the fixation point may be, 1he perceived properties of a square with shifting gaze or al different distances ..... force a square peg into a round hole. It is akin to ...
Pe rc e p l o n1,9 8 5v, o u me1 4 ,p aqes403 425
Visualspaceas physicalgeometry
Deparlmenlot Phirosophy, Uniw6,ry ol Carforn'aar SanDrego,La Jorla,CA 92093,USA Fec ev €d 10 Nov c m be.1983 ln r e ! s e d l o r m 2 M a r c h '1 9 8 5
. c l \ c c . | r t e l i s i 'r r i s u r l s p r c e . h d ( t u c l u r e s x n d f a r l e r n s Abs r hr t , Th. lc . nr dr ic nl in( on S r u c n c h , , i nc ( t r i1yin r he v is ur Lot c x . l o n ! k i d {. r o i n \ *r i s n k , n . s ^ c s a s I c r i t c ) n i t r e \ a l u i n s ot d.tcrminin! tht' $ohctrt of thc \irurl Norld nhrsi.al lheoric\ ol \nul sp.cc. l-h( tr'Ncn 1\ is ud s c , , f r dr v i\ c oDr r r ! d \ j 1 1 , r h d t i i l d c r e r m j n i n Sr h c S c o n r . t r vo l t h c p h v s u l u ( t r l d L r h v \ i c a l r c , n. r y r . lh* , r ' . s a\ r i, r h( t ^ t i b l c p h ) s i . r l l o ( u s , 'l r n u l s p r N '. $ h c t h e r i n r l k h r a n ' o ' e l s c \ her ( . r r ( Nid\ c d. r Dr l! z ! d. r , ( l . r j i i c i / c ( l r c . , t r ( l i n g l l . l r n o n d u d c d r h t r r o i l h c b a s i \ o l c or r r u( f c . r l( r c ir $ou! d hc l i r c d ( t ( l r r r ( ' ! i {L n l \ t r c e i s n , , r r o h c l i n r n d i , ' r h . h f u i n . ! \ c n th.u$h ir i\ \ecnrnr!l! ||nte! h n cr{\nlh. r\ crperinr.nhl ncunn(,!r and r.!tu't)hfsnnor! donon' s r r nr ( AlLr r nr r iv 0t hc lir c \ r a n) t h r i n N r . ( n l i s o r l \ f n c c r r c c o n \ i d c r e d .h u l a f u r l n ) f o u n d n i b 0 n' ad. ( p. r c n' ! r plir nr ' ! v n' r ils p i c n ' r . , N . . f ! p r i b l c r 1 , . , D t e n l b r i , ! s c i L n ( r
I In tro d u c n rn n o tr $ h i l c s o n rc n rrl d i s n )i s sr hc i nk^ri ng drl i b.rrri (nrs r\ hei rg j u\r phi l x{,ph! i l i ! s L rg Ac s l cl hd rl Ih o .' l trc ()I c cnl rrl i nrpo rnce (o l hc(nv i n l i ri on sci cnccas regrrds thc A l (,b n l u n d !rs l rn d i n g o l !i sual l orm nerccpti on.l -hi \ i s sti rl !(l i n rcsponscl o v' nrc c x p c ri n rc n ri rl i \l$sh o a ro o l r en i ncl i nedk, l i rbclrnd rcj ect !s phi k,sopht qhrr i s i n h.r s c i c n ti l i ( rh c o r\. Al rh ,)u 8 h sr)' rc,' l rhc l crnri n,to!! rn(l conccfl s ol phi l on' phv arc ,rc c r\n rn rl l J "p n r l o u s . i r N hl l n)l l ors. thc l fi i rcti \( i \ chci d l i (' n i n \ci cnce. not Ih i ' o s o th ) As r p o i n r,n d c I)l n u re . i l D i 8hr bc l vcl l ro coD si (l errhc l l ,l l o$i n! conrmcnl snradcby p h t\i c i s r (j c rtl (l H o tr(i n i l 9 6st $i th rcgur(l l o th. d!!ek)pmcrt ol Li nrt!i ns S tcci rrl -th c o r) o t l l c l a !i \.i t!: " l :i h r.i ' r r^ ^ ru (r frd n rh ( hcgnD i r! rh( t' ,^drnrl onl t,dl l l ui ' \ of thr\i rs qi r,' r he u D d e r\ro ,{ul rri l !D .tl n c D r ol ' i gl c!l ual' h!' !\i s i \ crrri & l our.p!rri currl } * ) tri 1hrc\fccr ro rhc n rc ri i i s o i th c(i n c !p ri o n so l \ti rc. 0d ri nrc. P e rh a p s\i n ri l a rc o n s i d e ra ri ons nri ghrbe prrJdrcti rei n \' i sn,nrcsei rrch. 2 Thr problcDr N hj ch h.tre bcen ndv:rnccdr) A c o n c e l i (l l rla n rl y s i sta k i n g i nl o i rcco nl rhe B eonrerri cs v i \u a l s trc e g e o netri .rl l !. gcomctri crl dcs.ri pl i or( gi !!n b! neuroc h n ra c ts i z e rnd thr p h !\i o l o l ] o f th c \i s u a l p ( )j ccttun arca! (mrtsl i n i hc vi l utrl corl ex. soggesl sthat e i tl re r th c g e o m .l ri c rl ru l e r appl i ed to physi cal space do nol appl ] to l i sual sl acc a D d l i c e !c rs .r. o r l h a l v i s L ' alspacci ( nor i n the brai n i s ncu' 1)\ci cl ccw oul d haw i l E i rh c r rl l e u l i v c w o u l d s e crnto hal e i rnporl i rnrcon$eql encesfor rhcori esol sface a n c lth c o ri c so f v i s i o n . 3 l he Bcomcf.t of risull space B y l h c g e o n l e l r!o { a s p rc ew hal i ! usual l ymeanri s i he serofS eomel ri calaxi omsand rul es \th i c h a rc i n l e rn !l l y c o n s i sl enri n l comel ri cal l y characreri zi ngthrt space.In r more resnicled seDsc.ftc geonetrr of a snace rcters to a specific geomel cal sysrem.for exa n ]fl e . \\rh e th €ar s p a c ei s b esrcharacteri zed by E ucl i deanor nor E ucl i deangeom€rri es. l T Pre s eandr (l .e \sDi e p a rrn rconlf tstchol ogv, U ni !e.si r)of C al i fo.D iLos a, A nFel cs, C A 900?.1, USA
visual space.or'phcnonenal spaceas il is alsocalled,is defineda5 $e 5pacewhich \re perceivethrough lision. We can lhink of lisual tpace as bcing part ol 3 hrger spatials(ucture. often callcd perceptualspace,whicfi conlainsspatialsensalionsfrom The presenr study.horcver. orhersensenodalhies{namelr.auditionandsomaesllresis). herc shouldto someex(enl wili be dclorcdonll lo visualspace.ahhoughwhatis said s a $hole applyro pcrcepruI|lspace LuDcburg( l9'l7l exnlainedl oivilualspace, As to rhestructure ''jlhe obJecrs qu!lilicsoi color.id brighrnes, iD vlsualst0cclhave.besides.harrcrctislic In a visualscrs ion *c lhu\ arc or onl mnediar.lrr$rrc ol . lormrnd k)c.1izari.n. bur al sool rhel acr rharcerl ri r oi rhe!cquLi l i ct N ,c dis rri h u ri oonf c (n o r!a n d b ri Bh rn c\ses, bcal i za' nD ,n o bj ects,w hi cl tharc a dcti ni reS comcr,i cal c om b i n .dre l o rn u n i ri e sn, a rn e rr. a r h rc e -d i m .n s i o n\ta a l c c .' Lunc b u r!s s ra te rrre Dwl o u l d \€ e n r kr endorsel rci tl y rhc appl i c,rl i onl o !i sual spaceof r hc s a m eg e o n re tri c rlc o n c e p rsa n d pri nci pl csordi nl ri l y appl i ed l o l l re phl si ci i l w orl d. l hrl . accordi D sl o l -uneburg,Iherr F or ou r p u rp o s e \ h e rc i r i s i mp o rhnt l () errrphr$i ze r ur cob l .r? r i n v i s u a ls p a c ca n d rh a l l hesc ohj ectsexhi bi l defi ni teS eonrel ri cl propcrl i cs ( s om c th i n gc o n rn ro ns e n s ca l r' ra d )' tcl l sus. ri ncc $c no" nal l y trke rhc \i \ual \orl d k) be r hc ' p h y s i l a l{ o rl d , a n d rh u s l i s u al obj ects10 bc phl si crl obj l cts).Il i \ on l hc l )asi s 1n r hc g c o m c rri c al n n l y s k o l rh e o hi cctsi n l i surl space(hai a guomcl r] (' l \i \t1' space is corrccilablc. Lcl us be-qir rhc'r hI trriefl) cxa inirrS thc lheorics rs k, the Aernnctr)_(t v is ulll s p rrcw c h i c h h l !e l )!c n p r()p o s cd. A u c m p rs ro d c re rm i n cth c S c o mel r)ot l i surrlappl j arancc\i w hi ' l $c atu crl l i ng vi \ttnl s px c c o r l h c l i s u rl $ o rl d ) d rtc h o m [rcl i d. { ho sl l gcsl cd thrl !i $.1 !con]cr,\ rrs c onic rl S u h s c q u c nirn !c s ri g .ti o n \ l )y Il .i d, I)r| l i cl s, rn(l A ng.l l prol oscd i nncrd l hrl i l $a\ s p h c ri c i l o n rh c b .s i s o f rh r s h npcof rhc cY .s i scc S unpe\ l 97l tl . Luncl )ur8r l 917l was lh c Ii rs l l o a tl c mp l l o c s l a b l i shl Ie ge()mcl rfol !i \url sfdcc by conrbi ni ngpsycho t hy s ic!l d a l r $ i rh .ri d .n r m l l l h c n r Iti crl rnrl y\i s. Ih. gfonrctry troposL' db] I utrcbnrg was ba \c d ml i n l y o n d n tn I' o m rh e \o cnl l ed al l ct erpcri menl \ ol H i l l cbri ' ndI l 90l l rnd I llum c n l c l d (1 9 1 3 ). l h c c rp c ri n \c n t.l l \l i i n rhcsecxpoti mrnrsconsi stcdoi posi ri (,ni ng allels o f l i g h r p o i n ts n n d mrk i n S i dgme r\ al )IN r thei ' parl l l el ncss,cqui di st nce. i ' n(l or hc r c i ,n fi g u rrl p ro l c rl i c s . A n u m ber ol ()rhc' i nvcni gal oft rLl l ned.cxl end!d. and/(rr (c8 Il Lrnk, H rdy, Zaj rczko$sLr, v,)n n c lif i e d L u n c b u tg r b rs i c n l a l h c mati ctlnn)d!l l S c hc l l i n g ,F i ,l e y , l n d o w . rn d s h i p l ey: Id rc!i e* see S upfcs l 9Ti l j . l hc;nrcrcsl i ng c lai' n n d c b y L u n e b u rgw a s l h a r l h c dal r from l bc l l c)' experi menl r(aD dol hcr cxpeF im c nc j c o u l d b c i n re rp re te dto s h o w rhar l hc geom!rry ol ri sual sp:rcci s non-E ucl i dcrn (possessingnon-rcro Gaussiar curururci. Specilic,lly. Lunehurg proposcd th iLsgconr eir y is h y p e ro l i c (p o rs e s s i nngc g a ti vcGaussi ancurvl rturcifor a good btrsi cexpl antrl i on ot G aus si a nc u rv a tu rec o n tra s te dw i th our ordi nary conceptof pl anc E ucl i deancurvaturc. s eeNe rl i c h I9 7 6 ). A iie r L u n e b u rgo th e f i n v e s ri g a l d .s proposedal rernari velrhal y vi sur)tspace i s ctl i pri cal (possesshg constanr posilive Gaussian curvature; see Caelli, HoffmaD, and Lindmanand D ro e s l c r-i n L c o u w e n b e rg n d l l ufi ol i 1978i sec al so Musdl ov l 97rr). S hi pl e! ( 1957 1fo u n d th r th e s i g n o f l h e c url arure i n l i sual spLrce di ffered from pers(' nk) person, varling from ncgalive curvature lo posilile curvalure. l'olcy {196.1. 19721, while maintaining thal visual space is non-Euclidean. argLredthar il does nor exhjbit constanl cu.varure and is rherefore nol hyperbolic. Borh Shipley and Foley suggcned lh:rl rhe geomeiry of visual spacemight be contingenrupon .orr?xr .,/J?./r,ils gconerry !arr-ing as a funclion of tho configuration of lhe stimulus, and thal rheref(re il mighl be rhal no one g€omerry could uniquely characre.ize lisual space under aI condilions. Sinilarly. Morgan (1979, 1980) auempt€d !o a.gue thar thcre js no unique geomcrry io visuAl space. bur Ihat it merely rcnecls th€ geometry of rhe physical sorld, moreolcr, rhe geomelry ol our a.ronr,
Visuir 3pa.c as PhYsi.argeomelly
a Seonrclr).e\e,r ln anycasc.thescslodicsassumcdthlt !i\ual spaceindeedpossessed if pcrhrpsa murrtrlcone.and rli.rl il could bc dclermiDedempiricallyb! pslchoph!\ical 4 ((,ordinalirc dclidlions a'rd phyricalgeo elrJ 'lhr gcomerririrrionr ol \isLralsnacr s mmllrizcdabore enlril cerlainfundanre'thl qhich Iinf tre cqLial€d conccprs surhas poinl Ddslr:righl rssumprions in mirlhcmxrical (tr i|s Lunehursmirhrsr\. !\irh r)bjcctsin lisualspacc.The\e \irh \isurl expericnc$. r!(,ukl sccnrr() corr(sp(rxlck,scll lo $'hrt Reichcnbrch ssunrnrxnrs 1195())callcd 'co(n(linfli\e ol fhlsic\.Ilcichenbach cxplrincd: dclinit()niiDrhccorrlc]il ''Prr)sicnl bo$l.(lsui\ ch r.r(ri7(dhr rlc hcr rhrr.onc.prs.rcnoronl)d(linedhr orher hl .o n c c th . h u r rtc rl q , c , ' (trl uurrd r,' ,frl (' bi c.l r.Tl i \ .,!otrl i i N Ll otoni .r h0 ' cfh0.l t t)dttknlo rn .\rl x rrl i !!r,n rre i D l rg\.I \ i ,r ! \Ld(\ thnrthi r coi c.tJri \ ttonl i ttt^\l k1 Il ti
S L rh s l i tu tr' !i \u rl In (tr\l cdgc l o' th!si crl l i D o\l edge and vi sual obj ecrs l br ' rc al o b i c c l \' i n l { e i rh .l l h r!fi \ Iornl uhri (i l l ol c(\)rdi nrri rc dcfi ni rr}ns.aD (l $c fi n(i rhrr r hc tro c e d u rc u s c d i n th \' \i c\ hrs hctn thc sanrc,rncu\rd i n l hc sl u(l ! (' l l he gcomcl r) ai \i s u x l s p i rc L .L r l h . c r\r t' l dcrcr| rl i nrr! thc gc()nrcl r!t)l l hc phrsi (rl so (l l ph\\i !ll l $i rh fhl si !rl obl ecr\.l o r g .()n rrrry jl h i s h n s n rc n nrc,r' r' (l i nrl i n! rnuhcD i tri ei ' c,r)c!pr\ c \r.rl l (. rh c i (l c n l i 4 (l .u rhenr,ti cxl foi rr i \ c,!)r(l i nrl e(lsi l h rnl ri l l turti cl cs,u stl l right l i n c i s c ,!n ' (l i n i rl c (l$ i rh r ri r\' rn l i -uh1i n tl \l c!unr. (n \\i 1h I ri gi cii od. cre i l or m(,r. on fh y \i c rl !ro n re tr]_s ( l tri (henbrch 1956. Ii nc 196.1.V rrr l !.rsen It)70,4;ti i D bi unr l L )1 .1 i,r(1 A n rrd rn 1 !N 01. l hi \ i \ i r .\\rncr l hc fr{,cc(l ur. u\c(l bI I rD eburg rD( l ()rh .i s i n d (t(rn ri n i n g l hc gconrcrr\ rt l hL !i sual s(nl d:\i \url gc(nncl ry! r' pl )inr l l c i n g r s n ri ' 1l,i g h r,x n ^ \ ,)' sr.h p()i nr\ b(i og n \trri l l hr l i nc. ctc. l -utrchu' t crl l rJ rhi\ p rl tc c \\' t\\c h r' trrc ri i c c , r,ri i D rrnD . \herchl ntr.thcr\ rre c,!)r(l i nrrcd l o scD \rl i , ) n\ i n i , f.\.h ,)1 ,){ i .:rl .ru i ri l ,,l d. A \ l l ,,pl i rrs I l !71l t,,)i nl c(l ,)Lrl : ' \\' r:h .rl !l rrt! t)h rD , ,D rrnrl vi {rrl t !(nD !l r\ \i ,ntti \ .n r tn' \nh fh\\i Lnl !r(n.l r\. u, l h ,' l (irh rr i ( trt' tr\i ' rD ' i i ri n!. rr! rtdrr!u1l r_ l rue l .r. \.Ifnnl i .i l i \. i f tJurLrrg th\\ 1. .rl !rri !l rr rfr' rr,l a L r ri !hrl i nf f L !q,D c1r\ l )rnLL(e\r nrrl rn!rnrtl r(,tr\rh.rr th\{ c r l \L rri g h Ll L n f\. rl r!r trl ri o! trhrtrnerrl \r{rrl l { rrr!hr Ln! sh(\nJ trtrh,.. r .onrnr s. nl rh fo r\ rh ' { ' r p h u ,n n rn rll rr\nrl rsrr,* hr Lre\. J u \r r\ l < e l c h .n l ' rc h.rphi nci t thrt (he gc,nnetr! ol nhy\i cl l sl xce i \ n.l rn i nrmc!l i l ' l c r.\u l r o J .\f.!i c n !.. l )ur dcf.' r(l s,)n rhc ch(' i ccol La!' r(l i nnti \cdcl i ni r,)r . sr)i r is $ i rh th ! g ro rre rD ()l l i s urrl spauei l or.rn exrensi v,idi scussk)noi rhi \ p(,i nl s.c C raig l e r)9 .rn d H o fk i n s l e 7 i i.Ol cenrrri i rp(trrucfi srhfrrdn.ofcoordi nrl i red!' l i ni ri l xr p ' o l c s s o l .o o rd i n xrnrsphf\i Lal {)r \i \tal ohi ectsr\i l h ni l l l hdn ti c:rlconccpl \ .Ns in 'h. ll.icherhrch slre\\e(l: ' ' S i n .. rh ..,)n ..p ^ rrL ii r!' c(' nrc.' .d l ,f rchrnn}-rh! c(udi rurnD nd! b. \.fi i ild ' c{ rl rl ri \ !!l d.d. i i r\ r.!(,tr h l \.. i l rh . k {urr.mcnr,n !A i qu!n!$ rul c l hrLthc \r!re tuncct il 'rihc i l $ !\s d c n o l e \th r rrmc ohi e0r. I)tl l ni l i di \ l h !rc n.r onLquc e i fudmi s\rbl nr c a sci enr ir i. A r i n re rc s rig o b s e f!ari on$ar mrd. | \ Jul !szi l 97l t. ' ' l r i s rn i n r,i s u i n rrh o u gh| hrrd\c. rl l ,ul h si dD n.r kno$ \hi l I pcl cctrts!.h rs x r{d lt r h l u ec o l t)i\c n \d rk l h ! Acl frs.$. cander.rnri i ii \ di nl cnri oral ix' ' ) l (lrncui cl -' l n l a c t. B l rn l , 1 1 9 5 8 i e tpl i ci i l ! e\chi ' \red an\r arempr on hi s pai i or I-uneburg' srk) e x p l o re l a fg c r p h i l (x o p l i cal or psl chol ogi cali rnpl i cari onsof rhe mal bemari calrhco r y L u n e h u rg a n d h e d e i e l o ped. Ii * as B l anl \ opi ni on rhar phi l osophi calconsi derations had no bearing on lhc corrcclness of lhe th€or}, and rhal diftercnces in philosophies co'rld be reduccd lo difllr.nces in languaere.Hc explained lhal a glossary could be
406
coDllructed for ihc purposeof conlerting . dualistictcrminology inb operalional language. AsBlank e)tplnin€d: _T\o sy\reD\ $hich hrre rhe samcsrn,clurcand diiler onlr it langu.Sclre srid 10 he i(l heD i s i nesscnri rl . .crhc sctnnD ! of frescnrrtn' n - c l 0D suagc Io rh c m rh c n rri c i rnrh ' notirp h re i c n (l .re | o rl c n h i l o !' p h i ci l poi nroi\i cs. nx ffc ll lo rc e d to l a k c s i d e s . B l a n k di d adni 1. ho$c\er. l hal he aD d l -uncburg w oul d pr ob rb l y f.rl o r l o g i c a l p o s i ti v i s mand bchavi (rri smH o$cver. (r. rhe di fl trences rn phik ,\o p h i c sl ' ' i \i a l n d a re l h c s e di fl ei €nccsdrl r a Inal rcr ol di l l el i ng l rrrgul l gelFor ex am p l e .i s i r rc a l l y s a ri s l s c to l yto sr\ thal dro l ti nguageshi ch descri bcsrhe ohscrl er' s m r ni p u l a ti o n o f l h e s l i mu l u s l i g h l poi nl s i n l hc nl l cy c\pcri menl s i s equi \al t' rrt1o the ohs c rl e r' s d e s c ri p ri r)nr)l h i s p e rcepl ' l D o.s rhe l /i rrnal coni i gural i (' nresul l i ngIronr t he c x tc ri m e n t e r(l rc rl ]n ri L rc r the i )trscr\er' sr1| ' rrrIlconti g rati (nr?| \l ti l l l rc!urn l r) r h. s e q u e \l i ()n \ s h o n l J , h rrl n l t hi s fl ,i nt. l shi tU no\ enden\or l o \ho$ l hrt l h. i nrfl i cri ti rrns.som! l- un e h u rArh c o r,- ,/o (s h a \e l a rg er phi l osofhi etrlrnd ps' -ch(nogi cal ol l hc al l c! erfcrrnrel l \ for of w h i c h n ry rfl e c l i ts l a l i (l i l y S omc of rhe i mpl i cati ons | )cU l ored C ;ri j nbrrLr l 1973r.Ihrt(l h r!c l )cf' r rrLcl th t he e p i \te n m L ,8 !o l g c o n re l r)H cel rrr i l eS .:i ) (t{r79, l 9fi 0i i nd Mofga,r H (' p k i n s 11973i , 1197 ? i . C f i g tl 9 6 9 i , i i ,r l hcori c\ ol i nrnl i cl l rr)Il s rht h r!c n ,rr ertkn' cd th c \c s rs d i { s H, r rc !e r. f{rtsi hl e v is io n .s p c c i l i c rl l " 'h. o w th c g c o m.l r! ol !i turrl tP ac0i s rcl rtr!d10!' sual fn)ccssts 5 Thc ps].honcural idenlilt lhtor\ ' lhe l h c o rt o l p c rfc ' 1 tx )ric rre n l l ! consi (l erc!ll (, bc sci cnl i l i crrl l rct.P l i thl L' sri rl .\ l hrt \ pc r cc l l n n r o c c u rs i n l h e b rl i n .:rod thl l i rt ei l ccl . l h. n)i l (l \i ntl l l i s l hc hrl i D - or p.rl ol il . Ph i l o s o fh c rsc r1 1l h i s h !p ,n hc\i s l hc fs!chonLurrrli (l cnl i l r l htor\' i l or n re\i t$ r nd c ri ri (l L re rc r l \c c e rti a n d l )y l i .s 1978i . l f rhc psl chontu' nl i dcnri rl thcor) i s r rc. t hc n ti s u rl \p rc f s 1 ' rl l l p r.s L rn l l bl !bc \onrt' l hi ngi n rh( btrri n A s l l ]hr\i crl ohi ..r. rhc gc on rc r' t d l l h c b r.ri n i \. i n tti n c ipl c. !t l uncl i on oI Ih\si (rl gc(' rn!try rrnd rh. c({ n' (l i Dr r i \( (l c l i n i ri ,)n \rn p h \s i c rl g c o nrcl r\ rtfpl ). H o\c\ct. Ih! P ' {)((\\ (,1 c(!)r(l rni )1r\r i s l \ol ol d: i i r l he deiin i l i o n m u n b c c rrrri c d ,' n c \l . P i url hcr. ti D !! thc c(r) i r)trl i ()r) ! i{ r rl c l c n re trli s c o o (l i rrr' i d w i r h x n)xl hc rxl i ci rl c(nrccIt rcg n sl rxi ghl l i rci i ' n(l i i i i r he !i s u a l e l c m e n t i s c o o rd i n l l c d \' i l b somc physi cultl ri ri ghl l i nc. P rcsunl hl l In l h. br ai n , i f rh e l s -!c h o n .u ra l i d e D l i l y theory i s correct.' thus, i n thc(,ry !t !i \ul l l st!.i 8hl a l u i g h t l i ' re : ph)si caI stftri ghll i rrcti n thc brai rr. linc : n rn rh c n ra ri c\u A c c o rd i n A l o l h i s l n rl y s i s . l he cxpcri ncD l s k) dcl crmi rrc l he gconrcLryof !i sunl s pr cc h rv e rl rl l y h c e n m rp p i n g c onfi gur tnnrs i D rhc bfti n ro corrcst,)ndi ngthrsi txl ones $ h i c h c o mfri s c rh c \l i n ru l u s(i c thc l i gh1poi ntsl .H osevcr.l hcrc ntrr l )! i nhcreD l lhq\ i n i h c rs s u n )p ti o n so i th i r mrppi ng. Onr such assumpl i oni \ l hi tl l hc l conr(l fy of rhe brain ior rclevanr parts or slalcs thcreofr and the 8co'nelry ol lhe Ph)'siclllsumulu\ ieg th e l i g h rs u s e rl i n l h c l l l c ! c xperi mentstrrc i e)mcrri c i eg a E ucl i de n p| rnt i s rot is ome rri cB i th rh e s u rf.c e o f a s p here-one cannot bc dck)rmed i | rl (' l hc ol hff s' i l hout s r . e rc h i n ga n d re a ri n g l$ h e re a srhe suri accoi a cl l i ndcf i s i somel ri csi l h a phne l he onc s u rl c e c i rnh e fo rm c d fro m th e other $i { hoursrrerchi ngl . wrrhour direcllj- measuring rhe contigurations in rhe brain il i\ impo\siblc to know whe l h e r th c y mi g h l u n d e rg o l ra n si orm ti ons i n the coutse oi rhe rl l e} extcri mcnl s which \\ould be reflecred in visual spacc bur no( in lhe posilions of the correspondi[g phy s i c a lc o n fi g u ra ti o n so. r \i c e l e rsa. Thus, onc cannot assumel hai thc geoneny of ! is u a l q p a c ea n d th a l o f th e p h y si calconfi gurati onsare i somctri c.l t l i sual spaccand phlsical space are ndr isomctric. rhen a mapping assuming isomen_r'sould result in a
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s p L rri o ugse o me l ri z a l i o no l vi surl sprce.A s Lei hol i c cl rl (l 97l j l pul i t: ' ()u r u .d e Arr.d l n ! o l s tr.r pcr(.tl i on mu\l runrrnrhmi l od . as k,n! !s i r i r bascdonl ) , r ) nslrh,)ltrt\icrr obs0^Nri('s \r mun ld)l f(tr r nfur.l ba\n in ord.r lo afpturch rhc tro b l c n ,\h { N \p rrrrl (i Dul i mar bc,rrrc.t!cr..li h. brri n. Thcn \\c \houl drl \o hc i n r b e u c r fo \i ri o n ro ( s i d er rhc epi srcmol 08Lcrl rcl nl () shi fs hcr\ee. spdceperc(fri rDrn d s c i rn ri l ith c (o ri .s ,,1 f h \' i crl \p.ce.In d re d . mo s t r)i te ri m c nti l i n!c\ti gi rl i ursi rs t{) l hc ecomctrvof l i sual sfracci $i th th L' ro ra h l c e \c e n ti u r o l l h c $orl of tci bo\j c ct al i nrLrdcno efi on ro i deD ri l \ thr l eo m(tr\ $ i l h rn l p h \\i c a l l Lrh\l rrl eol h.r thl n l he ph\si calsl i mul usand onl \ assumcdrh r r v i s u a l ro n l i g u ra ri o n rc o u l d tre rccural cl y D rapt.d ro arraysof phl si crl l i ghts,and rhar { )t Ii B hl sl l rni \hcd r rcl i i rhl crcprcse' l l xri (nr th r p h ts i c rl c o n fi g u ra (i ,) n r)f rhr \i st| i ' l oD. It w :rs n o r i r\ th o u g h :t !i \u l srri ri S ht l i ne i tsrl l $:rs l l ci nr nrcr\tl red di rccrl ) $i rh x n re L rs u ri nr!d g . \i n c c th i s \oul d | re\Lrmrbl \ enl .i i l nci rsuri r: \onfrhi r! i n Ihc b]' l rin. A \ a l rc rd ,- i n d i u rrc d . fre(Lrmrbl ! thc \i surl srrai rhr l i ne. as a hl tothcri cri l e n l i ty . r!(' u l d b r c i !)rd i n rl cd $i l h l i n. i n l h! l rrr r. j ul l i r\ i n th)\i crl g.(,1| cr' \ cr rl ' rhysi n l rh c mrti c i rl s ttri ts h tl i n c i s c(!r(l i ni {cd $i l h a rr\' of l i ghl i ,r:' \rcL' rnr ,rr ri fo( i. g Id c rl l !. rh i ! p ' o c e ri u ' e $ (rrkl ,c\ul l i r r ct!,rdi nrri \! (l cl i ni l l l )n{t \hxt soul' i d /)r$ f (? //i (o n \ri l u rc \i \u rl \rr i ghrnf\\. 6 (t,n s n re n (e rrrs u \ i s o n x' rphi sn' In g !D c rrl fu rn x . hr\ xtl cnrfl c(l t,, i denri i \ \i \url \l )r.! ,! rst)ccl s()1i1 i .u r(,\ci (n(e $ i l h l h e h fri r ti ( 'rh i u \i \url 5l ]rrc!i \ i D (i r i \ trrLrlol rh( h11ri l | )r i r\ i L(l r\j r\r.l )ur r\ $ r \h rL l ls !n r \c r th i ! rrrt!r\or hi L\h!fn h,rnrfej f(1h\ i i rcl rj tl eLl \( l nd uni Lnl hi gLr t {r l c (\,r(l i rx ri \. rl .l i n i ri o n \. i \s l tri ch.nl )rch.ruftnL(l . ' t)\!ud(FIr' ,l rl c' rl \rri \r i l $c l ,! , 1 l o r r rrh $ h rr( d e t| | )i ri (rrs arc rectl c . ' l h ( d c l i rri ti ,!r,)l .,,n g rrcl | .! rrr,l l h. fh,' i r.,)l r.,f)gfurrer \txr(| r(l l r! | r$utri ' s j l e 1 ,) (l !r!rrrn rn g rh r !r,r cl r\ ol r sl rLff /\\ \\' r\l l (r.{tr, srrufchl rt nd\t)(xl e( l: ' ' (i )n g ru rrrc e\h o u l \l h ! rnrl el | l . ()rc i rrl (' nl \ hi si ( c()nc.pl i D 8(,nutr!.- l n ph\rcir l !L o l l ].rr1 , i r i \ ri !i tl l ' (x l i .s shi .h c,,D rri ruttthf th\\i crl pn' r i D l hc (i !,r(l i | l l ri \c dcl i iri (n r o t e ,,n rtrc D c . l l l | d . rr,\l i nrl ,,rrl rnrl \.h\ dfj i ni l i (nr thr\ (l ,r rhl cIrn,!f l hei r sr/ ( rh e r) rfrn \fo rl c d . Ii rr e | rnrt)l e.u !i gi J ni .r\uri nS r)!l fhccd, rhe s!LrJr((oj r \l ll rn d u s c (l ro th . di sri ne. A l l $i l l rrnri ri n i dcnri (l l i n l (nsrh \hc ,r)(^((l r , , ' r.rs !rc rn o l h c r p rrt o l l h c s u ,J rfr a,)d rhr tl i \l xr)c. U ( i ! nr.i t{ r' ((l l l i t i \ i i trIrJ l hl l l th! l $ r ' d i s l ru rc e sA l t ru rn l l a l | | q (l l . rher rhr l (ngrh\ A B rn.l I,( rr. \ri (l ri , b( c{ )nsru enl l r\ \i rrL r. rrf l l .i n r n r!rs ur.(l l r\ r nrer\uri n! ]rj d r.nrri D i ns ri gi d und!r rfl nsfr) r t S tl re s \h i c h Ic ' n r1 r' tre ! nrobi l i l \' or l hL' tr.r' l rpo ol ri S nl rr)(l ssi l h{)r' r rh.i r l (r)rlh c h a n g i g i ]r. c i rl l c (i,? rrg,rrl r,r rf.r..\. (r. nr.re c,' nnnrrl \' , rkr)i t strkr\ b\ \i ' ru!. r ) i lhe l h x l l h .\ p o s s .\ s hoN ,!er)c,rr\.r .on\l rnl C ru\si l D cur\l l urc i j i ! l D )uch c tc c o u D Ls e . l l c i th c nb.!uh 1956r.W !rc rhe cur!rl ufe o,j l cl )r)sl nn1, l u l l e' tx n rs l of er(rmll. ()n l h e s u rl L t.e()f rn e g g ,r n)d i n rhl r sfrc! ${ i rLILl ch ng! i r\ l enN l hrs i t nrL{ ed hom r | ()c a l r(Dfo s s c s ri n So n e radi us,)l curl l tl urc l o rnothcr l { )cal i onposse\si n!a di fl i renl ri d i L rs i )fc u rrn ru rc . i f !rc L h i n L o l Ih c d i \ l ance A II .rnd l l ( as hei ng l i nc \cgnrcnrsol cqurl l crgl h(o n l rl r!,r l L n e s c g mc n r\ -l h!n $e cl n geD cftrl i z€Lhr mersurcmentprocc\\ to pl rnc i i g u l e s .If o n e m e a s u re !th. \i d.s and i rl l eri or i rnsl esof r\{ o rri angl esand rhe si desnn d r e ri o r rn g l c \ o l h rth tri ln{l e\ ar. ti )uD dl r) h. cqual .thcn rhe t\o rri nrgl e\ xr. \ri d l( ' be coDgruenl- If oD. lrianglc scre moled by a figid moti(nr in sltncc lllrrsl.Iion ol ro ra l i o n i n l h e p h D c t d nd c rri cd i nl o rhc ol her rri ngl .. l he l ro rri ngl cs \roul d tr e c o n g ru e n l i f l l e s i d e r $ erc found to be coi nci dcnl .Thus, pl anc U gu.es arc crl l e d coneruent it lhe) arc oI lhe sarnc shnpe and rhc $mr'sire. ilt follos's lhat an! fi.urc is afso corgruent *irh irsell. or i\ s?4:.o gnte t.) ln dislirguishing Euclidca! Jrom nonE u c l i d e u n g e o m e u i e s ,th e mcasLrrcD enr oi l ri angl esi s tyi ri cal l )' B i !en as an exrmplc.
O n a Eu c l i d c a n p l rn c l h e s u n of the i ntcri or angl esof a l ri angi c w i l l cq nl i l 30' $here a s(,n a n o n tu c l i d c l D s u tce l he sum oI l he i nl eri or angl es{i l l he l ess l han or morc lhan isl)'. This ca bc delermiDed b)_ tntdltrcnrct s mrde on llt suftaccs in que s ri o n .R i e n ;rn n ts e . Ii ri c h e n hach 1956) ad\ocal cd l hrl thi s nethod ot m;rki rg _prrclica' nrcasurcmenls rlirs ho\r thc Seonrctr'tof .t qracc coLrldbc delcfnrnred cmpiri o l c allr. \p c c i l i c a l l )rh c e e o n re rr ) thl si ci l sprcr. i dcnl i t-t" ol th€ psl ch(trcuI.r1 n s S n r)' th i e stl 9 5 6 t p o i n tc d o ut. I l ogi calcons.-qucnce ) grucnt\i l h l bc hl ai t. A s $c Lhc o r\ i s l h a l !i s u a l s p c e s h o u l (l | l c ge()nretri crl l coD \ hal l s o o n s e c .Smrl h i e s i i s i g h l hrt mi uv i mfort0nt rl nri l i c.tri ons.bol h i or the p\l choneL rrl i d c D ti l r' th .o ry a n d n )r t hc cfi sl cmokrgl ol gconcl r) l hi s.rnhunl s k) l hc ps t c h o n e u ftl i d e n l i l ! l h c o r! b c i n g i nl crfrcl cd S eoIncl ri ci l l ' ],si ncc congruencci s l hc \ i, r ( q u r (n r o l i d e D l i l \ i n S c o nrcr\. A s i r hrptcns. l hi \ \\' rtscss!' nri rl l t thc l i re d r er s o n n rgp u rs [c d b )' l h ! C e s l rl l ps\chol ogi rl si n th! 1920s,w h(, cl n). l ht cl oscsll o s ug g c \l i D grh rl l h c rc $ l s S.()n rcl ri (l l c()rrgl ucr)c!hel \!.!n ri $rl i orns xr)d ti rl tcrl )s i n t hc b fa i n i o th c i r l h c (tr) o f l i ' n pcrccpl rnr Ol thi \. (i csrrl r i r\!chol og\' s l trdi nS e\ p. n L n r. K i j h l .r i I (rl 9 i ' i . r\ e rt(d l ' O i ,rr \l \. I n \r | r\f v ,n rf l u (li r! l rri i (i l )l r i D m0l i n! nr\ Lnl (r.n.(\nLrn !nen ffuTr.' l i .s , , f (l i r(t .\l ).ri rr.! l o l l rf fr{ ,t.nri \.1 !L$c, i !i Ltrr Il v\i ol opi .rl Ir)tr$(\ l r i \ l .s{hl ! l (, trl i . o(l .rs. l hrl i )f im r!i rr r 8 r!r1 D rr\ (l i fl q rrrr r0Lrl r,nnrtxhe1" 0ef l | . l \t):\\tr r' nl rr(n\ i ,r rl rn8 ! \ f(,l o 0 e \ rra rh x l,n fh \\trrh i !i .nlnrL{r\sLsl \htrrkl hrrc evcrv, r. r\(trtrrc(,r. \p(ci i i c lo rrl rl r (j rl i ri l f r\ttrL C rc c sl o (lrl i ti r( !)r(' (.sr\ x, l ,n! r\ | frrl r(l' nu(h r(h rri n \h L l ,l )e 1 s !(r rrrr r\1 , ri (lfr\. ri /.Ihrr ,)l (nrFn,cne.o, i \,tn,trthi nn i i rhLi , \!\ _ lri i rl i r tr(i fe rri (s 'lhc l rri n c i fL r 1 ,j \!\l !r) l i c c o n!fuerrce.r\ I((i hl cr erl l e(l i r. nar!(l thrl trl l e)i l )!' ri enc .d r)rd .r i n \p r.e i \ r rru r rcfrrscnl xri orrol r rorrrspon(i i nt o er i n thc unl cr l) iD ! ri l n rfl ri .rl c i mre \r (n p h l si ()l ol i (tl l pmce\scs i K i ;hl .r l ' l :eri . S ub\cqucnr' \, K iil rl fl rl ' o tp c (i th ( $ o rrl (x rg ru .r)cc Irr)h hi \ l (' rnrul ui ,!i s. i rn!l r.nr ed hi s l ut(i i nr in f f inc i fl e . rh c tri n c i fl c (n p s \rh ,ph\' \i cr' l i \i ' nr,thi \l n i K i ;hl !r l eJTi . l hi \ chrLrrgc r . r n ri n l J l o g \n r y h i r! h l c n p i )m tl .d b\ the l ;rcl thrl r(r)S ren.( rl i d rrn x.(urrl eh c hirfrfl e ri r. th c \p i rri rl frl x l i (rx h ip b.r\ccn \i strrl l ornrs rnd prl rern\ i rrnd l ,) cxi \l i n r I ! b rri n l i ! D ru rJ th !s i o l ()g i \r\ hr hct. thi \ $r\ !rncl hi n! r' l \hi ch K i ;hl er urr r \ N f. r\ !!i d .,' c c (l b v rh . n )l l o \ i Ig cxegL' si s: ' l r n i n i l l \\i l n ( rh rr th f s | rx trxrt/r' l i ,xrnri i ).i n fhrn,!nrn!L\l )rrr \i nr| ]\ .tj j .\tr, rLr(j rhr ! ( .D re l rn rl r.l l o ,!x h rf\ (,1 rh .i r rr\t(uti \r t)rti ce\\r\i n thf h drf ]cl l (i I N l rLl rrtl ri nr!l ( r r r l ,,n { rtn rem,, rh rr th i \ i J In cfnre \rL r brcru\.. l rr .\i ni tl r, r\ { rr! \nre. rct\ ti l r i lri i \ u n i i ,/m c o n ri i u u n r.e l rl ( l h q (,,fr.\thi rl i rS tr)ce$!\,,1 th. tr rri ti rtLt.re i rnrr.nri c !l l \.!to t)rrr.n l l \ J i \1 rl )!L e (l ,i \rr rl i . r\i i h( nri sI h. | | \ i I . d j h.j i ntr(. | !nr T r(l ) g..D r!1, r i c rl c .r\i (l c rrri o n \.v ) rc l h i f! l l Lr o !rf Lf rr l !r:r r.!:tui \sdrnu.hrdr. ot c.D rrrui tj$.utrl h rv r ro b c b rL rth r rh ,D 1 h \ rli i \ i nh,,!),)srrci rv ot rhr !(,rn.tncnt Jnr.i butrrr ,,t l h( r n rc c \\e \ Ir.:rmf trri n gn )r| l )s\fi .n hu rtr.guhr rraD tcnr.nr (n bi (ut \.\!,1\ i n rhe n L r!o !sl rs { c i n l n rrn rth i z c dh l N tul l uriOui rLn!d.l nrn q' (h cdn\i d(rrri .n\_ thrndntrj r.l s t... h r\ r l .rg . ru D h rr rn c h rr r.teri {' c\ \i ki r \,N nl be.l l (' r!rhcr i !.r!ntrc[.n\i htr on r h . r\\u tri ({ rl trr i r\ \r(rc ru r. xnd r i .ol l rn' tri n.rch c.ncr!r. r,k \erc (]ct.rnri i c(l ' t\dnsoi urti \i dul l o.rt pn)c($.\. b t n o ' h i n ! b u r p u re l \s c o N ,tri .rl rcl rti OD h th( funrl i .orL di < ri b l rn D (' f p ro .c $ .\.,\ \c l l a\ gfud l xr\ !!d !,l l crtrti o.\ i r \i .h I co.1c\1..i . b. r c g n n l c dr\ l h c p h r\i o l o l i c .ib r\i s ol rhc fh.hrn!nrLl\t i xt ofttrr A ccordi D * t!.1tjth!sb. li ,l i c a l rh c .rr- o f n h c n .n c ra l \ti.0 mr\t bc d,-D nmi c. D 01!e.mr| l i crl LK i ' d r():91]. r r .r\l a l c dn rl l .n l e l ' )l l :c l Ko h l c r l ol 9r 1 1s e e mso d d rh a r Ki i h l c r w o L l d on l he on. hand l ppc:tl ro \prl i al conccpl s and r c r mtn o l o S) ($ h e l h e r c o n g ru e n ceor i sornorphi smlonl ! i o (hen * anl l o rej cct i rs r ele \a n c cw h e n ri g o ro u s l ya p p l i e d Thi s mal €s i l di i fi cul t to Ino$ j usr w hat qas bci oS a\ s u mc d o r p ro p o s e d l h c c o n c cpl ualambi gui ryi s parl i cul art),apparenr i n rhe ofrcn-
v6!a/ space as phys'.al geomelr!
409
ridiculed c)iample ol pslchophysiologica) isonorphism (h t rhcre is something tquarc' l i l ,e i n th c b ra i n w h e n one seesa squarc.(w hrl i s meaD lbr' squrrrel i ke i f not l i Le t he to rm o I a s q u a re ? i- Ihe ki nd oi spati al rcl al i onshi pshi ch the C estal t psychologisls th o u g h l e x i s l e d b e t \\ecn pcrcep(s xnd hrarns sas nel er spcci l i cd-i n Iact. r l \ ! as s c a rc c l yd e ti n c d a r al l . I' an ol rhe di fl i cuhy l i e\ i n thc Gesl al l i stschoi ce ol rhe lcr m i \o rl o rp h i \n 1 .W i l b o ul preci sedefi ni ti on.l he w ord i somorphi smi s s(' rmhi gtou: as lo b c a l m o s t m c a n i n g l ess. srD c€i l has not oD e hul \evcral speci l l cmeannrgsi n l echnicr ll u s a g e .C o n rra ry ro & )ri ng i l 93(,). rhc sord $as n(' r l nvenl cd bv K 6hl er. but rfas f ir \ t u s c d b y b rd o g i s r\ i n d nrarher| rri ci l | nsi r rhe l nre l 8l )l )s. L-i l eral l !-i s(,norphi smm cr ns ' s a n i c s h rp c . n n d i n generali t nrerns' bei nq (" i dcnri crl (tr si nri l l . I(' m or \hr f c ( 'r s l ru c ru re. Il i s i n rh c l arl cr scnscrhat Gesrnl lpsl chol ogi sl suscd thc $' ord i s(,mo r phisnr . H o $ c v c .. i r i s j u s r rhi s dcl i ni l i on w hi ch i s mosl ambi guoussi ncc i dtnftul sht pt is \i r1i l tt \hd| t i r) A concrf\. A s sL ha!c s(n. b.ing of c a re l o ri c a l l l ' d i l l !r.n l l ro i d c n l i c n l s h n p c ro rfcstutl s l o I$o \hafr\ bei ng (,,r!/rf,rl . rl hercr\' bci ng of \ ilnililr \h n p c c o rrc s l )o n d s10 \hl ' pc\ bei nr g(ontdri (al l ! Jn,;l r -l -hU s. therc i s r i unda nr cnr r l a n rb i g u i (yu n d p o l c n ti rl s(N rc. ()l \Li l :c(!tox(l i cl i i $ i nhcrcnlal rfnLl ] i D l hf dcl i nilr {nr{) l i s o mo | .1 ]h i s inrs r e l l . (i nl orrun rLl y. K (i hl cr n.!cr nrcnri , Lal \hi ch ol rhc !i ri { {r\ llchn i c a l s c n s c \ o I th c \or1l sLrgte\redl () hi nr i rs rpphcrr' (rr l (' l hc tr)l tcnr o l lor n l )c rc c p ri < Dl.ri n rl l \. i r i s,)j c,)nsi der.rhl\iegni l i urnrc hos l i ,i hl !r y,u!hr r(, rcd,rrilc r hf d i fl c rc n c c l )c t$ c c n Ihr ' phcn(nnl D rl rl rrcl ur! ol \j sLrl snrcc $i rh i rs phrsi ( 'l( 'gic. l b rs i s b ! n p p u l i ' rg r o r 1r' n(ti {,rrl { l i srri bIri ,!r ,i l pn,.cs\!\ i n rh. brl i n. rn( l in ! ) d ,J i o gs h i l ti n s rh c f('cusol rnrl tsi \ l rnn u rnt11 tt, l l tkl i )I- r\ l houl h r /i ,k / &, r r l l c c o u Ir { )l rh . p h !si {)l ogi crlfrr)cfss(s ((trtl (l :,de(l !rtcl ) r' ((, ,)r 1,,. rh. varrrI r 'l !i s u rl l o rn rsrn (l rh ei s\uc ot consru.ncccorkl l l e ci rc(| ,r\cnl ed ri r,' S .rherhl s(!d,' ing ' l h . d c !c l r)tn rc n t oi l hi \ \h.l ! c{ )rfusi n! !h.(' rcti crl c(rr\t i cti (nr.\i th i l \ \ r r ious n mb i s u i l i c s ,rl 1 ri i n p x hr\f b.er) rrrol i \r1edl tr the des$i pti on rnd i nt.rprcl ali, , n, , 1 c l i n j c rl l i n (i i n g \ i n n cur(n,,r) (l c\p.ri nrcrrrl \,)rl i r \i surl nr!rr)ffJ-\i ,nos\ , li) r r n a a l r:i s rD d c ri ri c i s D ,)i (,rh!r c{ )l l ccpl ui rl(,)rrl Lr\i l D \ol K i ]hl er \ \\' orl \.! S rro nb. r t 1 9 7 5 1 .K i i h ' .r w r\ r N rr| j ,n nLtrr()l ogi crl\tu(l i r\.(rr(hrel e(l i n l h! er \ !c!r\ {'l lhi\ c !n tu ry t!fi i c fi h d d i se,' !crcd rhrt rhL sprti rl t!rri rni /rl n' rr (' l rhe r.l i r)rl \udre r \ r li) r $ o n l ()l rt h c rtc r fh rr \cr !!i r\ ro \onrc.xl .nt rcpnx| rc((l i D l hd \rri rtc co' r!\ i n n u t cl K i j h l e r l 9 2 9 rr !rc I'{ )l yl k l e.l l j . Ii r\i fri rg \(nn( o' rh! nrni r)l i ndi rrgss;l l \h, t r \ t he b rs i \ o i l h c e r)n l !\i ,D j D K i ;hl cr\ thl or! l l s { cl l l s i r) \uhs.(tu!nt l h.(i | l rs frl ta h h} 7 'Nt.rps' in th( hr)in F ' l o n r th c o u t\c r. i ( i s n.ccssl r] k) di \ti ngui shhcr$ccl thc oh:;L^rrrtruts pertxioingl, ) rh c c o D i i g u rri ,)n src poncd to exj sr i n l b! vi surt c{ ' cr. and rhe i utrl ,k i on !;\ t n b l h o s e c o n l i g u ri tx )n rsi l h rc-rrfd l o !i sual pcrccp!i {n. In y, doi ng i l w i bccomc r pp. r , _ e n r h o r rh c a n rh i g uj j i esol r rheof) ti tc K i j hl crs pri ,rci pl eot psychophl si cl ti s ( ; nr or p h i s n r' .o u l d l | ri s e .Unforl unl reh, mrl l ef\ rre conl l ti ci rl edsrj mc h! l he tacr i hlt il is n o l a l w a l s a p p a re nr $l l rr consri tul esobscr!rrhn rnd $har i s i D l crpretati onijr r hc rc l e v a n rl i te ra tu rc .;ind thi r crl cnds el err l () dc\cri pl i ons ol tbe reudi ngsmrdc bJ-t he i n s l ru m o n rsu s e d i n srudyi ngrh. br.ti n.A s K rhn ! 1970t poi nl cd out: -Oi rcn . . rhd; r ) - is i n p l ,rJ l .d d r' e c ' l ) i n thL d(.rfn,,l :,ttrratJ, Jt\t..1,,.,,t\( l h! l r^hl cm. N ,,ncr hel( s. rl ,. L r\c l J l I' m J \. u r, uph drrr.i o l .(ru.(n , h..r{i ,,i .r rnJ i nl ..rTrerr' r..r,, n ll. r b a s i so l w h a l h a s b e e n rcponed l o bc observrnon!ersus cxpti cj l or i mpl i ci l i nrc r pr er ati o n . In s o me c a \e s , addi l i i )nrl i nl erprcl al i o' rrusl be i erj ccl cd. si nce rfrcr e aLc instanccs$hcre inrcrpretationsmusr be intcrpreted in lhc inlere\t otclaril!_
A sunrmrrr_ de\cnplionol lhe configuralsimilaril)het$ce lhc retinreand lheir n lllan'ii 1957i: in !i\url rrea\of lhebfri'rwasgilenb._lhernalhcmrlici thc n('iecrion t\ cdtarl .m 01di l ' ' ' fh . tN L l $ no l l i s l rri rl l i n ! o n th c r.l i n i nduc$ r rN o di nensi ,)nrl ordc' l .r.rr,rrc d rc \l )o r\r\ i n rh c.e l l \ ol rh. rcri nnlnn^ai c l hi \ prrre' nrtner6 ro l .( pr.\(r\.(l rl l rh c s n \ Iro n i r\ i ri l L rl i o ri n th c r.ti fr 1on\ dLsri na(i on i n rh( ri {,rr corr!\ Thc Irescr\rl i ,,rr o f Ih . ,c \t,rl c rJ rrl ri j ,i \ c L l !r1 (dby nai nrri ni r.s l h. rcri nrlorrl !ri n{rl i .l ,D rgrhf (,fri c l r1Ihd.l ,rni nri on l n l h c c ,,| ri c rltrrl .i r i ' th c rd ,\ ' cIreLIro rhr feri naltrrl .rr l ]\ r l n| or,)gi cnl .rh rr \,rd \ l h ! ()l i c rl l )rrre r f c.n hr ft' fl nR l nr)n)l hr rcrnrr!prl l cnr l r] srrd(hi nSrnd r' 1 h c(l ni \i oi oi rh. i N i Fr bcrs(enhrnri \thcr.si s. or c,n,r\c.rn b c i n i o s $ rh ,ri r ' .r,i n s . Ir s h o u l (lh e l } ()i D r.(lo r rh n l rherr xf(,)l l en s!tcl rl l c!cl \ oj i nrcrfrcrrl i on i nl ohed ol l en sruti nB nt l h! l el cl ol dcscri fri on (,1cnl ti l in rh c n !u ro fh )' \n )k rg i c L rl j i rr!l i n g s . c nnrtrrc. thc choi (e o' tc' nrs u5& l and thc t[l i ni rnns gi ]en n,r ic rl r1 \ I(n i n \rrn'ci te t hc n r F (tr € \l rfl r, x l rh r)u rh Il l rnl chfi 0cl ui rcd l h( strl i rl rel i r(i (,rshi phchl .cD rh€ r c r i o i l l p rrtc rl r rn d c d rl i c rl frl l eD r\ b!i D S /rrl r,/r{nrl i l i s rrr,re l l equl Jntl rrrtcn' nl r o r\ h c i n g ft,/,()r,1 /tr( i i )r to l l )gri rthi ci ' l r.l hrl l htr{ i \ r topogfrtl hi c l !t,e\cnrari ,,1r' l t!' r,l t)ri crl ,,r l dpou:rphi !-or i \i 1 r r ' -m rt,i l rh ( rc ri rrt( i n th . l rrl i l ] Ii rl \hi cb;\i l 1 o rhi s qu(sri (rr, i t \i l l be r| \.tu1 r,) consi dcr hri .fl \ l ht h) l h l Irr rl l rn rl l i n ! l tri \\c r ( l( ri ri ti { ,rN(' l l h c s ,n l \ I()p (n (,S i crl l nd l ofogrl trhi c. l l i s t.n rp ti ' rS r,, th rn l Ih rr l hc l $o $or(l s. N hi !h sl )rrc rh( c,nnnrnr (i r..k nn)t. ' lo t1 ,\' . n rc ro i n g /[r,. n )i g h l h r \. si n)i l xr ,,. rrl rl ((l nrcrni n!\. l ]r(| t.,1.i n I rri nl c(h niri r! \rn \!. rh ! \o r(l \ rrru \i ft' rl l t s\' noD \nr' r\. l ' )r r rl nl l (. orrc,' l Ih( nl xrl !(hni c!l r l. l i n i l i ,n rs o l l o t()l (' !\ i \ l l f l(' l l )rrrthi c \1tr(l ! ol x trrl i r!| l ,' ti rc( 11,,$r\ef. i r) l( ch r)i r:rlr\a g ( l h ! l s ,) \i ,rd \ h r\' ! rMch l (ss i r) c,nrnr(n)i rl rr! hi r\r l h(tr l \ nru(h i n . , D n n n ' r\ g .(,!r.p h \ rr(l !.{ ,1 ,,S \d,) \h!n l fchl rrci rl l \' (l el l Icd. l .ch| l i (xl ' \. rofi )l (i q\ is i L h trr)(ho l rrl h !n h l i (\$ h .rc i r\topo(ri rph\ i \rhri rnchr)l cl rft,)sri rt,h\ Il s .e n s r rc i rto n rrh l cg u c \r t'rrt th. $rrri k,p(,!rrph\ $rs b(' rr,$ed h\ n!ufottr\\i , nr i !\ l rri r1 rn re d i .i rr..$ h (r. i 1 ,) ce!rs i n l h. rtu(l r (' 1 xnl t,,rr1-I(' f(urqrhi . rr)rt(!n\' . , nl rrN i \. L D (tr\rtl \ ' r!!i ,' l l l l rrrl r)n)\' LrIl orl rni !l \. \ci !| ti s(s stu(l vi n! \i \ui rl r)(ur,! ph \\i ,)l o ,rt h r\. n c \(i d L l i n c d () f d.\.ri brJ !\i r(tl \ \hrl //kr nrcl r h\ l tr. st)r(t t()t)LF gr i tp h i r. 1 ,, d \rn rl rl d s h ftr \n \i n g thrl rl rcrc i \ l l dpo{nphi c trl rp rt th! j el i nuc j I th! l\ r i L i ri Ih u \ l l \h l (\ L l t/l l r(l (\(ri h edl l c rryrgraphi t rrr' r' anrcrD .l,,l t l h.r.l i nx r!| r,)du rtd L n l h ! l rrri n !1 th e trts.r\rl i 0n 0' th. r()t\)!' nthi . r.l nti or)\ (t rhf \crn)r\ \ ur i i e . i n l h ! c ,,ftr\' . \i l h L i u t e\trhl ni n: l l l . .l ni rr!\,j l fi l h.r .1,,1,)grxthi lcrrrng.(,r nr ! .n r l o p )g | ' p h i . re l x ri r!i \' Lngl i \b l D i l l i ngti \h t!5fi r gi \. l h! ti j (^\i n! !trti nr lr " n ' ,1 l l ,c r,i r' g rrp h k trrIn rI,l ( I' r ru ,,l ,,tt ' 1 h e I\r,i l ,.s i . rh t( d l e te .i th ./r t,)ri !i !\. i D ctu!,Drh! S { P rrrt ,(tl l l ,of\.tj l r| .r.f1r\orrLj ,!j i r( i .l re rre dr' r .o n L n !(d i r rh . orl rri Trl i rr) .t tl ). 1| rct\ N \.rrJj nt l rr l j r t,rri tj . i i Ll j ( rh .,l rn ' ,.,.k ). rn (li n rl r..o rk \ " Lr n fri ri L ra rc l t. th e !' u c i l l th r.rse. strti rt fctl ri { rn!. i s not d(ti o.d i ni r .' r. N hrl ti l ,.1 ol-s p rri n l .c l 1 rrj l )s l r. Al l h o u g h a suA c\ of thc fete\ant ti l c11[ur(l i ri t\ r,, r,i et,tl ctca, del i n i rl (' r o f $ h a r n e d tu rfh )s i o l ogi \t\hr\e nrcaD rb\ I l l 4rosr,rfhi c,nrp.,: l ." p," r" nrulk )n . r l i u l u p h i l (to g i c a l a n a l )si sol rhr descri pri onsgi r:en tr: rarnrus uri rcrs ot rhe f er rn c n l n c u rc i rn o m i c rt fi n d i n gsh.l p\ etuci dl l c rr l easr\\hat r/x1.nrer t to connotc l' ! rh , r.l tJ .ri .( l rtr,J r.,th rc L ,r e\J .l ,.L,,,sf.rrt-r.. ,,r ;,r: f' e. rhq ,-crl ' .J I . | ' n..( ln | h e \h L ' | t1 ' | l< \i' Jl' .' li' ' | r | t/' ' | -.,| .
ic a ponnon lhc rerir! hasa corre\pondirg Hnr"rcr.'frci,r" loiDl in rl","r,of one ro-on. or poinr-tor-Jtoinris nor sufficienrlo ditjtfenliale lhe ""t.,,. spatiatrelaljon\hi; reflected in $r ncuroanalomicat confilurxrion in quesrion from o^oig un, ,".fr.r,ii on.'ro-onerelalionshins $hich a.e m^$emaricalty fosribte.t hc malh;niiicr,t!,u\ctul rnf.,rnr..rion., rlr( neuroph\rinl.,giJ..l liDJi.SrhJr rh. ,.1, ,, p,,.irr.n.Jt f.r;n.rtt,,cj are repr.(rLrcL\d ,I lh( c,,rk\. r! (Jch quJJrrnrjjr rl,c \i\J.,1rrctJ.t,, Ir,l.Jr.\l ,,r, rh,
v iuaLs pac eas pnls c aL9 e 0 m e t r y
retiDt|c.corresponds ro r quadranr oi lhe visual conical rrea- Thc rcproducti(rr oi lhese spatial relalionshir|s corrcsponds lo frcrerving lhe lr)pobsical properlt oi o/?1fl tsJ" ordcr is mea'rl rhnl r€lalirxr uhich a group ol poinrs erhibils \,"hcn (h.! are alwal"s in rb c s a n rcs c q u e n c eF. br e-rrmpl e.consi derrhreepoi nrs.a. h. c.In thi s grcup of poinls. if th c p o i n l b n l s a \s o c ctrrshel \r!en Ihc foi nl s a rnd c (l hi s rchl i on i s sornehmcscr llcd ' b e t\e rn n c s rl . l h i :n rhi s i s rn exampl t of l op(nogi c!l ordcr. S o rl re o,?/r7of thr ret innl s u ri n c e si s p re s rn c d i D thc co e\. Thus rel rrdcd, l hc $ cal l ed topographi cm lp rfi p ro \i n r.rl e \Ih e d e l i ni ti on oi a phne pr)j .cti on i n proj eeti !cgcometr!.anLll hc Dcur o .rn x l o l ' l o p o s l l ' p h rcl n p l ' nounts l o r l ofol (,!rcrl l y detofnredfhnc proi cclioD( ) f 'cal l l r hrl tcns thrr thne proi r(ti on i s (D e ol l hc mrthenr ir icill l h c rc l i n n l c o n l i l L rr.rl i ol r. l o o l s u s e (l i n n rn k i rg l o tl o.rraj rhi cnr!l )s l l n o p l ()s i l i o n 1 o th esc con\i (l crrl i on\.h()rc!cr. ol hcrs hn!f.rgLrcd l hi tr l hc s pr r r iir l rc l rl i .n s h i l u n (l e f d i s cussron i s rol rof,)tfl rl hi crl . In rhi s !egrr(1.H rhh LIt).l tl r\ror e: ' ' T l r re p n tl u .ri ,n ',,1 rfl i i .rl prl l .rr\ i tr r,u l 7 i \ l .,trtr,g(rl . n,t r,,l \,!rrfhi ol : r nr l l' i rl .n l ' l \ \r' r.' 4 tl fre i \ drrohi ndl h\ Ll )r\hrtc,,1 i hr r,)nr.i l c\cLl fl i ,i h. r.!rrrl l .$ 1 ) i\ hr L l h . i r\rl 0 n p o n rrrl r! h!.l he t.' ..r\(l ti ,,f(!l L.\ i i l r !t!0ru $r1hshi l rl nrgn,.e,,rrl Ll ill( r ef r (l l s rfr.c s\h ,i rl { Lrh rd!r mrrl | (l l \-' $rrrri rr. i r n rnc. r,ti r(r,i hr.rrl t,,tr,l !)!i .rlrfl l , lr l i i i n t)rr\ n (\ l o r th i \ .1,(l ri i r rrl l rnti F l | . sr . ttr,t!trrnrrs l hrt r\..ror\ n!rrkl ,)cf ur . i! rh c l !rc c t)rn n r,nrtu rLi hrrrnl \.\rhr.h(1,'n" r ,,(r' !. i n rhLl ' .r(.trrrr.l rrrn![\] i \),{ .\ e r.l ! i D,n rcrn !l ( ,n r(S rrl \l !!.l l b( ci !ri u\rl \rl h rtr fl l i l ' \r i I l noLhrrrngl ! OD r r r L!iL t,\r u ir l.
r L lll.' ( n lL n l ..l l (l rn$1\ Lr c!,r I r(r rl i f tl i { Lf i i ,i ,,1 l L,l JL)g! rfh rrL rrl l i Li n
l l c rd i n g b c t$ (c rr th c l i ,r.\. shrt l l rbh s(cn).rl l (, h! Ir\i rr! t() c\trcs\ h\ \r\i n! rhll t h. fc p rts c n l i rl n )Do l l h c r (l i rr( i n l hc \i \url cl ,tl c\ (l { )r\ nr)l r!l i ri r) thc sInrf I11' l )or lr or r r i s rh rr th r ,rv l k .r/ \| rri rl r!l rl r(,o\l ri p\,,1 rh( rLrrrre e nLnr.In\l u!!(l l \ l hu\ \ , , 1[ l b c o n i r l o fo s rl ' rh i c l {l | ther.l l fhb $.r\ l l l u(l i nr l () Ihe l rrt l h.t (h( rr.l frcl l slr r t ir l ' r rn| . \h i ch r.l r' n trs h i ti \ rth rt Il .hh rt,tl rr(ntl \ l ,i ,rl I() .rL l .t(' n11rIhi cl lt ,)t l he rr t iI r f u ' x l c rs ,) r .l x \l i . trrn\l i rnl l i l xr i n l hr hmi n. l { i j th. rrl l nl l c0nl i !ul rti orr h,r( ih( er r p l rc ((l (' n r ftrh l ).r sh!rt l n(l \ etfh.{l rl :ri | . 1l )i \ \r!nr\ t(' he shrl h! rI \ lr \ ' Ir ' l (' p o l (' !i e r' lr(p rtr| r.ti ( )rr' r.Il i \ i n rhi \ s !. i rs Ij h l !\| | ri n!,(1. thl l l h. frti nrLl frL cr r r rs rc h l .d Ir) l h e (,),t i cal l j nf b\ 1,)f,' ]t)!i ci rl(l rl j rrr)rl i (!r ' 1,) l hi s !\l .r . H !hl ) $r \ L o re c r i l h f n l e i rn t 1 o \l l \ thi rt l hf \l )i rl i rl r!| i oD \hi | \ rLrr nr)t l i k. l ho\e 1)t Lt t ot , , F F fa p h ' c n l rp l 1 i \ fr!. i s.l \ th( ,l rfl ri (i rl \tui rLl fcl i rl i (i n\hi | \ shLch rrr l J ndxrn. J) t iLt c h rn c rc rj tl i f r)l l o l !)A rrt)hi ( rp\ l -r)re\rrIfl .. l he nrel | i crt r.t. i or\hi | \ 0t l guologc ()rr(\l l i n (l l {) rh(\r (!r rhr t()t)()grrIhj !nrrl ,)f i r h\ tLc(rr\l rnt ri rl i o k r o\ |l ' frl ' !-rrr)n rr l h r s c x l r. { h e fc rtr) D I di strncf r)D rh! nrxI i s eqLri !i Ltcnt t,j I (ti nl l nceIn th.. n! iro n n .n l c g l k i l o n r.l . r = J!.nti nr.l !fr L Ifl i ) u l rrl .l \,. i l N ()U l dfrcl te contu\i on l () frtl t i he cr) i cl t nILp l .tofr)t,,gi crLln r np. . l )...ru s r i r ro fo l o !!' rh . \\ord nrrp h| \l nrc ni ngqui l cfenrj !.dtr.on)rhccr;r(,rrrpt ; ic s e D s . o l th . { o | 1 l e o n r0teLli n rhi \ conrc\l tt r0ukt hr I nl i \l xt! t()r l hrl !!i l s() n l( ) rs k )c i l t( to fo g frIh i c n rnfs $ i rh k)l x)to{i cl t(rr!s s thoul h l he\ \ !r. h()rhi n rhf \ r nr . c rl e a o r) A 1 1 )t{ )l o l i cl l nl f i ! r l rf i n l he ml rh.n)xl i (nl sen\. i i . l ti !r)cri ( r shit . I I' rf trrfh c f' .f i , i I n.t , I prcr.[( ,,, tr,i (.' rr,n. I Int,,t,.rr.,t nrrt.,r\r rn. r lt r , . . n .i | .. I rr.n .' ..i r. r. ,h ( r(t.rl | ,,n\l .rt.,., , i \\,rr.r.rrr.\:rS ,r!q (r,rrr!urrtx,o, ( r i s q L rrr!j N h a d .l o n r i or of i l ht etrni c' t..$\r.h nr,,l i r)nji c-sr l rrpczoi d) I hc nap i s nor r h. d rl o rn u ri o n i l s e l f rs t he cnrr(tgrrphi . u\c ol l hc \ord mi rp m if hl h i s rh u sc (D c l u d e dfi ,r rhe rcasonsgi !cn ntrol c rhxr rhe $cal ted .n:rps.;n rh., ri\ uxl c .)rl c \ , e n c rrh d rr,' p ,\ !r.,thr. n,r t,,t,,touj (at,n d| n.prr(.r\(\erN (. tr i , sug!c\te,t th r t . r n s n i l e i ' l l h ( i ,' n l tr.rd i ti ,' I i n nf r,rptr\!ot,,rr ,,r rr.rnel h( q,rJ l ,,foprcpnrc. r. nol tr' e l l< u rl c dn \ J J c \c rrf' \( tcrm i n thrsr,,t)k,\r.h( r.ru\( th(rr Jre l o., m.rnt e\c(r,l k, n. t n thc corrc\poodcnce ol thc tirain maps lo lhe definirion ot a lopographic m;p f.,:'irr., i.,r,r,
412
r o co n v c y m u c h u s l l u l i n f(trm a rion.l r ri cal l ). i hc ol der ncuroanal onri .aldc\j gl l al i {)n. ' pr o i e c ri o n . h rp n e n s to b e th e !r(' rd $hi ch coi ncnl esbcsl !ri l h a m.tl he al i crl l Feon. Lr i c n l r d !\c r' i p l i o n $ h i c h $ 1 )ul d hc $)nsi stenl \\' i Ll i l he D eor(,tnal omi call i ndi ngr des c ri b .d i n rh c l i k r0 tu re . H o $ c r cr. rhe rsc of thi s ki fi co0l d ei rsi l )_ l ei d to further bccnuscan! geo c onl u \i o n ss i i rc ci l \r\ n o l i n i ti rl l f Lr\e!li n r acurcanal onri cal coD tcrl nr er ri c rlre l rti ,l n \h i p\ a ( b ri n ! d e n ored. l' h e s c i d i { \tn c ri n i c i x c \ o t th c {ords l ri po!rath} and bpok)gt i and. ar norcd ca i cr. ilr no fp h i s i rrr e rrn rp l rs o f a r u rl l cr ol trcud(' sci cnri [i cor pscudo-mrl hcmrti cx] lc r ' t \ h u n d i r l h c l c c h n i c i l ln (l D ! nchl urc ol nc rot)h\si ol og!l nd l i sual \ci cncc \\,hi ch r r e o l (h b i o u s e \p h n rl o r \t| l u e i cf Go(xl d\ l !5(,: P i rcnn! l t)51i . -l hc l \o terD r\ ( lis cu \s e d i b (trl J r:rs \c l l :rs th r co ccl l \ l hc! rcfrcsenl r urr fscu{l o nrrl h.mrl i cal hc c rn s eth .\ s l ri \e r,)c \p rc \\ i D l l h e ti crl (on(.pr\. bnl r( u\!d ri l hfr i mfrcci \cl J' i ar. nor g i \c n p r!c i \c n ri rth c mi rl i c id!lcti ni l l ni s i n l hc coD l crl i n shi ch Ihe\ afpcrrr. or i n s! hr\c \rcn. l hfi t s . r \ s (n l l c r\i s c a r !rri i rrc ( $ i l h \ rl ,rdl l (l D r thcnrrl i (i l l usl se ^\ r nr b i g L r(' r\m c rn i rg l i n ri r\ rh .i ' u s.ful ncssi n n, i nr cl .r' d.scri pl i trr\ ot concrpl \. lr ) r r i c rl l \. th (s r t\!!i l (!n rl tl )c n rx l i ci tl co| l c.' rl \ r' l rrn rfl ).t| | si de l r\ \i cl ( \i rh ((r1' .(rh u\ c d n rrl h fn ri (rl l rn l i fo l o g ! rrrl l i )rnruhri on\.rl l houl h l hc ,/k,i .l of l hc prrl i cul nt nr ! lh | D ]l tl i C l l | 1 ()l | l i | 1 i \n r1 l .)| !x |l nr| | !.(h.chl ' i | cInC o()fu| i nt| ti \edc| i D i l i l ' l ln \ti r! ()j l h c (n ,\i ()u \ (l i \!rrIr nci .\ her$c.| l rI. oi rfi . hri ' r n(l rnri rl ' rru.rurc l \u (h l \ l h ! d i \i s i (tr l r.1 $e.n th. l $r,.fr.brxl h.rrri \fhfrc\, \!i ' .rnl i \l \ sl n(l yi D { t ic r .(Pl \ \ ^u:rl r)(!,,,Ih \\r' l o !\ Ih ri u !h r l ()r r l ()r! ri fr. thrr \i \url \| l cc xr(l i r\ nn)to\.(' ,rruri ) t hl\ i ,n ,,!i c rl \u h s trrl ( i r th f b rri r $crc !cn!rrl l \ \i nri hr 1rrsr rctur! A s $. hx\. \e.n. lhe\ l \i ) i N { rn r.(l l h x l l h . c ,)rri(rl nrl tl \' rcl l (.t((1 r \i rfl . f.i n1 trri j .cti ()| (i f l hr r Lt r rc , i u rJ l h n s ,,l l h . (' tl i c x l i n IS .\ j ]roi (cl cd{ )l ]th.nrr. I l ' rt r\ k rr,r\1 ((l rr,,1l h e r).u r,,r rrrt(nn\,,r ' i un(l i { u:rl i !(hi l (!l rr( ()l th( \i \0rl cort.\ ir . ( |r ru l x rc rl .tn . \i n rp l r tro i c c ri , )tr (l ..cri bL(l l ,t Il hr)l \:r\ rrtl l cc(l h\ f\fr nr)r! ! , , f r t 1 l (\,,rrc s ..r.h n r. i r(,trrrr!c t$i l h th. pl rrno, fnxl \l rr( ! r' l \i \!l l \l )i r.r r ir n rl r! l r\r l ,)' .\rn rfl . rn r,)r)gl h( nn\r rcl c\r' l i (l i D g\ N ere the (i i \r,^l .r\ ,)l rhe ' f , , r l i c rl h c to f. \h .r.l he xr' r i n l hc (,tr1.\ c,nrfsl \!xl i fl S t,) thc l i r.i r i . ' rIrnl h i l ii rr c i rl i \' n()l t r r ! h T rr!.r Ih rl tI. r fti Ii rl t).i i fhfr\ , $ hi t[r i (hc i rn(lI)l i (l l t](' l i \\ hi l rcr' i (l se lLr 6 5 ril h f t)ri !,rl rti ,,r-\fl rc ti \f c .1l h\rr\ nd oruhr (l onri nxn.. c,,l unl r)sol H trb!t nn(i \ \ e\ ( l 1 !7 7 . l rl !:l r)(l . r,j r!r.c eni h.rh.!ti \e{)\ef\,,t s.\L' rl l tti fl crr r c{ )rl i rIt \i \url nr t \ rh ! l rrri s ()j c r1 s rn rl fl )r)l f\\. frLchttl rfrf.ntt\ rLrhs!ri n! (l i .rrnt t n.ri (rr\ ' r'c k l t)7 { r,. \ ( c (ri In !r\| r-! l () (l f\ rri bc thLrfr)rri cl t !i \ul l rrrn\ r\ r cr),ri ur' i rIl g. l{ r nr \(j ni l L )N i l r.c rn tl \ \ro t.: ' j\i rh r r\j .\. u fh (n rh ( \\trrt trrtJ n rutrrr\.D rrJD rrr\ | D r\,trrr tr\ rhf rfri \l \ {n ' r!i !j r , \,,,.' r 1 ,, |l|'tt{|tJl''n'||(ll('t|it(''|'nii||\|niiil|i|
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Ih !c !n rrrl \c rtn e s s . l i rl l nl ' (1.' s rn\(nt i ng l D r' l \si s rord(co tl o\i l rtri ol l hc\it ur l \ri n ru l u \ i s rh i rl l l l e ! l r. i n(on:i sl cnl\rl h.{rri su:' l c\' ^- i cn(c !\hi ch \l rent\ uni l nr \ A\ h \ r h( ' l l u h c l l I](l \v i c s .l L l (r7(7N dnri rr.d: l l o\l rnl cnti rcl i rrni srnnl rzcd(' rhandl c(l l )l ri D h o { rh i s i n fo rn i rri rnri s \ortcd on rn(l s\nrh.\i /!d t htcr sl rtsc\.i I i ttul ul t I t \ Ii l rl i c s r(l d fd l -i s n o r k t (N n.' i rl c(} | rtl l l Ltrn.s\t" l hc ti nd tn l isor l S o l c $ ()rk c rs s r,u ck h! l h! rn rl \!i s (l e \.ri l te d h \ l hh!l l frl W i .\cl tr\e rl [' r]f[(l l (] (l (\ck' l ) D r' rc gi (' h.l ' rl , ] dcl\ ,)l \i ru rl l l n fl i o n .()l h c r\l !rS ch$rrrl ;, l (rl l ' u. l t)S oh:fi ().nd.nrrl rt(l rrtr l )t)()n) l97l': I,(l Il ,' n i \/ rn rl l .l i ru \ l Lrsl ri s()ul d ht(e i r thnr rh.fe i \ a foncri drl l si rni l i cl ncc t,) t h! p c fu l i rr !c ti n r!1 r\ t\l l hu \l \uLrl rrl l t)\ i n thf hl 1l i n.l hx( the gc(nncl ,i crlcrrrl l guIrti( r r ( ] l l h . \i !rx l n t\ tfr \c f!rl ,rnr\ | tun(1i rnr1 \i surl xrrxl \si srr(i Il rl l crn | tci )!r'r ili{r r crrntrul rl i ,,ni rl xfrt,)i nt,)r ' .()frfutxl i onrl geonrcl r!r. ;S (h \rrl /h r\u rl l !(l l h i \ ll s{rinA t.(r: nrlllr(||)nli(rl Dlrrl(cas ()n . 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Il u r rg ri n . th .r nradeno r(cn)tt l .) nddrcs\thc prohi r ol congruoD cc.fhrr( , xr c ts o c h i .l ,)h j c c ti o n \ to thfi r nr{ )dcl rn.l ol hcrs,uf ti ^l !r 197:: H o nran tt)S { )i .the f ir sl o b i e c l i o ni \ rh i h e u r h!mrt' cal rrrn\tbrnl l rri ol Li nl ol i cd k, rctal cl i surtspncc l o hr ajn s p u c ci l b e re h d e l c rl r. turl (xe rt hand. i n l hi rl i r \pnti rl pi rl rcrncl n{ n bc cha n! . d l l n d s ri l l h c i J c n ri c rl con!ruenl i \ri rh i rs i ni l i rt unchrnr.d \hrpel C omnronsensca t onc t€ l l \ u \ rh i \ mu c h . Ir $ oukl consl i l urc \i otrri ()n ot se' Lcorgnrencetl soul d bc ralhcr l i k c c ru p l i n g a n d rel ri ng a (| i angl e m dc ()ur ol prf,ef aj rd i her si ryi nc rha l t he c ru m fl e d a n d to rr l fj r ngl c i oul Ll sri tl bu congruent$i th l he $.1! i l w rr before b r inS d c l o rmc d . l ' h u s .n o s l r i ctl ! physi calbasi si s gi \en ror rhe resuhi ngri suatseomerryir set t i n th e s cn ro d e l \.Ih e s e c(D dohj ccri oni s thal l Jrcrransformati ons cnti sred(o do i he j ob of re c ()n c i l i n gth e s l ru c rureof vi sualspac. $i rh rhe brai n exi sl ont) ahsl racrty i or mrt hcn o l rc a l l y l . ,rr /td .i l (? /4}.A D d cve! i l l hev di d e)i i stthl si ca v. no l ransfofmal i ol rot hcr tl ra n $ e n ra L h e nl i c rl l l! rri !i al ;.l r,ri n t tnsfo tutl i ol i i c I rransformal i Lrn $hi ch mr k. \ n o c h a n g ei D a c o D fi g ural i on or funcl i oD -eg.r' : -!, t.' : rl shoul dbe requj redl C )ret ale s o m e rh j n Sto i l s e l f-T h ar i s to sr)_ l i surt spaccshoul d hc i denl i cat{i rh i l scf. and ihc
hriin should bc idenlical $irh ir\elf. Hcre asain rhe lacli of corrrucncc hel$den visual an d b r.ri r p n trc rn s$ o u l d \tro D eh i ndi cutei hat therc i s no basi sl or assc' 1i ng rharthc 1\o r r e re trl l \o r)h (rre s tru c tu rep. rr l i cul adya si ngl crc4' 1rr!,1drl st,' !rcrure. nri ghlanrounr l l i \ a d i s ru rb i n gl h o rg h r th t rhe el fons i r thi s reS ard.\hi l e :rmtri rrcus. fi cti (' n,or s(rsc. l e8erdcmri r.I h. ri turti on i \ si mi l 0rl o t ( ) l ;rl l c m o r. Ih x n ma rh c n ra l i c al L,i \l c i ri s e .rl \ re \c n d l i o n s rh oul the u\e ol nrathemrti csi n the dcl ebpmcnt of hi s t h r(' ri c s .Ar L u n s ro sI1 9 6 5 t $ ro tc: j l :i nstci nj$rs afrai d thi rtrl rc cl egarccoI rhe nri rrhe mltical nccha isnr nrighr ohscur€ the physical problem and gife n nurel)- tornrillisric an s \e ' s h i c h n i g h rs x rl h € r th c de.pcr es\cnccol rh. fh!si crl si l !i rl i on. \\I01 D akes r h c ro l e (' j m 0 i h c n u ri c s n )n rc w hrt suspccti n ncur)ph!\l ol ogi crl h h!l cd theori esof \ isi o n i s l h rl u l l l (x r Ie q L re n tl j nri rthcmal i crlmodcl sarc $el conrcdotrl y i n\otrr rrsrhc\ r g r.. \\i l h l j rrri !i ne \f' c ri rc n rrl dl l x. l rul shoul dl het prcdi crfi n(l i ngsci nr r\ l () cri sri ne r ss u p ti (' r\. rh !\ l r' c ru l e i i (,u l o l coun. l \hl hrmrl i cIl rr-!unr.rr\ \,,ul i l thLrssr.nrrri hc us e dl l fl e l \ 1 ord d c i !d e n c el r) e nrti ri crl l i ndi ngs,r N (herl hl n l o l .a(l rl ) n($ (l i sco!cri es. 9 Ih., credibilill lnp r \ \ c r ! l \ Ih c l ()l l r\ s { ,n rr n r!r)\ci c ti sts hr(l he!ur) tr) (tu.\1i ,nr\l rerhfr or n,,r l hc s h r| . o i rrN r)n rl c o n j i { u rx l i o s hr(1 r' r)_nr.rni n!l ul rchl i on\hi t to l (nnr f!rc.fti ,)n r r ' th ,trr(hi t i \ rft)r' c n r fr()D rKi t hl cr \ rc' r)l rl s thrl Ihc suc(l so' (l (ul )l \c!e 1i (i ,(i \ \c\D h\' l \.l i i l l rt i n rh c l e l h c c n tu r\r. Ih( (hi ci d(){rhl crsr\ $r" rn l \1c(ul l ,)!h. r\ I' rIfn ' l h r rh .,rt ,n N i r.frr{ r ) \ l ) r(D | [!rrLl l ,\ | rr rL]rL rhrj r j ! . frr\L l )f Lnrl rr hrri r \,D r \L ,n i i l !r,,i i r1 rL .rl l \l rrl h rrl rrf re\eftrr,,n fl rhr L\rbi { l r\Lr In rh{ hrrrD l th,N !h thr rn rrl rn ri n r,n \,' rtl \ l !1 . i !D ,nl l ri \r' rnn r(,txn(,!i .rl ' rl i trri nrrcrl r| . nr!e.l ri r.rri Lr\ f r LLi( ni\ . \ . 1lr . ! i i \ r r L r i, f h\ \ , , i i l i r i l h \ t , , 1 h . ! \ r l r { I r r r r | L L n rL ( i l \ L l ( \ f l '( r l r r r i \ ( l( ' r il no r f ! r h. lir n hr ll ! n r h r r \ ! n r ! t h c ( r r , r 1 q r r e r h ! \ r I n r i , h r n ! \ n n ( ! ' ,n (tu.^i. \ t r lr . , i r t r t ! l! lr r r lt r hr r ir lh. r ) , t n r r t h d e \ r r r \ r r i h . ir:ir(!iu( i e \ r r \ | ] | \ {. r l n i\. r. iLri liLr \ L r I r ] [ ! t r r r r r i\ . r ] $ ( i r l ( l h t r i l . i r l . r n r r s r . h r f r i . 1 , f \ i t l e r ( ( l : h r r r i L )! i f r I r k i r t i l \ 1. ( ull. ' r ir r t r . l l' . r \ ! t r ir t . \ ln n h ( c n , r t r l ( r , r l ( \ . l t 't ) ( , r r r r . . I i f r l t r \ . i r n r r , r ( . I i ( i. ii l\ r iLl! ' r t r ( lni, ! L. lr r if \ r ir i n i h | i i t \ ! i r l l l r n r r " {)l
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Ii rr l hat ml l l ef. l h. i dcnl j cal m e a n j n g(' l rh . l .rn rs d , rh c c q uari ()ni s sonrethi ngqui tc aprul l nD rhc nl l rts on l he pn J re .l p rg e -i r i s s u p p l i c db ! t he krl .,r, \ho i nrpansrhc meani D sl (, rh( m: ts.-t.h. s o i l o l i d e n ri l y re h ri (,r C ;rc s i ) ri tropo\c\ nri l hr j Lrs rrsuetl equri e i mousr \i rh i rn ! l. p h .rn t. l t S $ i s \ (h c e s c $ i th 1C rmcnrb.n. or I ptum $j rh a f,runc-that i r to sl \. I : I l h e .rrh ' l l rry i d e n ri fi c a ri on ot unti te rhi ngsi \ pl ai ntt a scl t-dcrcnri ng corerpri sc. I t lhc doubl€-aspectIheory Cr .s o ry s i d e n ri l } o i n e a n i n g i s some$h:tlsi m;tari | l i l \ coD c)u\i on() r l rl i ;rnt oi thc ps )c h o n e u ra li d c n ri l v rh c o rv c a l l ed l hc .doubtc-aspecr rhcor). i W l burn ct rt 196_ti . llhich lllrtes drar rh. mind as experjencedand rh. brain as observcrtb_tscicnlins arc nr, ot thc safie lhing-nanr.lr, drc brain. 'fhc analogy of InoLrnranrsor ck)uds looted '?!/)(.,J ai lrom drflerent perspediles i$ often given in an . rcur ro \hos thar rhinls rhnl crn secn vel-! dissi'l]ilar {rom difterent vanrage points can nonelhelcss bc rhe samc ihing.
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