Structure Mapping in Analogy and Similarity

8/13/2019 Structure Mapping in Analogy and Similarity

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Dedre GentnerArthur Markman

Anal ogyands im l a r i t y are often assumd t o be di st i nctpsychol ogi cal processes I n contrast t o t h i s posi t i on, t heauthors suggest that both s im l a r i t y andana ogy i nvol veaprocess of structural a i gnmnt andmppi ng, that i sthat s im l a r i t y i s l i k e anaogy I n t h i s art i c le , t he authorsf i r s t descr i be t he structure-mappi ng process as i t hasb+en workedout foranaogy Then, t h i s vi ew s extendedt o s im l a r i t y , where i t i s used t o gener at e newredi c t i ons Final l y, t he authors expl ore broader i mpl i cat i ons ofstructural a i gnmnt for psychol ogi cal processi ng

nalogy and s im l a r i t y ar e central i n cogni t i vepr ocessi ng They ar e often vi ewedas qui t e sepa-at e Anal ogy i s a cl ever , sophi st i cat ed processused i n creati ve di scovery, whereas s im l a r i t y i s abr ut eper cept ual process that we share w t h t he ent i re ani malki ngdomThi s vi ewof s im l a r i t y has i mportant i mpl i ca-t i ons f or t he waywemdel human t hi nki ng, because

s im l a r i t y i s demnstrabl y i mportant across many areasof cogni t i on W store exper i ences i n categori es l argel yon t he basi s of thei r s im l a r i t y t o a cat egory representa-t i on or t o stored exemlars (SmthMedi n, 1981 I ntransfer ; newprobl em ar e sol ved us i ng procedures t akenf rompr i or si m l ar probl em (Bassok, 1990 Hol yoakKoh 1987 Keane, 1988 Kol odner , 1993 Novi ck, 19881990 Ross 1987, 1989 Wnston 1980) , and i nf erencesabout peopl e are i nf l uenced by thei r s im l a r i t y t o ot herknown i ndi vi duals (Andersenol e, 1990 Read 1984) 1?ven t he waywe respond aff ect i vel y t o a si tuat i on maybe based i n part on our responses t o previ ous s im l a rat i ons (Kahnemanl l e r , 1986 Thus, an under -st andi ng of s im l a r i t y pr ocessi ng may provi de generali ns i ght i nto human thi nking

I n our research, wehave t aken a very di f f erent routefrom he stars above, mudbel ow vi ewof anaogyands im l a r i t y Wsuggest that t he process of carr y i ng out acomari son i s t he sam i n both cases The general i deai s summari zedby t he sl ogansi m l ar i t y i s l i k e anaogyGentnerarkman, 1995 Markmanent ner , 1993al k l d di n Gol dst one,ent ner , 1993) Wsummari ze r e-c c ; nt evi dence suggest i ng that t he process i nvol ved i n boths im l a r i t y andanaogy comari sons i s one of structuralal i gnment andmappi ng between mental r epr esentat i ons(Fal kenhai ner , For bus, ent ner , 1989 Gentner, 19839989 ; GentnerMarkman, 1993 1994 1995 ; Gold-st one, 1994b Gol dstoneMedi n, 1994 Gol dstoneMedi n,ent ner , 1991 ; Markmanent ner , 1993a1993b Medi n et al 1993) Wbegi nw th creati ve anal -ogy and then t ur n t o s im l a r i t y

Structure Mappi ng i n Anal ogy and S im l a r i t y

J anuary 1997 Amri can Psychol ogi stCopyri ght 1997 by t he Ameri can Psychol ogi cal Associ ati on, I nc 0003- 066x/97/ 2. 00Vol 52 No 45-56

Northwestern Uni vers i t yCol umi a Uni vers i t y

Anal ogyJ ohannes Kepl er was agreat di scoverer and a pro l i f i canal ogi zer He was an ear l y chami on of Coperni cus' s(1543/1992) pr oposal that t he earth an ot her pl anet smved, rather than t he sun I n 1596, i n t he course oft ry i ng t o work out t he l aws of pl anet ary moti on Kepl erfound hi mel f aski ng a seemngl y si mpl e questi on : Whyi s i t that t he outermst pl anets mve sl ower than t hei nnermst pl anet s? Accordi ngt o t he best exi st i ng model st he pl anet s' mti on was caused by pl anetary s p i r i t s orsoul s that i mpel l edthe pl anet s on thei r cour ses As Kepl ernot ed, one possi bi l i t y was that t he sp i r i t s that mved t heout er pl anets j ust happened t o be weaker than t he s p i r i t sthat mved t he i nner pl anet s ; but he proposed i nst ead t heradi cal i dea that there i s one s p i r i t or power emnati ngfrom he sun that mves al l t he pl anets that i s t h a t t hesun causes t he mti on of t he pl anets [ Kepl er had hi tupon am or i dea, an i mportant precursor of gravi t y Butthere was a seemngl y fatal obj ect i on For t he sun t omve t he pl anet s woul d requi re act i on at adi st ance, anabhorr ent not i on t o any physi cal sci ent i s t ( i ncl udi ngNewon, when he developed t he f u l l theory of gravi t ysom 80 years l a t e rKepl er ' s response t o t h i s sel f - posed chal l enge wast o consi der an anaogy t o l i ght I n hi s AstronomaNova(TheNewAstronom 1609/1992) , Kepl er developed t h i sanaogybetween t he moti vepower and l i ght (see Gentneret a l i n press, f or detai l s) :But l e s t I appear t o phi l osophi ze w th excessi ve i nsol ence, Is h a l l propose t o t he r eader t he clearl y aut hent i c exampl e ofl i g h t si nce i t a l s o mkes i t s nest i n t he s u n t hence t o breakforth i n t o t hewhol eworl d as a comani ont o t h i s mot i ve power

Dedre Gen tner Depar tment of Psychol ogy, Nort hwestern Uni v er s i t y ;Ar t hur Mar kman, Depar t ment of P s y c h ol o gy Col umbi a Uni v er s i t y T hi s wor k was support ed by Na t i o na l Sci ence Foundati on (NSF)Grant SBR-95-11757, O f f i c e of Naval Research Gr ant N00014- 89-J 1 2 72 andNS Career Awar d SBR- 95-10924 We t hank Doug Medi n, KenF o r b u s and t he S i m l a r i t y andAnal -ogy group f or di s c u s s i o ns of t h i s wor k and Mar k Keane, Bri an Ross,and Col l een S i e f e r t f or h el p f u l comment s on t h i s a r t i c l e Cor r espondence concerni ng t hi s ar t i c l e s houl d be a d d r e s s e d t oDedre Gen tner Depar tment of P s y c h ol o gy Nort hwestern Uni v er s i t y2029 Sheri dan Road, Evanst on 11, 60208 E l e c t r o ni c mai l may be s en tv i a I n t e r ne t t o geni nerCnwu. e du ' Thi s c a u s a l i n t er p r e t at i o n whi ch went we l l beyond Coperni cus so r i g i n a l p r o po s a l a l s o account ed f or a n o th e r r e gul a r i t y Kepl er notednamel y, t h a t ea c h i n di v i d ua l p l anet moves f as t er i n i t s o r bi t t he cl oseri t i s t o t he sun

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Dedre Gent ner

Who a s k , w l l say t h a t l i g h t i s somet hi ng materi al ? Nevert he-I c ss, i t carves out i t s operati ons w t h respect t o pl a ce , s uf f e r sa l t e r a t i o n , i s r e f l e ct e d and r e f r a c t e d , andassumes q u a n t i t i e s soas t o be dense or r a r e , and t o be capabl e of bei ng taken as asurf ace wherever i t f a l l s upon somet hi ng i l l umnabl e Nowus tas i t i s s a i d i n opt i c s, t h at l i gh t does not ex i s t i n t h e i nt ermedi atespace bet ween the source and t he i l l umnabl e, t h i s i s equal l yt r u e of the moti ve power AstronomaNova, p 383)

I f l i ght can travel undet ectabl y on i t s waybetweent he source anddest i nati on, yet i l l um nat e i t s dest i nati on,t hen so toocoul d t hemtive f orce be undet ectabl e on i t sway fromsun t o pl anet , yet af f ect t he pl anet s mti ononce i t arr i ves at t he pl anet But Kepl er was not contentw t h amre proof of possi bi l i t y He pushed t he ana ogyf urther Heused i t t o state why t he moti ve power di mn-i shes w t h di st ance : J ust as the l i ght froma l am shi nesbri ght er on near obj ects t han on f urt her ones, so i t i sw t h t he sun s moti ve power , and f or t he sam reason :Themoti vepower l i k e t he l i ght) i s not l ost as i t di spers esbut i s spread out over agreat er area Becausenothi ng i sl os t as t he emssi on spreads fromt he source, Kepl er1609/1992) ar gued, The em ssi on, t hen, i n t he sammanner as l i g h t , i s i mmater i al , unl i ke odours, which areaccomanied by adi mnuti on of substance, and unl i keheat froma hot f ur nace, or anythi ng s i m l a r which f i l l st he i nt er veni ng space p . 381 Her e, odors and heatare used as near-msses Wnston, 1980)-potentiaanal ogs that di f f er wth respect t o t he key behavi or andserve t o sharpen t he paral l el between l i ght and t he moti vepowerKepl er s anal ogi cal mdel faced f urther chal l enges

l l e had t o expl ai n why, gi ven thi s power emanatingfromt he sun t he pl anets moved cl oser and f urt her on thei rorbi ts i nst ead of mai nt ai ni ng a const ant di st ance fromt he sun To met these chal l enges, he again turned t oana ogy For exampl e, he i nvokeda boatman anal ogyt o expl ai n the i n- and-out mti onof the pl anets Hepostu-46

l ated t h a t t he sun rotated around i t s axi s, creat i ng awhi rl i ng ci r cul ar r i v er of moti ve power that pushed t hepl anet s around Then, as a ferrymn can st eer hi s boat t he pl anet ) back and forth orthogonal l y t o t he ri ver scurrent, so the pl anets coul dmove i n and out w t h onl yaconst ant s i dew s e current of moti vepower But al t houghKepl er worked t h i s ana ogy f or decades, he was neversati sf i ed w t h i t ; i t seemd t o requi readegreeof sent i enceon t he part of t he pl anets t o sensehowo st eer I n anothermch expl ored anal ogy, he l i kened t hesunand pl anet t otwomagnets that approach or r epel each ot her dependingonwhich poles are proximteKepl er s wri ti ngs demnstrate t he central f eaturesof ana ogy F i r s t , ana ogy i s adevi ce f or conveying thattwo si tuati ons or domains share rel ati onal structure des pi t e ar bi t r ar y degrees of di f f erence i n t he obj ects thatmake up t hedomains Gentner, 1983) Themagnet anal -ogy, f or exampl e, w l l stand or f a l l accordi ng t o whethert he causal rel ati ons between twomagnets are the samas those betweent hesunandpl anet , andnot accor di ng t ot he resemlancebetweenamagnet and t he sun ommonrel ati ons are essent i al t o ana ogy commnobj ects arenot . Thi s promti ngof rel ati ons over obj ects makes anal -ogy a usef ul cogni ti ve devi ce, f or physi cal obj ects arenormal l y hi ghl y sal i ent i n human processing-easy t of ocus on, r ecogni ze, encode, retr i eve, and so on

But thi s i s s t i l l not speci f i c enough There i s, i ngeneral , an i ndef i ni te numer of possi bl e rel ati ons thatan anal ogy coul d pi ck out Goodman, 1972) , andmstof these are i gnored For examle, wemayf i n d a spi der-weband a f i shi ng net ana ogous because both trap thei rprey, both remin stati onary whi l e thei r prey enters, andsoon But i t woul dnot contr i bute t o t he anal ogy t o not ethat Both are smal l er than the Taj Maha , or Bothare smal l er than t he Kremin Howdowe sel ect whichcommnrel ati ons t o payattenti on t o? Them or goal oft h i s art i cl e i s t o demnstrate that t heprocess of comari -son-both i n ana ogyand i n siml ari ty-operates so ast o f avor i nt erconnect ed system of rel ati ons and thei rargumnts As t he abovedi scussi on shows, t o capture t he pro-cess of anal ogy, we mst make assumtions not onl yabout t he processes of comari son, but about t he natureof typi cal concept ual cogni ti ve represent ati ons andhowrepresent ati ons andpr ocesses i nteract Pal mer, 1978 I npart i cul ar, wemst have a r epresent ati onal systemt h a ti s suf f i ci ent l y expl i ci t about rel ati onal s t r uct ur e t o ex-press t he causal dependenci es that match across the do-mains We need a represent ati onal schem capabl e ofexpressi ng not onl y obj ects but al so t he rel ati onshi ps andbi ndi ngs that hol dbetweenthem i nc l udi ng hi gher orderrel ati ons such as causal rel ati ons . Oneclar i f i cat i on i s i n

z I n K ep l e r s pre-Newt oni an p hy s i c s , t he sun was r e q ui r e d t o pusht he p l a n e t s around i n t h e i r o r b i t s , not merel y t o a t t r a c t t hem F or ma l l y , t h e e l emen t s of our r e p r e s en t a t i o n s ar e ob j ec t s ( o r enti -t i e s ) , o b j e c t d es c r i pt o r s ( c a l l e d attri butes), f uncti ons which exp r e s sdi mensi onal i n f o r ma t i o n) , and relat i ons bet ween r e p r e se nt a t i o n al el ement s A t t r i b u t e s and r e l a t i o n s ar e p r e di c a t e s w i t h t r u t h v a l u e s Func-t i o n s d i f f e r f rom p r e di c a t e s i n t hat t h e y map f rom a se t of arguments

J anuary 1997 Amri can Psychol ogi st


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Arthur BMarkman

order here To di scuss al i gnment processes, we need t otake repr esent at i on s er i o us l y , but t h i s shoul d not be takent o i mpl y a commtment t o any part i cul ar repr esent at i onas t he bes t or onl y possi bl e representat i on of a s i t u a t i o n Logi cal l y, such a pos i t i on woul d be i ndef ensi bl e .Rat her , weassume t h a t t he compari son process operat esover a pers on s current r epresent at i ons, however they areder i ved Thus, t o predi ct t he outcome of a compari son,we shoul d knowt he per son s current psychol ogi cal con-s t r u a l of t he t hi ngs bei ng compar ed, i nc l udi ng goal s andcontext ual i nf ormat i on as wel l as l ong- t ermknowedgeStru c tu ra l Al i gnment V ewof Anal ogyandSi m l ar i t yThe def i ni ng c ha r ac t e r i s t i c of anal ogy i s that i t i nvol vesan al i gnment of rel ati onal s t r u c t u r e There are three psy-chol ogi cal const rai nt s on t h i s al i gnment F i r s t , the al i gn-ment mus t be structural l y consi stent : I n other wor ds, i tmus t obser ve p ar a l l e l connecti vi ty and one- t o- one corre-spondence Para l el connecti vi ty requi res t h a t mat chi ngr e l a t i o n s must have mat chi ng ar gument s , and one-to-onecor respondence l i m t s any el ement i n one represent at i ont o at most onemat chi ng el ement i n t he other representa-t i on Fal kenhai ner, Forbus, Gentner, 1986, 1989 ; Gent -n e t , 1983, 1989 ; Gent ner Cl ement , 1988 ; Hol yoak Thagar d, 1989) For exampl e, i n Kepl er s 1609/ 1992)anal ogy, t he pl anet corresponds t o t he boat and t he sun spower t o t he r i v e r s c u r r e n t , because t hey pl ay s i m l a rrol es i n a common r e l a t i o na l structure Thi s al so showsa second c h a r a c t e r i s t i c of anal ogy, namel y, rel at i onal fo-cus : As di scussed bove, anal ogi es roust i nvol ve commonr e l a t i o n s but need not i nvol ve common obj ect descr i p-ont o val ues ot her t h an t r u t h val ues For exampl e, a functi on l i k e col or b a l l ) r ed may be used t o represent the di mensi on of col or Thesameassert i on could be represented usi ng col or as an a t t r i b u t e , as i n red b a l l ) , or us i ng c ol or as a r el at i on, a s i n color b a l l , red) W assumet h a t howa property i s represented w l l af f ect t he way i t i s processed

J anuar y 1997 Ameri can Psychol ogi st

t i o n s e g . i t does not detract f r o m t he anal ogy t h a t t hepl anet does not l ook l i k e a boat) The f i n a l characteri sti cof anal ogy i s systemati ci ty Anal ogi es tend t o mat c h con-nect ed s ys t ems of r e l a t i o ns Gentner, 1983, 1989) Amat chi ng s et of r e l a t i o n s i nt erconnected by hi gher orderconstr ai ni ng r e l a t i o ns makes a b e t t e r anal ogi cal mat cht han an equal number of mat chi ng r e l a t i o n s that are un-connect ed t o each other Thesystemat i ci t y pr i nc i pl e cap-tures a t a c i t pref erence f or coherence and causal pre-d i c t i v e power i n anal ogi cal processi ng Weare not muchi nterested i n anal ogi es t h a t capture a s e r i e s of coi nci -dences, even i f t her e ar e a gr eat many of themAp a r t i c u l a r l y s t r i k i n g exampl e of structural dom -nance i n anal ogy i s t h a t of cr oss- mappi ng Acrossmappi ng i s a compari son i n whi chtwo anal ogous scenari os cont ai n s i m l ar or i de nt i c al obj ect s t h a t pl ay d i f f e r e n trel ati onal rol es i n t he two scenar i os Gent ner Toupi n,1986 ; see al s o Gent ner Rat t er mann, 1991 ; Gol d-stone Medi n, 994Markman Gentner , 993b Ross,1987, 1989) Asi mpl e exampl e of a cr oss- mappi ng i st h i s si mpl e proport i onal anal ogy : : 3 : 3 : 9 Theobvi ous p o s s i b i l i t y of mat chi ng t he two i d e n t i c a l 3si s di sm ssed because t o do so woul d r n i s a l i g n t he r e l a -t i o na l rol es of t he t er ms I nst ead, t he obj ect correspon-dences are 3 and 3 9, preservi ng t he rel ati onalcommonal i t y t he i d e n t i c a l r a t i o ) across t he pai r Gi ven an al i gnment of s t r u c t u r e , f u r t h e r i nf erencescan often be made f r o m t he anal ogy The i mpl i c i t pref er -ence f or s ys t emat i c i t y- f or al i gni ng of connect ed syst ems of knowedge-i s c r u c i a l here I t i s what permtsus t o gener ate spont aneous i nferences Wen we haveal i gned a system i n t he base domai n w t h a t y p i c a l l yl e s s compl et e) systemi n t he t a r g e t domai n, t hen furtherst at ements cand date i nferences connect ed t o t he basesystemi n t he base can be proj ected i nt o t he t a r g e t Thesecandi date i nf erences are onl y guesses Thei r f act ual c o r -rectness mus t be checked separat el y Thi s uncert ai nt y i sappropri ate Anyprocess capabl e of produci ng novel truei nf erences i s al so capabl e of gener ati ng f a l s e i nf erences Thi s ki nd of spont aneous anal ogi cal i nf erenceabounds i n Kepl er s w i t i n g s Hef ol l owed hi s i n i t i a l anal -ogy es t abl i s hi ng t hat t he mot i ve power l i k e l i g ht ) canoperate at a di st ance w t h a s e r i e s of further proj ect i ons t h a t t he mot i ve power [ l i k e l i g h t ] spreads out throughspace, t h a t i t becomes di f f used w t hout di m n i s hi ng i nt o t a l q ua nt i t y , etc . He even asked whet her i t coul d un-dergo an ecl i pse he deci ded not and used t h i s di sanal ogyt o concl ude t h a t t he mot i ve power cannot be t he samethi ng as t he sun s l i g h t ) Si m l ar i t y I s L i ke Anal ogyKepl er s anal ogi cal f e a t s are nothi ng short of amazi ng Ref l ect i ng on hi s power s makes i t cl ear why t he a b i l i t yt o formanal ogi es has been taken as a s i gn of i nt e l l i genc e,maki ng t he fo ur - t e r m anal ogy probl ema stapl e of a p t i -tude t e s t s But consi der t he f o l l ow ng more prosai cexampl e

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L u c a s , a 25- mont h- ol d c h i l d , p l a y s w t h a newt oy t h a t h as s i xcol or eddoor s Each door has i t s ownkey-a r ed key f o r a r eddoor a bl ue key f or a bl ue d o o r , and so on Lucas opens eachdoor w t h t he key of t h e corr espondi ng c ol o r Then he s e e s as e v e n t h whi t e key He c ar e f u l l y i n s pe c t s t h e t oy f r om t op t obottom Then he t u r n s t o h i s p a r e n t s and a s k s , Wher e t h ewhi te door?Chi l d devel opment i s f u l l of t hese moment s , as i n t heexampl e of Aar on' s anal ogy f r om s el f t o other di scussedi n t h e a r t i c l e by Hol yoak and Thagar d ( 1997, t h i s i s s u e)or t h i s exampl e cont r i but ed byLi s eMenn ( per sonal communi cat i on, Febr u ar y 1995) Her t wo- year- ol d sonwat ched f asc i nated as some pet duckl i ngs at e Then hehel d h i s ar ms t o h i s si des and bent down and up l i k e t h educkl i ngs Fi nal l y he announced, poi nt i ng at t he duck-l i ng s, Haveno hands He had f i gured out why theyat e so di f f erent l y f r omhi mThese ki nds of compar i son-based di s cover i es ar e so commonpl ace that they ar ehardl y not i ceabl e as anythi ng s pe ci a l , and yet they con-t a i n t h e same e s s en t i a l character i st i cs of anal ogi cal pro-cessi ng that marks Kepl er ' s use of anal ogyI n a f undament al sense, s i m l a r i t y i s l i k e anal ogy,i n t h a t both i nvol ve an al i gnment of rel ati onal st ructure( Gentner Markman, 1995) The di f f e rence bet weenthem i s t h a t i n anal ogy, onl y r e l a t i o na l pr edi cates ar eshared, wher eas i n l i t e r a l s i m l a r i t y , both r e l a t i o na l predi -cates and obj ect a t t r i but e s ar e shared I n Kepl er ' s anal -ogy, there i s no physi cal r esembl ance bet ween a boat ona r i ve r and a pl anet r evol vi ng ar ound t he sun I n Lucas'ss i m l a r i t y compar i son, each key and door pai r i s s im l a rt o every o t h e r , maki ng i t easy f or Lucas t o al i gn t he pa i r s Thi s contrast bet ween anal ogy and l i t e r a l s i m l a r i t y i s i nf a c t a cont i nuum not a di chot omy Yet i t i s an i mpor t antcont i nuum psychol ogi cal l y, because overal l s i m l a r i t ycompar i sons ar e f a r e as i e r t o not i c e and map than purel y

anal ogi cal compar i sons, espec i al l y fo r novi ces l i k e Lucas( Gent ner , Rat t er mann, Forbus, 1993 ; Hol yoak Koh,1987 ; Keane, 1988 ; Ross, 1989) Fi gure 1 pl aces t h i s di s t i nct i on bet ween anal ogy ands i m l a r i t y wi th i n a s i m l a r i t y space def i ned by t he degr eeof a t t r i but i o na l s i m l a r i t y and t h e degr e e of r e l a t i o na ls i m l a r i t y Anal ogy occurs when compar i sons exhi bi t ahi gh degr ee of r e l a t i o na l s i m l a r i t y wi t h very l i t t l e a t t r i -hute s i m l a r i t y As t he amount of at t r i but e s i m l a r i t y i n-c r e a s e s , t he compari son s h i f t s toward l i t e r a l s i m l a r i t yMer e- appear ance mat ches share obj ect descr i pt i ons butnot r e l a t i o ns For exampl e, compar i ng a pl anet wi t h ar ound b al l woul d consti tute a mer e- appear ance mat ch Mer e- appear ance matc hes a r e , i n a sense, t he oppos i t e ofanal ogi es Such mat ches ar e of course shar pl y l i m t ed i nt h e i r predi ct i ve u t i l i t y Nonet hel ess, they ar e i mpor t antto consi der, because t hey of t en occur among chi l dren andother novi ces and may i nt e r f e r e wi t h t h e i r l earn i ng Thebot tom l e f t cor ner of t he space i s anomal ous com a r i -sons, which share no si gni f i cant at t r i but e or r e l a t i o na lcommonal t i es F i n al l y , Fi gure 1 shows t h a t met aphor sspan t he r ange fromrel ati onal compar i sons e . g twol overs l i k e twi n compass es ) t o at t r i but e compar i sons( e g amoon l i k e a s i l v e r coi n ) 48

Fi gur e 1S i m l a r i t y Space, Showng D f f er ent Ki nds of Matchesi n Term of t he Degree of Rel at i onal Ve r s u s Ob j e c t -Desc r i pt i on Overl ap

Analogy/Re ati onametaphordobgai l

Att ri butes shared

ProcessModel ofAl i gnment andMappingThStructure-Mappi ngEngi ne

L i t e r a ls i m l a r i t ymatch( P r i s on l a i l )

Mere-appearance/Attr i butemetaphor( z e br a l l a i l )

Wehave argued t h a t t he compari son process i nvol ves ar a t h e r sophi st i cated process of structural al i gnment andmappi ng over r i c h compl ex r epr esent ati ons Askept i calr eader m ght j u s t i f i a b l y i nqui re at t h i s poi nt whet her therei s any pl aus i bl e real - t i me mechani sm h at coul d computesuch a s t r u c t u r a l al i gnment Thi s probl em s not t r i v i a l ,and some ear l y model s made t he assumpt i on t h a t the top-l e ve l concl us i on or goal of t he anal ogy was known i nadvance t o ease t he comput at i onal bur den Gr e i n er , 1988 ;Hol yoak, 1985 ; see Gent ner Cl ement , 1988, f o r a d i s -cussi on) However , these sol ut i ons ar e l i m t e d , becausepeopl e can process anal ogi es wi t hout advance knowedgeof t h e i r meani ng Wen you read Phi l osophy i s l a n-guage i d l i n g , you pr obabl y underst and i t s meani ngwi t h-out apri or goa l context (a l though a r el evant pr i or contextwoul d of c our s e f a c i l i t a t e compr ehensi on) Thus, a pr o-cess model of compari son shoul d be abl e t o operate wi th -out advance knowedge of t he f i n a l i nterpretat i onThe st r uctur e- mappi ng engi ne SW Fal kenhai neret al 1986, 1989 Forbus, Gentner , Law 1995) uses al ocal - to-gl obal al i gnment process t o a r r i v e at a s t r u c t u r a lal i gnment of twor epr esentat i ons Fi gure 2 shows SME'sthree s t a g e s of mappi ng I n t he f i r s t s t a g e , SMEbegi nsbl i nd and l o ca l by mat chi ng a l l i d ent i c al pr edi cates andsubpr edi cates i n t he two r epr esent ati ons Thi s i n i t i a l

S im l a r al gor i thms have been i ncorporat ed i nt o other comput a-t i o na l model s of anal ogy (Burst ei n, 1988 Gol dstone, 1994b Gol d-stone Merl i n, 1994 ; Hol yoak Thagar d, 1989 ; Keane, Ledgeway, Duff , 1994)3 Wmake t he t h e o r e t i c a l assumpti on t h a t s i m l a r i t y of r e l a t i o na lpredi cates ca n be express ed as p ar t i a l i dent i ty The i dea i s t h a t whentwo s i t ua t i o ns ar e anal ogous, they must have some systemof i d ent i c al

r e l a t i o ns Thi s i d e n t i c a l i t y appl i es t o t he under l y ing concepts ; t h e actualsur face words used t o expres s t he re l a t i on need not be i d ent i c al , f orexampl e, J upi te t t r a v e l s s l ower than Mercury i s anal ogous t o J upi -t er moves s l ower t han Mercury or J u p i t e r ' s r a t e of moti on i s l owerthan Mercur y' s (see Gent ner Cl ement, 1988)



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FigureOver vi ewof t he Al gor i t hm Used by t heStr ucture- Moppi ng Engi neBase Target


stageLoca matches

StageStructura

coa escencei n t o consi stent

mapp ngs

StageSma l structures

comb ned i n t omaxi ma I nterpretati on

cand date i nferences

mappi ng i s t y p i c a l l y i n co ns i s t e n t , cont ai ni ng many- t o-one mat ches I n t he second phase, t hese l o ca l mat ches arecoal esced i n t o s t r u c t u r a l l y consi st ent connect ed c l u s t er s c al i ed kerna s F i n a l l y , i n t he t h i r d s t a g e , t hese kernal sare merged i n t o one or afewmaximal s t r u c t u r a l l y consi s-t e n t i nt e r p r e t at i o ns i e mappi ngs di spl ayi ng one- t o- onecorrespondences and pa r al l e l connect i vi t y) SME t henproduces a structural eval uat i on of t he i nterpret ati on s ,usi ng a k i nd o f cascade- l i ke al gor i t hm i nwhich evi dencei s passed down frompredi cates to t h e i r ar gument s Thi smethod f avors deep syst ems over s hal l ow syst ems, eveni f t hey have equal number s of mat ches ForbusGent ner ,1989) F i n a l l y , predi cates connect ed t o t he commons t r u c t u r e i n t he base, but not i n i t i a l l y present i n t he t a r g e t ,are proposed as cand date i nferences i n t h e t arget Thus,s t r u c t u r a l compl et i on can l ead t o spont aneous unpl annedi nf erences SMEhas t he psychol ogi cal l y appeal i ng f eature thati t can deri ve more than one i nt erpretati on f or an anal ogyI t normal l y produces two or t hr ee best i n t e r p r e t a t i o n F ofan anal ogy- t hat i s i nterpret at i ons recei vi ng the hi ghests t r u c t u r a l eval uat i ons F or exampl e, s uppo se we askedSMEt o i n t e r p r e t another of Kepl er s anal ogi cal conj ec-wres, namel y, t h a t t h e eart h m ght i mpel t he moon j ustas t he sun does t he earth

1 CAUSE [TRAVEL mot i ve power, sun, ea r t h , REVOLVEAROUND ea r th , sun ]2 CAUSE[TRAVEL mot i ve power, ea r t h , moon) , REVOLVEAROUND moon, ea r t h ] Gi ven t h i s cr oss- mapped p a i r , SMEwoul dproduce a r e l a -t i o na l i nterpretati on i n which t he ear th i n Sent ence 1corresponds t o t he moon i n Sent ence 2, as wel l as anobj ect - based i nt erpret at i on i n which t he ear t h c o r r e -sponds t o t he earth Because of i t s pref erence f or deepl yconnect ed rel at i onal s t r u c t u r e , t he r e l a t i o na l i n t e r p r e t a -t i o n woul d r ecei ve a hi gher s t r u c t u r a l eval uat i on andwoul d wn over t he obj ect i nterpret ati onAgood expl anator y anal ogy can oft en be ext ended,as i n Kepl er s anal ogi cal extensi ons Comput at i onal mod-el s have t r i e d t o capt ure t h i s propensi t y w t h t he not i onof i ncrementa mapp ng Fo r exampl e, SMEcan ext endan exi sti ng anal ogi cal mappi ng by addi ng f u r t h e r con-nect ed mat eri al fromt he base domai n e i t h e r drawn f r o mcurr ent cont ext or froml ong- t erm memory [ Forbus, Fer-guson, Gent ner, 1994 ; see al so Burst ei n, 1988 ; Keane,Ledgeway, Duff , 1994] ) These model s operat e on t heassumpt i on whi ch we di scuss l a t e r t h a t ext endi ng aconnect ed mappi ng i s e as i e r than cr eat i ng a newmappi ngStructure Mapp ng at WrkCommonal i t i es andDi f f erencesThe exper i ence of compari son i s s e l e c t i v e : Only c e r t a i ncommonal i t i es are highl i ght ed Wehave suggest ed t h a ta central f a c t o r c ontr o l l i ng what i nformat i on i s consi d-ered i n a compari son i s systemati ci ty t he presence ofhi gher order connect i ons bet ween l ower order r e l a t i o n s Cl ement Gent ner, 1991 ; Forbus Gent ner, 1989 ;Gent ner, 1983) For exampl e, compari ng t he p i c t u r e s i nF i gure 3A and 3Bhi ghl i ght s t he commonal i t y t h a t bothshowa c h i l d l oo ki ng at a pet I n c o n t r a s t , compari ngFi gure 3Aw t h 3Chi ghl i ght s t he commonal i t y t h a t bothshow an ani mal bei ng f ri ght ened by another ani malMarkmanGent ner, i n press) I n both cases, t he i n f or -mat i on highl i ghted by t he compari son f or ms a connect edrel at i onal syst em and commonal i t i es not connect ed t ot he mat chi ng syst em such as t he f a ct t hat t here are dress-er s i n both 3A and 3B) seemt o recede i n i mport ance Thi s pattern has al so been demonst r at ed usi ng passages Cl ement Gent ner, 1991) I n t h i s s t u d y , peopl e whowere gi ven anal ogous s t o r i e s j udged t h a t corr espondi ngsent ences wer e more i mport ant when t he corr espondi ngsent ence pai rs wer e part of amat chi ng rel at i onal syst emt han when they wer e not More surpri s ingl y, structural al i gnment al so i n f l u -ences what di f f erences are psychol ogi cal l y s al i e nt Forexampl e, when compari ng Fi gure 3A and 3B, we noti cet h a t i t i s a snake t h a t t he boy i s l ook i ng at i n one pi ctureand a f i s h i n t he ot her Both t he snake and t he f i s h pl ayt he samer ol e i n t he mat chi ng structure Di f f erences t h a tare connect ed t o t he common syst em l i k e t he f i s h- s nakedi f f erence) we c al l a i gnab e di f ferences Gent ner Markman, 1994 ; Markman Gent ner, 1993b, 1996)

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50

Fi gureThe Rol e of Commnal i ti es andD fferences i nS im la r i t y

Note T h i s t r i a d of pictures demonst rat es t h a t commonal i t i es becom i mortantwhen they are part of a matc hi ng systemandthat di f ferences becom i mortantwhen they are related t o t he commonal i t i es

Al i gnabl e di f f erences can be contrasted w t h non-al i gnabl e d i f f e r e nc e s , which are aspects of one s i t u a t i o nt h a t have no correspondence at al l i n the other s i t u a t i o n For exampl e, i n the compari s on of Fi gures 3Aand 3B, thec l o g i n Fi gure 3Ahas nocorrespondence w th anythi ng i n1 i gure 3B, and hence i t i s a nonal i gnabl e di f f erence .J us t as commonal i t i es gai n i n i mpor t ance when theyare part of a matchi ng system so t oo do di f f erences Thati s al i gnabl e di f f er ences are mre s a l i en t than nonal i gnabl e di f f erences I n t ui t i v el y , t hi s focus on al i gnabl edi f f erences makes s ense, f or i t l eads t o a focus on thosedi f f erences t h a t are r el evant t o t he commn causal orgoal s t r u c t u r e t h a t spans t he si tuati ons Howeve r , i f wef o l l ow t h i s l o g i c a f ew steps f u r t h e r , we a r r i v e at t her a t h e r i ntri guing predi ct i on t h a t there s houl d be mores al i ent di f f erences f o r hi gh- s i ml ar than f or i ow- si ml arp a i r s (because i n general , hi gh- s i mlar i ty pai r s w l l have

l a r g er commn system and mre al i gnabl e di f f erences) For exampl e, i f you i magi ne l i s t i n g l l poss i bl e d i f f e r -ences f or t he pai r hotel- ~ote l and contrast t h a t w t hl i s t i n g l l possi bl e di f f erences f or t he p ai r magazi nek i t t e n , you wi l l probabl y f i n d t h a t i t i s much eas i er t ol i s t di f f erences f or t he f i r s t hi gh-s i mlar i ty pai r Experi -mntal r e s ul t s bear out t h i s obser vati on Part i ci pants whowere asked t o l i s t di f f erences between hotel and mot elreadi l y l i s t e d ( al i gnabl e) di f f erences Hotel s are i nc i t i e s , motel s are on t he highway ; you stay l onger i nh ot e l s than i n motel s ; hotel s have many f l o o r s , mot el sonl y one or two ; and so on Whengi ven a l ow-s i ml ar i typai r l i k e magazi ne-ki t t en, part i ci pants tended t o l i s t non-al i gnabl e di f f erences, such as You pet a k i t t e n , youdon t pet a magazi ne, or kit tens have f ur and magaz i nes don t . Thi s f i ndi ng of a greater numer ofal i gnabl e di f f er ences f or hi gh- s i mlar i ty pai r s has beenobt ai ned i n empi ri cal s t u d i e s i nvol vi ng both word pai rsMarkmanGentner, 1993b ; MarkmanWs ni ewski ,i n press) and picture p a i r s MarkmanGentner , 1996) An i nf ormal observati on i s t h a t part i ci pants often ex-pres sed conf us i on or i r r i t a t i o n over t he l ow-s i ml ar i typ ai r s , perhaps r e f l e c t i n g t h e i r f ee l ing t h a t i t makes nosense t o t a l k about di f f erences i n t he absence of a meani n gf u l al i gnment I f t he compari s on process f ocuses on al i gnabl e d i f -f erences rather than on nonal i gnabl e di f f erences, thenal i gnabl e di f f erences shoul d be l i s t e d more f l uent l y thannonal i gnabl e di f f erences Thi s mans t h a t peopl e shoul df i n d i t e as i e r t o l i s t di f f erences fo r p a i r s of s imlar i t emthan f o r p a i r s of di s s imlar i t em, because hi gh - s i m l a r i t ypai rs have many commonal t i es and, hence, manyal i gnabl e di f f erences Sucha predi cti on runs agai nst t hecommnsense vi ewand t he most natural predi ct i on off eature-i ntersecti on mdel s-that i t shou ld be easi er t ol i s t di f f erences the mre of themt her e ar e t o l i s t - t ha ti s the more d iss imlar t he t wo i t em are . I n a study byGent ner and Markman (1994) , part i c i pants were gi vena page contai ni ng 40 word p a i r s , hal f s im lar and hal fd i s s i m l a r , andwer e gi ven f i v e mnutes t o l i s t one d i f f e r -ence f o r as many di f f e r e nt p a i r s as they cou l d Theywereto ld t h a t they woul d not have ti me t o do l l 40 p a i r s ,and so they shoul d do the eas i est pai r s f i r s t The r e s ul t sprovi ded strong evi dence f o r the al i gnabi l i ty predi cti ons Part i ci pants l i s t e d many more di f f erences f o r s imlarpai rs M= 11. 4 than f o r di ss i ml ar p a i r s M= 5 . 9Fur t hermore , t h i s di f f erence was concentrated i n theal i gnabl e di f f erences Over t w c e as many al i gnabl e d i f -f erences wer e gi ven f or s im lar pai rs M 9. 0 than f o rd iss imlar p a i r s M=3. 9Because peopl e focus on al i gnabl e di f f erences r a t h e rthan on nonal i gnabl e di f f erences whenmaki ng compari -sons, al i gnabl e di f f erences have a greater i mpact on peo-ple s percepti on of s i m l a r i t y than do nonal i gnabl e d i f f e r -ences . Thus, l l e lse bei ng equal , al i gnabl e di f f erencescount more agai nst s i m l a r i t y than nonal i gnabl e d i f f e r -ences . Oneway to t es t t hi s predi ct i on i s t o pi t compari -sons i nvol vi ng a gi ven al i gnabl e di f f erence agai nst compar i sons i nvol vi ng t he same contrast as a nonal i gnabl e

J anuary 1997 Ameri can Psychol ogi st


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Fi gure 4The I mpor t ance of Al i gnabi e and Nonal i gnabl e Di f f erences i n S imlar i ty

Note T h i s s a f orced-choi ce t r i a d used t o demonst rate t hat ali gnabl e di f f erences decrease s i m l a r i t y more t han do nonal i gnabl e dif f erences Repri nted from Commonal i t i es and Di f f erences n S i m l a r i t y Compari sons byB Markmn andDGentner , 1996 MemoryC og ni t i o n 24, p 243 Copyri ght 1996 by the( ' sychonomc Society

d i t t y . r e u c e For exampl e, i n the t op f i g u r e of the t r i a d i nf i gure 4 themn shoots an arrow at a t a r g e t I n t henonal i gnabl e- di f f erence opti on, theman shoot s an arrowat a t a r g e t but there i s al s o a bi rd a nonal i gnabl e d i f f e r -ence) i n the pi cture I n t he al i gnabl e- di f f erence opt i on,t he mn shoot s an arrow at a bi r d ( an al i gnabl e d i f f e r -ence) ; the t a r g e t has been moved t o t he t r e e behi nd thet nan When asked which opt i on i s most si m l ar t o t het a r g e t part i ci pant s chose the nonal i gnabl e- di f f erence op-t i o n suggest i ng that the al i gnabl e di f ference decreasedthe s imlar i ty of the p ai r more than di d the nonal i gnabl edi f f erence MarkmnGentner , 1996) I n summar y, the process of structural al i gnmentl eads t o a f ocus on mat chi ng r e l a t i o na l system Thi sf ocus determnes both whi ch commonal i t i es are s al i e ntand whi ch di f f erences are s al i e nt Thi s l a s t my seemparadoxi cal Why shoul d the common al i gnment d e t e r -mnewhi ch di f f erences are i mpor t ant ? Y e t i f we r e f l e c tt h a t most pai rs of i tem i n t he worl d are d i s s i m l a r t h i spattern seem f uncti onal l y sensi bl e I n t u i t i v e l y t i s whena pai r of item i s s im la r t h a t t h e i r di f f erences are l i k e l yt o be i mport ant Anal ogi cal I nf er enceAnal ogi es can l ead t o newi nf erences, as Kepl er' s ( 1609/199 exampl e demonst rates, and the same i s t r u e ofJ anuary 1997 Ameri can Psychol ogi st

Nonal i gnabl e dif f erence choice A i gnabl e dif f erence choice

s imlar i ty compari sons As i n anal ogy, when there i s amatch between a base and t a r g e t domai n, f a c t s about thebase domai n t h a t are connect ed t o the matchi ng i nforma-t i o n my be proposed as candi dat e i nf erences ( Fal ken-hai ner e t al 1986, 1989) For exampl e, i magi ne you havea f r i end w th a s ar c a st i c sense of humor t h a t mkes herd i f f i c u l t to get al ong w th but a hel pf ul t emper ament t h a tw ns her the l oyal ty of her f r i e nds I f you met a newperson and di scovered that he had a s a r c as t i c sense ofhumor , t hen based on hi s s imlar i ty to your other f r i e n dyou woul d probabl y bemorew l l i ng t o suppose t h a t hei s d i f f i c u l t t o get al ong w th than to i n f e r t h a t he has ahel pf ul t emper ament t h a t w ns him oyal f r i e nds Thi s poi nt was demonst r ated i n a study by Cl ementand Gentner ( 1991) They asked peopl e t o read p ai r s ofanal ogous s t o r i e s Thebase story had two key f a c t s eachof which was connect ed to a causal antecedent Nei t herof these key f a c t s was stated i n the t a r g e t story However ,the t a r g e t story di d have a f a ct t h at corr esponded t o oneof the causal ant ecedent s fromthe base When p a r t i c i -pants were gi ven the anal ogy and asked tomke a new I n t he t r i a d i n Fi gure 4 the mani pul ati onof al i gnabl e- and non-ali gnabl e-di f f erence opt i ons a l s o i nvol ves mvi ng the t a r g e t whichcoul d be a conf ound See Markmn and Gentner ( 1996) f or anothervari ant of the study t h a t escapes t h i s probl em

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predi c t i on abou t _ t he t a r g e t s t o r y , they predi cted t he keyf ac t that was connect ed t o t he mat chi ng causal ant ecedentmore than t w c e as o f ten as t hey predi cted t he other keyf a c t Conver gent f i ndi ngs have been obt ai ned by Read(1984), Spel l man and Hol yoak i n p r e s s ) , and Markman( 1996) Li kew se, Lassal i ne (1996) showed t h a t peopl e sw l l i ngness t o i n f e r new f a c t s i n a cat egory- i nduct i ont a s k i ncreased whenthese f a c t s wer e connect ed t o sharedcausal re l at i ons These r e s u l t s showhows t r u c t u r a l a l i g n -ment andmappi ng al l ow peopl e t o predi ct newi nf orma-t i o n f r omol d Connecti vi t y andAsymmetryPeopl e o f ten f i n d compar i sons muchmore s im l a r i n onedi r e ct i on than t he o t h e r , as Tvers ky ( 1977) noted i n hi ssemnal t r e at i s e on s im l a r i t y For exampl e, we prefer Ascanner i s l i k e a copy machi ne t o Acopy machi ne i sl i k e a scanner . As Tvers ky poi nted out , t hi s di r e c t i on al -i t y i s at odds w t h t he per vasi ve i n t u i t i on t hat s im l a r i t yi s a symmet r i c r e l a t i o n a f t e r a l l i f A i s s im l a r t o B,t hen shoul dn t B be equal l y s i m l a r t o A?) Structuremappi ng of f e rs a nat ur al expl anati on We propose t h a tasymmet r i es t ypi c al l y ar i s e whenone of t he compar i soni t em i s more syst emat i c than the other Bowdl eGent -t i r 1996 ; Gent ner Bowdl e, 1994) Accordi ng t o s t r u c -t ure- mappi ng t heor y, i nf e r ences ar e proj ect ed f r om t hebase t o t he t a r g e t Thus, havi ng t he mre systemati c andcoherent i t e mas t he base maxi m zes t he amunt of i n f o r -mat i on t h a t can be mappedfrombase t o t a r g e t Consi st entw t h t h i s c l a im Bowdl e and Gent ner f ound t h a t whenpart i c i pants wer e gi ven pair s of passages varyi ng i n t h e i rcausal coher ence, they a) consi stent l y preferred compar -i sons i n whi ch t he mre coherent passage was t he baseand t he l e s s coherent passage was t he t a r g e t , b) gener at edmore i nf erences fromt he mre coherent passage t o t hel e s s coherent one, and c ) rated compar i sons w t h mre

coherent bases as mre i nf ormat i ve than t he r ever s ecompar i sons ExtendedMappingOne par t i cul ar l y i nterest i ng use of anal ogy i s i n ext endedmappi ngs They a r i s e i n creat i ve t h i n k i n g, as whenKepl erexpl ored t he i mpl i cat i ons of anal ogi es bet ween t he mo-t i v e power and l i g h t or magnet i sm Ext ended anal ogi esar e used i n i ns t r uc t i on as wel l f or exampl e, whene l e c t r i ccurrent and vol t age ar e descr i bed i n t e rm of wat er f l o wand pressure ( Gent ner Gent ner , 1983) They al so a r i s ei n ordi na ry l anguage, w t h met aphor i c system l i k eMar r i age i s aj our ney t h a t can be extended ( e . g Youhave t o sl og through t he r ough spots but event ual l y t heroad wi l l get smoot her [ G bbs, 1994 ; Lakof fohnson,19801 We have f ound, consi st ent w t h t he structure-mappi ng account, t h a t i t i s e as i e r t o ext end an exi st i ngdomai n mappi ng than t o i n i t i at e a newone [Boronat Gent ner , 1996 ; Gent ner Boronat, 1992] ) Peopl e whoread passages cont a i ni ng ext ended met aphor s one s e n -tence at a t i me were f a s t e r t o read t he f i n a l sentencewhen i t was acons i stent ext ens i on of t he met aphor of t hepassage, as i n Exampl eA( bel ow) , than when i t u t i l i z e d a 2

di f f e r en t met aphor , as i n Exampl e B( bel ow) For examp l e , one passage descr i bed a debat e i n t er ms of a race A Dan saw t he bi g debat e as a race Heknewt hat he hadt o s t eer h i s course c a r e f u l l y i n t he compet i t i on H s s t r a t e g ywas t o go c r u i s i n g through t he i n i t i a l p oi n t s and t h e n make hi smove He r evved up as he made hi s l as t key p oi n t s H ss k i l l l e f t hi s opponent f ar behi nd hi m a t t he f i n i s h l i n e B Dan saw t he bi g deba t e as a war Heknew t hat he hadt o use e v e r y weapon a t hi s command i n the competi t i on Hemapped out hi s s t r at egy t o e n s u r e t hat he e s t a bl i s h ed a dom-n a n t p os i t i o n He i n t e n s i f i e d t he bombar dment as he madehi s l a s t key p oi n t s H s s k i l l l e f t hi s opponent f ar behi nd hi mat t he f i n i s h l i n e I f ; xt endi ng anexi st i ng connect edmappi ng i s e as i e r thancreat i ng a newmappi ng, then peopl e shoul d be f a s t e r t oread t he f i n a l sentence i n Exampl eA than i n Exampl eB Thi s i s exactl y what happened Thi s f i ndi ng f i t s w t ht he comput at i onal not i on of i ncremntal mappi ng, i nwhichmet aphor i c passages can be under s t ood by addi ngt o an i n i t i a l mappi ng ( For bus et a l 1994 ; Keane et al 1994) I n t er es t i n gl y , t h i s r e s u l t he ld onl y f or novel meta-phors and not f or convent i onal met aphor s I t i s possi bl ethat convent i onal met aphor s have t h ei r met aphor i c mean-i ngs stored l e x i c a l l y , maki ng i t unnecessary t o car ry outa domainmappi ng ( Bowdl e Gentner , 1996 ; Gent ner Wol f f , 1996) Connect i vi t y andPure Mappi ngLearners ar e o f ten cal l ed on t o map i nf ormati on f r omone s i t u at i on t o another For exampl e, whenwe buy anewVCR, cl i mb i n t o a r e n t a l c a r , or f i r e up an updat eof Wndows, we must deci de which aspects of our pr i orknowedgeappl y t o t he news i t uat i on To study t he d e t e r -mnants of t h i s mappi ng process, Gent ner and Schu-macher ( 1986 ; Schumacher Gent ner , 1988) t aught par-t i c i p a n t s how t o p i l o t a shi p usi ng a si mul at ed devi cepanel Agame- l i ke task was used i n which part i c i pantscoul d d i r e c t l y mani pul at e cer t ai n par amet er s (such as en-gi ne t h r u s t or cool ant val ve openi ng) that cont r ol l ed otherpar amet er s (such as vel oc i t y or engi ne t emper atur e) I fthey per f or med c o r r e c t l y , t he shi p made port i n t i me ;otherw se, they l o s t t he game Af t er t he f i r s t devi ce hadbeen wel l l e ar n e d , part i c i pants were transferred t o a s e c -ond anal ogous devi ce panel , and t he number of t r i a l s t oreach c r i t e r i o n on t he newpanel was measured P a r t i c i -pants speed of l earni ng was af fected bot h by transpar-ency- pa r t i c i pant s l earned t he new panel f a s t e r whenthere wer e physi cal r esembl ances bet ween s t r u c t u r a l l ycorr espondi ng el emnts- and by sys temat i c i ty - par t i -ci pant s l ear ned t he new panel f a s t e r when they hadl ear ned a causal expl anati on f or t he procedures Consi st ent w t h these p a t t e r n s , bot h Ross ( 1987,1989) and Reed ( 1987) have f ound transparency e f f e c t s They have shown t h a t par t i c i pant s ar e bet t e r at t r a n s f e rr i ng al gebr ai c s ol ut i ons when corr espondi ng base andt a r g e t obj ect s ar e s im l ar Reed meas ur ed the tr anspar-ency of t he mappi ng bet ween two anal ogous al gebr apr obl ems by aski ng part i c i pants t o i d e n t i f y pair s of corre-



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spondi ng concept s He f ound t h a t t r anspar ency was agood pr edi ctor of t h e i r a b i l i t y to not i ce and appl y sol u-t i o n s f romone pr obl emt o t he other Ross ( 1989) f oundt h a t p a r t i c i p a n t s a b i l i t y t o t r a n s f e r t he pr obl emsol vi ngsol uti on corr ectl y was di srupt edwhen cr oss- mapped cor-r espondences wer e used Research w t h chi l dren showsearl y e f f e c t s of transparency and somewhat l a t e r e f f e c t sof systemati ci t y ( Gentner Toupi n, 1986) We suspectt h a t t o deri ve the b e n e f i t s of systemati c expl anati ons mayrequi re possessi ng some degr ee of domain knowedgeThree general i zati ons emer ge from he t r a n s f e r st ud-i es F i r s t , t r anspar ency makes anal ogi cal mappi ng easi er Cl ose, l i t e r a l s im la r i t y mat ches are t he e as i e s t sort ofmappi ng and t he ki nd f or which par ti ci pant s are l e as tl i k e l y t o make e r r o r s Second, possessi ng a syst emati chi gher order structure can permt t r a n s f e r even under ad-verse t r anspar ency condi t i ons Having a strong causalmodel can enabl e a l ear ner t o t r a n s f e r even when t heobj ects msmat ch percept ual l y t h i r d po i n t , on whi chwe expand bel ow i s t h a t di f f e r ent ki nds of s im la r i t ymay enter i nto d i f f e r e n t subprocesses of t r a n s f e r Furt her Impl i cati onsUbi qui tyofA i gnmentOur st r uct ur e-mappi ng a b i l i t i e s const i tute a rather r e-mar kabl e t a l e nt I n c r e a t i v e t hi nki ng, anal ogi es serve t ohi ghl i ght i mpor t ant commonal i t i es, t o proj ect i nferences,and t o suggest newways t o r epr esent t he domai ns Yet,

t would be wrong t o thi nk of anal ogy as e s ot e r i c , t heproperty of geni uses On t he contrary, we often take anal -ogy f or grant ed, as i n exampl es l i k e t he fol l ow ng fromHofst adt er ( 1995, p 76) S he l l e y I mgoi ng t o pay f or my beer now7 iMe, t oo [ T imhad a coke ]Ti mdoes not mean t h a t he t oo i s goi ng t o pay f or Shel -l e y s beer t he nonanal ogi cal i nt e r p r et a t i on) , nor event h a t he t oo i s goi ng t o pay f or hi s own b e e r , but rathert h a t he i s goi ng t o pay f or what i n hi s s i t u a t i o n bestcor r esponds t o Shel l ey s beer namel y, hi s coke Thisa bi l i t y t o carry out f l u e n t , apparent l y e f f o r t l e s s , structuralal i gnment andmappi ng i s a hal l mark of human cogni t i vepr ocessi ng Pl ur al i t y of Si ml ari tyW have r evi ewed evi dence t h a t s imlar i ty i s a processof s t r u c t u r a l al i gnment and mappi ng over art i cul ated rep-r esentati ons However , s imlar i ty does not al ways appearso s t r u c t u r a l l y di scer ni ng part i cul arl y str i ki ng caseoccurs i n si ml ari ty- based r e t r i e va l Several f i ndi ngs sug-gest t h a t siml ar i ty-based r e t r i e v a l froml ong- t ermmemory based ono . e r a l l s i m l a r i t v , w t h surface s im la r i t yheavi l y wei ghted, rather than by t he ki nd of s t r u c t u r a lal i gnment t h a t best support s i nf erence ( Gent ner , 1989Hol yoakKoh 1987 ; Keane, 1988 ; Ross, 1989 S e i f e r t ,McKoon, Abel son, R a t e l i f f , 1986) For exampl e, Gent -t i e r et l ( 1993) gave parti ci pants amemory s et of s t o r i e sand l a t e r probed themw t h s t or i e s t ha t were s iml ar i nJ anuary 1997 Ameri can Psychol ogi st

var i ous ways Thegreater t he surface s im la r i t y betweent he probe and a t a r g e t i n memory i n terms of sharedobj ects and characters), t he more l i k e l y the target was t obe retr i eved I n c o n t r a s t , t he greater the degr ee of sharedhi gher order rel ati onal structure (such as shared causals t r u c t u r e ) , t he hi gher t he rated i nf e r e nt i a l soundness ands im la r i t y of t he pai r Thus, t he ki nd of s im la r i t y t h a tmost r e l i a b l y l e d t o r emndi ngs was not t he ki nd p a r t i c i -pant s most val ued i n maki ng i nferences I n f a c t , p a r t i c i -pant s often rated t h e i r own r emndi ngs as l ow i n bothsoundness and s i m l a r i t y Fi ndi ngs l i k e t h i s suggest t h a t s imlar i ty i s p l u r a l i s -t i ( Gent ner , 1989 ; Gol dst one, 1994a; Medi n et al 1993) I ndeed, a p a r a l l e l di sassoci ati on has been f ound i n probl emsol vi ng t r a n s f e r : Retr i eval l i kel i hood i s s e n s i t i v e t osurface s i m l a r i t y , wher eas l i kel i hood of successf ul prob-l emsol vi ng i s s ens i t i v e t o structural si mlar i ty ( Keane,1988 ; Ross, 1987, 1989 but see Hammond, S e i f e r t , Gray, 1991) This suggest s t h a t di f f e r e nt ki nds of s i m l a r -i t y may have d i f f e r e n t psychol ogi cal r o l e s i n t r a n s f e r The si mul ati on Many are cal l ed- but f ew are chosenMAC-FAC For bus et al 1995) model s t h i s phenome-non w t h a t wo- st age system The f i r s t stage MAC) i san i ndi scri mnate, comput at i onal l y cheap search f or anyki nds of s i m l a r i t i e s i n memory and t he second st ageFAQc ar r i es out a s t r u c t u r e mappi ng of t he candi dat esfromt he f i r s t st age Another way i n which s im la r i t y i s p l u r a l i s t i c i s t h a td i f f e r e n t ki nds of s im la r i t y emer ge at d i f f e r e n t poi nt si n pr ocessi ng Response deadl i ne s t u di e s of r e l a t i o na lcompar i sons suggest t h a t when part i ci pants are r equi r edto r espond qui ckl y ( under 700 ms or under 1, 000 m,dependi ng on t he t ask and materi al s) , they base t h e i rsense of s im la r i t y on l o c al mat ches ( even cr oss- mappedobj ect mat ches) rather than on r e l a t i o na l mat ches ( Gol d-stone Medi n, 1994 ; Ratel i f f McKoon, 1989) Atl onger r esponse deadl i nes, t h i s pattern i s reversed Thi st i me cour se of s imlar i ty has been successful l y model edf or pr ocessi ng features conj oi ned i n t o obj ects by Gol d-st one and Medi n s ( 1994) Si m l a r i t y , I nteracti ve Acti va-t i o n , andMapping SIAM model , usi ng a l ocal - t o- gl obalprocess l i k e that of SME Overal l , the di f f erence betweenearl y and l a t e pr ocessi ng seem t o be a s h i f t from o c a lmat ches t o gl obal structural al i gnment i mpl i cati ons forOher Cogni t i veProcesses

Categori zat i on Structural al i gnment and mappi ngcan pr ovi de i nsi ght i n t o other cogni ti ve processes (seeFi gure 5) As one exampl e, s im la r i t y i s oft en gi ven ac e n t r a l r ol e i n categori zati on ( Hampt on, 1995 ; Rosch,1975 ; Smth Medi n, 1981) I t i s common t o assumet h a t obj ects can be cat egori zed on the basi s of per ceptual ,behavi oral , or f unct i onal commonal i t i es w t h t he c a t e -gor y r epr esent ati on e . g r obi ns are seen as bi rds becauseof t h e i r per ceptual and behavi oral s i m l a r i t y t o a proto-type bi rd or t o many other bi rds t h a t have been encoun-t e r e d ) However , manyresearchers have poi nt ed out casesi n which rated s imlar i ty and probabi l i ty of categorymembershi p are di ssoci ated Gel manWel l man, 1991 ;

53


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54

Fi gure 5ame Uses of Conpari son i n Cogni t i ve Processi ngAl i gnment and mappi ng processes are used i n

percei vi ng s i m l a r i t y( al i gnment )

percei vi ng di f f erences

categori zi ng( sel ecti ng best match f rommemory

di scoveri ngnewcategory( abstracti ngcommonsystem

potent i alcategoryabstr acti ons

K e i l , 1989 ; Ri ps, 1989) For exampl e, bats have the per-ceptual and behavi oral characteri sti cs of bi rds ( they aresi ml ar t o bi r ds i n t h i s s e n s e ) , but t hey are c l a s s i f i e das mmml s because of i mportant ( though nonobvi ous)propert i es, such as gi vi ng birth t o l i v e young On thebasi s of exampl es l i k e t h i s , s i m l a r i t y s rol e i n categori za-t i o n has been chal l enged has been ar gued t h a t categorymembershi pj udgments are theory based rather than sim-l a r i t y based K e i l , 1989 MurphyMedi n, 1985) The process of al i gnment and mappi ng poi nts theway to a reconci l i at i on of sim l ari ty-based and theory-based account s (see al so Gol dstone, 1994a) I f we f ocuspurel y on perceptual s imlar i ty among obj ects, we arel ed to concl ude t h a t bats shoul d be categori zed w thbi rds On t h i s vi ew t heory- based knowedge ( such aswhy bats are mmml s must i ntervene f romel sewheret o overr ul e t h i s assi gnment However , i f the s imlar i tycomput at i on s assumed tobethat of structural al i gnment ,t hen the s imlar i ty bet ween two i nstances w l l be basedr i o t onl y on obj ect- l evel commonal i t i es but also on com

monr e l a t i o ns such as commoncausal r e l a t i o n s and common ori gi ns Assumng t h a t our represent ati ons i ncl udei nf ormati on about t heory- based r e l a t i o ns , such as t h a tbats bear l i v e young, as wel l as i nf ormati on about f e a -t u r e s , then t h e schi smbetween sim l ari ty-based and t h e -ory- based categori zati onmy be more apparent than r e a l Devel opment al l y, we assume t h a t t h e o r et i c alknowl edge s acqui red gradual l y, t h i s vi ewwould accountf or the characteri sti c-t o-def i ni ng s h i f t ( Kei l Bat t erman,1984) i n chi l dren s i nt e r p r e t at i o ns of wordmeani ng f r oml o c al obj ect f eatures e . g a t a x i i s bri ght yel l ow andhas a checkered si gn) t o deeper r e l a t i o n a l commonal i t i es( e. g a t a x i s a vehi cl e t h a t my be hi red t o transportpeopl e) Choi ce and deci si on Structural al i gnment al sosheds l i g h t on the processes under l yi ng choi ce behavi or Medi n, Gol dst one, and Markmn ( 1995) r evi ewed paral

l e l s bet ween phenomna i n deci si on processi ng and phe-nomna i n compar i son processi ng that suggest an i mportant rol e f o r s t r u c t u r a l al i gnment i n deci si onmaki ngStructural al i gnment i nf l uences which f eatures to paya t t e n t i o n t o i n choi ce opt i ons Research suggest s t h a tali gnabl e di f f erences are gi ven more wei ght i n choi ces i t u a t i o n s than are nonal i gnabl e di f f erences ( Li nde-mnn Markmn 1996 ; Markmn Medi n, 1995 Slovi c MacPhi l l amy, 1974) For exampl e, Markmnand Medin ( 1995) asked parti ci pants t o choose bet weenvi deo games and to j u s t i f y t h e i r choi ces Thei r j u s t i f i c a -t i o n s were more l i k e l y to cont ai n al i gnabl e dif f erencesthan nonal i gnabl e di f f erences As another exampl e, Kah-nemn and Z versky ( 1984) descri bed t o parti ci pants ahypotheti cal s t o r e i n whi cha j acket coul d be bought f or125anda cal cul ator f or 15 They off ered parti ci pantst he opport uni t y to go to another store and save 5 on thet o t a l purchase Parti ci pants whowere of f ered aj acket f o r125 and a cal cul ator f or 10were morew l l i ng t o mkethe e f f o r t to go t o another s t o r e than those offered aj acket f o r 120 and a cal cul ator f o r 15 Even t houghthemonetar y r ewar d f or goi ng t o the other s t o r e was thesame f or both groups, parti cipants were i nf l uenced bythe al i gnabl e di f f erenceConcl usi onsCompari son processes f o s t e r i nsi ght They hi ghl i ghtcommonal i t i es and rel evant di f f erences, t hey i n v i t e newi nf erences, and t hey promot e newways of const rui ngsi tuati ons Thi s creati vepotent i al i s easi est to noti cewhenthe domai ns compared are very d i f f e r e n t , as i n Kepl er sanal ogi es or J ohn Donne s metaphor s But even prosai cs imlar i ty compar i sons can l ead t o i n s i g h t s Somet i mesthese i n s i g h t s are so obvi ous t h a t wemght f a i l to noti cet hem as when two-year- ol d Lucas noti ced the repeatedpattern of keys openi ng doors or Aaron i n Hol yoakThagard s a r t i c l e , 1997) spont aneousl y sw t ched rol es i nthe ki ss- and- make- bet t er schema or whena six- year- ol dreal i zed that t u l i p s must need w a t e r , because peopl e do( I nagaki Hat ano, 1987) At f i r s t gl ance, thesemndaneexampl es mght seemto have nothi ng i n common w ththe bol d anal ogi es of s c i e n t i f i c di scovery But l et us cl ose



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wth n i i r ownanal ogy Anal ogi es are l i k e comet s, f l as hi ngt hrough our awar eness and r i v e t i n g our a t t e nt i o n L i t e r a ls i m l a r i t y l i k e pl anetary mot i on : s t e a d y , predi ctabl e,and prosai c But t he pl anets are c e n t r a l t o t he behavi orof t he s o l a r system and ( l i k e l i t e r a l s i m l a r i t y compari -sons) they are al ways w t h us F i n a l l y , both pl anet s andcomet s are gover ned by t he same f undament al l aws REFERENCES

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Structure Mapping in Analogy and Similarity

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