ,9 ! fir/ place1 words mean diff]5t ?+s on diff]5t occasions4 ,! ^w 8l9e10 = example1 has m ?an fifty mean+s li/$ 9 a big diction>y4 ,h[ d we h&le ! puzzle ( _m mean+s8 ,z we gr[ old] we ga!r exp]i5ce & we develop a truly m>vel\s capacity to li/5 to a s5t5ce & !n fit ! words toge!r into a patt]n t makes s5se4 ,sometimes we notice ! "t lag :ile our bra9 hunts = ! mean+ ( a ^w we h he>d b n grasp$4 ,!n sudd5ly we guess ! ne$$ mean+1 :]eupon we grasp ! mean+ ( ! s5t5ce z a :ole 9 mu* ! same way z ! p>ts ( a puzzle click into place :5 solv$4 ,ano!r tr\ble ) words is t (t5 !re is no good way to tell someone :at a ^w means4 ,( c\rse1 if ! ^w d5otes a physical object1 we c %[ sev]al examples ( ! object & utt] ! ^w ea* "t4 ,9 fact1 sev]al good illu/rations ( a ^w d5ot+ a physical ?+ (t5 tell mo/ ( its mean+4 ,b ! re/ ( its mean+ we (t5 d n le>n = ye>s1 if ev]4 ,= in/ance1 two p w\ld m likely disagree ?an agree ab\t :at %\ld be call$ a 8rock0 & :at %\ld be call$ a 8/one10 if we %[$ !m two doz5 examples4 ,9 ! case ( words n d5ot+ physical objects1 l 8&10 8heat10 8responsibility10 we are worse (f4 ,we _c %[ some?+ & say1 8,t is a 40 ,! usual diction>y is ( "s help1 b x has a t5d5cy to tell u :at "s ^w ,a means by us+ ano!r ^w ,b1 & :5 we look up ! o!r ^w ,b we f9d ! ^w ,a giv5 z its mean+4 ,ma9ly1 h[ev]1 to det]m9e ! mean+s ( words1 we ga!r exp]i5ce3 we soak up words 9 our bra9s & sl[ly e/abli% _! mean+s4 ,we seem to use an unconsci\s reason+ process3 we notice h[ words are us$ toge!r 9 patt]ns1 & we conclude :at !y mu/ mean4 ,cle>ly1 !n1 words be+ clumsy in/rum5ts1 ! m exp]i5ce we h _h ) a ^w1 ! m likely we are to be able to use x1 "w ) x1 & und]/& x4 ,!re=e explanation %\ld be bas$ *iefly on words ) :i* we h _h ! mo/ exp]i5ce4 ,:at words are ^!8 ,!y w be ! well-kn[n words4 ,a great _m ( !m w be %ort4 ,,set ,,( ,,words ,,= ,,expla9+ ,n[ :at is ! set ( all ! words ne$$ to expla9 simply a te*nical subject l ma*9es t ?9k8 ,= we %all ne$ m words ?an j ! well-kn[n & %ort ones4 ,?is "q d\btless has _m answ]s2 b ! answ] us$ 9 ?is book 0 bas$ on ! foll[+ reason+4 ,9 a book devot$ to explanation1 !re w be a gr\p ( words 7#a7 t are suppos$ to be kn[n already or to be le>n$ :ile read+1 & 7#b7 t are us$ z build+ blocks 9 lat] explanation & def9itions4 ,suppose t we call ^! words ! words = expla9+4 ,!re are at lea/ ?ree gr\ps ( su* words3 ,gr\p #a4 ,words n specially def9$ t are s famili> t e read] w "k all ( !m2 = example1 8is10 8mu*10 8tell40 ,gr\p #b4 ,words n specially def9$ t are famili>1 b p]haps "s read] may n "k "s ( !m2 = example1 8alt]native10 8cont9u\s10 8indicator40 ,gr\p #c4 ,words t are n famili>1 t _m read]s are n expect$ to "k1 & t are specially def9$ & expla9$ 9 ! body ( ! book2 = example1 8abacus10 8trajectory10 8torque40 ,9 writ+ ?is book1 x 0 n h>d to keep track ( ! words 9 ! ?ird gr\p4 ,^! words are n[ li/$ 9 ! index1 toge!r ) ! page :]e !y are def9$ or expla9$4 7,! index1 ( c\rse1 also li/s phrases t are specially def9$47 ,b :at division %\ld be made betwe5 ! o!r two gr\ps8 ,a practical1 easy1 & cons]vative way to sep>ate mo/ words betwe5 ! fir/ & second gr\ps seem$ to be on ! basis ( numb] ( syllables4 ,all words ( "o syllable--if n specially def9$--7 put 9 ,gr\p #a4 ,also1 if a ^w became two syllables only because ( ! addition ( "o ( ! end+s 8-es10 8-ed10 8-+10 x 0 kept 9 ,gr\p #a1 = ^! end+s probably d n make a ^w any h>d] to und]/&4 ,9 addition1 !re 7 put into ,gr\p #a3 #a4 ,numb]s2 = example1 8#ahf1jjj02 8_/04 #b4 ,places3 8,philadelphia02 8,massa*usetts04 #c4 ,nations1 organizations1 p1 etc43 8,sw$i%02 8,bell04 #d4 ,ye>s & dates3 8,febru>y02 8#aidf04 #e4 ,names ( curr5t books or articles & _! au?ors4 ,( c\rse1 n all ^! words w\ld be famili> to e read] 7= example1 8,maya071 b 9 ! way !y occur1 !y are usually n puzzl+1 = we c tell f ! context j ab\t :at !y mu/ mean4 ,all rema9+ words = expla9+--*iefly1 words ( two or m syllables & n specially def9$--7 put 9 ,gr\p #b & 7 li/$ dur+ ! writ+ ( ?is book4 ,_m ,gr\p #b words1 ( c\rse1 w\ld be entirely famili> to e read]2 b ! li/ _h sev]al virtues4 ,no h>d words w\ld sudd5ly be sprung l a trap4 ,! same ^w w\ld be us$ = ! same idea4 ,e ^w ( two or m syllables 0 cont9ually *eck$3 is x ne$$8 c x be replac$ by a %ort] ^w8 ,x is p]haps rem>kable t !re 7 few] ?an #ahjj diff]5t words all[$ to /ay 9 ?is li/4 ,?is fact %\ld be a com=t to a read]1 z x 0 to ! au?or4 ,n[ !re are m words 9 ?is book ?an words = expla9+4 ,s we %all d well to recognize3 ,gr\p #d4 ,words t d n ne$ to be kn[n or le>n$ & t are n us$ 9 lat] explanation & def9itions4 ,^! words occur 9 ! book 9 su* a way t und]/&+ !m1 ?\gh helpful1 is n ess5tial4 ,"o subdivision ( ,gr\p #d are names t appe> j once 9 ! book1 z a k9d ( side rem>k1 = example1 8a *emical1 call$ acetyl*ol9e40 ,su* a "n w also appe> 9 ! index1 b x is n a ^w = expla9+4 ,ano!r subdivision ( ,gr\p #d are words occurr+ only 9 quotations4 ,= example1 9 ! quotation f ,frank5/e9 on page #aih1 a doz5 words appe> t occur n[h]e else 9 ! book1 includ+ 8daemon10 8dissoluble10 8maw10 8satiate40 ,cle>ly we w\ld de/roy ! entire flavor ( ! quotation if we *ang$ any ( ^! words 9 any way4 ,b only ! g5]al drift ( ! quotation is ne$$ = und]/&+ ! book1 & s ^! words are ,gr\p #d words4 ,9 ?is way ! ef=t to a*ieve simple explanation 9 ?is book proce$$4 ,b ev5 suppos+ t we c\ld rea* ! be/ set ( words = expla9+1 !re is m to be done4 ,h[ d we g f simple explanation to und]/&+8 ,,und]/&+ ,,ideas ,und]/&+ an idea is basically a /&>d process4 ,fir/1 we f9d ! "n ( ! idea1 a ^w or phrase t id5tifies x4 ,!n1 we collect true /atem5ts ab\t ! idea4 ,f9ally1 we practice us+ !m4 ,! m true /atem5ts we h ga!r$1 & ! m practice we h _h 9 apply+ !m1 ! m we und]/& ! idea4 ,= example1 d y und]/& z]o8 ,"h are "s true /atem5ts ab\t z]o4 #a4 ,z]o is a numb]4 #b4 ,x is ! numb] t c\nts none or no?+4 #c4 ,x is m>k$ #j 9 our usual num]al writ+4 #d4 ,! anci5t ,romans1 h[ev]1 _h no num]al = x4 ,app>5tly1 !y did n ?9k ( z]o z a numb]4 #e4 #j is :at y get :5 y take away #ag f #ag1 or :5 y subtract any numb] f itself4 #f4 ,if y add #j to #bc1 y get #bc2 & if y add #j to any numb]1 y get t numb] un*ang$4 #g4 ,if y subtract #j f #dh1 y get #dh2 & if y subtract #j f any numb]1 y get t numb] un*ang$4 #h4 ,if y multiply #j by #ga1 y get #j2 & if y multiply toge!r #j & any numb]1 y get #j4 #i4 ,usually y are n all[$ to divide by #j3 t is aga9/ ! rules ( ari?metic4 #aj4 ,b if y d1 & if y divide #ab by #j1 = example--& !re are times :5 ?is is n wrong--! result is call$ inf9ity & is m>k$ 1 a sign t is l an #h on its side4 ,?is is n all ! /ory ( z]o2 x is "o ( ! mo/ important ( numb]s4 ,b1 if y "k ^! /atem5ts ab\t z]o1 & h _h "s practice 9 apply+ !m1 y h a good und]/&+ ( z]o4 ,incid5tally1 a me*anical bra9 kn[s all ^! /atem5ts ab\t z]o & a few m2 !y mu/ be built into x4 ,= u to und]/& any idea1 !n1 we pursue ?ree aims3 #a4 ,we f9d out :at x is call$4 #b4 ,we collect true /atem5ts ab\t x4 #c4 ,we apply ^? /atem5ts--we use !m 9 situations4 ,we c d ?is ab\t any idea4 ,!re=e1 we c und]/& any idea1 & ! degree ( our und]/&+ increases z ! numb] ( true /atem5ts ma/]$ increases4 ,p]haps ?is seems to be a ra% claim4 ,( c\rse1 x may take a good deal ( "t to collect true /atem5ts ab\t _m ideas4 ,9 fact1 a sci5ti/ may sp5d ?irty ye>s ( 8 life try+ to f9d out f exp]im5t ! tru? or falsehood ( "o /atem5t1 ?\gh1 :5 he has succe$$1 ! fact c be swiftly told to o!rs4 ,also1 we all v>y 9 ! spe$1 p]sev]ance1 skill1 etc41 ) :i* we c collect true /atem5ts & apply !m4 ,besides1 "s ( u h n be5 taught well & h little fai? 9 our ability to c>ry out ?is process3 ?is is ! greate/ ob/acle ( all4 ,b1 !re is 9 reality no idea 9 ! field ( exi/+ sci5ce & k :i* y or ,i _c und]/&4 ,! road to und]/&+ lies cle> be=e u4 ,supplem5t #b ,,ma!matics ,9 ! c\rse ( our discussion ( ma*9es t ?9k1 we h _h to ref] )\t mu* explanation to a numb] ( ma!matical ideas4 ,! purpose ( ?is supplem5t is to expla9 a few ( ^! ideas a little m c>efully ?an seem$ easy to d 9 ! text &1 at ! end ( ! supplem5t1 to put d[n briefly "s additional notes = ref]5ce4 ,,devices ,,= ,,multiplication ,suppose t we h to multiply #cgb by #dfe4 ,) ! ord9>y s*ool me?od1 we write #dfe "u ! #cgb & proce$ ab\t z foll[s3 #e times #b is #aj1 put d[n ! #j & c>ry ! #a2 #e times #g is #ce1 #ce & #a is #cf1 put d[n ! #f & c>ry ! #c2 #e times #c is #ae1 #ae & #c is #ah1 put d[n ! #h & c>ry ! #a2 444 ,! me?od is bas$ ma9ly on a well-le>n$ subr\t9e ( cont9ually *ang+ /eps3 #a4 ,select a multiplic& digit4 #b4 ,select a multipli] digit4 #c4 ,ref] to ! multiplication table ) ^! digits4 #d4 ,obta9 ! value ( _! product1 call$ a p>tial product4 #e4 ,add ! prec$+ c>ry4 #f4 ,set d[n ! "r-h& digit4 #g4 ,c>ry ! left-h& digit4 ,we c1 h[ev]1 simplify ?is subr\t9e = a ma*9e by delay+ ! c>ry+4 ,we collect 9 "o place all ! "r-h& digits ( p>tial products1 collect 9 ano!r place all ! left-h& digits1 & delay all addition until ! end4 ,= example1 let u multiply #cgb by #dfe ) ?is me?od3 ,,"r-,,h& ,,left-,,h& ,,usual ,,me?od1 ,,digits ,,digits ,,= ,,comp>ison #cgb #cgb #cgb #dfe #dfe #dfe ------------ ------------ ------------ #eej #aca #ahfj #hbb #ada #bbcb #bhh #abj #adhh ---------- ---------- ------------ #cgegj #aceda #agbihj ,,f9al ,,addition #cgegj #aceda ---------------- #agbihj #cgegj is call$ ! "r-h& compon5t ( ! product4 ,x is conv5i5t to fill 9 ) #j ! space at ! end ( #aceda & to call #acedaj ! left-h& compon5t ( ! product4 ,?is process is call$ multiply+ by "r- & left-h& compon5ts4 ,x has ! great advantage t no c>ry+ is necess>y to complete any l9e ( ! orig9al multiplications4 ,"s comput+ ma*9es use ?is process4 ,built into ! h>dw>e ( ! ma*9e is a multiplication table up to #i #i4 ,! ma*9e1 !re=e1 c f9d automatically ! "r-h& digit & ! left-h& digit ( any p>tial product4 ,9 a comput+ ma*9e t uses ?is process1 all ! left-h& digits are automatically add$ 9 "o regi/]1 & all ! "r-h& digits are add$ 9 ano!r regi/]4 ,! only c>ry+ t is ne$$ is ! c>ry+ z ! "r-h& digits are accumulat$ & z ! left-h& digits are accumulat$4 ,at ! end ( ! multiplication1 "o ( ! regi/]s is automatically add$ into ! o!r1 giv+ ! product4 ,ano!r device us$ 9 comput+ ma*9es = multiply+ is to *ange ! multipli] into a set ( digits #j to #e t are ei!r positive or negative4 ,= example1 suppose t we want to multiply #hig by #ahb4 ,we note t #ahb equals #bjj m9us #bj plus #b1 & s we c write x z #bbb4 ,! m9us ov] ! #b m>ks x z a negative digit #b4 ,!n to multiply we h3 #hig #bbb -------- #agid - #agid #agid ------------ #afcbed ,! middle #agid is subtract$4 ,?is process is usually call$ %ort-cut multiplication4 ,ev]ybody discov]s ?is trick :5 he decides t multiply+ by #ii is too mu* "w1 t x is easi] to multiply by #ajj & subtract once4 ,,b9>y ,,or ,,two ,,numb]s ,we are well accu/om$ to decimal notation 9 :i* we use #aj decimal digits #j1 #a1 #b1 #c1 #d1 #e1 #f1 #g1 #h1 #i & write !m 9 comb9ations to designate decimal numb]s4 ,9 b9>y notation we use two b9>y digits #j1 #a & write !m 9 comb9ations to designate b9>y numb]s4 ,= example1 ! fir/ #ag numb]s1 f #j to #af 9 ! decimal notation1 correspond ) ! foll[+ numb]s 9 b9>y notation3 ,,decimal ,,b9>y ,,decimal ,,b9>y #j #j #a #a #i #ajja #b #aj #aj #ajaj #c #aa #aa #ajaa #d #ajj #ab #aajj #e #aja #ac #aaja #f #aaj #ad #aaaj #g #aaa #ae #aaaa #h #ajjj #af #ajjjj ,9 decimal notation1 #aja means "o times a hundr$1 no t5s1 & "o4 ,9 b9>y notation1 #aja means "o times f\r1 no twos1 & "o4 ,! successive digits 9 a decimal numb] f "r to left c\nt #a1 #aj1 #ajj1 #ajjj1 #ajjjj1 444--successive p[]s ( #aj 7= ?is t]m1 see ! end ( ?is supplem5t74 ,! successive digits 9 a b9>y numb] f "r to left c\nt #a1 #b1 #d1 #h1 #af1 444--p[]s ( #b4 ,! decimal notation is conv5i5t :5 equipm5t = comput+ has t5 positions1 l ! f+]s ( a man1 or ! positions ( a c\nt] :eel4 ,! b9>y notation is conv5i5t :5 equipm5t = comput+ has j two positions1 l 8yes0 or 8no10 or curr5t fl[+ or no curr5t fl[+4 ,addition1 subtraction1 multiplication1 & division c all be c>ri$ out unusually simply 9 b9>y notation4 ,! addition table is simple & consi/s only ( f\r entries4 #j #a ------------ #j #j #a #a #a #aj ,! multiplication table is also simple & conta9s only f\r entries4 #j #a ------------ #j #j #j #a #j #a ,suppose t we add 9 b9>y notation #aja & #ajja3 ,,b9>y ,,addition ,,*eck #aja #e #ajja #i ------------ ------ #aaaj #ad ,we proce$3 #a & #a is #aj2 write d[n #j & c>ry #a2 #j & #j is #j1 & #a to c>ry is #a2 & #a & #j is #a2 & !n we j copy ! la/ #a4 ,to *eck ?is we c conv]t to decimal & see t #aja is #e1 #ajja is #i1 & #aaaj is #ad1 & we c v]ify t #e & #i is #ad4 ,"o ( ! easie/ ways to subtract 9 b9>y notation is to add a ones complem5t 7t is1 ! analogue ( ! n9es complem5t7 & use end-ar\nd-c>ry 7= ^! two t]ms1 see ! end ( ?is supplem5t74 ,a ones complem5t c be writt5 d[n at sight by j putt+ #a = #j & #j = #a4 ,= example1 suppose t we subtract #aja f #aaaj3 ,,subtraction ,,by ,,direct ,,add+ ,,ones ,,subtraction ,,*eck ,,complem5t #aaaj #ad #aaaj - #aja -#e #ajaj ---------- -------- ------------ #ajja #i 7#a7ajjj #a ------------ #ajja ,multiplication 9 ! b9>y notation is simple4 ,x am\nts to 7#a7 add+ if ! multipli] digit is #a & n add+ if ! multipli] digit is #j1 & 7#b7 mov+ ov] or %ift+4 ,= example1 let u multiply #aaa by #aja3 ,,b9>y ,,multiplication ,,*eck #aaa #g #aja #e ------------ #aaa #aaa ------------ ------ #ajjjaa #ce ,! digit #a 9 ! #f? 7or n?7 b9>y place f ! "r 9 #ajjjaa /&s = #a times #b to ! #e? 7or n-#a ?7 p[]1 #b #b #b #b #b #cb4 ,! result #ajjjaa is translat$ into #cb plus #b plus #a1 :i* equals #ce & v]ifies4 ,division 9 ! b9>y notation is also simple4 ,x am\nts to 7#a7 subtract+ 7yield+ a quoti5t digit #a7 or n subtract+ 7yield+ a quoti5t digit #j71 & 7#b7 %ift+4 ,we nev] ne$ to try multiples ( ! divisor to f9d ! l>ge/ t c be subtract$ yet leave a positive rema9d]4 ,= example1 let u divide #ajaj 7#aj 9 decimal7 into #ajjjaaaj 7#adb 9 decimal73 #aaaj 7#ad 9 decimal7 -------------------- #ajaj7ajjjaaaj #ajaj ------------ #aaaa #ajaj ---------- #ajaa #ajaj ---------- #aj 7rema9d]1 #b 9 decimal7 ,9 decimal notation1 digits to ! "r ( ! decimal po9t c\nt p[]s ( 4 ,9 b9>y notation1 digits to ! "r ( ! b9>y po9t c\nt p[]s ( 3 1 1 1 _/4444 ,= example1 #j4ajaa equals _/1 or _/4 ,if we 7 accu/om$ to us+ b9>y numb]s1 all our ari?metic w\ld be v simple4 ,fur!rmore1 b9>y numb]s are 9 _m ways mu* bett] = calculat+ ma*9]y ?an any o!r numb]s4 ,! ma9 problem is conv]t+ numb]s f decimal notation to b9>y4 ,"o me?od dep5ds on /or+ ! p[]s ( #b 9 decimal notation4 ,! rule is3 subtract successively small] p[]s ( #b2 />t ) ! l>ge/ t c be subtract$1 & c\nt #a = ea* p[] t goes & #j = ea* p[] t does n4 ,= example1 #hf 9 decimal becomes #ajajaaj 9 b9>y3 #hf #fd #fd goes #a ------ #bb #cb does n g #j #af #af goes #a ------ #f #h does n g #j #d #d goes #a ------ #b #b goes #a #b #a does n g #j ------ #j ,x is a little tr\blesome to rememb] long s]ies ( #a's & #j's2 9 fact1 to write any numb] 9 b9>y notation takes ab\t #c times z mu* space z decimal notation4 ,= ?is reason we c sep>ate b9>y numb]s into triples beg9n+ at ! "r & label ea* triple z foll[s3 ,,triple ,,label #jjj #j #jja #a #jaj #b #jaa #c #ajj #d #aja #e #aaj #f #aaa #g ,= example1 #ajajaaj w\ld become #a #jaj #aaj or #abf4 ,?is notation is (t5 call$ octal notation1 because x is notation 9 ! scale ( eight4 ,,biqu9>y ,,or ,,two-,,five ,,numb]s ,ano!r k9d ( notation = numb]s is biqu9>y notation1 s call$ because x uses bo? #b's & #e's4 ,ess5tially ?is notation is v l ,roman num]als1 anci5t /yle4 ,by anci5t /yle we mean1 = example1 ,,viiii in/ead ( ,,ix4 ,9 ! foll[+ table we %[ ! fir/ two doz5 numb]s 9 decimal1 biqu9>y1 & anci5t ,roman notation3 ,,decimal ,,biqu9>y ,,roman #j #j #a #a ,i #b #b ,,ii #c #c ,,iii #d #d ,,iiii #e #aj ,v #f #aa ,,vi #g #ab ,,vii #h #ac ,,viii #i #ad ,,viiii #aj #ajj ,x #aa #aja ,,xi #ab #ajb ,,xii #ac #ajc ,,xiii #ad #ajd ,,xiiii #ae #aaj ,,xv #af #aaa ,,xvi #ag #aab ,,xvii #ah #aac ,,xviii #ai #aad ,,xviiii #bj #bjj ,,xx #ba #bja ,,xxi #bb #bjb ,,xxii #bc #bjc ,,xxiii ,! biqu9>y columns alt]nate 9 go+ f #j to #d & f #j to #a4 ,! digits f #j to #d are n *ang$4 ,! digits f #e to #i are *ang$ into #aj to #ad4 ,we see t ! biqu9>y digits are #j to #d 9 odd columns & #j1 #a 9 ev5 columns1 c\nt+ f ! "r4 ,?is is ! notation actually express$ by ! abacus4 ,! beads ( ! abacus %[ by _! positions gr\ps ( #b & #e 7see ,fig4 #a74 ,illu/ration3 ,,fig4 #a4 ,abacus & notations4 ,,"s ,,op]ations ,,( ,,algebra ,"o ( ! op]ations ( algebra t is important = a me*anical bra9 is approximation1 ! problem ( gett+ close to ! "r value ( a numb]4 ,take1 = example1 f9d+ squ>e root 7see ! end ( ?is supplem5t74 ,! ord9>y process taught 9 s*ool is r tr\blesome4 ,we c set d[n ano!r process1 h[ev]1 us+ a desk calculator to d division1 :i* gives u squ>e root ) great spe$4 ,suppose t we want to f9d ! squ>e root ( a numb] ,n1 & suppose t we h x z a guess$ squ>e root correct to "o figure4 ,= example1 ,n might be #fg4b & x might be #h1 *os5 because #h #h is #fd1 & #i #i is #ha1 & x seems z if #h %\ld be ne> ! squ>e root ( #fg4b4 ,"h is ! process3 #a4 ,divide x into ,n1 & obta9 ,n_/x4 #b4 ,multiply x ,n_/x by #j4e & call ! result x4 ,n[ repeat3 #a4 ,divide x into ,n & obta9 ,n_/x4 #b4 ,multiply x ,n_/x by #j4e & call ! result x4 ,e "t ?is process is repeat$1 ! new x comes a great deal clos] to ! correct squ>e root4 ,9 fact x c be %[n t1 if x is correct to "o figure1 !n3 ,,approximation ,,is ,,correct ,,to ,,figures x #b x #d x #h x #af ,let u see h[ ?is actually works out ) #fg4b & a #aj-;column desk calculator4 ,r\nd #a3 #h divid$ into #fg4b gives #h4d4 ,"o half ( #h plus #h4d is #h4b4 ,?is is x4 ,r\nd #b3 #h4b divid$ into #fg4b gives #h4aieabb4 ,"o half ( #h4b plus #h4aieabb is #h4aigefa4 ,?is is x4 ,r\nd #c3 #h4aigefa divid$ into #fg4b gives #h4aigefjbbe4 ,"o half ( #h4aigefa & #h4aigefjbbe is #h4aigefjfabe4 ,?is is x4 ,*eck+ x1 we f9d t #h4aigefjfabe divid$ into #fg4b gives #h4aigefjfabf approximately4 ,9 ?is case1 !n1 x is correct to m ?an #aj figures4 ,9 o!r words1 ) a reasonable guess & two or ?ree divisions we c obta9 all ! accuracy we c ord9>ily use4 ,?is process is call$ rapid approximation1 or rapidly conv]g5t approximation1 s9ce x conv]ges 7po9ts or comes toge!r7 v quickly to ! numb] we are seek+4 ,ano!r important op]ation ( algebra is int]polation1 ! problem ( putt+ values smoo?ly 9 betwe5 o!r values4 ,= example1 suppose t we h ! table3 x y #e #bf #f #cg #g #ej #h #fe #i #hb ,suppose t we want to f9d ! value t y 7or y7 ought to h :5 x has ! value ( #g4b4 ,?is is ! problem ( int]polat+ y s z to f9d y at ! value ( #g4b1 y4 ,"o way ( do+ ?is is to discov] ! =mula t expresses y & !n to put x into t =mula4 ,?is is n always easy4 ,ano!r way is to take ! diff]5ce betwe5 y & y1 #ae1 & %>e ! diff]5ce appropriately ov] ! di/ance #g to #g4b & #g4b to #h4 ,we c1 = example1 take _/ ( #ae #c1 add t to y #ej1 & obta9 an e/imat$ y #ec4 ,?is is call$ l9e> int]polation1 s9ce ! diff]5ce #j4b 9 ! value ( x is us$ only to ! fir/ p[]4 ,x is a good practical way to c>ry out mo/ int]polation quickly & approximately4 ,actually "h y x #a1 & s ! true value ( y is 7#g4b #g4b7 #a1 or #eb4hd1 :i* is r close to #ec4 ,types ( int]polation proc$ures m accurate ?an l9e> int]polation w come mu* ne>] /ill to ! true value4 ,,algebra ,,( ,,logic ,we turn n[ to ! algebra ( logic4 ,! fir/ half ( ,*apt] #i1 8,reason+0 7?r\gh ! section 8,logical-,tru? ,calculation by ,algebra071 introduces ?is subject4 ,!re ! t]ms tru? values1 tru? tables1 logical connectives1 & algebra ( logic are expla9$4 ,! "p ( ,*apt] #c1 8,a ,ma*9e ,t ,w ,?9k10 t discusses ! op]ations great]-?an & selection1 also expla9s "s ( ! algebra ( logic4 ,x introduces1 = example1 ! =mula p ,t7a b7 #a1 #j ,?is is a way ( say+ briefly t ! tru? value ( ! /atem5t 8a is great] ?an b0 equals p2 p is #a if ! /atem5t is true & #j if ! /atem5t is false4 ,! tru? value #a corresponds ) 8yes40 ,! tru? value #j corresponds ) 8no40 ,) me*anical bra9s we are especially int]e/$ 9 h&l+ ma!matics & logic )\t any %>p divid+ l9e betwe5 !m4 ,= example1 suppose t we h a regi/] 9 :i* a t5-digit numb] l #a1gfe1dch1hij may be /or$4 ,we %\ld be able to use t regi/] to /ore a numb] consi/+ ( only #a's & #j's1 l #a1ajj1ajj1jaj4 ,su* a numb] may designate ! answ]s to #aj successive que/ions3 yes1 yes1 no1 no1 yes1 no1 no1 no1 yes1 no4 ,or x may tell #aj successive b9>y digits4 ,! regi/] !n is ?ree times z useful3 x c /ore ei!r decimal numb]s or tru? values or b9>y digits4 ,we ne$1 ( c\rse1 a way to obta9 f ! regi/] any desir$ digit4 ,= ?is purpose we may h two in/ructions to ! ma*9e3 7#a7 read ! left-h& end digit2 7#b7 %ift ! numb] ar\nd 9 a circle4 ,! second in/ruction is ! same z multiply+ by #aj & !n putt+ ! left-mo/ digit at ! "r-h& end4 ,= example1 suppose t we want ! #crd digit f ! left 9 #a1ajj1ajj1jaj4 ,! result ( ! fir/ circul> %ift is #a1jja1jjj1aja2 ! result ( ! second circul> %ift is #j1jaj1jja1jaa2 & read+ ! left-mo/ digit gives #j4 ,a process l ?is has be5 call$ extraction & is be+ built into ! newe/ me*anical bra9s4 ,us+ tru? values1 we c put d[n v neatly "s tru?s ( ord9>y algebra4 ,= example3 7! absolute value ( a7 a 7! tru? ( a great] ?an or equal to #j7 - a 7! tru? ( a less ?an #j7 a a ,t7a #j7 - a ,t7a #j7 ,= ano!r example3 ,ei!r a is great] ?an b1 or else a equals b1 or else a is less ?an b ,t7a b7 ,t7a b7 ,t7a b7 #a ,_m common logical op]ations1 l select+ & comp>+1 & ! behavior ( _m simple me*anisms1 l a light or a lock1 c be express$ by tru? values4 ,*apt] #d1 on pun*-c>d me*anisms1 conta9s a numb] ( examples4 99 99 99 99 99 pron\n1 v>iable ,9 ord9>y language1 a pron\n1 l 8he10 8%e10 8x10 8! =m]10 8! latt]10 is a ^w t usually /&s = a n\n previ\sly ref]r$ to4 ,a pron\n usually /&s = ! la/ prec$+ n\n t ! gramm> all[s4 ,9 ma!matics1 a v>iable1 l 8a10 8b10 8x10 8m10 8m0 closely resembles a pron\n 9 ord9>y language4 ,a v>iable is a symbol t usually /&s = a numb] previ\sly ref]r$ to1 & usually x /&s = ! same numb] ?r\gh\t a p>ticul> discussion4 multiplic&1 divid5d1 aug5d1 etc4 ,,9 ,,! ,,! ,,"n ,,! ,,"n ,,! ,,"n ,,equation3 ,,( a ,,is3 ,,( b ,,is3 ,,( c ,,is3 a b c aug5d add5d sum a - b c m9u5d subtrah5d rema9d] a b c multiplic& multipli] product a b c divid5d divisor quoti5t ,aug5d & add5d are names ( regi/]s 9 ! ,h>v>d ,m>k ,,ii calculator 7see ,*apt] #aj74 subtraction by add+1 n9es complem5t ,two digits t add to #i 7#j & #i1 #a & #h1 #b & #g1 #c & #f1 #d & #e7 are call$ n9es complem5ts ( ea* o!r4 ,! n9es complem5t ( a numb] a is ! numb] b 9 :i* ea* digit ( b is ! n9es complem5t ( ! correspond+ digit ( a2 = example1 ! n9es complem5t ( #agc is #hbf4 ,ord9>y subtraction is ! same z addition z ( ! n9es complem5t1 ) a simple correction2 = example1 #efb less #agc 7equal to #chi7 is ! same z #efb plus #hbf 7equal to #achh7 less #ajjj plus #a4 end-ar\nd-c>ry ,! correction 8less #ajjj plus #a0 ( ! =ego+ example may be ?\ght ( z c>ry+ ! #a 79 ! result #achh7 ar\nd f ! left-h& end to ! "r-h& end1 :]e x is !re add$4 ,s ! #a is call$ end-ar\nd-c>ry4 t5s complem5t ,two digits t add to #aj are call$ t5s complem5ts ( ea* o!r4 ,! t5s complem5t ( a numb] a1 h[ev]1 is equal to ! n9es complem5t ( ! numb] plus #a4 ,= example1 ! t5s complem5t ( #agc is #hbg4 ,:5 subtract+ by add+ a t5s complem5t1 ! left-mo/ digit #a 9 ! result is dropp$4 ,= example1 #efb less #agc 7equal to #chi7 is ! same z #efb plus #hbg 7equal to #achi7 less #ajjj4 p[]1 squ>e1 cube1 reciprocal1 etc4 ,a p[] ( any numb] a is a multipli$ by itself "s numb] ( times4 a a a 444 a :]e a appe>s b times is writt5 a & is read a to ! b? p[]4 a1 a to ! #bnd p[]1 is a a & is call$ a squ>$ or ! squ>e ( a4 a1 a to ! #crd p[]1 a a a1 is call$ a cub$1 or ! cube ( a4 a1 a to ! z]o p[]1 is equal to #a = e a4 a1 a to ! p[] #a1 is a itself4 ,! fir/ p[] is (t5 call$ l9e>4 a to "s negative p[] is ! same z #a divid$ by t p[]2 t is1 a #a_/;a4 a1 a to ! p[] m9us #a1 is #a_/;a1 & is call$ ! reciprocal ( a4 a1 a to ! "o-half p[]1 is a numb] c su* t c c a1 & is call$ ! squ>e root ( a & (t5 d5ot$ by a4 table1 tabul> value1 argum5t1 etc4 ,an example ( a table is3 #j4jbe #j4jc ------------------------------------ #a #a4jbejj #a4jcjjj #b #a4jejfc #a4jfjij #c #a4jgfhi #a4jibgc ,! numb]s 9 ! body ( ! table1 call$ tabul> values1 dep5d on or are det]m9$ by ! numb]s along ! edge ( ! table1 call$ argum5ts4 ,9 ?is example1 if #a1 #b1 #c are *oices ( a numb] n1 & if #j4jbe1 #j4jc are *oices ( a numb] i1 !n ea* tabul> value y is equal to #a plus i rais$ to ! n? p[]4 n & i are also call$ indep5d5t v>iables1 & y is call$ ! dep5d5t v>iable4 ,! table expresses a function or =mula or rule4 ,! rule c\ld be /at$ z3 add i to #a2 raise ! result to ! n? p[]4 con/ant ,a numb] is said to be a con/ant if x has ! same value "u all conditions4 ,= example1 9 ! =mula3 7area ( a circle7 7radius71 is a con/ant1 equal to #c4adaei 4441 apply+ equally well to all circles4 inf9ity ,ma!matics recognizes sev]al k9ds ( inf9ity4 ,"o ( !m occurs :5 numb]s become v l>ge4 ,= example1 ! quoti5t ( #ab divid$ by a numb] x1 z x becomes clos] & clos] to #j1 becomes indef9itely l>ge1 & ! limit is call$ inf9ity & is d5ot$ 4 equation1 simultane\s1 l9e> ,an example ( two l9e> simultane\s equations is3 #gx #ht #bb #cx #et #aa x & t are call$ unkn[ns--t is1 unkn[n v>iables--because ! objective ( solv+ ! equations is to f9d !m4 ,^! equations are call$ simultane\s because !y are to be solv$ toge!r1 at ! same "t1 = values ( x & t :i* w fit 9 bo? equations4 ,! equations are call$ l9e> because ! only p[]s ( ! unkn[ns t appe> are ! fir/ p[]4 ,values t solve equations are said to satisfy !m4 ,x is easy to solve ^! two equations & f9d t x #b & t #a is _! solution4 ,b x is a long process to solve #aj l9e> simultane\s equations 9 #aj unkn[ns1 & x is almo/ impossible 7)\t us+ a me*anical bra97 to solve #ajj l9e> simultane\s equations 9 #ajj unkn[ns4 d]ivative1 integral1 diff]5tial equation1 etc4 ,see ! sections 9 ,*apt] #e entitl$ 8,diff]5tial ,equations10 8,physical ,problems10 & 8,solv+ ,physical ,problems40 ,!re ^! ideas &1 to "s ext5t1 also ! foll[+ ideas 7 expla9$3 =mula1 equation1 function1 diff]5tial function1 in/antane\s rate ( *ange1 int]val1 inv]se1 integrat+4 ,see also a textbook on calculus4 ,if y is a function ( x1 !n a ma!matical symbol = ! d]ivative ( y ) respect to x is ,d y1 & a symbol = ! integral ( y ) respect to x1 is y dx4 ,an integral ) giv5 initial conditions 7see p4 #hc7 is a def9ite integral4 expon5tial ,a fam\s ma!matical function is ! expon5tial4 ,x equals ! con/ant e rais$ to ! x p[]1 e1 :]e e equals #b4gahbh4444 ,! expon5tial lies betwe5 ! p[]s ( #b & ! p[]s ( #c4 ,x c be comput$ f3 x x e #a x ------------ ------------------ 444 #a #b #a #b #c ,x is a solution ( ! diff]5tial equation ,dy y4 ,see also a textbook on calculus4 ,! expon5tial to ! base #aj is #aj4 log>i?m ,ano!r important ma!matical function is ! log>i?m4 ,x is writt5 log x or log x & c be comput$ f ! two equations3 log uv log u log v x x log7#a x7 x - ------------ ------------ - 4441 x #a #b #c ,x is a solution ( ! diff]5tial equation ,dy #a_/y4 ,if y is ! log>i?m ( x1 !n x is ! antilog>i?m ( y4 ,! log>i?m to ! base #aj ( x1 log x1 equals ! log>i?m to ! base e ( x1 log x1 divid$ by log #aj4 ,see also textbooks on algebra & calculus4 s9e1 cos9e1 tang5t1 antitang5t ,^! also are important ma!matical functions4 ,! s9e & cos9e are solutions ( ! diff]5tial equation ,d7,dy7 -y & are writt5 z s9 x & cos x4 ,!y c be comput$ f x x s9 x x - ------------ ------------------ - 444 #abc #abcde x x cos x #a - ------------ ------------ - 444 #ab #abcd ,! tang5t ( x is simply s9e ( x divid$ by cos9e ( x4 ,if y is ! tang5t ( x1 !n x is ! antitang5t ( y4 ,see also ref]5ces on trigonometry & on calculus4 ,trigonometric tables include s9e1 cos9e1 tang5t1 & relat$ functions4 ,bessel functions ,^! are ma!matical functions t 7 nam$ aft] ,fri$ri* ,w4 ,bessel1 a ,prussian a/ronom] :o liv$ f #aghd to #ahdf4 ,bessel functions are f\nd z "s ( ! solutions ( ! diff]5tial equation x ,d7,dy7 x ,dy 7x - n7y ,o ,?is equation arises 9 a numb] ( physical problems 9 ! fields ( electricity1 s\nd1 heat fl[1 air fl[1 etc4 matrix ,a matrix is a table 7or array7 ( numb]s 9 r[s & columns1 = :i* addition1 multiplication1 etc41 ) simil> tables is specially def9$4 ,= example1 ! matrix #a #b #c #d plus ! matrix #e #bj #fj #ajj equals ! matrix #f #bb #fc #ajd4 7,c y guess ! rule def9+ addition87 ,calculations us+ matrices are useful 9 physics1 eng9e]+1 psy*ology1 /ati/ics1 etc4 ,to add a squ>e matrix ( #ajj t]ms 9 an array ( #aj columns & #aj r[s to ano!r su* matrix1 #ajj ord9>y additions ( numb]s are ne$$4 ,to multiply "o su* matrix by ano!r1 #ajjj ord9>y multiplications & #ijj ord9>y additions are ne$$4 ,see ref]5ces on matrix algebra & matrix calculus4 diff]5ces1 smoo?ness1 *eck+ ,on p4 #bba1 a sequ5ce ( values ( y is %[n3 #bf1 #cg1 #ej1 #fe1 #hb4 ,suppose1 h[ev]1 ! second value ( y 0 report$ z #dg in/ead ( #cg4 ,!n ! diff]5ces ( y z we pass d[n ! sequ5ce w\ld n be #aa1 #ac1 #ae1 #ag 7:i* is c]ta9ly regul> or smoo?7 b #ba1 #c1 #ae1 #ag 7:i* is c]ta9ly n smoo?74 ,! second set ( diff]5ces w\ld /rongly sugge/ a mi/ake 9 ! report+ ( y4 ,! smoo?ness ( diff]5ces is (t5 a useful *eck on a sequ5ce ( report$ values4 ,supplem5t #c ,,ref]5ces ,a book l ! pres5t "o c cov] only a "p ( ! subject ( ma*9es t ?9k4 ,to obta9 m in=mation ab\t ^! ma*9es & o!r topics to :i* !y are relat$ !re are _m ref]5ces t may be consult$4 ,!re are /ill few books directly on ! subject ( ma*9es t ?9k1 b !re are _m articles & pap]s1 mo/ ( !m r specializ$4 ,! purpose ( ?is supplem5t is to give a numb] ( ^! ref]5ces & to provide a brief1 g5]al introduction to "s ( !m4 ,! ref]5ces are subdivid$ into gr\ps1 ea* deal+ ) a bran* ( ! subject4 ,! ref]5ces 9 ea* gr\p are 9 alphabetical ord] by "n ( au?or 7) 8anonym\s0 la/71 & "u ea* au?or !y are 9 *ronological ord] by publication date4 ,"s publications1 especially a =um or symposium1 are li/$ m ?an once1 accord+ z ! topic discuss$ falls 9 diff]5t gr\ps4 ,9 ?is supplem5t1 ! sign ?ree dots 7 4447 next to ! page numb]s = an article indicates t ! article is cont9u$ on lat]1 nonconsecutive pages4 ,x seem$ undesirable to try to make ! gr\p ( ref]5ces deal+ ) a subject absolutely complete1 s long z en\gh 7 giv5 to provide a good introduction to ! subject4 ,x prov$ impractical to try to make ! citation ( e s+le ref]5ce te*nically complete1 s long z en\gh citation 0 giv5 s t ! ref]5ce c\ld c]ta9ly be f\nd4 ,fur!rmore1 9 a li/ ( m ?an #bej ref]5ces1 errors are almo/ c]ta9 to occur4 ,if any read] %\ld s5d me additions or corrections1 ,i %all be m ?an grateful4 ,,! ,,human ,,bra9 ,no "o yet kn[s specifically h[ p>ticul> ideas are ?\ght ab\t 9 ! human bra94 ,! ref]5ces li/$ 9 ?is section1 h[ev]1 conta9 "s in=mation ab\t su* topics z3 ,! /ructural diff]5ces1 developm5t1 & evolution ( ! bra9s ( animals1 apes1 primitive man1 & mod]n man4 ,! effect on ! bra9 ( blood composition1 body temp]ature1 supply ( oxyg51 & o!r bio*emical factors4 ,! /ructure & physiology ( ! bra91 ! n]v\s sy/em1 & n]ve impulses4 ,! !ory ( le>n+1 intellig5ce1 & memory4 ,,b>cr(t1 ,,joseph1 ,! ,bra9 & ,its ,environm5t1 ,new ,hav53 ,yale ,univ]sity ,press1 #aidh1 #aag pp4 ,,bea*1 ,,frank ,a41 ,payday = ,primates1 ,natural ,hi/ory1 vol4 #ef1 no4 #aj1 ,dec4 #aidg1 pp4 #ddh-dea4 ,,bea*1 ,,frank ,a41 ,c ,animals ,reason8 ,natural ,hi/ory1 vol4 #eg1 no4 #c1 ,m>4 #aidh1 pp4 #aab-aaf 444 ,,b]ry1 ,r4 ,j4 ,a41 ,bra9 & ,m9d1 or ! ,n]v\s ,sy/em ( ,man1 ,new ,york3 ,! ,macmillan ,co41 #aibh1 #fjh pp4 ,,bor+1 ,,edw9 ,g41 ,a ,hi/ory ( ,exp]im5tal ,psy*ology1 ,new ,york3 ,c5tury ,co41 #aibi1 #fii pp4 ,,franz1 ,,%eph]d ,i41 ,! ,evolution ( an ,idea2 ,h[ ! ,bra9 ,works1 ,los ,angeles3 ,univ]sity ( ,cali=nia1 #aibi1 #ce pp4 ,,h]rick1 ,c4 ,,judson1 ,! ,?9k+ ,ma*9e1 ,*icago3 ,univ]sity ( ,*icago ,press1 #aibi1 #cgd pp4 ,,h]rick1 ,c4 ,,judson1 ,bra9s ( ,rats & ,m51 ,*icago3 ,univ]sity ( ,*icago ,press1 #aicj1 #chb pp4 ,,la%ley1 ,,k>l ,s41 ,bra9 ,me*anisms & ,intellig5ce1 ,*icago3 ,univ]sity ( ,*icago ,press1 #aibi1 #ahf pp4 ,,pi]on1 ,,h5ri1 ,?\ght & ! ,bra91 ,london3 ,kegan1 ,paul1 ,tr5*1 ,trbn] ,co41 #aibg1 #bfb pp4 ,also ,new ,york3 ,h>c\rt1 ,brace ,co4 ,,s*r,,d+]1 ,,erw91 ,:at is ,life81 ,new ,york3 ,! ,macmillan ,co41 #aide1 #ij pp4 ,,%]r+ton1 ,,*>les ,s41 ,! ,bra9 & ,its ,me*anism1 ,cambridge1 ,engl&3 ,! ,univ]sity ,press1 #aicc1 #ce pp4 ,,tilney1 ,,fr$]ick1 ,! ,bra9 f ,ape to ,man1 ,new ,york3 ,p4 ,b4 ,hoeb]1 ,inc41 #aibh1 #b vol41 #ajge pp4 ,,wi5]1 ,,norb]t1 ,cyb]netics1 or ,control & ,communication 9 ! ,animal & ! ,ma*9e1 ,new ,york3 ,john ,wiley ,sons1 #aidh1 #aid pp4 ,,anonym\s1 ,t5 ,billion ,relays1 ,"t1 ,feb4 #ad1 #aidi1 p4 #fg4 ,,ma!matical ,,biophysics ,!re has rec5tly be5 ano!r approa* to ! problem3 ,h[ does a bra9 ?9k8 ,a gr\p ( m51 _m ( !m 9 & ne> ,*icago1 h be5 say+3 8,we "k ! prop]ties ( n]ves1 n]ve impulses1 & simple n]ve networks4 ,we "k ! activity ( ! bra94 ,:at ma!matical model ( n]ve networks is necess>y to acc\nt = ! activity ( ! bra980 ,^! m5 h us$ ma!matics1 /ati/ics1 & ma!matical logic 9 ! ef=t to attack ?is problem1 & !y support a ,bullet9 ( ,ma!matical ,biophysics4 ,,h\sehold]1 ,,al/on ,s41 ,a ,neural ,me*anism = ,discrim9ation1 ,psy*ometrika1 vol4 #d1 no4 #a1 ,dec4 #aici1 pp4 #de-eh4 ,,h\sehold]1 ,,al/on ,s41 & ,h]b]t ,d4 ,l&ahl1 ,ma!matical ,biophysics ( ! ,c5tral ,n]v\s ,sy/em1 ,bloom+ton1 ,ind43 ,pr9cipia ,press1 #aide4 ,,l&ahl1 ,,h]b]t ,d41 ,contributions to ! ,ma!matical ,biophysics ( ! ,c5tral ,n]v\s ,sy/em1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #a1 no4 #b1 ,june #aici1 pp4 #ie-aah4 ,,l&ahl1 ,,h]b]t ,d41 ,,w>r5 ,s4 ,,mccullo*1 & ,,walt] ,,pitts1 ,a ,/ati/ical ,consequ5ce ( ! ,logical ,calculus ( ,n]v\s ,nets1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #e1 no4 #d1 ,dec4 #aidc1 pp4 #ace-acg4 ,,l&ahl1 ,,h]b]t ,d41 ,a ,note on ! ,ma!matical ,biophysics ( ,c5tral ,excitation & ,inhibition1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #g1 no4 #d1 ,dec4 #aide1 pp4 #bai-bba4 ,,lettv91 ,,j]ome ,y41 & ,,walt] ,,pitts1 ,a ,ma!matical ,!ory ( ! ,affective ,psy*oses1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #e1 no4 #d1 ,dec4 #aidc1 pp4 #aci-adh4 ,,mccullo*1 ,,w>r5 ,s41 & ,,walt] ,,pitts1 ,a ,logical ,calculus ( ! ,ideas ,imman5t 9 ,n]v\s ,activity1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #e1 no4 #d1 ,dec4 #aidc1 pp4 #aae-acc4 ,,ra%evsky1 ,n41 ,ma!matical ,biophysics1 ,*icago3 ,univ]sity ( ,*icago ,press4 ,revis$ edition1 #aidh1 #ffi pp4 ,,ra%evsky1 ,n41 ,ma!matical ,biophysics ( ,ab/raction & ,logical ,?9k+1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #g1 no4 #c1 ,sept4 #aide1 pp4 #acc-adh4 ,,ra%evsky1 ,n41 ,"s ,rem>ks on ! ,boolean ,algebra ( ,n]v\s ,nets 9 ,ma!matical ,biophysics1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #g1 no4 #d1 ,dec4 #aide1 pp4 #bjc-baa4 ,,ra%evsky1 ,n41 ,a ,sugge/ion = ,ano!r ,/ati/ical ,int]pretation ( ! ,fundam5tal ,equations ( ! ,ma!matical ,biophysics ( ! ,c5tral ,n]v\s ,sy/em1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #g1 no4 #d1 ,dec4 #aide1 pp4 #bbc-bbf4 ,,ra%evsky1 ,n41 ,! ,neural ,me*anism ( ,logical ,?9k+1 ,bullet9 ( ,ma!matical ,biophysics1 vol4 #h1 no4 #a1 ,m>4 #aidf1 pp4 #bi-dj4 ,,languages3 ,,words ,,& ,,symbols ,,= ,,?9k+ ,h>dly any field ( te*niques = ?9k+ is m fasc9at+ ?an language4 ,! foll[+ li/ ( ref]5ces1 ( c\rse1 is %ort2 x is meant *iefly z an introduction po9t+ out a numb] ( diff]5t pa?s into ! field ( language & languages4 ,su* topics z ! foll[+ are introduc$ by ! ref]5ces 9 ?is li/3 ,! orig9 ( languages & alphabets4 ,! languages ( ! _w1 & spee* communities4 ,! comp>ison ( words & /ructure f language to language4 ,! significance ( gramm> & syntax4 ,! problem ( cle> mean+s4 ,writ+ & speak+ t is easy to und]/&4 ,,bloomfield1 ,,leon>d1 ,language1 ,new ,york3 ,h5ry ,holt ,co41 #aicc1 #efd pp4 ,,bodm]1 ,,fr$]ick1 & ,,launcelot ,,hogb51 ,! ,loom ( ,language1 ,new ,york3 ,w4 ,w4 ,norton ,co41 #aidd1 #fib pp4 ,,fles*1 ,,rudolf1 ,! ,art ( ,pla9 ,talk1 ,new ,york3 ,h>p] ,bro!rs1 #aidf1 #baj pp4 ,,graff1 ,,willem ,l41 ,language & ,languages3 ,an ,introduction to ,l+ui/ics1 ,new ,york3 ,d4 ,appleton ,co41 #aicb1 #dhg pp4 ,,hayakawa1 ,s4 ,i41 ,language 9 ,action1 ,new ,york3 ,h>c\rt1 ,brace ,co41 #aida1 #cde pp4 ,,jesp]s51 ,,otto1 ,! ,philosophy ( ,gramm>1 ,new ,york3 ,h5ry ,holt ,co41 #aibi 7?ird pr9t+71 #cei pp4 ,,jesp]s51 ,,otto1 ,analytic ,syntax1 ,9 ?is book1 by means ( a well-contriv$ sy/em ( lett]s & signs1 ! great l+ui/ic s*ol> ,jesp]s5 depicts all ! important int]-relations ( ,engli% words & p>ts ( words 9 connect$ spee*4 ,,ogd51 ,c4 ,k41 ,! ,sy/em ( ,basic ,engli%1 ,new ,york3 ,h>c\rt1 ,brace ,co41 #aicd1 #cbj pp4 ,,s*lau*1 ,,m>g>et1 ,! ,gift ( ,tongues1 ,new ,york3 ,mod]n ,age ,books1 #aidb1 #cdb pp4 ,,walpole1 ,,hugh ,r41 ,semantics3 ,! ,nature ( ,words & ,_! ,mean+s1 ,new ,york3 ,w4 ,w4 ,norton ,co41 #aida1 #bfd pp4 ,,languages3 ,,ma*9es ,,= ,,?9k+ ,= _m ye>s1 ne>ly all ref]5ces ab\t ma*9es z a language = ?9k+ h be5 specializ$ & limit$4 ,colleges ) s*ol>s :o write textbooks usually h n _h a v>iety ( exp5sive & v]satile comput+ ma*9]y4 ,z a result1 ! ma9 environm5t = /imulat+ possible au?ors has until rec5tly be5 miss+4 ,! li/ ( ref]5ces is accord+ly brief4 ,,aik51 ,,h[>d ,h41 & o!rs1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 #cjb pp4 ,,comrie1 ,,john ,,leslie1 ,! ,application ( ,comm]cial ,calculat+ ,ma*9es to ,sci5tific ,comput+1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #b1 no4 #af1 ,oct4 #aidf1 pp4 #adi-aei4 ,,crew1 ,e4 ,w41 ,calculat+ ,ma*9es1 ,! ,eng9e]1 vol4 #agb1 ,dec4 #aida1 pp4 #dch-dda4 ,,fry1 ,,macon1 ,design+ ,comput+ ,me*anisms1 ,clevel&1 ,ohio3 ,p5ton ,publi%+ ,co41 #aidf1 #dh pp4 7,repr9t$ f ,ma*9e ,design1 ,aug4 #aide ?r\gh ,feb4 #aidf47 ,,h>tree1 ,d4 ,r41 ,calculat+ ,ma*9es3 ,rec5t & ,prospective ,developm5ts & ,_! ,impact on ,ma!matical ,physics1 ,cambridge1 ,engl&3 ,! ,univ]sity ,press1 #aidg1 #dj pp4 ,,horsburgh1 ,e4 ,h41 ,mod]n ,in/rum5ts & ,me?ods ( ,calculation1 ,london3 ,g4 ,bell & ,sons1 ,ltd41 #aiad1 #cdc pp4 ,,lilley1 ,s41 ,ma!matical ,ma*9es1 ,nature1 vol4 #adi1 ,apr4 #be1 #aidb1 pp4 #dfb-dfe4 ,,murray1 ,,francis ,j41 ,! ,!ory ( ,ma!matical ,ma*9es1 ,new ,york3 ,k+'s ,cr[n ,press1 #aidg1 #aaf pp4 ,! au?or /ates t a ma!matical ma*9e is a me*anism t provides in=mation conc]n+ ! relation%ips among a specifi$ set ( ma!matical concepts4 ,,turck1 ,j4 ,a4 ,v41 ,! ,orig9 ( ,mod]n ,calculat+ ,ma*9es1 ,*icago3 ,we/]n ,society ( ,eng9e]s1 #aiba4 ,rec5tly1 h[ev]1 "s magaz9e & newspap] publi%]s h se5 news value 9 ma*9es t ?9k1 & "s good g5]al articles ) appeal to a wide audi5ce h appe>$4 ,= ! ref]5ces to ^! articles1 see ! section ( ?is supplem5t entitl$ 8,digital ,ma*9es--,miscellane\s40 ,,pun*-,,c>d ,,calculat+ ,,ma*9es ,!re are a few g5]al ref]5ces on pun*-c>d calculat+ ma*9es3 ,,baehne1 ,g4 ,,walt]1 editor1 & o!rs1 ,practical ,applications ( ! ,pun*$ ,c>d ,me?od 9 ,colleges & ,univ]sities1 ,new ,york3 ,columbia ,univ]sity ,press1 #aice1 #ddb pp4 ,?is is a collection ( _m contributions f a numb] ( au?ors1 describ+ v>i\s applications1 *iefly educational4 ,,eck]t1 ,w4 ,j41 ,pun*$-,c>d ,me?ods 9 ,sci5tific ,computation1 ,new ,york3 ,columbia ,univ]sity1 ,! ,?omas ,j4 ,watson ,a/ronomical ,comput+ ,bureau1 #aidj1 #acf pp4 ,?is is a sci5tific treatise1 *iefly relat+ to ! computation ( orbits 9 a/ronomy4 ,,h>tkemei]1 ,,h>ry ,,pelle1 ,pr9ciples ( ,pun*-,c>d ,ma*9e ,op]ation 7,subtitle3 ,h[ to ,op]ate ,pun*-,c>d ,tabulat+ & ,alphabetic ,acc\nt+ ,ma*9es71 ,new ,york3 ,?omas ,y4 ,cr[ell ,co41 #aidb1 #bfi pp4 ,?is is bas$ on ! au?or's exp]i5ce 9 tea*+ /ati/ical analysis us+ ,,ibm tabulators4 ,! book does n deal ) ! collator or multiply+ pun*4 ,,h$ley1 ,k4 ,j41 ,! ,developm5t ( ! ,pun*$-,c>d ,me?od1 ,actu>ial ,society ( ,au/ralasia1 #aidf1 #bj pp4 ,,int]national ,,bus9ess ,,ma*9es ,,corporation1 ,int]national ,bus9ess ,ma*9es 7=m no4 ,a-#djcf-f-de71 ,new ,york3 ,int]national ,bus9ess ,ma*9es ,corporation1 #aide1 #fe pp4 ,pages #f to #ca %[ pictures & brief descriptions ( ab\t #bj pun*-c>d ma*9es1 available 9 #aide4 ,,s*nackel1 ,h4 ,g41 & ,h4 ,c4 ,,lang1 ,acc\nt+ by ,ma*9e ,me?ods1 ,new ,york3 ,ronald ,press ,co41 #aici1 #ec pp4 ,,wolf1 ,,ar?ur ,w41 & ,,edmund ,c4 ,,b]keley1 ,advanc$ ,c\rse 9 ,pun*$ ,c>d ,op]ations1 ,new>k1 ,n4 ,j43 ,prud5tial ,insurance ,company ( ,am]ica1 #aidb1 #ih pp4 ,a useful & au?oritative description ( ,,ibm pun*-c>d calculat+ ma*9]y is ! foll[+3 ,,int]national ,,bus9ess ,,ma*9es ,,corporation1 ,,dep>tm5t ,,( ,,education1 ,ma*9e ,me?ods ( ,acc\nt+1 ,endicott1 ,n4 ,y43 ,int]national ,bus9ess ,ma*9es ,corporation1 #aicf-da1 #che pp4 ,?is is a collection ( #bh sep>ate booklets tell+ ! detail$ op]ation ( ,,ibm pun*-c>d ma*9]y4 ,!y 7 writt5 = employees ( ,,ibm & us]s ( ,,ibm equipm5t4 ,! foll[+ li/ ( ! booklets is useful 9 locat+ !m3 ,,no4 ,,( ,,title ,,=m ,,no4 ,,date ,,pages ,ma*9e ,me?ods ( ,acc\nt+--,=eword ,,am #aicf #f ,developm5t ( ,,ibm ,corporation ,,am-#a-a #aicf #ad ,pr9ciples ( ! ,electric ,acc\nt+ ,ma*9e ,me?od ,,am-#b #aicf #ab ,! ,tabulat+ ,c>d ,,am-#c-a #aicf #bj ,design ( ,tabulat+ ,c>ds ,,am-#d-a #aicf #af ,prep>ation & ,use ( ,codes ,,am-#e #aicf #bh ,organization & ,sup]vision ( ! ,tabulat+ ,dep>tm5t ,,am-#f #aicf #af ,selection & ,tra9+ ( ,key ,pun* ,op]ators ,,am-#g #aicf #ab ,acc\nt+ ,control ,,am-#h #aicf #h ,pun*es ,,am-#i #aicf #ab ,alphabetic ,pr9t+ ,pun*es ,,am-#aj #aicf #g ,facts to ,"k ab\t ,key ,pun*es ,,am-#aa #aicf #d ,v]ifi]s ,,am-#ab #aicf #d ,gang ,pun*es ,,am-#ac #aicf #h ,c>d-,op]at$ ,sort+ ,ma*9es ,,am-#ad #aicf #ab ,facts to ,"k ab\t ,sort]s ,,am-#ad;a #aicf #d ,electric ,tabulat+ ,ma*9es ,,am-#ae #aicf #bj ,electric ,acc\nt+ ,ma*9es 7,type #bhe & ,type #big7 ,,am-#af #aicf #af ,alphabetic ,direct ,subtraction ,acc\nt+ ,ma*9e ,,am-#ag #aicf #bh ,num]ical ,int]pret]s ,,am-#ah #aicf #h ,electric ,pun*$-,c>d ,int]pret] 7,type #eeb7 ,,am-#ah;a #aida #h ,reproduc+ ,pun*es 7,type #eab7 ,,am-#ai #aicf #af ,automatic ,summ>y ,pun*es = ,use ) ! ,num]ical ,acc\nt+ ,ma*9es 7,type #bhe-big7 ,,am-#bj #aicf #af ,automatic ,summ>y ,pun*es = ,use ) ! ,alphabetic ,acc\nt+ ,ma*9es 7,type #dje7 ,,am-#bj;a #aidj #af ,multiply+ ,pun*es ,,am-#ba #aicf #af ,application ( ,ma*9es to ,acc\nt+ ,functions ,,am-#bb #aicf #bd ,o!r ,int]national ,products ,,am-#bc-b #aicf #ai ,! ,int]national ,automatic ,c>riage 7,type #iba7 ,,am-#bd #aich #ae ,! ,dep>tm5t ( ,education ( ,,ibm has begun a second s]ies ( booklets on ! pr9ciples ( op]ation ( pun*-c>d calculat+ ma*9]y3 ,,int]national ,,bus9ess ,,ma*9es ,,corporation1 ,,dep>tm5t ,,( ,,education1 ,pr9ciples ( ,op]ation1 ,endicott1 ,n4 ,y43 ,int]national ,bus9ess ,ma*9es ,corporation1 #aidb & lat] 7except = "o publi%$ 9 #aici74 ,_m ( ! booklets 9 ?is s]ies h good examples ( ma*9e op]ation & applications4 ,also1 = ! fir/ "t1 lett]s & numb]s h be5 us$ z coord9ates to label ! hubs on ! plugbo>ds4 ,?is s]ies includes ! foll[+3 ,,no4 ,,( ,,title ,,=m ,,no4 ,,date ,,pages ,,c>d ,,pun*es ,,& ,,v]ifi]s ,c>d-,pun*+ & ,v]ify+ ,ma*9es #eb-cagf-j #aidf #ba ,alphabetical ,v]ifi]1 ,type #jee #eb-cbie-a #aidf #d ,,int]pret]s ,c>d ,int]pret]s1 ,type #eej1 #eea1 & #eeb #eb-cagh-j #aidf #ad ,,reproduc]s ,automatic ,reproduc+ ,pun*1 ,type #eac #eb-cahj-j #aide #bb ,end ,pr9t+ ,reproduc+ ,pun*1 ,type #eai #eb-cbib-a #aidf #bf ,electric ,docum5t-,orig9at+ ,ma*9e1 ,june ,type #eai #eb-cbib-b #aidh #bf ,,collators ,collator ,,am-#be #aidc #ca ,collator ,c\nt+ ,device ,c4,r4 #iagh #aidb #ab ,,calculat+ ,,pun*es ,electric ,multipli]1 ,type #fja #eb-cdjh-a #aidg #dg ,calculat+ ,pun*1 ,type #fjb #eb-cdji-j #aidf #hc ,calculat+ ,pun*1 ,type #fjb #eb-cdji-e #aidg #ic ,calculat+ ,pun*1 ,type #fjb-;,a 7,prelim9>y ,manual7 #bb-edhi-j #aidh #ei ,electronic ,multipli]1 ,type #fjc #eb-cefa-j #aidf #e ,electronic ,calculat+ ,pun*1 ,type #fjd #bb-ebgi-j #aidh #ea ,,tabulators ,acc\nt+ ,ma*9e1 ,type #djb & #djc 7,prelim9>y ,manual7 #bb-efed-j #aidi #adf ,alphabetical ,acc\nt+ ,ma*9e1 ,type #djd #eb-ccie-a #aidf #if ,typical ,applications1 ,alphabetical ,acc\nt+ ,ma*9e1 ,type #djd1 ) ,multiple ,l9e ,pr9t+ #bb-cgga-a #aidg #dg ,alphabetical ,acc\nt+ ,ma*9e1 ,type #dje ,,am #ag 7#a71 #aidc #ij ,revis$ #a_/a_/dc ,nov4 ,alphabetical ,acc\nt+ ,ma*9e1 ,type #dje #eb-cagi-b #aidh #ha ,,automatic ,,pr9t+ ,,c>riages ,bill ,fe$1 ,type #ibj #eb-cahd-j #aide #ba ,=m ,fe$+ ,device #eb-cbce-j #aidf #aa ,automatic ,c>riage1 ,type #iba #eb-cahc-j #aide #cf ,tape-,controll$ ,c>riage 7,prelim9>y ,manual1 ,revis$7 #bb-edae-a #aidh #bg ,,te/ ,,scor+ ,,ma*9e ,te/ ,scor+ ,ma*9e #id-bccc-j #aici #ai ,may ,te/ ,scor+ ,ma*9e #cb-iade-a #aidf #bj ,publi%$ ,te/s ,adapt$ = ,use ) ,june ! ,,ibm ,electric ,te/ ,scor+ ,ma*9e #bg-dbhf-i #aidh #h ,9 addition to ! new types ( pun*-c>d ma*9es ref]r$ to 9 ! above li/1 an elaborate pun*-c>d calculat+ ma*9e is describ$ 9 ! foll[+ ref]5ce3 ,,eck]t1 ,w4 ,j41 ,! ,,ibm ,pluggable ,sequ5ce ,relay ,calculator1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bc1 ,july #aidh1 pp4 #adi-afa4 ,a description ( pun*-c>d ma*9]y 9 r a light ve9 is conta9$ 93 ,,anonym\s1 ,speak+ ( ,pictures3 ,new ,me*anical ,mon/]s ,ease ,life's ,gr[+ ,pa9s1 ,life1 ,sept4 #ae1 #aidg1 pp4 #ae-af4 ,,anonym\s1 #edj1 ,*icago3 ,"t-,life-,=tune ,magaz9e1 ,subscription ,fulfillm5t ,(fice1 #aidh1 #ae pp4 ,new types ( pun*-c>d ma*9]y are cont9ually com+ into use4 ,among !m are3 ma*9es t take 9 pun* c>ds & make pun*$ pap] tape 7su* z teletype tape71 & vice v]sa--useful = transmitt+ pun*-c>d in=mation ov] wires2 an electric typewrit] op]at$ by pun* c>ds--useful = prep>+ almanacs = sea & air navigation1 etc42 a calculator programm$ by pun* c>ds1 consi/+ ( an assembly ( a tabulator1 an electronic calculat+ pun*1 & an auxili>y /orage unit1 all cabl$ toge!r--useful = "s types ( long calculation2 etc4 ,= in=mation ab\t su* ma*9]y1 ! manufactur]s may be consult$4 ,,pun*-,,c>d ,,calculat+ ,,ma*9]y3 ,,applications ,!re are _m articles 9 sci5tific j\rnals on applications ( pun*-c>d calculat+ ma*9]y to te*nical problems4 ,! fields ( eng9e]+1 education1 index+1 ma!matics1 survey+1 /ati/ics1 & o!rs are all repres5t$ 9 ! foll[+ li/ ( sample ref]5ces3 ,,alt1 ,,franz ,l41 ,multiplication ( ,matrices1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #b1 no4 #ac1 ,jan4 #aidf1 pp4 #ab-ac4 ,,bailey1 ,c4 ,f41 & o!rs1 ,pun* ,c>ds = ,index+ ,sci5tific ,data1 ,sci5ce1 vol4 #ajd1 ,aug4 #bc1 #aidf1 p4 #aha4 ,,b[]1 ,e4 ,c41 ,on ,subdivid+ ,tables1 ,lick ,obs]vatory ,bullet91 vol4 #af1 no4 #dee1 ,nov4 #aicc1 pp4 #adc-add4 ,,b[]1 ,e4 ,c41 ,sy/ematic ,subdivision ( ,tables1 ,lick ,obs]vatory ,bullet91 vol4 #ag1 no4 #dfg1 ,apr4 #aice1 pp4 #fe-gd4 ,,clem5ce1 ,g4 ,m41 & ,,paul ,,h]get1 ,optimum-,int]val ,pun*$-,c>d ,tables1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #a1 no4 #f1 ,apr4 #aidd1 pp4 #agc-agf4 ,,culley1 ,,frank ,l41 ,use ( ,acc\nt+ ,ma*9es = ,mass-,trans=mation f ,geographic to ,milit>y-,grid ,coord9ates1 ,wa%+ton1 ,d4 ,c43 ,national ,rese>* ,c\ncil1 ,am]ican ,geophysical ,union ,transactions ( #aidb1 "p #b1 pp4 #aij-aig4 ,,dem+1 ,w4 ,,edw>ds1 & ,,morris ,h4 ,,hans51 ,on ,"s ,c5sus ,aids to ,sampl+1 ,j\rnal ( ! ,am]ican ,/ati/ical ,association1 vol4 #ch1 no4 #bbe1 ,sept4 #aidc1 pp4 #cec-ceg4 ,,dunlap1 ,,jack ,w41 ,! ,computation ( ,means1 ,/&>d ,deviations1 & ,correlations by ! ,tabulator ,:5 ! ,numb]s ,are ,bo? ,positive & ,negative1 ,proce$+s ( ! ,educational ,rese>* ,=um1 ,int]national ,bus9ess ,ma*9es ,corporation1 ,aug4 #aidj1 pp4 #af-ai4 ,,dwy]1 ,,paul ,s41 ,! ,use ( ,tables 9 ! ,=m ( ,prepun*$ ,c>ds1 ,proce$+s ( ! ,educational ,rese>* ,=um1 ,int]national ,bus9ess ,ma*9es ,corporation1 ,aug4 #aidj1 pp4 #abe-abg4 ,,dwy]1 ,,paul ,s41 ,summ>y ( ,problems 9 ! ,computation ( ,/ati/ical ,con/ants ) ,tabulat+ & ,sort+ ,ma*9es1 ,proce$+s ( ! ,educational ,rese>* ,=um1 ,int]national ,bus9ess ,ma*9es ,corporation1 ,aug4 #aidj1 pp4 #bj-bh4 ,,dwy]1 ,,paul ,s41 & ,,alan ,d4 ,,mea*am1 ,! ,prep>ation ( ,correlation ,tables on a ,tabulator ,equipp$ ) ,digit ,selection1 ,j\rnal ( ! ,am]ican ,/ati/ical ,association1 vol4 #cb1 #aicg1 pp4 #fed-ffb4 ,,dy]1 ,h4 ,s41 ,mak+ ,te/ ,score ,data ,effective 9 ! ,admission & ,c\rse ,placem5t ( ,h>v>d ,fre%m51 ,proce$+s ( ! ,rese>* ,=um1 ,int]national ,bus9ess ,ma*9es ,corporation1 #aidf1 pp4 #ee-fb4 ,,eck]t1 ,w4 ,j41 & ,,ralph ,f4 ,,haupt1 ,! ,pr9t+ ( ,ma!matical ,tables1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #b1 no4 #ag1 ,jan4 #aidg1 pp4 #aif-bjb4 ,,fe9/e91 ,,lillian1 & ,,m>t9 ,,s*w>z*ild1 ,automatic ,integration ( ,l9e> ,second-,ord] ,diff]5tial ,equations by ,means ( ,pun*$-,c>d ,ma*9es1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #ab1 no4 #h1 ,aug4 #aida1 pp4 #dje-djh4 ,,hotell+1 ,,h>old1 ,"s ,new ,me?ods 9 ,matrix ,calculation1 ,! ,annals ( ,ma!matical ,/ati/ics1 vol4 #ad1 no4 #a1 ,m>4 #aidc1 pp4 #a-cd4 ,,int]national ,,bus9ess ,,ma*9es ,,corporation1 editor1 & o!rs1 ,proce$+s ( ! ,educational ,rese>* ,=um1 ,endicott1 ,n4 ,y43 ,int]national ,bus9ess ,ma*9es ,corporation1 #aida4 ,,int]national ,,bus9ess ,,ma*9es ,,corporation1 editor1 & o!rs1 ,proce$+s ( ! ,rese>* ,=um1 ,endicott1 ,n4 ,y43 ,int]national ,bus9ess ,ma*9es ,corporation1 #aidf1 #id pp4 ,,k+1 ,,gilb]t ,w41 ,pun*$-,c>d ,tables ( ! ,expon5tial ,function1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #ae1 no4 #ab1 ,dec4 #aidd1 pp4 #cdi-cej4 ,,k+1 ,,gilb]t ,w41 & ,,george ,b4 ,,?omas1 ,prep>ation ( ,pun*$-,c>d ,tables ( ,log>i?ms1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #ae1 no4 #ab1 ,dec4 #aidd1 p4 #cej4 ,,kormes1 ,,m>k1 ,a ,note on ! ,integration ( ,l9e> ,second-,ord] ,diff]5tial ,equations by ,means ( ,pun*$ ,c>ds1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #ad1 no4 #d1 ,apr4 #aidc1 p4 #aah4 ,,kormes1 ,,m>k1 ,num]ical ,solution ( ! ,b\nd>y ,value ,problem = ! ,pot5tial ,equation by ,means ( ,pun*$ ,c>ds1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #ad1 no4 #h1 ,aug4 #aidc1 pp4 #bdh-bej4 ,,kormes1 ,,m>k1 & ,,j5nie ,p4 ,,kormes1 ,num]ical ,solution ( ,initial ,value ,problems by ,means ( ,pun*$-,c>d ,ma*9es1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #af1 no4 #a1 ,jan4 #aide1 pp4 #g-i4 ,,kud]1 ,g4 ,,fr$]ic1 ,use ( ! ,,ibm ,scor+ ,ma*9e = ,rapid ,computation ( ,tables ( ,int]correlations1 ,j\rnal ( ,appli$ ,psy*ology1 vol4 #bb1 no4 #f1 ,dec4 #aich1 pp4 #ehg-eif4 ,,maxfield1 ,d4 ,k41 ,libr>y ,pun*$ ,c>d ,proc$ures1 ,libr>y ,j\rnal1 vol4 #ga1 no4 #ab1 ,june #ae1 #aidf1 pp4 #ijb-ije 444 ,,mclaughl91 ,,ka?le51 ,add+ ,ma*9es ,nip ,,aef ,epidemics1 ,new ,york3 ,new ,york ,times1 ,apr4 #bg1 #aide4 ,,mcph]son1 ,,john ,c41 ,on ,me*anical ,tabulation ( ,polynomials1 ,annals ( ,ma!matical ,/ati/ics1 ,sept4 #aida1 pp4 #cag-cbg4 ,,mcph]son1 ,,john ,c41 ,ma!matical ,op]ations ) ,pun*$ ,c>ds1 ,j\rnal ( ! ,am]ican ,/ati/ical ,association1 vol4 #cg1 ,june #aidb1 pp4 #bge-bha4 ,,milliman1 ,,w5dell ,a41 ,me*anical ,multiplication by ! ,use ( ,tabulat+ ,ma*9es1 ,transactions ( ! ,actu>ial ,society ( ,am]ica1 vol4 #ce1 "p #b1 ,oct4 #aicd1 pp4 #bec-bfd2 = discussion see also vol4 #cf1 "p #a1 ,may #aice1 pp4 #gg-hd4 ,,roy]1 ,,elm] ,b41 ,a ,ma*9e ,me?od = ,comput+ ! ,bis]ial ,correlation ,coeffici5t 9 ,item ,validation1 ,psy*ometrika1 vol4 #f1 no4 #a1 ,feb4 #aida1 pp4 #ee-ei4 ,,:itt51 ,c4 ,a41 ,triangulation ,adju/m5t by ,int]national ,bus9ess ,ma*9es1 ,wa%+ton1 ,d4 ,c43 ,national ,rese>* ,c\ncil1 ,am]ican ,geophysical ,union ,transactions ( #aidc1 "p #a1 p4 #ca4 ,! foll[+ bibliography may be obta9$ on reque/ to ! ,watson ,sci5tific ,comput+ ,laboratory1 ,columbia ,univ]sity1 #fab ,we/ #aaf ,/reet1 ,new ,york #bg1 ,n4 ,y43 ,,watson ,,sci5tific ,,comput+ ,,laboratory1 ,bibliography3 ,! ,use ( ,,ibm ,ma*9es 9 ,sci5tific ,rese>*1 ,/ati/ics1 & ,education1 ,new ,york3 ,int]national ,bus9ess ,ma*9es ,corporation 7=m no4 #ej-chac-j71 ,sept4 #aidg1 #be pp4 ,! organization & equipm5t ( ?is laboratory are describ$ 93 ,,eck]t1 ,w4 ,j41 ,facilities ( ! ,watson ,sci5tific ,comput+ ,laboratory1 ,proce$+s ( ! ,rese>* ,=um1 ,int]national ,bus9ess ,ma*9es ,corporation1 #aidf1 pp4 #ge-hj4 ,,! ,,diff]5tial ,,analyz] ,! basic sci5tific articles on ! two diff]5tial analyz]s at ,massa*usetts ,in/itute ( ,te*nology are3 ,,bu%1 ,,vannev>1 ,! ,diff]5tial ,analyz]3 ,a ,new ,ma*9e = ,solv+ ,diff]5tial ,equations1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bab1 no4 #d1 ,oct4 #aica1 pp4 #ddg-dhh4 ,,bu%1 ,,vannev>1 & ,,samuel ,h4 ,,caldwell1 ,a ,new ,type ( ,diff]5tial ,analyz]1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bdj1 no4 #d1 ,oct4 #aide1 pp4 #bee-cbf4 ,"s ( ! less te*nical articles ab\t ! second diff]5tial analyz] at ,m4,i4,t4 are3 ,,caldwell1 ,,samuel ,h41 ,educat$ ,ma*9]y1 ,te*nology ,review1 vol4 #dh1 no4 #a1 ,nov4 #aide1 pp4 #ca-cd4 ,,g5et1 ,n41 #ajj-,ton ,bra9 at ,m4,i4,t41 ,s*ola/ic1 vol4 #dh1 ,feb4 #d1 #aidf1 p4 #cf4 ,,anonym\s1 ,ma!matical ,ma*9e2 ,new ,electronic ,diff]5tial ,analyz]1 ,sci5ce ,news ,lett]1 vol4 #dh1 ,nov4 #aj1 #aide1 p4 #bia4 ,,anonym\s1 ,robot ,e9/e93 ,diff]5tial ,analyz] at ,m4,i4,t41 ,newsweek1 vol4 #bf1 ,nov4 #ab1 #aide1 p4 #ic4 ,,anonym\s1 ,m4,i4,t4's #ajj-,ton ,ma!matical ,bra9 is ,n[ to ,tackle ,problems ( ,peace1 ,popul> ,sci5ce1 vol4 #adh1 ,jan4 #aidf1 p4 #ha4 ,,anonym\s1 ,! ,great ,electro-,me*anical ,bra92 ,m4,i4,t4's ,diff]5tial ,analyz]1 ,life1 vol4 #bj1 ,jan4 #ad1 #aidf1 pp4 #gc-gd 444 ,,anonym\s1 ,all ! ,answ]s at ,y\r ,f+]tips2 9 ! ,laboratory ( ,m4,i4,t41 ,popul> ,me*anics1 vol4 #he1 ,m>4 #aidf1 pp4 #afd-afg 444 ,a diff]5tial analyz] 0 built at ! ,moore ,s*ool ( ,electrical ,eng9e]+3 ,,travis1 ,,irv51 ,diff]5tial ,analyz] ,elim9ates ,bra9 ,fag1 ,ma*9e ,design1 ,july #aice1 pp4 #ae-ah4 ,a diff]5tial analyz] 0 built at ! ,g5]al ,electric ,company1 ,s*5ectady1 ,n4 ,y4 ,in/ead ( us+ a me*anical or electrical amplifi] ( ! motion ( ! little turn+ :eel rid+ on ! disc1 ?is ma*9e foll[s ! motion us+ pol>iz$ light4 ,?is ma*9e is describ$ 93 ,,b]ry1 ,t4 ,m41 ,pol>iz$ ,light ,s]vo ,sy/em1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #fc1 ,apr4 #aidd1 pp4 #aie-aig4 ,,kuehni1 ,h4 ,p41 & ,h4 ,a4 ,,pet]son1 ,a ,new ,diff]5tial ,analyz]1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #fc1 ,may #aidd1 pp4 #bba-bbg4 ,a diff]5tial analyz] has be5 put into use at ! ,univ]sity ( ,cali=nia3 ,,boelt]1 ,l4 ,m4 ,k41 & o!rs1 ,! ,diff]5tial ,analyz] ( ! ,univ]sity ( ,cali=nia1 ,los ,angeles3 ,univ]sity ( ,cali=nia1 #aidg1 #be pp4 ,a diff]5tial analyz] 0 built at ,man*e/] ,univ]sity1 ,engl&4 ,x 0 built fir/ f 8,meccano0 p>ts1 at a total co/ ( ab\t #bj p\nds1 & lat] ref9$ = m exact "w4 ,"s articles deal+ ) ?is diff]5tial analyz] are3 ,,h>tree1 ,d4 ,r41 ,! ,diff]5tial ,analyz]1 ,nature1 vol4 #ace1 ,june #h1 #aice1 p4 #idj4 ,,h>tree1 ,d4 ,r41 ,! ,me*anical ,integration ( ,diff]5tial ,equations1 ,! ,ma!matical ,gazette1 vol4 #bb1 #aich1 pp4 #cdb-cfd4 ,,h>tree1 ,d4 ,r41 & ,a4 ,,port]1 ,! ,con/ruction ( a ,model ,diff]5tial ,analys]1 ,memoirs & ,proce$+s ( ! ,man*e/] ,lit]>y & ,philosophical ,society1 vol4 #gi1 ,july #aice1 pp4 #ea-gb4 ,o!r small scale diff]5tial analyz]s built 9 ,engl& are cov]$ 93 ,,be>d1 ,r4 ,e41 ,! ,con/ruction ( a ,small ,scale ,diff]5tial ,analys] & ,its ,application to ! ,calculation ( ,actu>ial ,functions1 ,j\rnal ( ! ,in/itute ( ,actu>ies1 vol4 #ga1 #aidb1 pp4 #aic-bbg4 ,,massey1 ,h4 ,s4 ,w41 ,j4 ,,wylie1 & ,r4 ,a4 ,,buck+ham1 ,a ,small ,scale ,diff]5tial ,analys]3 ,its ,con/ruction & ,op]ation1 ,proce$+s ( ! ,royal ,iri% ,academy1 vol4 #de1 #aich1 pp4 #a-ba4 ,a diff]5tial analyz] con/ruct$ 9 ,g]many is briefly describ$ 9 ! foll[+3 ,,sau]1 ,r41 & ,h4 ,,poes*1 ,integrat+ ,ma*9e = ,solv+ ,ord9>y ,diff]5tial ,equations1 ,eng9e]s ,dige/ 7,am]ican ,edition71 vol4 #a1 ,may #aidd1 pp4 #cbf-cbh4 ,f ! hi/orical po9t ( view !re are "s int]e/+ pap]s on a ma*9e = solv+ diff]5tial equations by ,sir ,william ,?omson 7,"l ,kelv971 includ+ "o by 8 bro!r ,james ,?omson4 ,!y are 9 ! ,proce$+s ( ! ,royal ,society1 vol4 #bd1 ,feb4 #ahgf1 pp4 #bfb-bge4 ,! me?od ( integration by a ma*9e is describ$1 b ! /ate ( ma*9e tools at ! "t 0 su* t no accurate me*anism 0 con/ruct$4 ,ano!r int]e/+ pap] =e%ad[+ ! diff]5tial analyz] is3 ,,wa9wright1 ,,lawr5ce ,l41 ,a ,balli/ic ,eng9e1 ,*icago3 ,univ]sity ( ,*icago1 !sis = ,ma/]'s ,degree1 #aibc1 #bh pp4 ,"s ( ! applications & ma!matical limitations ( diff]5tial analyz]s are cov]$ 93 ,,bu%1 ,v41 & ,s4 ,h4 ,,caldwell1 ,?omas-,f]mi ,equation ,solution by ! ,diff]5tial ,analyz]1 ,physical ,review1 vol4 #ch1 no4 #aj1 #aica1 pp4 #ahih-aijb4 ,,h>tree1 ,d4 ,r41 ,a ,great ,calculat+ ,ma*9e3 ! ,bu% ,diff]5tial ,analys] & ,its ,applications 9 ,sci5ce & ,indu/ry1 ,proce$+s ( ! ,royal ,in/itution ( ,great ,brita91 vol4 #ca1 #aidj1 pp4 #aea-agj4 ,,h>tree1 ,d4 ,r41 & ,a4 ,,port]1 ,! ,application ( ! ,diff]5tial ,analys] to ,transi5ts on a ,di/ortionless ,transmission ,l9e1 ,j\rnal ( ! ,in/itute ( ,electrical ,eng9e]+1 vol4 #hc1 no4 #ejc1 ,nov4 #aich1 pp4 #fdh-fef4 ,,h>tree1 ,d4 ,r41 & ,j4 ,r4 ,,wom]sley1 ,a ,me?od = ! ,num]ical or ,me*anical ,solution ( ,c]ta9 ,types ( ,p>tial ,diff]5tial ,equations1 ,proce$+s ( ! ,royal ,society ( ,london1 s]ies ,a1 vol4 #afa1 #aicg1 pp4 #cec-cff4 ,,mag9niss1 ,f4 ,j41 ,diff]5tial ,analyz] ,applications1 ,g5]al ,electric ,review1 vol4 #dh1 no4 #e1 ,may #aide1 pp4 #ed-ei4 ,,%annon1 ,,claude ,e41 ,ma!matical ,!ory ( ! ,diff]5tial ,analyz]1 ,j\rnal ( ,ma!matics & ,physics1 ,cambridge1 ,mass43 ,massa*usetts ,in/itute ( ,te*nology1 vol4 #bj1 no4 #d1 #aida1 pp4 #ccg-ced4 ,,h>monic ,,analyz]s ,,& ,,syn!siz]s ,ano!r bran* ( ! analogue calculat+ ma*9e is ! h>monic analyz] & syn!siz]4 ,^! are ma*9es t /udy wave motions & relat$ physical & ma!matical functions4 ,a brief li/ ( articles on ?is type ( ma*9e foll[s3 ,,ar*]1 ,r4 ,m41 ,project+ ,app>atus = ,comp\nd+ ,h>monic ,vibrations1 ,j\rnal ( ,sci5tific ,in/rum5ts1 vol4 #ad1 #aicg1 pp4 #djh-daj4 ,,br[n1 ,s4 ,l41 ,a ,me*anical ,h>monic ,syn!siz]-,analyz]1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bbh1 #aici1 pp4 #fge-fid4 ,,br[n1 ,s4 ,l41 & ,l4 ,l4 ,,:eel]1 ,a ,me*anical ,me?od = ,graphical ,solution ( ,polynomials1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bca1 #aida1 pp4 #bbc-bdc4 ,,br[n1 ,s4 ,l41 & ,l4 ,l4 ,,:eel]1 ,use ( ! ,me*anical ,multih>monograph = ,graph+ ,types ( ,functions & = ,solution ( ,pairs ( ,non-,l9e> ,simultane\s ,equations1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #ac1 ,nov4 #aidb1 pp4 #dic-die4 ,,br[n1 ,s4 ,l41 & ,l4 ,l4 ,,:eel]1 ,! ,use ( a ,me*anical ,syn!siz] to ,solve ,trigonometric & ,c]ta9 ,types ( ,transc5d5tal ,equations1 & = ! ,d\ble ,summations ,involv$ 9 ,patt]son ,cont\rs1 ,j\rnal ( ,appli$ ,physics1 vol4 #ad1 ,jan4 #aidc1 pp4 #cj-cf4 ,f,,r?1 ,r41 & ,r4 ,w4 ,,pr+le1 ,a ,new ,photo-,electric ,me?od = ,f\ri] ,syn!sis & ,analysis1 ,london1 ,ed9burgh & ,dubl9 ,philosophical ,magaz9e & ,j\rnal ( ,sci5ce1 vol4 #ce1 s]ies #g1 #aidd1 pp4 #fdc-fef4 ,,int]national ,,hydrographic ,,bureau1 ,tide ,pr$ict+ ,ma*9es1 ,int]national ,hydrographic ,bureau1 ,special ,publication #ac1 ,july #aibf4 ,,kranz1 ,,fr$]ick ,w41 ,a ,me*anical ,syn!siz] & ,analyz]1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bjd1 #aibg1 pp4 #bde-bfb4 ,,m>ble1 ,f4 ,g41 ,an ,automatic ,vibration ,analyz]1 ,bell ,laboratories ,record1 vol4 #bb1 ,apr4 #aidd1 pp4 #cgf-chj4 ,,maxwell1 ,l4 ,r41 ,an ,electrical ,me?od = ,comp\nd+ ,s9e ,functions1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #aa1 ,feb4 #aidj1 pp4 #dg-ed4 ,,mill]1 ,,dayton ,c41 ,a #cb-;,elem5t ,h>monic ,syn!siz]1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #aha1 #aiaf1 pp4 #ea-ha4 ,,mill]1 ,,dayton ,c41 ,! ,h5rici ,h>monic ,analyz] & ,devices = ,ext5d+ & ,facilitat+ ,its ,use1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #ahb1 #aiaf1 pp4 #bhe-cbb4 ,,milne1 ,j4 ,r41 ,a 8,duplex0 ,=m ( ,h>monic ,syn!tis] & ,its ,ma!matical ,!ory1 ,proce$+s ( ! ,royal ,society ( ,ed9burgh1 vol4 #ci1 #aiah-ai1 pp4 #bcd-bdb4 ,,montgom]y1 ,h4 ,c41 ,an ,optical ,h>monic ,analyz]1 ,bell ,sy/em ,te*nical ,j\rnal1 vol4 #ag1 no4 #c1 ,july #aich1 pp4 #djf-dae4 ,,raymond1 ,w4 ,j41 ,an ,h>monic ,syn!siz] ,hav+ ,compon5ts ( ,incomm5surable ,p]iod & ,any ,desir$ ,decrem5t1 ,physical ,review1 vol4 #aa1 s]ies #b1 #aiah1 pp4 #dgi-dha4 ,,rob]tson1 ,j4 ,m41 ,a ,simple ,h>monic ,cont9u\s ,calculat+ ,ma*9e1 ,london1 ,ed9burgh & ,dubl9 ,philosophical ,magaz9e & ,j\rnal ( ,sci5ce1 vol4 #ac1 #aicb1 pp4 #dac-dai4 ,,som]ville1 ,j4 ,m41 ,h>monic ,syn!siz] = ,demon/rat+ & ,/udy+ ,complex ,wave ,=ms1 ,j\rnal ( ,sci5tific ,in/rum5ts1 vol4 #ba1 ,oct4 #aidd1 pp4 #agd-agg4 ,,/raiton1 ,a4 ,w41 & ,g4 ,k4 ,,t]hune1 ,h>monic ,analysis by ,photographic ,me?od1 ,j\rnal ( ,appli$ ,physics1 vol4 #ad1 #aidc1 pp4 #ece-ecf4 ,,wegel1 ,r4 ,l41 & ,c4 ,r4 ,,moore1 ,an ,electrical ,frequ5cy ,analyz]1 ,bell ,sy/em ,te*nical ,j\rnal1 vol4 #c1 #aibd1 pp4 #bii-cbc4 ,,network ,,analyz]s ,a ?ird bran* ( ! analogue calculat+ ma*9e is ! network analyz]4 ,to solve problems1 ?is ma*9e uses ! laws gov]n+ a network ( electrical circuits4 ,= example1 an electric p[] company ) a sy/em ( p[] l9es ov] hundr$s ( miles may h a problem ab\t electrical p[]3 w an accid5t or a sudd5 dem& cause a breakd[n any:]e 9 ! sy/em8 ,9 ! ,g5]al ,electric ,company 9 ,s*5ectady1 ,n4 ,y41 !re is a ma*9e call$ ! ,a4,c4 ,network ,analyz]4 ,all ! prop]ties ( ! p[] company's network ( l9es c be f$ on a small scale into ! analyz]4 ,c]ta9 dials are turn$ & c]ta9 plugwires are connect$4 ,!n v>i\s k9ds ( 8accid5ts0 & 8sudd5 dem&s0 are f$ into ! ma*9e1 & ! response ( ! sy/em is not$4 ,! answ]s giv5 by ! ma*9e are multipli$ by ! prop] scale factor1 & 9 ?is way ! problem ( ! p[] company is solv$4 ,!re are two k9ds ( problems t network analyz]s are built to solve3 ! /eady /ate conditions & ! transi5t conditions4 ,= example1 y may n ov]load a fuse ) an electric iron :5 x is plugg$ 9 & be+ us$1 b z y pull out ! cord1 y may bl[ ! fuse3 ! /eady /ate does n ov]/ra9 ! sy/em1 b ! transi5t does4 ,"s articles on network analyz]s are3 ,,enns1 ,w4 ,e41 ,a ,new ,simple ,calculator ( ,load ,fl[ 9 ,a4,c4 ,networks1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #fb1 #aidc1 pp4 #ghf-gij4 ,,haz51 ,h4 ,l41 & o!rs1 ,! ,m4,i4,t4 ,network ,analyz]1 ,cambridge1 ,mass43 ,massa*usetts ,in/itute ( ,te*nology1 ,dep>tm5t ( ,electrical ,eng9e]+1 ,s]ial ,no4 #fi1 ,apr4 #aica4 ,,kuehni1 ,h4 ,p41 & ,r4 ,g4 ,,lorra9e1 ,a ,new ,a4,c4 ,network ,analyz]1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #eg1 #aich1 pp4 #fg-gc4 ,,p>k]1 ,w4 ,w41 ,dual ,a4,c4 ,network ,calculator1 ,electrical ,eng9e]+1 ,may #aide1 pp4 #ahb-ahc4 ,,p>k]1 ,w4 ,w41 ,! ,mod]n ,a4,c4 ,network ,calculator1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #fj1 ,nov4 #aida1 pp4 #igg-ihb4 ,,pet]son1 ,h4 ,a41 ,an ,electric ,circuit ,transi5t ,analyz]1 ,g5]al ,electric ,review1 ,sept4 #aici1 pp4 #cid-djj4 ,,v>ney1 ,r4 ,n41 ,an ,all-,electric ,integrator = ,solv+ ,diff]5tial ,equations1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #ac1 ,jan4 #aidb1 pp4 #aj-af4 ,"s ( ! articles on applications ( network analyz]s to v>i\s problems are3 ,,kron1 ,,gabriel1 ,equival5t ,circuits ( ! ,ela/ic ,field1 ,j\rnal ( ,appli$ ,me*anics1 vol4 ,a#aa1 ,sept4 #aidd1 pp4 #adf-afa4 ,,kron1 ,,gabriel1 ,t5sorial ,analysis & ,equival5t ,circuits ( ,ela/ic ,/ructures1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bch1 ,dec4 #aidd1 pp4 #cii-ddb4 ,,kron1 ,,gabriel1 ,num]ical ,solution ( ,ord9>y & ,p>tial ,diff]5tial ,equations by ,means ( ,equival5t ,circuits1 ,j\rnal ( ,appli$ ,physics1 vol4 #af1 #aide1 pp4 #agb-ahf4 ,,kron1 ,,gabriel1 ,electric ,circuit ,models = ! ,vibration ,spectrum ( ,polyatomic ,molecules1 ,j\rnal ( ,*emical ,physics1 vol4 #ad1 no4 #a1 ,jan4 #aidf1 pp4 #ai-ca4 ,,kron1 ,g41 & ,g4 ,k4 ,,c>t]1 ,a4,c4 ,network ,analyz] ,/udy ( ! ,s*rd+] ,equation1 ,physical ,review1 vol4 #fg1 #aide1 pp4 #dd-di4 ,,kron1 ,g41 & ,g4 ,k4 ,,c>t]1 ,network ,analyz] ,te/s ( ,equival5t ,circuits ( ,vibrat+ ,polyatomic ,molecules1 ,j\rnal ( ,*emical ,physics1 vol4 #ad1 no4 #a1 ,jan4 #aidf1 pp4 #cb-cd4 ,,pet]son1 ,h4 ,a41 & ,c4 ,,concordia1 ,analyz]s = ,use 9 ,eng9e]+ & ,sci5tific ,problems1 ,g5]al ,electric ,review1 vol4 #dh1 no4 #i1 ,sept4 #aide1 pp4 #bi-cg4 ,,ma*9es ,,= ,,solv+ ,,algebraic ,,equations ,ano!r bran* ( ! analogue calculat+ ma*9e is a type ( ma*9e t w solve v>i\s k9ds ( algebraic equations 7see ,supplem5t #b74 ,a li/ ( "s articles foll[s4 ,! article by ,mallock describes a ma*9e = solv+ up to #aj l9e> simultane\s equations 9 #aj unkn[ns1 & ! article by ,wilbur1 a ma*9e = solv+ up to #i4 ,,dietzold1 ,,rob]t ,l41 ,! ,isograph--,a ,me*anical ,root-,f9d]1 ,bell ,laboratories ,record1 vol4 #af1 no4 #d1 ,dec4 #aicg1 pp4 #acj-acd4 ,,duncan1 ,w4 ,j41 ,"s ,devices = ! ,solution ( ,l>ge ,sets ( ,simultane\s ,l9e> ,equations1 ,london1 ,ed9burgh1 & ,dubl9 ,philosophical ,magaz9e & ,j\rnal ( ,sci5ce1 vol4 #ce1 s]ies #g1 #aidd1 pp4 #ffj-fgj4 ,,frame1 ,j4 ,,su!rl&1 ,ma*9es = ,solv+ ,algebraic ,equations1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #a1 no4 #i1 ,jan4 #aide1 pp4 #ccg-cec4 ,,h>t1 ,h4 ,c41 & ,,irv5 ,,travis1 ,me*anical ,solution ( ,algebraic ,equations1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bbe1 ,jan4 #aich1 pp4 #fc-gb4 ,,h]r1 ,d4 ,l41 & ,r4 ,s4 ,,graham1 ,an ,electrical ,algebraic ,equation ,solv]1 ,review ( ,sci5tific ,in/rum5ts1 vol4 #i1 ,oct4 #aich1 pp4 #caj-cae4 ,,mallock1 ,r4 ,r4 ,m41 ,an ,electrical ,calculat+ ,ma*9e1 ,proce$+s ( ! ,royal ,society1 s]ies ,a1 vol4 #adj1 #aicc1 pp4 #deg-dhc4 ,,m]cn]1 ,r4 ,o41 ,! ,me*anism ( ! ,isograph1 ,bell ,laboratories ,record1 vol4 #af1 no4 #d1 ,dec4 #aicg1 pp4 #ace-adj4 ,,/ibitz1 ,,george ,r41 ,electric ,root-f9d]1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #cbh-cbi4 ,,wilbur1 ,j4 ,b41 ,! ,me*anical ,solution ( ,simultane\s ,equations1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bbb1 ,dec4 #aicf1 pp4 #gae-gbd4 ,,analogue ,,ma*9es--,,miscellane\s ,"s articles ref]r+ to v>i\s o!r k9ds ( analogue ma*9es & _! applications are "h li/$ toge!r3 ,,bu%1 ,v41 ,f4 ,d4 ,,gage1 & ,r4 ,r4 ,,/ew>t1 ,a ,cont9u\s ,integraph1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bjc1 #aibg1 pp4 #fc-hd4 ,,gray1 ,t4 ,s41 ,a ,photo-,electric ,integraph1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bab1 #aica1 pp4 #gg-ajb4 ,,haz51 ,h4 ,l41 ,g4 ,s4 ,,br[n1 & ,w4 ,r4 ,,h$eman1 ,! ,c9ema ,integraph3 ,a ,ma*9e = ,evaluat+ a ,p>ametric ,product ,integral 7two p>ts & app5dix71 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bcj1 ,july #aidj1 pp4 #ai-dd1 & ,aug4 #aidj1 pp4 #ahc-bje4 ,,mccann1 ,g4 ,d41 & ,h4 ,e4 ,,cr9]1 ,me*anical ,problems ,solv$ ,electrically1 ,we/+h\se ,eng9e]1 vol4 #f1 no4 #b1 ,m>* #aidf1 pp4 #di-ef4 ,,my]s1 ,d4 ,m41 ,an ,integraph = ! ,solution ( ,diff]5tial ,equations ( ! ,second-,ord]1 ,j\rnal ( ,sci5tific ,in/rum5ts1 vol4 #af1 #aici1 pp4 #bji-bbb4 ,,pek]is1 ,c4 ,l41 & ,w4 ,t4 ,,:ite1 ,diff]5tiation ) ! ,c9ema ,integraph1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bcd1 ,july #aidb1 pp4 #ag-bi4 ,,smi?1 ,c4 ,e41 & ,e4 ,l4 ,,gove1 ,an ,electrome*anical ,calculator = ,directional-,ant5na ,patt]ns1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #fb1 #aidc1 pp4 #gh-hb4 ,,yavne1 ,r4 ,o41 ,high ,accuracy ,cont\r ,cams1 ,product ,eng9e]+1 vol4 #ai1 "p #b1 ,aug4 #aidh1 #c pp4 ,,anonym\s1 ,electrical ,gun ,director ,demon/rat$1 ,bell ,laboratories ,record1 vol4 #bb1 no4 #d1 ,dec4 #aidc1 pp4 #aeg-afg4 ,,anonym\s1 ,developm5t ( ! ,electric ,director1 ,bell ,laboratories ,record1 vol4 #bb1 no4 #e1 ,jan4 #aidd1 pp4 #bbe-bcj4 ,,anonym\s1 ,old ,field ,=tune ,tell]3 ,electronic ,oil ,pool ,analyz]1 ,popul> ,me*anics1 vol4 #hf1 ,sept4 #aidf1 p4 #aed4 ,,h>v>d ,,ibm ,,automatic ,,sequ5ce-,,controll$ ,,calculator ,! basic sci5tific description ( ?is ma*9e z ( ,septemb] #a1 #aide1 is conta9$ 93 ,,aik51 ,,h[>d ,h41 & ,,/aff ,,( ,,! ,,computation ,,laboratory1 ,a ,manual ( ,op]ation = ! ,automatic ,sequ5ce-,controll$ ,calculator1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidf1 #efa pp4 ,! ma*9e has *ang$ r a good deal s9ce ,sept4 #a1 #aide4 ,"s circuits h be5 remov$4 ,o!r circuits h be5 add$4 ,! capacity ( ! ma*9e to d problems has be5 greatly increas$4 ,! ,computation ,laboratory at ,h>v>d ,univ]sity is cordial t[>ds sci5tific inquiries1 & "s unpubli%$1 mimeograph$ in=mation is available at ! laboratory reg>d+ ! details ( ^! *anges4 ,"s %ort] sci5tific & te*nical descriptions ( ! ma*9e are conta9$ 93 ,,aik51 ,,h[>d ,h41 & ,,grace ,m4 ,,hopp]1 ,! ,automatic ,sequ5ce ,controll$ ,calculator 7#c p>ts71 ,electrical ,eng9e]+1 vol4 #fe1 nos4 #h1 #i1 & #aj1 ,aug4 to ,nov4 #aidf1 p4 #chd 444 7#ba pp474 ,,blo*1 ,,ri*>d ,m41 ,m>k ,i ,calculator1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bc-cj4 ,,h>rison1 ,,joseph ,o41 ,,jr41 ,! ,prep>ation ( ,problems = ! ,m>k ,i ,calculator1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bjh-baj4 ,,int]national ,,bus9ess ,,ma*9es ,,corporation1 ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator1 ,endicott1 ,n4 ,y43 ,int]national ,bus9ess ,ma*9es ,corporation1 #aide1 #f pp4 ,"s ( ! less te*nical articles reg>d+ ! ma*9e are3 ,,g5et1 ,n41 ,got a ,problem8 ,h>v>d's ,amaz+ ,new ,ma!matical ,robot1 ,s*ola/ic1 vol4 #de1 ,sept4 #ah1 #aidd1 p4 #ce4 ,,torrey1 ,v41 ,robot ,ma!matician ,kn[s ,all ! ,answ]s1 ,popul> ,sci5ce1 vol4 #ade1 ,oct4 #aidd1 pp4 #hf-hi4444 ,,anonym\s1 ,giant ,new ,calculator1 ,sci5ce ,news ,lett]1 vol4 #df1 ,aug4 #ab1 #aidd1 p4 #aaa4 ,,anonym\s1 ,ma!matical ,robot ,pres5t$ to ,h>v>d1 ,"t1 vol4 #dd1 ,aug4 #ad1 #aidd1 p4 #gb4 ,,anonym\s1 ,_w's ,greate/ ,ma*9e = ,automatic ,calculation1 ,sci5ce ,news ,lett]1 vol4 #df1 ,aug4 #ai1 #aidd1 p4 #abc4 ,,anonym\s1 ,sup]bra91 ,nation's ,bus9ess1 vol4 #cb1 ,sept4 #aidd1 p4 #h4 ,,anonym\s1 ,robot ,works ,problems ,nev] ,be=e ,solv$1 ,popul> ,me*anics1 vol4 #hb1 ,oct4 #aidd1 p4 #ac4 ,,eniac1 ,,! ,,electronic ,,num]ic ,,integrator ,,& ,,calculator ,!re is z yet no full-scale1 publi%$ sci5tific acc\nt ( ! ,eniac4 ,at ! ,balli/ic ,rese>* ,laboratories1 ,ab]de51 ,md41 :]e ! ma*9e n[ is1 !re are a few copies ( "s long mimeograph$ reports on ! ma*9e & ! way x works4 ,^! 7 prep>$ by ,h4 ,h4 ,gold/9e & o!rs :5 at ! ,moore ,s*ool ( ,electrical ,eng9e]+1 z a "p ( ! contract "u :i* ! ma*9e 0 con/ruct$ = ! ,u4 ,s4 ,gov]nm5t4 ,x is possible t ^! reports might be consult$ on reque/ by s]i\s /ud5ts4 ,"s sci5tific descriptions ( ! ma*9e & its prop]ties are3 ,,burks1 ,,ar?ur ,w41 ,electronic ,comput+ ,circuits ( ! ,,eniac1 ,proce$+s ( ! ,in/itute ( ,radio ,eng9e]s1 vol4 #ce1 no4 #h1 ,aug4 #aidg1 pp4 #gef-gfg4 ,,clipp+]1 ,r4 ,f41 ,a ,logical ,cod+ ,sy/em ,appli$ to ! ,eniac1 ,b4 ,r4 ,l4 ,report ,no4 #fgc1 ,ab]de51 ,md43 ,balli/ic ,rese>* ,laboratories1 ,sept4 #bi1 #aidh1 #da pp4 ,,eck]t1 ,j4 ,,presp]1 ,,jr41 ,,john ,w4 ,,mau*ly1 ,,h]man ,h4 ,,gold/9e1 & ,j4 ,g4 ,,bra9]d1 ,description ( ! ,,eniac & ,comm5ts on ,electronic ,digital ,comput+ ,ma*9es1 ,appli$ ,ma!matics ,panel ,report #aga4b,r1 ,wa%+ton1 ,d4 ,c43 ,national ,def5se ,rese>* ,committee1 ,nov4 #aide1 #gh pp4 ,,gold/9e1 ,,h]man ,h41 & ,,adele ,,gold/9e1 ,! ,electronic ,num]ical ,integrator & ,comput] 7,,eniac71 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #b1 no4 #ae1 ,july #aidf1 pp4 #ig-aaj4 ,,h>tree1 ,d4 ,r41 ,! ,,eniac1 an ,electronic ,comput+ ,ma*9e1 ,nature1 vol4 #aeh1 ,oct4 #ab1 #aidf1 pp4 #ejj-ejf4 ,,h>tree1 ,d4 ,r41 ,calculat+ ,ma*9es3 ,rec5t & ,prospective ,developm5ts & ,_! ,impact on ,ma!matical ,physics1 ,cambridge1 ,engl&3 ,! ,univ]sity ,press1 #aidg1 #dj pp4 7,pages #ad to #bg are devot$ to ! ,eniac47 ,,tabor1 ,,lewis ,p41 ,brief ,description & ,op]at+ ,*>act]i/ics ( ! ,,eniac1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #ca-ci4 ,"s ( ! less te*nical articles on ,eniac are3 ,,rose1 ,a41 ,lightn+ ,/rikes ,ma!matics3 ,,eniac1 ,popul> ,sci5ce1 vol4 #adh1 ,apr4 #aidf1 pp4 #hc-hf4 ,,anonym\s1 ,robot ,calculator3 ,,eniac1 ,all ,electronic ,device1 ,bus9ess ,week1 ,feb4 #af1 #aidf1 p4 #ej 444 ,,anonym\s1 ,answ]s by ,,eny3 ,electronic ,num]ical ,integrator & ,comput]1 ,,eniac1 ,newsweek1 vol4 #bg1 ,feb4 #ah1 #aidf1 p4 #gf4 ,,anonym\s1 ,adds 9 _/ ,second3 ,electronic ,comput+ ,ma*9e at ! ,univ]sity ( ,p5nsylvania1 ,sci5ce ,news ,lett]1 vol4 #di1 ,feb4 #bc1 #aidf1 p4 #aac 444 ,,anonym\s1 ,,eniac3 at ! ,univ]sity ( ,p5nsylvania1 ,"t1 vol4 #dg1 ,feb4 #be1 #aidf1 p4 #ij4 ,,anonym\s1 ,x ,?9ks ) ,electrons2 ! ,,eniac1 ,popul> ,me*anics1 vol4 #he1 ,june #aidf1 p4 #aci4 ,,anonym\s1 ,electronic ,calculator3 ,,eniac1 ,sci5tific ,am]ican1 vol4 #agd1 ,june #aidf1 p4 #bdh4 ,,bell ,,laboratories ,,relay ,,comput]s ,z yet no full-scale sci5tific report is available on ! ,bell ,laboratories g5]al-purpose relay comput]s t w5t to ,ab]de5 & ,langley ,field4 ,h[ev]1 !re is "s in=mation ab\t ^! & o!r ,bell ,laboratories relay comput+ ma*9es 9 ! foll[+ articles3 ,,alt1 ,,franz ,l41 ,a ,bell ,telephone ,laboratories' ,comput+ ,ma*9e 7two p>ts71 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #ba1 ,jan4 #aidh1 pp4 #a-ac1 & vol4 #c1 no4 #bb1 ,apr4 #aidh1 pp4 #fi-hd4 ,,ces>eo1 ,o41 ,! ,relay ,int]polator1 ,bell ,laboratories ,record1 vol4 #bd1 no4 #ab1 ,dec4 #aidf1 pp4 #deg-dfj4 ,,juley1 ,,joseph1 ,! ,balli/ic ,comput]1 ,bell ,laboratories ,record1 vol4 #be1 no4 #a1 ,jan4 #aidg1 pp4 #e-i4 ,,williams1 ,,samuel ,b41 ,a ,relay ,comput] = ,g5]al ,application1 ,bell ,laboratories ,record1 vol4 #be1 no4 #b1 ,feb4 #aidg1 pp4 #di-ed4 ,,williams1 ,,samuel ,b41 ,bell ,telephone ,laboratories' ,relay ,comput+ ,sy/em1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #dj-fh4 ,,anonym\s1 ,complex ,comput] ,demon/rat$1 ,bell ,laboratories ,record1 vol4 #ai1 no4 #b1 ,oct4 #aidj1 pp4 v-vi4 ,,anonym\s1 ,comput] ,m>k #bb ,mod4 #j3 ,developm5t & ,description1 ,navord ,report ,no4 #agh-de1 ,wa%+ton1 ,d4 ,c43 ,navy ,dep>tm5t1 ,dec4 #f1 #aide1 #bbe pp4 ,,anonym\s1 ,relay ,comput] = ! ,army1 ,bell ,laboratories ,record1 vol4 #bf1 no4 #e1 ,may #aidh1 pp4 #bjh-bji4 ,,! ,,kal9-,,burkh>t ,,logical-,,tru? ,,calculator ,z yet !re are no publi%$ ref]5ces on ! ,kal9-,burkh>t ,logical-,tru? ,calculator4 ,"s books cov]+ a good deal ( ma!matical logic are3 ,,qu9e1 ,w4 ,v41 ,ma!matical ,logic1 ,new ,york3 ,w4 ,w4 ,norton ,co41 #aidj1 #cdh pp4 ,,rei*5ba*1 ,,hans1 ,elem5ts ( ,symbolic ,logic1 ,new ,york3 ,! ,macmillan ,co41 #aidg1 #ddd pp4 ,,t>ski1 ,,alfr$1 ,introduction to ,logic1 ,new ,york3 ,ox=d ,univ]sity ,press1 #aida1 #bci pp4 ,,woodg]1 ,j4 ,h41 ,! ,axiomatic ,me?od 9 ,biology1 ,cambridge1 ,engl&3 ,! ,univ]sity ,press1 #aicg1 #agd pp4 ,*apt] #b1 pp4 #ah-eb1 is an excell5t & und]/&able summ>y ( ! concepts ( ma!matical logic4 ,sev]al pap]s on ! application ( ma!matical logic to ! analysis ( practical situations are3 ,,b]keley1 ,,edmund ,c41 ,boolean ,algebra 7,! ,te*nique = ,manipulat+ 8,&10 8,or10 8,n10 & ,conditions7 & ,applications to ,insurance1 ,record ( ! ,am]ican ,in/itute ( ,actu>ies1 vol4 #bf1 ,oct4 #aicg1 pp4 #cgc-dad4 ,,b]keley1 ,,edmund ,c41 ,conditions ,affect+ ! ,application ( ,symbolic ,logic1 ,j\rnal ( ,symbolic ,logic1 vol4 #g1 no4 #d1 ,dec4 #aidb1 pp4 #afj-afh4 ,,%annon1 ,,claude ,e41 ,a ,symbolic ,analysis ( ,relay & ,swit*+ ,circuits1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #eg1 #aich1 pp4 #gac-gbc4 ,?is pap] has _h a good deal ( influ5ce "h & !re on ! developm5t ( electric circuits us+ relays4 ,! foll[+ report discusses ! solution ( "s problems ( ma!matical logic by means ( a l>ge-scale digital calculator3 ,,t>ski1 ,,alfr$1 ,a ,decision ,me?od = ,elem5t>y ,algebra & ,geometry1 ,report ,r-#aji1 ,cali=nia3 ,r& ,corporation1 ,aug4 #a1 #aidh1 #fj pp4 ,,o!r ,,digital ,,ma*9es ,,f9i%$ ,,or ,,"u ,,developm5t ,! ,aik5 ,m>k ,,ii ,relay ,calculator ,! ,computation ,laboratory ( ,h>v>d ,univ]sity f9i%$ dur+ #aidg a second l>ge relay calculator1 call$ ! ,aik5 ,m>k ,,ii ,relay ,calculator4 ,?is ma*9e is allud$ to briefly at ! end ( ,*apt] #aj & is describ$ m fully 9 ! foll[+3 ,,campbell1 ,,rob]t ,v4 ,d41 ,m>k ,,ii ,calculator1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #fi-gi4 ,,freel&1 ,,/eph5 ,l41 ,inside ! ,bigge/ ,man-,made ,bra91 ,popul> ,sci5ce1 ,may #aidg1 pp4 #ie-ajj4 ,,mill]1 ,,fr$]ick ,g41 ,application ( ,pr9t+ ,telegraph ,equipm5t to ,l>ge-,scale ,calculat+ ,ma*9]y1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bac-bbb4 ,! ,edsac ,! ,edsac is a ma*9e "u con/ruction 9 ,engl&4 ,,wilkes1 ,m4 ,v41 ,! ,design ( a ,practical ,high-,spe$ ,comput+ ,ma*9e3 ! ,,edsac1 ,proce$+s ( ! ,royal ,society1 s]ies ,a1 vol4 #aie1 #aidh1 pp4 #bgd-bgi4 ,,wilkes1 ,m4 ,v41 & ,w4 ,,r5wick1 ,an ,ultrasonic ,memory ,unit = ! ,,edsac1 ,electronic ,eng9e]+1 vol4 #bj1 no4 #bde1 ,july #aidh1 pp4 #bjh-bac4 ,! ,edvac ,! ,edvac is a ma*9e "u con/ruction at ! ,moore ,s*ool ( ,electrical ,eng9e]+1 ,philadelphia4 ,,koons1 ,,flor5ce1 & ,,samuel ,,lubk91 ,conv]sion ( ,numb]s f ,decimal to ,b9>y ,=m 9 ! ,,edvac1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bf1 ,apr4 #aidi1 pp4 #dbg-dca4 ,,anonym\s1 ,,edvac ,replaces ,,eniac1 ,! ,p5nsylvania ,gazette1 ,philadelphia3 ,univ]sity ( ,p5nsylvania1 vol4 #de1 no4 #h1 ,apr4 #aidg1 pp4 #i-aj4 ,! ,,ibm ,selective-,sequ5ce ,electronic ,calculator ,! ,,ibm ,selective-,sequ5ce ,electronic ,calculator 0 f9i%$ & ann\nc$ 9 ,janu>y #aidh1 & is allud$ to briefly at ! end ( ,*apt] #aj4 ,m in=mation ab\t ?is ma*9e is 9 ! foll[+ ref]5ces3 ,,eck]t1 ,w4 ,j41 ,electrons & ,computation1 ,! ,sci5tific ,mon?ly1 vol4 #fg1 no4 #e1 ,nov4 #aidh1 pp4 #cae-cbc4 ,,int]national ,,bus9ess ,,ma*9es ,,corporation1 ,,ibm ,selective-,sequ5ce ,electronic ,calculator1 ,new ,york3 ,int]national ,bus9ess ,ma*9es ,corporation 7=m no4 #eb-cibg-j71 #aidh1 #af pp4 ,! ,ray!on ,comput] ,! ,ray!on ,comput] is a ma*9e "u con/ruction at ! ,ray!on ,manufactur+ ,co41 ,wal?am1 ,mass4 ,,blo*1 ,r4 ,m41 ,r4 ,v4 ,d4 ,,campbell1 & ,m4 ,,ellis1 ,! ,logical ,design ( ! ,ray!on ,comput]1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #bhf-bie4 ,,blo*1 ,r4 ,m41 ,r4 ,v4 ,d4 ,,campbell1 & ,m4 ,,ellis1 ,g5]al ,design ,consid]ations = ! ,ray!on ,comput]1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #cag-cbc4 ,a 8,sy/em ( ,electric ,remote-,control ,acc\nt+0 ,dur+ ! #aicj's a sy/em us+ connect$ pun*-c>d ma*9]y 0 exp]im5t$ ) 9 a dep>tm5t /ore 9 ,pittsburgh4 ,! purpose ( ! sy/em 0 automatic acc\nt+ & analysis ( sales4 ,?is sy/em is describ$ 93 ,,woodruff1 ,l4 ,f41 ,a ,sy/em ( ,electric ,remote-,control ,acc\nt+1 ,transactions ( ! ,am]ican ,in/itute ( ,electrical ,eng9e]s1 vol4 #eg1 ,feb4 #aich1 pp4 #gh-hg4 ,! ,univac ,! ,univac is a ma*9e "u con/ruction at ! ,eck]t-,mau*ly ,comput] ,corporation1 ,philadelphia4 ,a simil> b small] digital comput] call$ ! ,b9ac is also be+ develop$4 ,,eck]t-,,mau*ly ,,comput] ,,corporation1 ,! ,univac ,sy/em1 ,philadelphia3 ,eck]t-,mau*ly ,comput] ,corp41 #aidh1 #h pp4 ,,electronic ,,control ,,co4 7n[ ,,eck]t-,,mau*ly ,,comput] ,,corp471 ,a ,t5tative ,in/ruction ,code = a ,/ati/ical ,edvac1 ,philadelphia3 ,electronic ,control ,co4 7n[ ,eck]t-,mau*ly ,comput] ,corp471 ,may #g1 #aidg1 #ai pp4 ,,snyd]1 ,,frances ,e41 & ,,hub]t ,m4 ,,liv+/on1 ,cod+ ( a ,laplace ,b\nd>y ,value ,problem = ! ,,univac1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #be1 ,jan4 #aidi1 pp4 #cda-cej4 ,! ,zuse ,comput] ,! ,zuse ,comput] is a small digital comput] con/ruct$ 9 ,g]many4 ,,lyndon1 ,,rog] ,c41 ,! ,zuse ,comput]1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #b1 no4 #bj1 ,oct4 #aidg1 pp4 #cee-cei4 ,,! ,,design ,,( ,,digital ,,ma*9es ,foll[+ are a numb] ( ref]5ces on v>i\s aspects ( ! design ( digital comput+ ma*9es3 ,organization ,,burks1 ,,ar?ur ,w41 ,sup]-,electronic ,comput+ ,ma*9e1 ,electronic ,indu/ries1 vol4 #e1 no4 #g1 ,july #aidf1 p4 #fb4 ,,burks1 ,,ar?ur ,w41 ,,h]man ,h4 ,,gold/9e & ,,john ,,von ,,neumann1 ,prelim9>y ,discussion ( ! ,logical ,design ( an ,electronic ,comput+ ,in/rum5t1 ,pr9ceton1 ,n4 ,j43 ,in/itute = ,advanc$ ,/udy1 #bnd edition1 ,sept4 #aidg1 #db pp4 ,,eck]t1 ,j4 ,,presp]1 ,,jr41 ,,john ,w4 ,,mau*ly1 & ,j4 ,r4 ,,we9]1 ,an ,octal ,sy/em ,automatic ,comput]1 ,electrical ,eng9e]+1 vol4 #fh1 no4 #d1 ,apr4 #aidi1 p4 #cce4 ,,=re/]1 ,,jay ,w41 ,,w>r5 ,s4 ,,l\d1 ,,rob]t ,r4 ,,ev]ett1 & ,,david ,r4 ,,br[n1 ,lectures by ,project ,:irlw9d ,/aff on ,electronic ,digital ,computation1 ,cambridge1 ,mass43 ,massa*usetts ,in/itute ( ,te*nology1 ,s]vo-me*anisms ,laboratory1 ,m>4 & ,apr4 #aidg1 #adi pp4 ,,lubk91 ,,samuel1 ,decimal ,po9t ,location 9 ,comput+ ,ma*9es1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #ba1 ,jan4 #aidh1 pp4 #dd-ej4 ,,patt]son1 ,,george ,w41 editor1 & o!rs1 ,!ory & ,te*niques = ,design ( ,electronic ,digital ,comput]s 7subtitle3 ,lectures ,giv5 at ! ,moore ,s*ool #h ,july #aidf-ca ,augu/ #aidf71 ,philadelphia3 ,! ,univ]sity ( ,p5nsylvania1 ,moore ,s*ool ( ,electrical ,eng9e]+1 vol4 #a1 lectures #a-aj1 ,sept4 #aj1 #aidg1 #afa pp42 vol4 #b1 lectures #aa-ba1 ,nov4 #a1 #aidg1 #agc pp42 vol4 #c & #d 9 prep>ation4 ,,/ibitz1 ,,george ,r41 ,relay ,comput]s1 ,appli$ ,ma!matics ,panel ,report #aga4a,r1 ,wa%+ton1 ,d4 ,c43 ,national ,def5se ,rese>* ,c\ncil1 ,feb4 #aide1 #hc pp4 ,,/ibitz1 ,,george ,r41 ,%\ld ,automatic ,comput]s be ,l>ge or ,small8 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #b1 no4 #bj1 ,oct4 #aidg1 pp4 #cfb-cfd4 ,,/ibitz1 ,,george ,r41 ,! ,organization ( ,l>ge-,scale ,calculat+ ,ma*9]y1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #ia-ajj4 ,,/ibitz1 ,,george ,r41 ,a ,new ,class ( ,comput+ ,aids1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bc1 ,july #aidh1 pp4 #bag-bba4 ,input & ,output ,devices ,,alex&]1 ,,samuel ,n41 ,input & ,output ,devices = ,electronic ,digital ,calculat+ ,ma*9]y1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bdh-bec4 ,,full]1 ,,h>rison ,w41 ,! ,num]oscope1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bch-bdg4 ,o',,neal1 ,r4 ,d41 ,photographic ,me?ods = ,h&l+ ,input & ,output ,data1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bfj-bff4 ,,tyl]1 ,,ar?ur ,w41 ,optical & ,photographic ,/orage ,te*niques1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #adf-aej4 ,,zworyk91 ,v4 ,k41 ,l4 ,e4 ,,flory1 & ,w4 ,s4 ,,pike1 ,lett]-,read+ ,ma*9e1 ,electronics1 vol4 #bb1 no4 #f1 ,june #aidi1 pp4 #hj-hf4 ,,anonym\s1 ,lett]-,pr9t+ ,ca?ode-,ray ,tube1 ,electronics1 vol4 #bb1 no4 #f1 ,june #aidi1 pp4 #afj-afb4 ,/orage ,devices ,,brill\91 ,,leon ,n41 ,electromagnetic ,delay ,l9es1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #aaj-abd4 ,,=re/]1 ,,jay ,w41 ,high-,spe$ ,electro/atic ,/orage1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #abe-abi4 ,,haeff1 ,,&rew ,v41 ,! ,memory ,tube & its ,application to ,electronic ,computation1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bd1 ,oct4 #aidh1 pp4 #bha-bhf4 ,,kornei1 ,,otto1 ,survey ( ,magnetic ,record+1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bbc-bcg4 ,,moore1 ,,b5jam9 ,l41 ,magnetic & ,phosphor ,coat$ ,discs1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #acj-acb4 ,,raj*man1 ,,jan ,a41 ,! ,selectron--,a ,tube = ,selective ,electro/atic ,/orage1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #b1 no4 #bj1 ,oct4 #aidg1 pp4 #cei-cfa & frontispiece4 ,,%>pless1 ,t4 ,,kite1 ,m]cury ,delay ,l9es z a ,memory ,unit1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #ajc-aji4 ,,%epp>d1 ,c4 ,,brad=d1 ,transf] ,betwe5 ,ext]nal & ,int]nal ,memory1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bfg-bgc4 ,programm+ or ,cod+ ,,ev]ett1 ,,rob]t ,r41 ,digital ,comput+ ,ma*9e ,logic 7memor&um ,m-#fc71 ,cambridge1 ,mass43 ,massa*usetts ,in/itute ( ,te*nology1 ,s]vo-me*anisms ,laboratory1 ,m>4 #ai1 #aidg1 #dh pp4 ,,gold/9e1 ,,h]man ,h41 & ,,john ,,von ,,neumann1 ,plann+ & ,cod+ ( ,problems = an ,electronic ,comput+ ,in/rum5t1 ,pr9ceton1 ,n4 ,j43 ,in/itute = ,advanc$ ,/udy1 #aidg1 #fi pp4 ,,gold/9e1 ,,h]man ,h41 & ,,john ,,von ,,neumann1 ,plann+ & ,cod+ ( ,problems = an ,electronic ,comput+ ,in/rum5t1 ,pr9ceton1 ,n4 ,j43 ,in/itute = ,advanc$ ,/udy1 "p #b1 vol4 #c1 #aidh1 #bc pp4 ,,mau*ly1 ,,john ,w41 ,prep>ation ( ,problems = ,edvac-,type ,ma*9es1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #bjc-bjg4 ,,digital ,,ma*9es--,,miscellane\s ,_m ( ! foll[+ articles are nonte*nical & conta9 mu* int]e/+ in=mation ab\t ma*9es t ?9k3 ,,alt1 ,,franz ,l41 ,new ,high-,spe$ ,comput+ ,devices1 ,! ,am]ican ,/ati/ician1 vol4 #a1 no4 #a1 ,aug4 #aidg1 pp4 #ad-ae4 ,,bu%1 ,,vannev>1 ,z ,we ,may ,?9k1 ,atlantic ,mon?ly1 ,july #aide1 pp4 #aja-ajh4 ,,condon1 ,,edw>d ,u41 ,! ,electronic ,bra9 ,means a ,bett] ,future = ,y 7broadca/71 ,columbia ,broadca/+ ,sy/em1 ,jan4 #d1 #aidh4 ,,davis1 ,,h>ry ,m41 ,ma!matical ,ma*9es1 ,sci5tific ,am]ican1 vol4 #ahj1 no4 #d1 ,apr4 #aidi1 pp4 #bi-ci4 ,,lagemann1 ,,john ,k41 ,x ,all ,adds ,up1 ,colli]'s ,magaz9e1 ,may #ca1 #aidg1 pp4 #bb-bc 444 ,,locke1 ,e4 ,l41 ,mod]n ,calculators1 ,a/\nd+ ,sci5ce ,fiction1 vol4 #eb1 no4 #e1 ,jan4 #aidi1 pp4 #hg-ajf4 ,,maclaughlan1 ,,lorne1 ,electrical ,ma!maticians1 ,a/\nd+ ,sci5ce ,fiction1 vol4 #ec1 no4 #c1 ,may #aidi1 pp4 #ic-ajh4 ,,mann1 ,,m>t91 ,want to ,buy a ,bra98 ,popul> ,sci5ce1 vol4 #aed1 no4 #e1 ,may #aidi1 pp4 #adh-aeb4 ,,newman1 ,,james ,r41 ,cu/om-,built ,g5ius1 ,new ,republic1 ,june #bc1 #aidg1 pp4 #ad-ah4 ,,pfeiff]1 ,,john ,e41 ,! ,ma*9e ,t ,plays ,g9 ,rummy1 ,sci5ce ,illu/rat$1 vol4 #d1 no4 #c1 ,m>4 #aidi1 pp4 #df-dh 444 ,,rid5\r1 ,,l\is ,n41 ,me*anical ,bra9s1 ,=tune1 vol4 #ci1 no4 #e1 ,may #aidi1 pp4 #ajh-aah4 ,,tumbleson1 ,,rob]t ,c41 ,calculat+ ,ma*9es1 ,f$]al ,sci5ce ,progress1 ,june #aidg1 pp4 #c-g4 ,,anonym\s1 ,almo/ ,human1 ,home ,(fice ,news1 ,new>k1 ,n4 ,j43 ,prud5tial ,insurance ,company ( ,am]ica1 ,feb4 #aidg1 p4 #h4 ,,applications ,,( ,,digital ,,ma*9es ,"s ( ! problems t me*anical bra9s c solve1 "s ( ! me?ods = controll+ !m to solve problems1 & "s ( ! implications ( me*anical bra9s = future problems are cov]$ 9 ! foll[+ ref]5ces3 ,solv+ ,problems ,,b]keley1 ,,edmund ,c41 ,electronic ,ma*9]y = ,h&l+ ,in=mation1 & its ,uses 9 ,insurance1 ,transactions ( ! ,actu>ial ,society ( ,am]ica1 vol4 #dh1 ,may #aidg1 pp4 #cf-eb4 ,,b]keley1 ,,edmund ,c41 ,electronic ,sequ5ce ,controll$ ,calculat+ ,ma*9]y & ,applications 9 ,insurance1 ,proce$+s ( #aidg ,annual ,conf]5ce1 ,life ,(fice ,managem5t ,association1 ,new ,york3 ,life ,(fice ,managem5t ,association1 #aidg1 pp4 #aaf-abi4 ,,curry1 ,,haskell ,b41 & ,,willa ,a4 ,,wyatt1 ,a ,/udy ( ,inv]se ,int]polation ( ! ,eniac1 ,b4 ,r4 ,l4 ,report ,no4 #fae1 ,ab]de51 ,md43 ,balli/ic ,rese>* ,laboratories1 ,aug4 #ai1 #aidf1 #ajj pp4 ,,h>rison1 ,,joseph ,o41 ,,jr41 & ,,hel5 ,,malone1 ,piecewise ,polynomial ,approximation = ,l>ge-,scale ,digital ,calculators1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bf1 ,apr4 #aidi1 pp4 #djj-djg4 ,,h(fleit1 ,,dorrit1 ,a ,comp>ison ( ,v>i\s ,comput+ ,ma*9es ,us$ 9 ,r$uction ( ,doppl] ,obs]vations1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #be1 ,jan4 #aidi1 pp4 #cgc-cgg4 ,,leontief1 ,,wassily ,w41 ,computational ,problems ,aris+ 9 ,connection ) ,economic ,analysis ( ,int]9du/rial ,relation%ips1 ,proce$+s ( a ,symposium on ,l>ge-,scale ,digital ,calculat+ ,ma*9]y1 ,cambridge1 ,mass43 ,h>v>d ,univ]sity ,press1 #aidh1 pp4 #afi-age4 ,,lotk91 ,,max1 ,inv]sion on ! ,eniac ,us+ ,osculatory ,int]polation1 ,b4 ,r4 ,l4 ,report ,no4 #fcb1 ,ab]de51 ,md43 ,balli/ic ,rese>* ,laboratories1 ,july #ae1 #aidg1 #db pp4 ,,l[an1 ,,arnold ,n41 ,! ,computation ,laboratory ( ! ,national ,bureau ( ,/&>ds1 ,scripta ,ma!matica1 vol4 #ae1 no4 #a1 ,m>4 #aidi1 pp4 #cc-fc4 ,,matz1 ,,adolph1 ,electronics 9 ,acc\nt+1 ,acc\nt+ ,review1 vol4 #ba1 no4 #d1 ,oct4 #aidf1 pp4 #cga-cgi4 ,,mcph]son1 ,,james ,l41 ,applications ( ,high-,spe$ ,comput+ ,ma*9es to ,/ati/ical ,"w1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bb1 ,apr4 #aidh1 pp4 #aba-abf4 ,,mit*ell1 ,,h]b]t ,f41 ,,jr41 ,inv]sion ( a ,matrix ( ,ord] #ch1 ,ma!matical ,tables & ,o!r ,aids to ,computation1 vol4 #c1 no4 #bc1 ,july #aidh1 pp4 #afa-aff4 ,,anonym\s1 ,revolutioniz+ ! ,(fice1 ,bus9ess ,week1 ,may #bh1 #aidi1 no4 #ajcj1 pp4 #fe-gb4 ,spee* ,"s ( ! possibilities ( ma*9es deal+ ) voice & spee* are indicat$ 93 ,,dudley1 ,,hom]1 ,r4 ,r4 ,,riesz1 & ,s4 ,s4 ,a4 ,,watk9s1 ,a ,syn!tic ,speak]1 ,j\rnal ( ! ,frankl9 ,in/itute1 vol4 #bbg1 ,june #aici1 pp4 #gci-gfd4 ,?is is an article on ! ,vod]1 :i* is an abbreviation ( ,voice ,op]ation ,demon/rator4 ,! ma*9e 0 exhibit$ at ! ,new ,york ,_w's ,fair1 #aici4 ,,dudley1 ,,hom]1 ,! ,vocod]1 ,bell ,laboratories ,record1 vol4 #ah1 no4 #d1 ,dec4 #aici1 pp4 #abb-abf4 ,?is is a m g5]al type ( ma*9e ?an ! ,vod]4 ,! ,vocod] is bo? an analyz] & syn!siz] ( human spee*4 ,,pott]1 ,,ralph ,k41 ,,george ,a4 ,,kopp1 & ,,h>riet ,c4 ,,gre51 ,visible ,spee*1 ,new ,york3 ,d4 ,van ,no/r& ,co41 #aidg1 #dda pp4 ,,anonym\s1 ,p$ro ! ,vod]3 ,a ,ma*9e t ,talks1 ,bell ,laboratories ,record1 vol4 #ag1 no4 #f1 ,feb4 #aici1 pp4 #agj-aga4 ,wea!r ,"s ( ! possibilities ( ma*9es deal+ ) wea!r in=mation are cov]$ 93 ,,lagemann1 ,,john ,k41 ,mak+ ,wea!r to ,ord]1 ,new ,york ,h]ald ,tribune3 ,?is ,week1 ,feb4 #bc1 #aidg4 ,,%alett1 ,,sidney1 ,electronics to ,aid ,wea!r ,figur+1 ,! ,new ,york ,times1 ,jan4 #aa1 #aidf4 ,,zworyk91 ,v4 ,k41 ,outl9e ( ,wea!r ,proposal1 ,pr9ceton1 ,n4 ,j43 ,radio ,corporation ( ,am]ica ,rese>* ,laboratories1 ,oct4 #aide1 #aa pp4 ,,anonym\s1 ,wea!r ,"u ,control1 ,=tune1 ,feb4 #aidh1 pp4 #ajf-aaa 444 ,! ,robot ,ma*9e ,,apek1 ,,k>el1 ,r4 ,u4 ,r4 7translat$ f ! ,cze* by ,paul ,selv]71 ,new ,york3 ,d\bl$ay1 ,page ,co41 #aibc4 ,,lagemann1 ,,john ,k41 ,f ,piggly ,wiggly to ,ke$oozle1 ,colli]'s ,magaz9e1 vol4 #abb1 no4 #ah1 ,oct4 #cj1 #aidh1 pp4 #bj-ba 444 ,,leav]1 ,e4 ,w41 & ,j4 ,j4 ,,br[n1 ,ma*9es ,)\t ,m51 ,=tune1 vol4 #cd1 no4 #e1 ,nov4 #aidf1 pp4 #afe 444 ,,pease1 ,m4 ,c41 ,devi\s ,weapon1 ,a/\nd+ ,sci5ce ,fiction1 vol4 #ec1 no4 #b1 ,apr4 #aidi1 pp4 #cd-dc4 ,,%annon1 ,,claude ,e41 ,programm+ a ,comput] = ,play+ ,*ess1 ,bell ,telephone ,laboratories1 ,oct4 #h1 #aidh1 #cd pp4 ,,%elley1 ,,m>y ,w41 ,frank5/e9 79 ,ev]yman's ,libr>y1 ,no4 #faf71 ,new ,york3 ,e4 ,p4 ,dutton ,co41 la/ repr9t$ #aide1 #bdb pp4 ,,spilhaus1 ,,a!l/an1 ,let ,robot ,"w = ,y1 ,! ,am]ican ,magaz9e1 ,dec4 #aidh1 p4 #dg 444 ,,anonym\s1 ,ano!r ,new ,product = ,robot ,salesm51 ,mod]n ,indu/ry1 vol4 #ac1 no4 #b1 ,feb4 #ae1 #aidg4 ,,anonym\s1 ,! ,automatic ,factory1 ,=tune1 vol4 #cd1 no4 #e1 ,nov4 #aidf1 p4 #afj 444 ,,anonym\s1 ,ma*9es ,pr$ict ,:at ,happ5s 9 ,y\r ,plant1 ,bus9ess ,week1 ,sept4 #be1 #aidh1 pp4 #fh-fi 444 ,,"n ,,index ,note3 ,?is li/ ( p]sons m5tion$ 9 ! text includes names ( fictional *>act]s4 ,! subject index1 :i* foll[s1 includes all o!r names4 ,aik51 ,h[>d ,h41 #ij-aab1 #agg-h1 #bcb1 #bde-f ,alex&]1 ,samuel ,n41 #bea ,alqui/1 #bjj ,alt1 ,franz ,l41 #adb1 #bcg1 #bdg1 #bec ,ar*]1 ,r4 ,m41 #bda ,ari/otle1 #aeb ,babbage1 ,*>les1 #hi ,baehne1 ,g4 ,walt]1 #bcb ,bailey1 ,c4 ,f41 #bcg ,b>cr(t1 ,joseph1 #bbi ,bea*1 ,frank ,a41 #bbi ,be>d1 ,r4 ,e41 #hh1 #bdj ,b]keley1 ,edmund ,c41 #bcc1 #bdh1 #bed ,b]ry1 ,r4 ,j4 ,a41 #bbi ,b]ry1 ,t4 ,m41 #bdj ,blo*1 ,ri*>d ,m41 #bdf1 #bej ,bloomfield1 ,leon>d1 #bca ,bodm]1 ,fr$]ick1 #bca ,boelt]1 ,l4 ,m4 ,k41 #bdj ,boole1 ,george1 #aeb ,bor+1 ,edw9 ,g41 #bbi ,b[]1 ,e4 ,c41 #bcg ,bra9]d1 ,j4 ,g41 #bdg ,brill\91 ,leon ,n41 #beb ,br[n1 ,david ,r41 #bea ,br[n1 ,g4 ,s41 #bde ,br[n1 ,j4 ,j41 #bee ,br[n1 ,s4 ,l41 #bda-b ,buck+ham1 ,r4 ,a41 #bdj ,burkh>t1 ,william1 #add1 #aee-f ,burks1 ,ar?ur ,w41 #bdf1 #bea ,bu%1 ,vannev>1 #gb1 #gd1 #bci1 #bda1 #bde1 #bec ,caldwell1 ,samuel ,h41 #gd1 #bci1 #bda ,campbell1 ,rob]t ,v4 ,d41 #bdi-ej apek1 ,k>el1 #aii1 #bee ,c>roll1 ,lewis1 #ab ,c>t]1 ,g4 ,k41 #bdd ,ces>eo1 ,o41 #bdh ,clem5ce1 ,g4 ,m41 #bcg ,clipp+]1 ,r4 ,f41 #bdf ,comrie1 ,john ,leslie1 #bcb ,concordia1 ,c41 #bdd ,condon1 ,edw>d ,u41 #bec ,crew1 ,e4 ,w41 #bcb ,cr9]1 ,h4 ,e41 #bde ,culley1 ,frank ,l41 #bcg ,curry1 ,haskell ,b41 #bed ,davis1 ,h>ry ,m41 #bec ,dem+1 ,w4 ,edw>ds1 #bcg ,dietzold1 ,rob]t ,l41 #bdd ,dom91 ,h>ry1 #aii ,dudley1 ,hom]1 #bed-e ,duncan1 ,w4 ,j41 #bdd ,dunlap1 ,jack ,w41 #bcg ,dwy]1 ,paul ,s41 #bcg ,dy]1 ,h4 ,s41 #bcg ,eck]t1 ,j4 ,presp]1 ,jr41 #aad1 #agh1 #bdg1 #bea ,eck]t1 ,w4 ,j41 #bcc1 #bcf-g1 #bci1 #bej ,edison1 ,?omas ,a41 #ae ,ellis1 ,m41 #bej ,enns1 ,w4 ,e41 #bdc ,ev]ett1 ,rob]t ,r41 #bea-b ,fe9/e91 ,lillian1 #bcg ,fles*1 ,rudolf1 #bca ,flory1 ,l4 ,e41 #beb ,=re/]1 ,jay ,w41 #bea-b ,frame1 ,j4 ,su!rl&1 #bdd ,frank5/e91 ,victor1 #aih1 #bjj ,franz1 ,%eph]d ,i41 #bbi ,freel&1 ,/eph5 ,l41 #bdi ,fry1 ,macon1 #bcb ,full]1 ,h>rison ,w41 #beb ,fr?1 ,r41 #bdb ,gage1 ,f4 ,d41 #bde ,g5et1 ,n41 #bci1 #bdf ,godw91 ,m>y ,w4 7,m>y ,w4 ,%elley71 #aih1 #bee ,gold/9e1 ,adele1 #bdg ,gold/9e1 ,h]man ,h41 #bdg1 #bea1 #bec ,gove1 ,e4 ,l41 #bde ,graff1 ,willem ,l41 #bca ,graham1 ,r4 ,s41 #bdd ,gray1 ,t4 ,s41 #bde ,gre51 ,h>riet ,c41 #bee ,haeff1 ,&rew ,v41 #beb ,hans51 ,morris ,h41 #bcg ,h>rison1 ,joseph ,o41 ,jr41 #bdf1 #bed ,h>t1 ,h4 ,c41 #bdd ,h>tkemei]1 ,h>ry ,pelle1 #bcc ,h>tree1 ,d4 ,r41 #bcb1 #bdj-a1 #bdg ,haupt1 ,ralph ,f41 #bcg ,hayakawa1 ,s4 ,i41 #bca ,haz51 ,h4 ,l41 #bdc1 #bde ,h$eman1 ,w4 ,r41 #bde ,h$ley1 ,k4 ,j41 #bcc ,h]get1 ,paul1 #bcg ,h]r1 ,d4 ,l41 #bdd ,h]rick1 ,c4 ,judson1 #bbi ,h(fleit1 ,dorrit1 #bed ,hogb51 ,launcelot1 #bca ,holl]i?1 ,h]man1 #dc ,hopp]1 ,grace ,m41 #bdf ,horsburgh1 ,e4 ,h41 #bcb ,hotell+1 ,h>old1 #bcg ,h\sehold]1 ,al/on ,s41 #bcj ,jesp]s51 ,otto1 #bca ,juley1 ,joseph1 #bdh ,kal91 ,!odore ,a41 #add1 #aee-f ,kelv91 ,"l1 #gb1 #bdj ,k+1 ,gilb]t ,w41 #bch ,koons1 ,flor5ce1 #bdi ,kopp1 ,george ,a41 #bee ,kormes1 ,j5nie ,p41 #bch ,kormes1 ,m>k1 #bch ,kornei1 ,otto1 #beb ,kranz1 ,fr$]ick ,w41 #bdb ,kron1 ,gabriel1 #bdc-d ,kud]1 ,g4 ,fr$]ic1 #bch ,kuehni1 ,h4 ,p41 #bdj1 #bdc ,lagemann1 ,john ,k41 #bec1 #bee ,l&ahl1 ,h]b]t ,d41 #bcj ,lang1 ,h4 ,c41 #bcc ,la%ley1 ,k>l ,s41 #bbi ,leav]1 ,e4 ,w41 #bee ,leontief1 ,wassily ,w41 #bed ,lettv91 ,j]ome ,y41 #bcj ,lilley1 ,s41 #bcb ,liv+/on1 ,hub]t ,m41 #bej ,locke1 ,e4 ,l41 #bec ,lorra9e1 ,r4 ,g41 #bdc ,lotk91 ,max1 #bed ,l\d1 ,w>r5 ,s41 #bea ,l[an1 ,arnold ,n41 #bed ,lubk91 ,samuel1 #bdi1 #bea ,lyndon1 ,rog] ,c41 #bej ,mac,laughlan1 ,lorne1 #bec ,mag9niss1 ,f4 ,j41 #bda ,mallock1 ,r4 ,r4 ,m41 #bdd ,malone1 ,hel51 #bed ,mann1 ,m>t91 #bec ,m>ble1 ,f4 ,g41 #bdb ,massey1 ,h4 ,s4 ,w41 #bdj ,ma/ukazi1 ,kiyo%i1 #ai ,matz1 ,adolph1 #bed ,mau*ly1 ,john ,w41 #aad1 #agh1 #bdg1 #bea1 #bec ,maxfield1 ,d4 ,k41 #bch ,maxwell1 ,l4 ,r41 #bdb ,mc,cann1 ,g4 ,d41 #bde ,mc,culloch1 ,w>r5 ,s41 #bcj ,mc,laughlin1 ,ka?le51 #bch ,mc,pherson1 ,james ,l41 #bed ,mc,pherson1 ,john ,c41 #bch ,mea*am1 ,alan ,d41 #bcg ,m]cn]1 ,r4 ,o41 #bdd ,mill]1 ,dayton ,c41 #bdb ,mill]1 ,fr$]ick ,g41 #bdi ,milliman1 ,w5dell ,a41 #bch ,milne1 ,j4 ,r41 #bdb ,mit*ell1 ,h]b]t ,f41 ,jr41 #bed ,montgom]y1 ,h4 ,c41 #bdb ,moore1 ,b5jam9 ,l41 #beb ,moore1 ,c4 ,r41 #bdb ,murray1 ,francis ,j41 #bcb ,my]s1 ,d4 ,m41 #bde ,newman1 ,james ,r41 #bec ,ogd51 ,c4 ,k41 #bca ,o',neal1 ,r4 ,d41 #beb ,p>k]1 ,w4 ,w41 #bdc ,patt]son1 ,george ,w41 #bea ,pease1 ,m4 ,c41 #bee ,pek]is1 ,c4 ,l41 #bde ,pet]son1 ,h4 ,a41 #bdj1 #bdc-d ,pfeiff]1 ,john ,e41 #bec ,pi]on1 ,h5ri1 #bbi ,pike1 ,w4 ,s41 #beb ,pitts1 ,walt]1 #bcj ,poes*1 ,h41 #bdj ,port]1 ,a41 #bdj-a ,pott]1 ,ralph ,k41 #bee ,pr+le1 ,r4 ,w41 #bdb ,qu9e1 ,w4 ,v41 #bdh ,raj*man1 ,jan ,a41 #beb ,ra%evsky1 ,n41 #bcj ,raymond1 ,w4 ,j41 #bdb ,rei*5ba*1 ,hans1 #bdh ,r5wick1 ,w41 #bdi ,rid5\r1 ,l\is ,n41 #bec ,riesz1 ,r4 ,r41 #bed ,rob]tson1 ,j4 ,m41 #bdb ,rose1 ,a41 #bdg ,rossum1 #aii ,roy]1 ,elm] ,b41 #bch ,sau]1 ,r41 #bdj ,s*lau*1 ,m>g>et1 #bca ,s*nackel1 ,h4 ,g41 #bcc ,s*rd+]1 ,erw91 #bbi ,s*w>z*ild1 ,m>t91 #bcg ,%alett1 ,sidney1 #bee ,%annon1 ,claude ,e41 #aec-e1 #bda1 #bdh1 #bee ,%>pless1 ,t4 ,kite1 #beb ,%elley1 ,m>y ,w41 #aih1 #bee ,%elley1 ,p]cy ,bys%e1 #aih ,%epp>d1 ,c4 ,brad=d1 #beb ,%]r+ton1 ,*>les ,s41 #bbi ,smi?1 ,c4 ,e41 #bde ,snyd]1 ,frances ,e41 #bej ,som]ville1 ,j4 ,m41 #bdb ,spilhaus1 ,a!l/an1 #bee ,/ew>t1 ,r4 ,r41 #bde ,/ibitz1 ,george ,r41 #abi-cj1 #bdd1 #bea ,/raiton1 ,a4 ,w41 #bdb ,tabor1 ,lewis ,p41 #bdg ,t>ski1 ,alfr$1 #bdh-i ,t]hune1 ,g4 ,k41 #bdb ,?omas1 ,george ,b41 #bch ,?omson1 ,james1 #bdj ,?omson1 ,william1 #gb1 #bdj ,tilney1 ,fr$]ick1 #bbi ,torrey1 ,v41 #bdf ,travis1 ,irv51 #bci1 #bdd ,tumbleson1 ,rob]t ,c41 #bec ,turck1 ,j4 ,a4 ,v41 #bcb ,tyl]1 ,ar?ur ,w41 #beb ,v>ney1 ,r4 ,n41 #bdc von ,neumann1 ,john1 #abd1 #bea ,wa9wright1 ,lawr5ce ,l41 #gb1 #bda ,walpole1 ,hugh ,r41 #bca ,watk9s1 ,s4 ,s4 ,a41 #bed ,wegel1 ,r4 ,l41 #bdb ,we9]1 ,j4 ,r41 #bea ,:eel]1 ,l4 ,l41 #bda-b ,:itt51 ,c4 ,a41 #bch ,wi5]1 ,norb]t1 #bbi ,wilbur1 ,j4 ,b41 #bdd ,wilkes1 ,m4 ,v41 #bdi ,williams1 ,samuel ,b41 #bdh ,wolf1 ,ar?ur ,w41 #bcc ,wom]sley1 ,j4 ,r41 #bda ,wood1 ,?omas1 #ai ,woodg]1 ,j4 ,h41 #bdh ,woodruff1 ,l4 ,f41 #bej ,wyatt1 ,willa ,a41 #bed ,wylie1 ,j41 #bdj ,yavne1 ,r4 ,o41 #bde ,zworyk91 ,v4 ,k41 #aij1 #beb1 #bee ,,subject ,,index ,notes3 ,phrases consi/+ ( an adjective & a n\n1 or ( a n\n & a n\n1 are ent]$ 9 _! alphabetical place accord+ to ! fir/ ^w4 ,= example1 8electro/atic /orage tube0 is "u e1 & 8pun* c>d0 is "u p4 ,a field1 #ii ,a tape1 #hb-c abacus1 #ag-i1 #acc1 #bbj abax 7,greek71 #ah absolute value1 #aja1 #bbb accumulator1 #aae-f accumulator decade1 #aah accuracy1 #fg1 #hi acetyl*ol9e1 #c add output1 #abj add5d1 #bbc add]1 #gg add] me*anism1 #gg-h add+1 #bd-e1 #bg1 #cg1 #ee1 #ajj1 #aai1 #aci addition circuit1 #cg ,aik5 ,m>k ,i ,calculator1 #aj1 #hi-aab1 #bde-f2 see also ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator ,aik5 ,m>k ,,ii ,relay ,calculator1 #agf-h1 #bdi ,aik5 ,m>k ,,iii ,electronic ,calculator1 #agg air resi/ance coeffici5t1 #hj-b algebra ( logic1 #bf1 #cf1 #ef-fb1 #aje1 #adj1 #aea-b1 #afd1 #bba-c1 #bdh algebraic equations1 ma*9es = solv+1 #bdd all-or-none response1 #c alphabet1 #ad alphabetic cod+1 #ac1 #ed alphabetic pun*+1 #df alphabetic writ+1 #ac amplify1 #gc analog\s1 #fe analogue1 #fe analogue ma*9es 7ma*9es t h&le in=mation express$ z measurem5ts71 #fe2 ,,mit ,diff]5tial ,analyz] ,no4 #b1 #fe-hh2 ref]5ces1 #bci-de analytical eng9e1 #ij analyz]1 #fh1 #bda-d2 see also diff]5tial analyz] &1 #adf-h &_/or1 #adi angle-indicator1 #gd-e animal ?9k+1 #d1 #h1 #ahh annuities1 #hh antec$5t1 #aeh antilog>i?m1 #aci1 #bbf antitang5t1 #aci1 #bbf approximation1 #bbj2 see also rapid approximation aptitude te/+1 #aij argum5t 79 a ma!matical table or function71 #if1 #ajc-d1 #abb1 #acf1 #bbd ari?metical op]ations1 #ee-f1 #agc armor ) a motor1 #ahj1 #aie array1 #agc1 #bbg ,atomic ,en]gy ,commission1 #bjc1 #bjh attitudes1 #bje aug5d1 #bbc aut 7,lat971 #adi automatic address-book1 #aha automatic c>riage1 #ec 8,automatic ,comput+ ,ma*9]y0 7section 9 ,ma!matical ,tables & ,o!r ,aids to ,computation71 #agg automatic control3 h\se-furnace1 #ahi2 lawn-m[]1 #ahh2 tractor-pl[1 #ahh2 wea!r1 #ahi automatic cook1 #aha automatic factory1 #ahi automatic libr>y1 #i1 #aha automatic ma*9]y1 #ahb automatic pilot1 #ahi automatic recogniz]1 #ahf-g automatic sequ5ce-controll$ calculator1 #ij2 see also ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator automatic /5ograph]1 #ahe automatic swit*+ circuits1 #bdh automatic translator1 #ahb automatic typi/1 #ahb1 #ahd axon1 #c ,b field1 #ii ,b tape1 #hb-c ,balli/ic ,rese>* ,laboratories1 #a1 #aac-e1 #abg-h1 #acb1 #adb base e1 #bbf base #aj1 #bbf beam ( electrons1 #agb behavior1 #d1 #g-h1 #bi ,bell ,telephone ,laboratories1 #d-e1 #abh-dc1 #bdg-h ,bell ,telephone ,laboratories' g5]al-purpose relay comput]1 #abh-dc1 #bdg-h2 co/1 #adb2 reliability1 #ada2 spe$1 #adb ,bessel functions1 #aaa1 #bbf ,b9ac1 #agi b9>y cod+1 #aa1 #ac b9>y digit1 #ad b9>y numb]s1 #ad1 #baf-i biophysics1 #bcj biqu9>y numb]s1 #acc1 #bai-bj blocks ( argum5ts1 #acg ,boolean algebra1 #aeb1 #bdh2 see also ma!matical logic bo?1 #adi b[w[ !ory1 #ab bra9 evolution1 #bbi bra9 ) a motor1 #ahj1 #aie ,,btl frames1 #ach-i bus1 #cb1 #aai button1 #ia1 #id ,c field1 #ii ,c tape1 #hb-c calcis 7,lat971 #ah calculat+ pun*1 #dg1 #ea-b1 #bce calculator frames1 #ach calculator programm$ by pun* c>ds1 #bcf cam1 #id-e cam contact1 #ia1 #id-e capacitance1 #aag capacitor1 #aag capacity3 c\nt]1 #ei2 select+1 #ei c>bon dioxide1 #aij c>d *annel1 #dg1 #eb c>d column1 #dh c>d fe$1 #dh1 #ia c>d pun*1 #ia1 #ig c>d read]1 #aaf1 #aah c>d sort]1 #if c>d /ack]1 #dh c>d /ation1 #dg ,c>negie ,in/itution ( ,wa%+ton1 #aac c>ry impulse1 #aah cell nucleus1 #b-c c5sus1 #dc1 #ec *annel1 #dg1 #eb1 #agj *>act]i/ic ( a log>i?m1 #ajg *eck c\nt]1 #aje *eck-m>ks1 #aea *eck+1 #aje1 #aaj1 #agi1 #bbg *ess game1 #aag *e/nut blight1 #bja *ortle1 #ab class selector1 #ei cle>+1 #ajj codes1 #bi1 #ed1 #if1 #ii cod+1 #cj1 #acj1 #beb-c cod+ l9e1 #ii column 79 a pun* c>d71 #de connective1 #adh1 #aeh-i connective gr\p+1 #aei collat+1 #ea1 #agc collator1 #dg1 #ea1 #bce collator c\nt+ device1 #ea1 #bce comb9+ in=mation1 #ae comb9+ op]ations1 #agc ,common1 #ei-fj comp>]1 #eg-h comp>+1 #ej1 #eg-h complem5t1 #ee2 see also n9es complem5t1 ones complem5t1 t5s complem5t ,complex ,comput]1 #abi-cj complex numb]s1 #abh-i comput]1 #f1 #bg ,comput] #a & ,comput] #b1 #acb1 #ach conflicts betwe5 /atem5ts1 #adi-ej consequ5t1 #aeh con/ant1 #bbd con/ant ratio1 #gg con/ant regi/]1 #if1 #ii con/ant swit*1 #ii ,con/ant ,transmitt]1 #aaf1 #aah consult+ a table1 #ajc1 #abb conv]g5t1 #bba ,conv]t]1 #aae context1 #add cont9u\s annuities1 #hh cont9u\s cont+5t insurances1 #hh cont9u\sly runn+ ge>1 #ic control1 #f1 #bh1 #ij-a control bru%es1 #ea-b control frames1 #ach-i ,control ,in/rum5t ,company1 #dc control ov] robot ma*9es1 #aif-bjh control tape1 #bh controv]sy1 #aig cos9e1 #ge1 #he1 #aci1 #bbf co/ ( me*anical bra9s1 #hg1 #aji1 #abf1 #adb1 #afe1 #afh c\nt]1 #eb1 #gd1 #ic-d c\nt] position1 #ic c\nt] :eel1 #ic1 #aah c\nt+1 #ee c\pl+ 7numb]s71 #ajf cube1 #aje1 #bbd ,curr5t 7input ( comp>]71 #eg cycle1 #bi1 #de ,cycl+ ,unit1 #aae-f ,cypriote1 #ac ,d>tm\? ,college1 #aca decade1 #aah decimal digit1 #aa1 #ad decimal position1 #aah deciph]+1 #ahd1 #ahh decod+1 #ahd1 #ahh def9ite integral1 #aaa1 #bbe delay l9es1 #ag1 #bj1 #aga-b d5drite1 #c d5ial1 #adg dep5d5t v>iable1 #ha1 #bbd d]ivative1 #fh-ga1 #bbe design ( me*anical bra9s1 #afg-gi1 #bea desk calculat+ ma*9es1 #d1 #aa1 #ag1 #ai detail c>ds1 #ej dial swit*1 #ib1 #ie-f dial telephone1 #ag1 #ai1 #abh diff]5ces1 #aaj1 #bbg diff]5tial1 #fh1 #gj1 #gh diff]5tial analyz]1 #fh1 #gb-hh1 #bci-da ,diff]5tial ,analyz] ,no4 #b1 #fe-hh2 accuracy1 #hf2 co/1 #hg2 reliability1 #hg2 spe$1 #hg diff]5tial equation1 #fh-i1 #ga1 #aaa1 #ada1 #bbe-f diff]5tial function1 #gj diff]5tial ge> assembly1 #gh digit1 #aa1 #ad ,digit ,pickup1 #fj digit selector1 #fj digit tray1 #aai digit trunk l9es1 #aai digit trunks1 #aai digital ma*9es 7ma*9es t h&le in=mation express$ z digits or lett]s73 ,bell ,laboratories' g5]al-purpose relay calculator1 #abh-dc2 ,eniac1 #aac-bg2 ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator1 #hi-aab2 pun*-c>d calculat+ ma*9]y1 #db-fd2 ref]5ces1 #bcb-i1 #bde-ee directions1 #bd disc1 #gh-hj discrim9ation1 #adj discrim9ator1 #adj-a di/ance1 #fh-i di/+ui%+ ,a & ,h1 #ahd divid5d1 #ajc1 #bbc ,divid]-,squ>e-,root]1 #aae-g divid+1 #ee-f1 #ih1 #ajb1 #aba1 #adj divisor c\nt]1 #ajb doorpo/1 #fe-f d\bl+1 #gf-g1 #ajj d\bl+ me*anism1 #gf-g draft+ rules1 #adi drag coeffici5t1 #hj drive1 #hf ,dry ,ice1 #aij e*o1 #aga ,eck]t-,mau*ly ,comput] ,corporation1 #agi1 #bej economic relations1 #aid ,edsac1 #bdi 8educat$0 ma*9e1 #aja ,edvac1 #agg1 #bdi ,egyptian1 #ab ei!r1 #adi electric *>ge1 #agb electric remote-control acc\nt+1 #bej electric typewrit]1 #ia1 #ig1 #bcf electromagnet1 #afh ,electronic ,b9>y ,automatic ,comput]1 #agi electronic calculat+ pun*1 #bcf ,electronic ,control ,company1 #bej ,electronic ,num]ical ,integrator & ,calculator 7,eniac71 #aac-bg1 #bdf-g2 see also ,eniac electronic tubes1 #ag1 #bj-a1 #agh-i2 ,ca?ode1 #ba2 ,grid1 #ba2 ,plate1 #ba electro/atic /orage tube1 #ag1 #bj1 #agb #aa position1 #de #aa pun*1 #eh else1 #adf-g end-ar\nd-c>ry1 #ie1 #bag1 #bbc eng9e1 #ij ,eniac1 #aac-bg1 #bdf-g2 co/1 #abf2 panels1 #aae2 reliability1 #abf2 spe$1 #abe2 unbalance1 #abd 8en\gh alike10 #ahd ,equal 7output ( sequ5c]71 #fa-b equation1 #fh1 #bbe equival5t1 #ad erase key1 #acd ,etruscan1 #ahh explanation1 #bji-ac explicit equation1 #hf expon5tial1 #he1 #ajf1 #bbe-f extraction1 #bbb falsity1 #adg f>ad1 #aag f+]s1 #af1 #ah fire-control in/rum5t1 #ag1 #ai1 #fg1 #aca #e impulse1 #ef flights1 #gj flip-flop1 #aai foll[+ logically1 #ade =m fe$+ device1 #bcf =mal logic1 #aeb =mula1 #fh1 #gj1 #bbd ,frank5/e9's mon/]1 #aih function1 #fh1 #gj1 #ha1 #ajc1 #aaf1 #aah1 #bbd function table1 #hj-a1 #aaf1 #aah gang pun*+1 #ej ge>box1 #gg-h ,g5]al ,electric ,a4,c4 ,network ,analyz]1 #bdc ,g5]al ,electric ,company1 #bdc geographic code1 #ed giant bra91 #a1 #e-h globe1 #fe-f graph1 #ha great circle1 #fi great]-?an1 #be-g1 #cg1 #bbb great]-?an circuit1 #cg ,greek lett]s1 #abj guid$ missile1 #aig1 #bjf gun1 #fi hail /orm1 #aij h& p]=ator1 #acb1 #acd h&l+ in=mation1 #aj-ah h>monic analyz]s1 #bda-b h>monic syn!siz]s1 #bda-b ,h>v>d ,computation ,laboratory1 #hi1 #agf-g1 #bde1 #bdi ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator 7,m>k ,i71 #aj1 #hi-aab1 #bde-f2 co/1 #aji2 effici5cy1 #aaa2 reliability1 #aaj2 spe$1 #aji ,h>v>d ,sequ5ce-,controll$ ,electronic ,calculator 7,m>k ,,iii71 #agg ,h>v>d ,sequ5ce-,controll$ ,relay ,calculator 7,m>k ,,ii71 #agf-h1 #bdi ,h>v>d ,univ]sity1 #a1 #d1 #h1 #hi1 #agf-g1 #bde1 #bdi hatr$1 #bjf hopp]s1 #ea hub1 #df1 #ih human bra91 #b-d1 #af1 #bbi humidity1 #fc ,,ibm 7,int]national ,bus9ess ,ma*9es71 #dc-fd1 #hi-ij1 #agg1 #bcc-i1 #bdi-ej ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator1 #aj1 #hi-aab1 #bde-f2 see also ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator ,,ibm c>d-programm$ calculator1 #bcf ,,ibm pluggable sequ5ce relay calculator1 #bcf ,,ibm pun*-c>d ma*9]y1 #dc-fd1 #bcc-i ,,ibm ,selective-,sequ5ce ,electronic ,calculator1 #agg-i1 #bdi ideographic writ+1 #ab if1 #adf-g if 444 !n1 #adi ignorance1 #bje illness1 #aia-b imitative s*eme1 #ab 9-code1 #ii 9-field1 #ii indep5d5t v>iable1 #ha1 #bbd inf9ity1 #hf1 #acc1 #bab1 #bbe in=mation1 #aj initial conditions1 #hc1 #bbe ,initiat+ ,unit1 #aae-f input1 #f1 #ij-a input devices1 #age1 #bea-b input regi/]1 #bg in/antane\s rate ( *ange1 #gj-a ,in/itute ( ,advanc$ ,/udy1 #abd in/ructions1 #bh1 #hc1 #ig1 #agh-i insurance company1 #db insurance policies1 #db insurance values1 #hh integral1 #fh1 #ga-b1 #bbe integral sign1 #he1 #bbe integrat+1 #ga-b1 #gh integrator1 #gh-hj integrator me*anism1 #gh-i ,int]national ,bus9ess ,ma*9es ,corporation 7,,ibm71 #dc2 see ,,ibm ,int]national ,hydrographic ,bureau1 #bdb ,int]national ,phonetic ,alphabet1 #ac int]polat+1 #aca1 #bba int]pos+1 #ajb int]pret]1 #dg1 #di1 #bce int]pret+1 #di int]val1 #fh1 #gj intuitive ?9k+1 #h inv]se1 #ga judgm5ts1 #aia ,kal9-,burkh>t ,logical-,tru? ,calculator1 #add-ff1 #bdh2 co/1 #afe2 reliability1 #aff2 spe$1 #aff key pun*1 #dg-h1 #if1 #bce keybo>d1 #dh knots1 #ag language ( logic1 #ef-fb1 #aje1 #adj2 see also ma!matical logic languages1 #aj-ba1 #bca lat* relay1 #dj-a left-h& compon5ts1 #ef1 #aba1 #bae libr>y1 #i1 #aha ,libr>y ( ,congress1 #ae lie detector1 #aib l9e ( cod+1 #ii l9e>1 #bbd-e l9e> int]polation1 #bba l9e> simultane\s equations1 #ada1 #bbe lobe1 #id-e log>i?m1 #fg1 #he1 #ajf-h1 #aci1 #bbe ,log>i?m-,9-,out c\nt]1 #ajg logic1 #add2 see also ma!matical logic logical *oice1 #d2 see also ma!matical logic logical connective1 #adh1 #bbb logical op]ations1 #ef-fb1 #agc logical patt]n1 #ade-f logical tru?1 #add-ef1 #aff ,logical-,tru? ,calculator1 #add-ff2 see ,kal9-,burkh>t ,logical-,tru? ,calculator loopholes1 #adi ,l[ ,prim>y 7output ( sequ5c]71 #fa-b ,l[ ,second>y 7output ( sequ5c]71 #fa-b ,l[] ,bru%es1 #eb loxodrome1 #fi-gj ma*9e call numb]1 #ii ma*9e cycle1 #ef ma*9e language1 #bi1 #ii1 #age1 #aia ma*9es z a language = ?9k+1 #ai-bj2 ref]5ces1 #bca-b ma*9es involv+ voice & spee*1 #ahe-f1 #bed magnetic surfaces1 #ag1 #bj1 #afh-gj1 #agi magnetic tape1 #afi-gj1 #agi magnetic wire1 #afh magnetiz$ spot1 #afh-gj ma9 connective1 #afj _m-wire cable1 #ej ,m>k ,i 7,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator71 #aj1 #hi-aab1 #bde-f2 see also ,h>v>d ,,ibm ,automatic ,sequ5ce-,controll$ ,calculator ,m>k ,,ii 7,h>v>d ,sequ5ce-,controll$ ,relay ,calculator71 #agf-h1 #bdi ,m>k ,,iii 7,h>v>d ,sequ5ce-,controll$ ,electronic ,calculator71 #agg ,massa*usetts ,in/itute ( ,te*nology1 #a1 #bj1 #fe1 #gb-hh1 #aec ,massa*usetts ,in/itute ( ,te*nology's ,diff]5tial ,analyz] ,no4 #b1 #fe-hh2 accuracy1 #hf2 co/1 #hg2 reliability1 #hg2 spe$1 #hg ma/] c>d1 #ej ,ma/] ,programm]1 #aae-f mat*+1 #agc ma!matical biophysics1 #bcj ma!matical logic1 #bf1 #cf1 #ef-fb1 #aje1 #adj1 #aea-b1 #afd1 #bba-c1 #bdh matrices1 #agc1 #bbg matrix1 #agc1 #bbg mean+s1 #bji1 #bca measurem5ts1 #fe-f1 #fh me*anical bra91 #a1 #e-h1 #bj2 crucial devices =1 #bj me*anical bra9s "u con/ruction1 #agf-i memory1 #bg1 #ij-a m5tality1 #bd1 #bg m]cury tank1 #aga1 #agi m]g+1 #agc metal f+]s1 #ace mica1 #agb microphone1 #ahe mimeograph /5cil1 #af ,m9oan1 #ahh miscellane\s field1 #ii mi/ake1 #acd ,moore ,s*ool ( ,electrical ,eng9e]+1 #g1 #aac-bg1 #agg1 #bdi multiplic&1 #bbc multiplic& c\nt]1 #aja multiplication s*emes1 #bad-f multipli]1 #aae-f multipli] c\nt]1 #aja multiply-divide unit1 #ajc multiply+1 #ee-f1 #aja1 #aba1 #adj multiply+ pun*1 #dg1 #eb1 #bce ,national ,advisory ,committee = ,a]onautics1 #abh1 #acb ,naval ,prov+ ,gr\nd1 #agg negation1 #bd-e1 #bg1 #cd-f negation circuit1 #cf negative1 #adg negative digit1 #bae neon bulb1 #aai n]ve1 #b-d n]ve cell1 #b1 #c1 #af n]ve fib]1 #b1 #c n]ve networks1 #bcj n]v\s sy/em1 #ahh network analyz]s1 #bdb-d neurosis1 #aia n9e-pulses1 #abj-a n9es complem5t1 #ie1 #aba1 #bbc ,no ,x1 #ei ,nor?rop ,aircraft1 ,inc41 #agi n1 #adf-h num]ic cod+1 #ac1 #ed num]ical ,x position1 #de num]ical ,y position1 #de occupation code1 #ed octal notation1 #agi1 #bai ohm1 #aag ,ojibwa1 #ab ones complem5t1 #bag only1 #adf-g op]ation code1 #ajc op]ations ) numb]s1 #bd-g or1 #adf-i organization ( digital ma*9es1 #bea out-code1 #ii out-field1 #ii output1 #f1 #ij-a1 #bea-b output devices1 #agf1 #bea-b output regi/]1 #bg pap] *annel1 #eb p>tial diff]5tial equations1 #hg p>tial products1 #aae1 #bad ,pe>l ,assurance ,company1 #hh pebbles1 #ag-h p5 ) a motor1 #ahj1 #aie p]man5t table frames1 #ach-i p]sonal income tax1 #ada phonetic writ+1 #ac phonograph1 #ae-f phonographic writ+1 #ac phototube1 #ha-b1 #ahc-d physical equipm5t = h&l+ in=mation1 #aa1 #ae-ba1 #ia physical problems1 #fi-gb physical quantities1 #fg-i pictographic writ+1 #ab plugbo>d1 #df1 #ih plug-9 units1 #aag-h po9t ( view1 #bjg pooh-pooh !ory1 #ab position 79 a pun* c>d71 #de position frames1 #ach-i p[]1 #dc1 #fe1 #acc1 #baf1 #bbd prejudice1 #bje ,previ\s 7input ( comp>]71 #eg ,prim>y 7input ( sequ5c]71 #fa-b ,prim>y ,bru%es1 #ea1 #fb ,prim>y ,fe$1 #ea1 #fa ,prim>y ,sequ5ce ,bru%es1 #ea pr9t]1 #acg pr9t] frames1 #ach problem frames1 #ach problem position1 #acb1 #ace problem tape1 #acd processor1 #acb1 #acd1 #age product1 #gj1 #ajb1 #bbc product c\nt]1 #ajb production s*$ul+1 #aic program1 #abb1 #agc1 #beb-c program-control swit*1 #abc program pulse1 #abb program-pulse input t]m9al1 #abc program regi/]1 #ch program tape1 #bh-i program trays1 #aai program trunk l9es1 #aai programm+ me?od ( von ,neumann1 #abd pron\n1 #bbc psy*ological te/+1 #aij psy*ological tra9]1 #aia-b pulses1 #abj1 #aga pun* c>d1 #ag1 #dd-e1 #ie1 #ig pun*-c>d column1 #de pun*-c>d ma*9]y1 #ag1 #bj1 #db-fd1 #bcb-i2 co/1 #fc2 reliability1 #fc-d2 spe$1 #fb-c pun* fe$1 #ea-b pun*$ pap] tape1 #ag1 #bc1 #hb1 #ie pun*+ *annel1 #ej pun*+ dies1 #dh1 #ea-b pyramid circuit1 #ci quantity ( in=mation1 #aa1 #ad-ae qu>tz1 #aga quoti5t1 #ih1 #ajc ,r4,u4,r41 #aii rad>1 #ahc railroad l9e1 #f1 #aai rapid approximation1 #ajf-h1 #bbj-a rate ( *ange1 #fh1 #gj-a ratio1 #gg1 #hc ,ray!on ,comput]1 #bej read+1 #eg read+ bru%es1 #ea-b read+ *annel1 #ej read+ ( pun* c>ds1 #dd reason+1 #add rebus-writ+1 #ac reciprocal1 #he1 #bbd recogniz+1 #h1 #ahb-e record]1 #acb1 #acg rectifi]1 #cb ref]5t1 #ab regi/]1 #bg reject1 #di relay1 #ag1 #bj-a1 #bc1 #ib1 #abi1 #acc1 #agh2 ,common1 #ba2 ,gr\nd1 #ba2 ,normally ,clos$1 #ba2 ,normally ,op51 #ba2 ,pickup1 #ba release key1 #dh reliability1 #fc-d1 #aaj1 #abf1 #abh1 #ada-b1 #aff1 #afh1 #agd ,rem+ton-,r&1 #dc rep]=ator1 #acg rephras+1 #afc-d reproduc]1 #dg1 #di-ej1 #bce reproduc+1 #di reset code1 #ajj resett+1 #ajj resi/ance1 #hj1 #aag resi/ance coeffici5t1 #hj resi/or1 #aag "r-h& compon5ts1 #ef1 #aba1 #bae robot ma*9e1 #aig1 #aih-bjh1 #bee robot salesman1 #bja robota 7,cze*71 #aii ,roman num]als1 #bab2 anci5t /yle1 #bai room1 #gj ,rossum's ,univ]sal ,robots1 #aii r\nd+ (f1 #ee-f r\t9e1 #h1 #afg1 #agc r\t9e frames1 #ach-i r\t9e tape1 #bh1 #acd rules1 #aia1 #bbd satisfy1 #bbe scale factor1 #gd1 #hf s*emes = express+ mean+s1 #aa-ae scre51 #agb screw1 #gh ,second>y 7input ( sequ5c]71 #fa-b ,second>y ,bru%es1 #ea1 #fb ,second>y ,fe$1 #fa ,select-,receiv+-,regi/] circuit1 #ci select+1 #bf1 #eh1 #ajd selection1 #bf-g1 #ch1 #bbb selection circuit1 #ch selection c\nt]1 #ajd selector1 #eh-fj s5s+ digits1 #ajh sep>ation sign1 #abi sequ5ce-control tape1 #ih sequ5ce-control-tape code1 #ih sequ5ce-controll$1 #hi sequ5ce-tape fe$1 #ih sequ5c]1 #fa sequ5c+1 #fa %ift+1 #bag %ort-cut multiplication1 #bae-f ,simon1 #bb-dj simultane\s1 #bbe simultane\s equations1 #he1 #bbe s9e1 #ge1 #he1 #ajf1 #aci1 #bbf s9k 7( a circuit71 #aed slab1 #ah slide rule1 #fe1 #fg smoo?ness1 #aaj1 #bbg social control1 types1 #bjc sort]1 #dg-i sort+1 #eg1 #agc s\ndtracks1 #af1 #ah s\rce 7( a circuit71 #aed space key1 #dh spe$omet]1 #fh spell+ rules1 #ahe spok5 ,engli%1 #aa squ>e1 #bbd squ>e matrix1 #bbg squ>e root1 #aaf-g1 #agc1 #bbj1 #bbd ,/>t ,key1 #ih /atem5ts1 #bf1 #add-ea /atic electricity1 #fc /orage1 #f /orage c\nt]1 #ic /orage devices1 #beb /orage regi/]1 #bh1 #ic /or+ in=mation1 #ae /or+ regi/] frames1 #ach /or+ regi/]s1 #aci /r+1 #fe-f /ylus1 #af subr\t9e1 #ajf ,subsidi>y ,sequ5ce ,me*anism1 #ij1 #ajf subtract output1 #abj subtract+1 #ee1 #ajj1 #aai1 #aci1 #bbc subtract+ by add+1 #bbc summ>y pun*1 #ej1 #aaf1 #aai summ>y-pun*+1 #ej swit* op5 & curr5t fl[+1 #aed swit*bo>d1 #gf swit*es 9 p>allel1 #aed swit*es 9 s]ies1 #aed swit*+ circuits1 #aee syllable-writ+1 #ac syllables1 #baa syllogism1 #adf1 #aeb symbolic logic1 #bba-c1 #bdh2 see also ma!matical logic symbolic writ+1 #ab synapse1 #c ,sy/em ( ,electric ,remote-,control ,acc\nt+1 #bej sy/ems = h&l+ in=mation1 #aj table tape1 #acd tables 7( values71 #ajc1 #acf1 #bbd tabul> value1 #acf1 #bbd tabulator1 #dg1 #eb1 #aai1 #bce tallies1 #ag tang5t1 #aje1 #bbf tank 7armor$71 #ahj1 #aie tank 7m]cury tank71 #aga1 #agi tape-controll$ c>riage1 #bcf tape fe$1 #ia1 #agh-i tape pun*1 #ia1 #ig-h1 #acg tape reels1 #agj tape transmitt]1 #ace1 #acg telegraph l9e1 #f1 #aai telephone c5tral /ation1 #ach teletype1 #ag teletype transmitt]1 #acc1 #ace teletypewrit]1 #acj1 #acg t5-position relay1 #ia-c t5-position swit*1 #ia-b t5-pulses1 #abj-a t5s complem5t1 #bbd te/ scor+ ma*9e1 #bcf !n1 #adf-g !rmo/at1 #ahg ?9k+1 #a-e1 #aj1 #ig tim$ electrical curr5ts1 #dd tim+ contact1 #id tol]ances1 #fg1 #aje torque1 #gc1 #hf torque amplifi]1 #gc trajectories1 #fi1 #aad1 #ada transf] circuit1 #cc transf]r+1 #ca1 #cd1 #ajj1 #aai1 #afg translat+1 #eg transmitt]1 #gd trigg]+ control1 #ahc1 #ahf-g trigonometric tables1 #bbf trigonometric tang5t1 #aje1 #bbf tru?1 #add tru? table1 #adg1 #aee1 #bbb tru? value1 #bf1 #eh1 #aje1 #adg1 #bbb tun+1 #ahc turn+ =ce1 #gb #ab position1 #de two-position relay1 #ba1 #ia-b2 see also relay two-position swit*1 #ia-b typewrit]1 #af1 #ah typewrit] c>riage1 #ec unatt5d$ op]ation1 #agd und]/&+1 #bab-c1 #bca unemploym5t1 #bja-b ,unequal 7output ( comp>]71 #eg unit ( in=mation1 #aa1 #ad-e1 #afi ,unit$ ,nations1 #bjc1 #bjh ,unit$ ,/ates ,army ,ordnance ,dep>tm5t1 #aac-d ,univac1 #bej ,univ]sity ( ,p5nsylvania1 #g1 #aac unkn[ns1 #ada ,upp] ,bru%es1 #eb value tape code1 #if value tape fe$1 #ie-f v>iables1 #hd1 #bbc vel 7,lat971 #adi v]ifi]1 #dg-h1 #bce vibration1 #fi ,vocod]1 #bee ,vod]1 #bed voltage1 #gd ,watson ,sci5tific ,comput+ ,laboratory1 #bci wea!r control1 #ahi1 #bee wea!r =eca/+1 #ahi1 #bee :eel 7( a c\nt]71 #gh :ite elephant1 #gc1 #aad w9*1 #gc words = expla9+1 #bji-ab ,x1 #ei ,x di/ributor1 #ei ,x ,pickup1 #ei ,x pun*1 #de1 #eh ,x selector1 #ei z]o1 #acc1 #bab zh 7s\nd71 #ac1 #ahe ,zuse ,comput]1 #bej