WECHSLER, Judith - On Aesthetics in Science

7/25/2019 WECHSLER, Judith - On Aesthetics in Science

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C o p y r i g h i 1 9 7 8 b y T h e M a s s a c h u s e t ts n s t i [ u i e f Te c h n c l c g y

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T h i s b o o k was se t n V- l -P O p t i m a by Wo o d l a n d Craphics , n d p r i n t e d

a n d b o u n d b y The M u r r a y P r i n t i n gC o m p a n y n t h e U n i t e d Sta tes f

A m e r i c a .

L i b r a r yo f C o n g r e s s C a t a l o g i n g n P u b l i c a t i o n D a t a

M a i n en t ry u n d e r i t l e :On a e s t h e t i c s n s c i e n c e .

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O N AESTHETICSN SCIENCE

f h e MIT P r e s sC a m b r i d g e , h 4 a s s a c h u s e t t s , n d L o n d o n , E n g l a n c

Ed re dbyJ u d i t hWechsler


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CONTENTS

INTRODUCTION 1

Judi th Wechsler

STRUCTURAL IEMRCHY N SCIENCE, RT, ANDHISTORY 9

Cyri lStanley mith

O N BROKEN YMMETRIES 55

Ph i l ipM o r r i s o n

VISUALIZATION OSTAND RECAINED: HE CENESIS FTHE QUANTUM THEORY N THE PERTOD 913-27 73

A r t h u r . Mi l l e r

THE MATHEMATICAL NCONSCIOUS 10 5

Seymour . Papert

DARWIN'S TREEOF NATURE" ND OTHER MACES O FWIDE SCOPE 121

Howard E. Cruber

RATIONALITY ND INTUITION 143

Ceoffrey Vickers

SELECTED IBLIOCRAPHY 165

I ND E X 1 7 1


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P R E FA C E O T H E1 9 B B E I S S U E

Nine years have passed irrce he firs t re lease f On Aesthet icsin Sclence.

The course rom which the dea or his volume develooed asnot been aught at MIT sirrce my departure n 1978. But i t hasbeen ewarding o have cont inual posi t ive esponse o the effor tsmade n the course and to this book.

Since he essays re concerned with issues lrat emain essential,we decided o reissue hem as hey appeared n the las t pr int ingwithout ur ther evis ion.

In recent years here have been many new developments nphysics, mathematics, iology, chenristry, and computer sciencewhich sug,Best rui t ful opics or fur ther aesthet ic xplorat ions. na sequel o t l r isbook, I hope o explore some of these ssues i ththe pa r t i c ipa t ion f s c i e n t i s t s nd t h o s e whose d i sc ip l ine s o r -ma l ly h u m a n i s t i c . l s t i l lbe l i eve ha t much of t h e b e s t w o r k insc i ence an be seen n a human i s t i c r a m e w o r k . )

New questions f aesthetics merge around phenonrena whichwil l not obey the order w,e have been taught o perceive or toimpose. We are forced to come to terms with t he not ion of auniverse n inf la t ionary movement , of pat terns rounded n dis-order and chaos-s ta tes hat diverge rom the radi t ional ot ionsof aesthetics n science. What are he aesthetic orollaries o theseneu, heories? ow does he s tudy of f ractals r of s t r ing heoryinfluence our sense f aesthetics? oes he attempt o incorporatenew forms of scient i f ic understanding hat ter xis t ing aesthet ic

assumptions? n a conrputer ge, can intui t ion play he sanre oleas i t did for the physicis ts , l remists , nd engineers n the f i rs tdecades f this century?

In sorne n,ays hese nelv discoveries nd tools paral le l devel-o p m e n t s n t h e v i sua l r t s , hang ing he o lde r no t ions f t h e sep -aratior.r etween order and disorder s well as betvveen he rationaland t h e i r r a t i o n a l . h e ime has c o m e t o e v a l u a t e he mean ingof beautv n aesthet ic onsiderat ions f both science and a r t .

F a l l , 9 8 7 ludi th Wecl-rs ler


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INTRODUCTION

Aesthetic ensibility lays he part of the de/icate ieve.Henri Poincare

Scient is tsalking bout heir wn work and hat of other c ient is tsuse he terms beauty," "elegance," and "economy" r,r,ith heeuphoria f praise more character is t ical ly ppl ied o paint ing,music , nd poetry. r here s he exclamation f recogni t ion-the"Aha" tha t accompanies he discovery f a connect ion r an Lrn-expected ut ut ter ly ight eal izat ion n arl and science. hese reepi thets f the sense f " f i t " -o f f inding he most appropriaie ,evocative nd correspondent xpression or a reality heretoforeunart iculated nd unperceived, ut s t rongly ensed nd act ivelyprobed. he ight ormalism r model which captures" his eal-i ty seems lmost magical n i ts potency. Both art and scienceevoke he previously neffable n making deas nd concepts lear,coSent , nd manipulable .

Heisenberg ecal ls ommenting o Einstein n the orce f rec-ogni t ion e associates i th aesthet ic xperience:Youmay bjecthat yspeaking fsimplci ty nd eauty am ntrod cingaesthetic riteria f ruth, nd rankly dmit hat am stronglv ttracted )'the simplicity nd beauty f the mathematical chemes 'hich atr.rrepresents s. ou must ave el t his oo: he lmost r ighteningimplici tyand vholeness f the ela t ionship, hich ature uddenly preads utb e f o r e u s . . . . '

D e f n i t i on

But he ole of aesthet ic udgment s arely mentioned n the cor-pus f science nd nrathematics . hen cient is ts , owever, ef lect

on heir work, he development f concepts , nd he heories ha texpound hem, t s evident hat ntui t ion nd aesthet ics uide heirsense f " this s how it has o be," heir sense f r ightness .

It s almost oo obvious o say hat fone bel ieves cience o havea s ingular nd exclusive elat ion o real i ty nd assume t to besynonymous i th truth, hen he dea of aesthet ics n scient i f icjudgment r cogni t ionmay seem apricious r marginal . ne ca nst i l regard he products f science s beaut i ful t ruth equalsbeauty) . ut f one views science s a t tenrpt ing o approximatereal i ty, ubject o experiment ut not necessar i ly o verif cat ion,then here s a t i tude, nd one can conceive hat he choice ofalternative hypotheses re subject to aesthetic actors. Karl


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2Judith Vechsler

Popper's heory hat not the verif abilitybut he alsif abilityof asystem be taken as a criteria of demarcation," llows or thatla t i tude. . . . t must e possible or an empir ical cient i f ic ystemto be refuted y experience," e writes n The Logicof ScientifcDiscovery 1959) .

The Oxford English Dict ionary efines esthet ics s "thingspercept ible o the senses , hings mater ia l" s opposed o "thingsthinkable r mm ater ia l ." es thet ics y his ef ini t ion ight ee minappl icable o hose reas f science hose perat ions ppear o

be purely intel lectual- logical rocesses , mathematical or-ma l i sms .

Kant understood he imitat ions f such a def ini t ion hen hecommented n The Cri t ique f Pure Reason, concepts i thoutfactual ontent re empty; ense-data i thout oncepts re bl ind.The senses annot hink.The understanding annot ee. By heirunion only can knowledge e produced,"

ln ts eal ings i th things ercept ible o he senses ," esthet icscomes o grips with rela t ions; t ructure , ontext , schemata,s im ari ty/dssimiar i y, consonance/d ssonance. About solated,s imple ense mpressions esthet ics as i t t le o say.) hese ela-t ions, hich are ometimes eparated rom heir factual ontent"or perceptual

ubstraten science, re stillsubject o aesthetic ref-

erence, s hey are n art or nature where his separation as no tbeen made.

In his ense, antwri tes , es thet ics s the science hich reatsthe condl t lons f sensuous ercept ion" my emphasis) .

A dichotomy xis ts n science etween hose ike Bohrwho as-sume hat heir tar t ing ointand base f ver i f icat ion s sense er -cept ion, nd hose, ike Heisenberg, ho bel ieve hat ense er -cept ion s an unnecessary imitat ion. uch a case s he contrastbetween Hertz and Mach: Hertz advocated purely ntel lectualprocess n his pure natural cience," hi le Mach bel ieved ev -ery statement n physics as o state elations etween bservablequant i t ies ." oth pure cience nd science elated o observat ionare subject o aesthet ic udgment . he aesthet ics f pure elat ionsengages urminds s musicdoesthrough armonic elat ionships .

Intui t ion s wel l as aesthet ic udgments perate n both ap-proaches o science. n ar t , nd n ife ,we acknowledge he placeof aesthetics nd intuition, but we don't readily associate hesemore aci t dimensions i th he ogical rocesses f science. e t ,as Norbert Wiener and Arturo Rosenblueth bserve,An ntuitive lair or what will urnout o be he most mportant eneralquest ion ives basis or select ing ome f the signif icantmong heindefni te umber f r ivial xperrmentsh ch ould e arr ied ut t hats tage. ui te ague nd aci t eneral izat ionshus nfluencehe elect ionof data a t the s taf t . ' ?

5cope

The contr ibutors o this book al l maintain hat aesthet ics s a cru-

cial actor n the scient i f ic rocess . es thet ics s discussed n this

col lect ion ot as a systematic iscipl ine n phi losol lhy, ut as a

mode f discr iminat ion nd esponse-a uidel ine or he appro-priateness f a scient i f ic xpression as n the chapters y Papert

and Vickers) .Aesthet ics s also associated i th visual izat ion Mil ler) , t ruc -

ture Smith) , e taphor, mage, nd analogy Morrison, ruber) 'The ouest ion s aised, ow do aesthet ic onsiderat ions ffect he

form, development , nd eff icacy f models?Aesthet ic ensibi l i ty lso nters he appreciat ive ocle For he

ma ori ty f pract ic ing cient is ts , es thet ic r i ter ia nter n he wa s

of iesponse. he aesthet ics f recogni t ion s at work when we

Brasp n dea, nderstand ow a principle perates , r how a sol t t '

t ion u, found. This ssue s discussed n al l he essays Our ad -

nrirat ion f Copernicus r Newton s of this orcler nd can be ik -

ened o our aesthet ic ppreciat ion f C6zanne, ach, r Mil ton '

Science oo can be a sr lurce f aesthet ic el ight .As n ar t , es ihet ics ssubiect o period tyles swell as personal

ones. t is bound o change n t ime, n bothsubiect nd ocus

There s ample vidence o suSSest hanges rr c ient i f ic tyle nc l

tas te , n the problems osed nd he methods osi ted While a

sense f "f i t" may be t imeless , he context nd conlrect ions n

which a theory irs t merges re af iected y schemata nd radi-

t ion. n the wentieth entury, esthet ics s he appreciat ion fform has expanded o include rocess s ' r 'e l l s procluct '

Process

The emphasis n this book s on process n science, he ssr ' re imodel ing. he inished ork, n scie .nce s n ar t , gi i 'es vicienceof ts process . owever, he balance etween roduct nd proces\

differ n a r tand science. n a r t , t s he inished aint ing, onnet , rsonata hich s normally he subject f our cr i t ic ism r apprecia-t ion. c ience . loesn ' txhibi t roducts or aesthet ic r i t rc ismn hisway; here s hardly ny ecognized ocabulary f aesthet ic r i t i -c ism nd esponse or science. he usual r i ter ion or success" - ri

a scient i fc product-an equat ion, physicalmodel , r a wri t tenpaper- is whether t works, hat s, predicts , xplains Aesthet icjudgments perate n the cognrt ive rocesses f arr iving t thatp od uct.

Our contemporary nterest n process as a history'At he end oithe nineteenth entury, evelopments ccurred n the a r t s an d

sciences hich chal lenged he bel ief n an object ive eal i ty n-

3l n t r o d u c l c n


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J u d i t h We c h s l e rmediated y he subject ive erceiver. n paint ing, he breakdownof "scient i f ic" erspect ive eant n end o an establ ished prior iwav of t ranslat ing eal i ty onto a two-dimensional urface.Cezanne sser led ubject ive ercept ion n the form of shif t ingperspect ives . imilar ly n l i terature , ames oyce omposed isnove l s r o m he mul t ip l e i ew p o i n t s f h i s c h a r a c t e r s .

I t s n this per iod hat science oo began o recognize he ndi-vidual , erceptual nd ntel lectual creen n construct ing odels

of real i ty, or example, n Poincare 's dvocacy f intur t ion ndEinstein 's heory f relat ivi t l , . hese evelopments n he arts ndsciences r t iculated he complex henomenological elat ionshipof subject ive erceiver nd object ive eal i ty.

Nolv more han ever we focus n he e ffec t f process n art an dscrence; ur age s par l icular ly elf-conscious fcogni t ive odes.Because f Freud e are ler l o a tent swel l as manifest ontent .The studies f Piaget , runer, nd other cogni t ive sychologis tsind ica t e he o l e mode l s l ay n our h ink ing . y s t e m s na lys i s n dconceptual r1 urther repare s o look at process ather ha nproouct .

Scient is t ' s redi lect ions re often evealed n their choices ftmagery nd metaphor. ie lsBohr, ecal led eisenberg, quatesthe anguage f poetry nd physics:. . when t comes o atoms, anguage an e used nlv s n poetry. hepoet oo s notnearly oconcerned vith escribingacts s l,ith reatingimages nd establ ishing ental onnect ions. euantum heory . .provides switha s t r ikingl lustrat ionf he act hat , . , , ean ul ly nder-s tand connect ionhough e can nJ '" .speaki t n mages nd arables

Aesthet ics iewed sa mode f scient i f ic ogni t ion ay paral le la scient is t ' s ut look and concern n other areas f l i fe .poincareobserved fmathematici ns , lt is he he erynature f hei mi ndwhichmakes hem ogic i ans r n t u i t i o n a l is t s ,nd heycanno t ay tas ide when hey approach new subiect ." . Werner Heisenbergand NielsBohr f t enwrote f hese inks.

erald Holton as xanr-ined he mapping fpersona ife nto cience n E nstein,s vork.

Intui t ion and Aesthet ics

Bohr, Dirac, Einstein, eisenberg, oinca16, and others ac -knowledge ntui t ive nd aesthet ic udgment s decis ive actors nthe acceptance r re ject ion f a part icular odel .

Poincare as convinced f the role of intui t ion n scient i f icprocess.Pure ogic ould never ead us o ant , thing ut autologies;t couldc r e a t e n o t h i n g n e w ; n o t f r o m it a l o n e c a n a n v s c i e n c e s s u e . n On e

s e n s e h e s e p h l l o s o p h e r s a r e r i g h t ; t o m a k e a r i t h m e t i c , a s t o m a k e

g e o m e t r y, r t o m a k e a n y s c i e n c e , o m e t h i n g l s e h a n p u r e o g i c sn e c e s s a r y. o d e s i g n a t e h i s o m e t h i n g lse v e h a v e o w ' o r d t h e r h a ni n t u i t i o n . 6P o i n c a r e g o e s u r t h e r , i n k i n g i n t u i t i o n w i t h a e s t h e t i c s :I t may a p p e a r u r p r i s i n gha t ens ib i l i ty h o u l d e n t r o d u c e d n c o n n e c -t i o nw i t h m a t h e m a t i c a l emons t ra t io t . t s ,h i c h , t w o u l d s e e t r , a n o n l yi n t e r e s th e n te l l ec t . u t n o t f w e b e a r n mi n d h e e e l i n g f n r a t h e m a t -i c a lb e a u t v, f he h a r m o n y f n u m b e r s n d o r n r s n d o f g e o m e t r i c le -g a n c e . t ' s r e a l es the t ic e e l i n g h a t l l m a t h e n l a t i c i a n se c o g n i z e , n dt h i s s r u l y e n s i b i l i t y , . T h e u s e f u l o n r b i n a t i o n s r e p r e c i s e l yh e n r o s tb e a u t i f u l. . '

R e i n f o r c i n g Poincare ' s t rus t o f aes the t ic j u c l g m e n t , D i r a c

c o m m e n t e d o n S c h r i i d i n g e r ' s o t p u b l i s h i n g h i s f i r s t v e r s i o n o f

t h e w a v e e q u a t i o n b e c a u s e t c o n f l i c t e d wi th empi r ica l c l a t a :I th ink here s a m o r a l o h i s t o r y, a m e l y h a t t s m o r e n l p o r t . r n toh a v e e a u t v n o n e ' s q u a t i o n s h a n o h a v e h e m i t e x p e r i m e n t . liseems hat f one s rvorking rom he point of vtew oi gett ing eauty rrone ' s q u a t i o n s , n d f o n e h a s e a l l y s o u n d n s ig h t , n e s o t r a s u r el ine of progress. f there s not complete greenrent et \^ 'een he resultso f o n e ' s w o r k a n d e x D e r i e n t , n e s h o u l d o t a l l o w o n e s e l i o be tood i s c o u r a g e d , e c a u s e h e d i s c r e p a n c y a y w e l l b e d u e o m i n o r e a -t u r e s ha t re no t p r o p e r l v a k e n n t o a c c o u n t r r d h a t v i l l e t l e a r e c l p

w, i t h u r t he r e v e l o p m e n t s f t h e h e o r v. u

P o l a r i t i e s

D i r a c a n d P o i n c a r e o t h a p p e a l o a e s t h e t i c . r i t e r i a et h e f r a m e

o f t h e i r a e s t h e t i c i ffe r s . P o i n c a r e ' s s a m o r e g e o m e t r i c e n s i b i l -i t y, Di ac ' s a n a b s t r a c t m o d e o f d e d u c t i v e r e a s o n i n g . But D i r a c

too i s c o n c e r n e d r v i t h t h e b e a u t v o f form, o f re la i iv i s t i c

c o v a r i a n c e o r p e r s i s t e n c e f form. T h e c a p a c i t y t o v i s u a l i z e ,Di rac m a i n t a i n s , d o e s n o t a d v a n c e n e w t h e o r i e s , b u t r a t h e r r e -f l ec t s a m o r e b a s i c n e e d t o p i c t u r e a n d r e p r e s e n t .

M a n y sc ien t i s t s a v e c o m m e n t e d o n t h e p o l a r i t i e s , v e n t f le

d i a l e c t i c , o f sc ien t i f i c m a g i n a t i o n . C e r a l d H o l t o nh a s

d e s c r i b e dt h i s p h e n o m e n o n a s h e " t h e m a a n d a n t i t h e m a " o f s c i e n c e . wo

bas ic o r m s o f s c i e n t i f i c h i n k i n g h a v e b e e n c h a r a c t e r i z e d s d e -

s c r i p t i v e s. s t r u c t u r a l c i e n c e Ar i s to t l e s . P la to ) , t h e c o n c e p tof space v s . t h e c o n c e p t o f n u m b e r " (Erns t C a s s i r e r ) , i c to r ia l

m o d e l s ( p r o c e s s f o p e r a t i o n s ) s . u n c t i o n a l m o d e l s f u n c t i o n a l

m a p p i n g ) Wi e n e r ) , o g i c i a n s a n d a n a l y s t s s . n tu i t iona l i s t s n dgeometers Poi ncar).

C o n t r a s t i n g m o d e s of sc ien t i f i c r n a g i n a t i o n s a r e c u r r e n t ssue

i n th i s b o o k . Vickers d i s t i n g u i s h e s e t w e e n a e s t h e t i c r i t e r i a a ndr a t i o n a l d e d u c t i o n in m a k i n g u d g m e n t s , P a p e r t b e t w e e n i n t u i -

t i o n a n d p u r e o g i c n m a t h e m a t i c s , M i l l e r b e t w e e n v i s u a l i z a t i o n

a n d n o n v i s u a l i z a ti o n n q u a n t u m t h e o r y, a n d G r u b e r b e t v v e e n

c lass ic a n d r o m a n t i c m a g e r y n n i n e t e e n t h e n t u r y b i o l o g y

)i n t r o d u c l r c -


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ludi th WechslerWe knorv rom he development fquantum heory hat l terna-

t iveexplanat ions an coexis t , e complementary: ave nd part i -c l e , con t inu i ty nd d i s c o n t i n u i t y, a t h e m a t i c a lo r m a l i s m ndvisual izat ion, ach of which "descr ibes" he nature f a tomicphenomena. Both are needed because ei ther saves / / t hepnenomena . )

I t may be more diff icul t o specify he aesthet ic ropert ies fsymbolic mathematical e la t ions han those of models ,

metaphors , nd mages ased n our experience nd observat ion.The aesthet ics f pure mathematical elat ions nd he strongemotion t evokes ecal l he ormalis t es thet ic n ar t - though at amore abstract evel-s i nce mathematical orm ations ometimesescher,v isual izat ion. he principal r i ter ion n hisaesthet ic astermed signif icant orm" by he art heoris t s l ive Bel l nd RogerFrya round 9 1 4 .S ign i f i can to rm mpl i e s he op t ima l n i ty ndcoherence f the composi t ional lements . ry 's osi t ionmarkedthe beginning f the modernis t es thet ic n ar t , v i th ts ack ofconcern or representat ion nd ts ocus n the beauty f formalrelat ions. ignifcant orm evokes part icular indof react ion ha tFry escr ibed s aesthet ic motion," hich, ccording o him, smore ntense nd ocused han he ordinarv nrot ion e experi-ence n ou da i ly i v e s . a themat i c i ans ave a id h e a m e f h e i rexperience f pure mathenrat ical elat ions.

Conc lus ion

The choice of or ientat ion s not necessar i ; , se t n science y theproblem ut by a mode of hinking. hough here re constraints ,there s no a prior i ssent ia l pis temological ay of seeing. here-fore he role of cogni t ive mode and aesthet ic ensibii ty plays avi ta l pa r t n the structure nd s tyle f the scient i f ic rocess .

In summary, es thet ics s presented n his ol lect ion s a modeof cogni t ion hich ocuses n orms nd metaphors sed n scien-

t i f ic conceptual iz ing nd model ing. he at tent ion o process nscience nd ar t leads o a considerat ion f the part played byparadigms Kuhn) nd personal tyle n discovery nd nvent ion.

Viewed sa way of knowing, esthet ics n science s concernedwith he metaphorical nd analogical elat ionship etween eal i tyand concepts , heories nd models . he search n science ormodels hat l luminate ature eems o paral le l er ta in rucialprocesses n a f t ,as Cyri lSmith oints ut : hey hare undamen-tal evocat ive ual i ty.

The orms f symbol zat ion re entral o he study f aesthet icsin science. c ience ses symbolic anguage, ost commonlymathematics . ew concepts ecessar iy expand he vocabularyand syntax f his anguage. he way new symbol c orms evelopis in parl influenced v aesthetic oncerns.

Scien t i f i c d e a s models , h y p o t h e s e s ) e v e l o p w i t h i n a c u l t u r a lf r a m e w o r k o o t e d n the sc ien t i s t ' s i m e i n h i s t o r y. T h e r e a r e c u l -t u r a l s t y l e s n d t r a d i t i o n s n sc ien t i f i c o n c e p t s . h o u g h h e r e h as

b e e n a h i s t o r i c a l l y r e c u r r e n t a p p r e c i a t i o n o f e l e g a n c e anc l

e c o n o m y, Vic tor ian s c i e n c e , o r e x a m p l e , o f t e n p r e f e r r e c lmorec o m p l i c a t e d o r m u l a t i o n s . An e x a m i n a t i o n of aes the t ic r i t e r i ar e v e a l s h e p r e s s u r e f v a l u e s y s t e m s h a t a r e r e l a t e d o t h e s c i e n -t i s t ' s o c i a l a n d c u l t u r a l con tex t . T h e a b i l i t y o r e l i n q u i s h h e p r e -

d i c t a b i l i t y of c lass ica l h y s i c s a n d a c c e p t n d e t e r m i n a c y, r o b a -b i l i t y, a n d c o m p l e m e n t a r i t y, we assoc ia te w i t h c o n t e m p o r a r ysens ib i l i ty. o t o o t h e e m p h a s i s o n p r o c e s s v e r p r o d u c t .

T h i s b o o k e x a m i n e s h e aes the t ics f f o r n r u l a e , h e o r i e s , o r l -cep t s , m o d e l s , a n d p r o c e s s e s . T h e a e s t h e t i c fac tors in

c o g n i t i o n - m a n i f e s t i n b o t h a r t a n d s c i e n c e , h o u g h u n t i l r e c e n t l ; 'm o r e r e c o g n i z a b l e n a r t - a r e c o n t i n u o u s a n d b r o a d e r t l r a r re i t h e r. The essavs v four s c i e n t i s t s n d t w o s o c i a l sc ien t i s t s .v r l l

h o p e f u l l y n r i c h h e r e a d e r ' s i e w o f t h e n a t u r e o f a e s t h e t i c o g n i -t i o n i n t h e s c i e n t i f c p r o c e s s .

N o t e s

' 1. We r n e r H e i s e n b e rg , h v s i c s n d B e y o n d New York: H a r p e r R o i v,1 9 7 1 ) , 1 t . 6 8 .

2. Arturo Rosenblueih nd Nortrert Wiener, "Roles of Motlels n Str-e n c e , " P h i l o s o p h y f Sc ience , X 1 9 4 5 ) : 1 7 .

3 . H e i s e n b e rg , hys ics nd Be t ,ond , . 2 1 0 .

4 . H e n r i P o i n c a r , h e Va l u e fS ,c ience ,r a n s . . B . H a l s t e a d N e r. - o r k :D o v e r u b l i c a t i o n s ,9 5 8 ) , . 1 5 . O r i g i n a l l yu b l i s h e d n 1 9 0 5 . )

5 . C e r a l d - l o l t o n ,N l a c h , i n s t e i n , nd h e S e a r c h or Rea l i ty, " h t ' r r. i t r cOrigins of Scienti / lc Thought: Kep/er o Einstern Cambridge: arvarclU n i v e r s i t v ress . 9 2 3 ) .

6 . P o i n c a r e , h e Va l u e f 5 c l e n c e , . 1 9 .

/. H e n r i Po incar , c i e n c e nd M e t h o d , r a r r s . ' l a i t l a n dN e r v Yo r k :Dover Publ ica t ions , . d . t , p . S l . ( O r i g i n a l l v u b l i s h e d n ' l 9 0 8 . )

B. P. A. M. D i r a c , T h e E v o l u t i o n f t h e Phys ic i s t ' s i c t u r e i Nature , 'Sc len t l f i c n t e r i c a n , a y 1 9 6 3 , p . 47 .

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WECHSLER, Judith - On Aesthetics in Science

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