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Int J. Man-Machine Studies (1985) 22, 39-57

Metaphor computing systems and active learning

JOHN M. CARROLL AND ROBERT L. MACK

Computer Science Department, IBM Watson Research Center, Yorktown Heights,

NY 10598

Received 17 January

1984)

Recent discussion has resolved the question of how prior knowledge organizes new

learning into the technical definition and study of "metaphor". Some theorists have

adopted an "operational" approach, focusing on the manifest effects of suggesting

metaphoric comparisons to learners. Some have resolved the question formally into a

"structural" definition of metaphor. However, structural and operation approaches

typically ignore the goal-directed learner-initiated learning

process

through which

metaphors become relevant and effective in learning. Taking this process seriously

affords an analysis of metaphor that explains

why

metaphors are intrinsically open-

ended and

how

their open-endedness stimulates the construction of mental models.

1 Introduct ion

Over the last few years, cognitive scientists have increasingly acknowledged the critical

role of prior knowledge in acquiring new knowledge. Of course, the bald fact that

prior knowledge limits and structures the acquisition of new knowledge was never

"missed", but it was often "abst racted away from" as being a complicat ion that theories

of human cognition could not well accommodate. This theoretical consideration focused

empirical work on simple and artificial concepts and skills, precisely to avoid the

complication of prior knowledge.

This situation has changed substantially in current Cognitive Science. The problem

of prior knowledge has become a central concern. There is growing interest in the

study of real world problems of human knowledge and learning. Indeed, there is a

natural confluence between the interest in the role of prior knowledge in learning, and

the interest in studying

real domains

of human knowledge and skill. All of this converges

directly upon the topic o f metaphor and the design of the human-compu ter interface:

can interfaces be designed to take advantage of the metaphors new users generate

spontaneously as they apply their prior knowledge to this novel learning situation?

Traditionally, metaphor is a topic for students of rhetoric. A metaphor--so con-

ceived--is a linguistic figure with the form "X is Y". Recent writing has more seriously

considered the metaphoricity of thought underlying these verbal figures, not only in

Cognitive Science (Lakoff & Johnson, 1980; Ortony, 1979) but in rhetoric itself:

"Thought is metaphoric, and proceeds by comparison, and the metaphors of language

derive therefrom." (Richards , 1965).

Several investigators have used this broadened concept of metaphor in their descrip-

tions of cognitive intercourse with complex domains. Carroll & Thomas (1982) claimed

that the activity of learning to use a computer system is structured by metaphoric

comparisons. For example, the metaphor "a text editor is a typewriter" could be

spontaneously referred to during early learning about text processors. Carroll & Thomas

39

0020-7373/85/010039+ 19503.00/0 9 1985 Academic Press Inc. (London) Limited



METAP HOR COMP UT ING S YSTEMS AND ACTIVE LEARNI NG 4

de l e t ed f r om a c om pu t e r f il e j u s t a s pa ge s c a n be i n s e r t e d a nd r e m ove d f r om a

c onve n t i ona l f il e) . R um e l ha r t & N o r ma n ( 1981) e mp l oye d t h r e e m od e l s i n t e a c h i ng

pe op l e a bou t t e x t p r oc e s s i ng f unc t ions . T he s e c r e t a r y mo de l w a s u s e d t o e xp l a i n

t ha t c om ma nds c a n be in t e r s pe r se d w it h t e x t i nput . T he c a r d f il e mo de l w a s u s e d

to desc r ibe the de le t ion of a s ing le nu mb ere d l ine f rom a f il e. Th e t ap e recor der

mo de l was used to conv ey the need for expl i c i t t e rmina tors in fi le s.

I t i s c l ea r these oper a t iona l m etaph ors for t ex t -ed i t ing exer t a mea surab le e f fec t on

lea rn ing . Observ a t iona l s tud ies of ac tua l lea rners have do cu me nte d th is ex tens ive ly

(Bot t , 1979; Carrol l & Mack, 1983, 1984; Mack, Lewis & Carrol l , 1983) . Typewri ter

know ledge i s rou t in e ly invoke d by lea rners f ir st enc oun te r ing t ex t ed i tors . Exp er im enta l

s tud ies a re beginning to document these e f fec t s a s we l l . Foss , Rosson & Smi th (1982) ,

i n t he e xpe r i me n t r e f e r r e d t o a bove , f ound s l i gh t l y be t t e r pe r f o r ma nc e f o r s ub j e c t s

who were provided wi th the advance organize r ( i . e . , t hese subjec t s requi red s l igh t ly

l es s t i me to c om pl e t e pe r f o r ma n c e t as ks a nd u s e d f e w e r c omma nds ) .

However , a s cogni t ive psychologica l ana lys i s , the opera t iona l theor ies don ' t go fa r

enough . F or desp i t e the l ea rn ing e f fi cac ies they co r rec t ly an t i c ipa te , i t r emains obsc ure

prec i se ly

ow

me t a ph or ope r a t e s in the mi nd t o a c h i e ve any o f th is . T he ope r a t i ona l

t h eo r ie s o f fe r e x a m p l e s o f g o o d m e t a p h o r s , a n d s o m e t im e s o f b a d m e t a p h o r s ,

bu t t he y o f f e r no p r i nc i p le s t ha t c ou l d p r e d i c t t he s e p r ope r t i e s e x t e ns ib l y . A nd i n a ny

c a se t he r e is muc h m or e t ha t one mi gh t l ike t o know : w h i c h me t a pho r s a r e na t u r a l ,

l ike ly to a r i se , pos s ib le , e tc . The opera t io na l theor ies have l i tt le to say he re . Such

que s t ions ha ve l e d t o the de v e l opm e n t o f s tr uc t u r al mode l s o f me t a phor .

3. Stru ctur al theories of metap hor

I n a n e f f o r t t o r e s o lve i ss ues r e ga r d i ng t he unde r l y i ng r e p r e s e n t a t i ona l me c ha n i s m o f

meta pho r , the no t ion h as been g iven de f in i t ion in re la t ive ly more s t ruc tura l t e rms (Bot t ,

1979; Gentner , 1983; Ortony, 1979) . A typical def ini t ion might run l ike this :

Give n two do ma ins A and B , t ak ing A as a me tap ho r for B i s equiva len t to

provid ing a formal mapping f rom the pr imi t ives de f in ing A in to the pr imi t ives

defining B.

S uc h a de f i n i t i on ma ke s t he me t a phor que s t i on a que s t i on a bou t r e p r e s e n t a t i ona l

formats , st ruc tura l p r imi t ives , and the pro per t i e s of form al mappings . F ro m the s t and-

po i n t o f c ogn i t ive p r oc e s s t he se ana l y s e s r e duc e me t a ph or t o p r i mi t ive pa t t e r n

matching ope ra t ion s de f ined over the e lements and re la t ions of a s t ruc tura l desc r ip t ion .

A typica l ana lys i s is tha t o f Ge ntn er (1980, 1983), who has dev e lop ed a s t ruc ture -

ma p p i ng a na ly s i s o f me t a p hor . T h is v i e w i n t e rp r e t s me t a pho r a s a ma p p i ng be t w e e n

t w o ( g r a ph t he o r e t i c a l ly e xp r e s s e d ) doma i ns , pa i r ing t he nod e s o f ea c h . T he r e l a t ions

o f the t w o dom a i ns a r e c ons t r a i ne d t o be i de n t ic a l . O ne o f G e n t ne r ' s c h i e f e xa mpl e s

is R u t he r f o r d ' s f a mou s a na l ogy be t w e e n t he s o l a r s y s te m a nd t he s t r uc t u re o f the

hydr og e n a t om. T he nod e s o f t he f o r me r dom a i n a r e t he s un a nd t he p l a ne t s : t hos e

o f t he l a tt e r doma i n a r e t he a t omi c nuc l e us a n d t he e l ec t r ons.

T h i s s t r uc t u r e - ma pp i ng i s a s uc c e s s f u l me t a phor be c a us e t he r e l a t i ona l p r e d i c a t e s

tha t apply to one se t o f nodes apply in l ike fash ion to the o the r . Thus , the p lane t s and

the e lec t rons revolve about the sun and the nuc leus , re spec t ive ly . The sun i s more

ma s si ve t ha n a ny o f t he p l a ne t s : a nd t h i s r e l a t ion t oo ho l ds be t w e e n t he nuc l e us a nd



42

JOHN M. CARROLL AND ROBERT L. MACK

t he e l e c t rons . I n c on t r a s t t o t he se c om mo n r e l a ti ona l p r e d i c a t es , G e n t ne r obs e rve s t ha t

a t t r ibu te predica tes genera l ly fa i l to ca r ry ac ross the mapping . Thus , the sun i s ye l low

a nd ho t ; w h i l e t he nuc l e us ma y no t be .

3.1 NEW METAPH OR CONCEP TS

T hi s s t r uc tu r a l f o rmul a t i on o f w ha t me t a pho r is al low s us t o de f ine ma ny fu r t he r

c onc e p t s r e ga rd i ng me t a ph or r e la t ions . G e n t n e r de f i nes a va r i e t y o f s uch r e l a t ions :

base specif ic i ty, c lar i ty, r ichness , abs t ractness , sys temat ic i ty, val idi ty, exhaust iveness ,

t ransp aren cy , and scope . Base spec i f i c i ty i s de f ined as the ex tent to which the

s t ruc tu r e o f t he me t a p hor ba s e , o r s ou rc e , is unde r s t oo d . C l a r i t y r e f e rs t o t he p r e c i s i on

o f t he nod e c o r r e s po nde n c e s a c ross t he ma pp i ng . R i c h ne s s i s t he de ns i t y o f p r e d i c a t e s

ca r r i ed ac ross the map ping . Ab s t rac tnes s re fe rs to the l eve l a t which the re la t ions

c a rd e d a c ros s t he ma p p i ng a r e de f ine d . I f t he y a r e t he i nd i v i dua l p r e d i c a t e s o f t he

base , the ma pp ing i s l es s abs t rac t than i f they a re re la t ions am ong predica tes in the base .

M e t a pho r s a r e s ys t e m a t i c t o t he e x t e n t t ha t t he ma ppe d r e l a ti ons a r e mu t ua l l y

c ons t r a i ne d b y me m be r s h i p i n s ome s truc t u r e o f r e l at i ons. I n t he R u t h e r fo rd m e t a phor ,

t he r e l a t ions a t t r a c t s a nd o rb i t s a ro un d a r e s ys t e ma t iz e d by t he i r me m be r s h i p i n

t he i nve r s e - s qua re r e l a t ions h i p (G e n t n e r , 1980; 1983) . M e t a pho r s a r e va l i d t o t he

extent tha t the base re la t ions ca r ry the i r t ru th va lues ac ross the the mapp ing . Base

e xha us t i ve me t a p hor s m a p e a c h o f t he i r r e l a ti ons i n to t he t a rge t ( t a rge t e xha us t i ve

me t a p hor s a r e de f i ne d a na l ogous l y ) . M e t a pho r s a re t r a ns pa re n t t o t he e x t e n t t ha t

i t i s obvio us which re la t ions in the base a re ab le to be ca r r i ed in to the t a rge t. Sc op e

re f er s t o t he e x t e ns ib i l it y o f t he ma pp i ng . F o r e xa mp l e , t he R u t h e r fo rd s o l a r s yst e m

ana logy appl i es l e s s use fu l ly to heavie r a toms .

T h i s i nve n t o ry o f me t a phor p rope r t i e s a f fo rds fu r t he r e xp l a na t o ry pow e r t o t he

me t a pho r c onc e p t . A s t udy o f r a t e d goodne s s fo r me t a p hor s s how e d t ha t bo t h e xp re s si ve

(o r li t er a ry ) me t a pho r s a nd e xp l a na t o ry (o r sc i en t if ic ) me t a phor s w e re r a t e d a s be t te r

w he n t he y w e re h i ghe r i n c l a r i t y ( i . e . , w he n t he node c o r r e s ponde nc e s w e re more

s e l f- e v i den t ) . E xp l a na t o ry m e t a phor s , how e ve r , d e pe n de d l es s on r i c hne ss ( i .e . on the

de ns i ty o f p r e d i c a t e s ma pp e d) . I n t hi s c on t r a s t, t he c on c e p t o f r i c hnes s a f fo rds a n

a na lys is o f the d i f f e r e nc e be t w e e n e xp re s si ve a nd e xp l a n a t o ry me t a phor . T h i s c o nc e p t

a nd t ha t o f s c ope a r e u s e d fu r t he r i n a n a t t e mpt t o a na l ys e t he d i f f e r e nc e be t w e e n

nov i c e s a nd e xpe r t s w i th r e s pe c t to t he t ype s o f me t a phor i c a l mode l s e a c h e nga ge .

.. . we speculate that a difference between experts and novices in a scientific do main is that

the expert has an abstract global model with broad scope, while the novice has a pastiche

of rich, only locally useful models . . . naive models of science appear more like expressive

analogies than do expert models (Gentner, 1980).

Tha t i s novices re ly more on lower l eve l re l a t iona l predica tes , appl i cable only in a

l i m i t e d doma i n - -pe rha ps on l y i n t he c u r r e n t c a s e . E xpe r t mode l s a r e more a bs t r a c t

and sys temat ic .

3.2. THE PROBLEM OF ARBITRARY PRIMITIVES

D e s p i t e t he s e p romi s i ng a c h i e ve me n t s i n p rov i d i ng a more a r t i c u l a t e d s t a t e me n t o f

the m eta ph or conc ept , s t ruc tura l theor ies suf fe r a va r i e ty of t echnica l problem s . F i r s t,

the s t ruc tura l pr imi t ives pos i t ed by the theor ies can be shown to be a rb i t ra ry in ways

tha t rend er som e of the i r desc r ip t ive c la r i ty spec ious . Second, the new co ncep t s (a lbe i t



METAPHOR COMP UTI NG SYSTEMS A ND ACTIVE LEAR NING 4

pr e c i s e l y e xp r e s s e d by t he s e t he o r i e s ) a r e s ome t i me s p r ob l e ma t i c i n t ha t t he y ma p

i nc ons i s t e n t l y on t o t he o r d i na r y me t a phor phe nome na t ha t mo t i va t e d t he a na l y s i s i n

the f i rs t p lace 9 F ina l ly , the formal chara c te r of these theor ies has so fa r fa i l ed to ac tua l ly

reso lve re levan t emp i r i ca l i ssues 9

A s no t e d , f r o m G e n t ne r ' s s t ruc t u r al r e nde r i ng o f t he R u t he r f o r d s o l a r sy s te m me t a -

phor , o ne ga the rs a ve ry nea t re su lt . How eve r , s c ru t in iz ing he r acco un t revea ls tha t

muc h ha s be e n l e f t ou t . O ne o f the mos t s a l i e n t r e la t ions ho l d i ng be t w e e n t he s un a n d

i ts p lane t s i s wha t we m ight ca ll the "w ar m s" re la t ion : T he sun warm s the p lane t s 9

N o t a b l y t hough , t h is r e l a ti on doe s no t ho l d be t w e e n c o r r e s p ond i n g node s o f t he a t om

mode l ; t he a t omi c nuc l e us o f hyd r oge n doe s no t w a r m t he e l e c tr ons ( s ub - a t omi c e n t it ie s

do no t ha ve t e mpe r a t u r e ) . T hus , t he ma pp i ng a s p r e s e n t e d by G e n t ne r a ppe a r s t o be

far bet ter than i t in fact i s .

T h i s w e a kne s s be c o me s c l e a r e r w he n t he r e l a t ions s he doe s e mph a s i z e a r e c r it i ca l ly

e xa mi ne d . F o r e xa mp l e , o f t he f ou r p r e d i c a te s G e n t ne r ' s s o l a r s y st e m me t a p hor

ana lyses , two a re "a t t rac t s " re la t ions : the p lane t s a t t rac t the sun and the sun a t t rac t s

t he p l a ne t s ; w i t h t he r e l a t i ons ho l d i ng a na l og ous l y i n t he a t omi c d oma i n . F o r s t a rt e rs ,

w hy c ons i de r t he s e t w o un i d i r e c t i ona l r e l a ti ons i n s t e a d o f one b i d i r e c t iona l r e l a t i on

( i . e . , t he sun and the p lane t s mutua l ly a t t rac t )? As fa r a s one can t e l l , t he re i s no

i nde p e nde n t l y mo t i va t e d p r i nc i p l e t o r u l e th i s pos s i b il i ty ou t f o r G e n t ne r , e xc e p t tha t

i t wou ld decre ase the app aren t r i chness of the m etaphor 9 But th i s begs the que s t ion .

B e yond t h i s que s t i on t hough , i t i s unc l e a r w hy " a t t r a c t s " s hou l d be t he p r e d i c a t e

a t all . W hy no t " g r a v i t a t e s t ow a r d " o r " e l e c t r om a gne t i c a l l y a t t r a c t s " ? A ga i n t he r e is

no pr inc ip le to ru le these out ; the re i s jus t the b a ld fac t tha t do ing so reduces the

r i chness of a me tap ho r which seems in tu i t ive ly ri ch . But g iven a l l these ap par ent ly

a r b i t r a ry de g r e e s o f f r e e dom one c a n a s k j u s t w ha t t he s t r uc t u r e ma p p i ng a na ly s is o f

me t a phor i s do i ng f o r u s ?

3.3. THE PROBLEM OF DESCRIBING REAL METAPHOR PHENOMENA

A second c las s of problem s wi th these theor ies pe r t a ins to the conc ept s tha t a re forma l ly

de f i ne d f r om s t r uc tu r a l r e p r e s e n t a t i ons. F o r e xa m pl e , c ons i de r G e n t ne r ' s de f i n i t ion o f

" t r a ns pa r e nc y" , na me l y a s t he e a s e w i t h w h i c h r e l a t i ons c a r de d a c r os s t he ma pp i ng

are de te rminable 9 C lea r ly , a f ir st o rd er fac t we wan t to ge t ou t is tha t "g oo d" me taph ors

a r e t r ans pa r e n t 9 H ow e ve r , i n l i gh t o f t h is , c on s i de r G e n t ne r ' s ow n r e ma r k t ha t t he

f a mi l ia r a na l ogy o f w a t e r w a ve s t o s ound w a ve s is r a t he r non - t r a ns pa r e n t ( G e n t n e r ,

1980) . The t rouble he re i s tha t the metaphor i s we l l -es tab l i shed , a t t e s t ed ly use fu l - - in

s ho r t ma n i f e s t ly " g oo d" . I t is t he t he o r e ti c a l c onc e p t o f t r a ns pa r e n c y t ha t i s n ' t w or k i ng

well .

A s i mi l a r p r ob l e m c r ops up r e ga r d i ng G e n t ne r ' s c onc e p t o f " ba s e s pe c i f i c i t y " : " t he

de g r e e to w h i c h t he s t r uc t u re o f t he ba s e i s e xp li c it l y un de r s t o od " ( G e n t ne r , 1980 ).

C l e a rl y , t he s uc c es s o f a me t a pho r de pe nds on ha v i ng a fa mi l i a r dom a i n t o a na l og i ze

f r o m a n d o n r e c o g n i z in g e n o u g h i n t h e ne w d o m a i n s o t h a t so m e c o r r e s p o n d e n c e c a n

be e s t ab l i she d . B u t a pp l y i ng G e n t ne r ' s f o r ma l r e c ons t r uc t i on o f th i s o r d i na r y l a ngua ge

wisdom i s prob lemat ic . She gives th is a s an ex am ple o f a met aph or tha t fa i l s on grou nds

of poor base spec i f i c i ty :

9 sometimes in introductory chemistry texts, molecular bonding is explained by analogy

with interperson al attraction, e.g. The lonely sodium ion searches for a com patible chloride

ion. Interper sonal attraction is certainly familiar, but its rules are unfo rtunate ly unclea r;



44 J O H N M . C A R R O L L A N D R O B E R T L. M A C K

so this m etaph or does n ot tell the student precisely what to map from the base. (Gentner,

1980).

The problem here i s tha t the fac t s a re wrong. The ion metaphor i s we l l e s t ab l i shed ,

f requent ly used , popula r , he lpfu l for f l edgl ing s tudent s of chemis t ry . A theory tha t

te l ls us why i t f i ls i s making the wrong predic t ion .

S t ruc tu r a l t he o r i st s ha ve t e nd e d t o foc us on l y on

simil rity

as a bas is for com par i so n .

T ha t is , me t a pho r s a r e go od i f a nd on l y if l o ts o f node s a nd r e l a ti ons ma p obv i ous l y

be t w e e n t w o doma i ns . B u t how e ve r e l a bo ra t e l y a r t ic u l a t e d , t he s e a r e c ou n t i n g

t he o ri e s: ma t c he s a re go od , m i s ma t c he s a r e ba d . I n t r a d i t iona l d i s cus s ions more

complexi ty i s envi s ioned . For example , i t i s o f t en noted tha t the disp rity be tween a

metaphor vehic le and i t s source can a l so be a potent fac tor cont r ibut ing to the force

of the me tap ho r (Deu tsch , 1962; R ichards , 1965). R icha rds ' exa mp le is Ham le t ' s

c o m p a r i s o n o f m e n t o v e r m i n t h r o u g h u se o f t h e w o r d c r a w l i n g in t h e r e m a r k , W h a t

s hou l d s uc h f e l low s a s I do c r a w l ing be t w e e n e a r th a nd h e a ve n? T he c ompa r i s on is

sa l ien t a s m uch in v i r tue of the d i f fe rences be tw een th e com par ed en t it i es a s i t i s in

v i r tue o f t he i r s ha r e d p rope r t i e s ( e.g . l oc omot i on ) .

An exa mp le f rom the h i s tory of phys ics shows tha t d i spar i t ie s in mappin gs can a l so

opera te e f fec t ive ly in sc ien t i fi c me tapho rs . E lec t rons a re charg ed; a nd mo ving charges

emi t e l ec t romagne t i c rad ia t ion which d imini shes the i r k ine t i c energy . Thus revolv ing

e lec t rons wou ld rad ia te away a ll the i r k ine t ic energy in a ve ry shor t t ime , caus ing the m

to p lunge them in to the nuc leus . The fac t tha t th i s does not h a p p e n p o s e d a p r o b l e m

in c las s ica l phys ics : on th i s mode l a l l a tomic mat te r should be uns tab le , wi th a toms

col l aps ing in a re lease of u l t rav io le t rad ia t ion ( see Misner , Th orn e & Whee le r , 1973).

I ts r e s o l u t i on l e d to t he ove r t h row o f c l as s ic a l me c ha n i c s a s a n a d e qua t e mode l o f

a tomic s t ruc ture (on which the so la r sys tem mode l i s based) , and l ed to the preva i l ing

qu ntum mech nic l

v ie w o f a t o m i c p h e n o m e n a .

A d i spar i ty in the map pe d com par i son , not a s imi la r i ty , l ed to the insight. Note a l so

tha t the metaphor in th i s case pe r t a ins to an a t t r ibu te of e l ec t rons ( the i r charge) , a s

wel l a s re la t ions they en te r in to (e .g . revolv ing a round the nuc leus ) . Gentner draws a

fun dam enta l d i s t inc t ion be twe en a t t r ibu tes and re la t ions , c l a iming tha t on ly the la t t e r

a r e r e l e va n t t o m e t a ph or ma pp i ngs . T h i s is qu it e i r on ic , si nc e c ouc h i ng t he R u t he r fo rd

sola r sys tem me tap ho r s t r i c tly on re la t iona l pred ica tes ob scures i t s ro le in de f in ing th i s

c ons e q ue nc e o f t he me t a ph or - -h i s t o r i c a l l y pe rha ps its mos t i mpo r t a n t de r iva t ive .

3 .4 . T H E P R O B L E M O F N O N E M P I R I C A L F O R M A L I S M

A th i rd problem a rea for the s t ruc tura l theor ies , somewhat i ronica l ly , devolves f rom

t he i r f o rma l c ha r a c t e r . F o r e xa mpl e , a l t hough t he s e t heo r i e s a t t e mpt t o ve ry p r e c i se l y

def ine pr imi t ive en t i t i es and re la t ions , d i f fe rent theor i s t s have i so la ted d i f fe rent pr imi t ive

types . G en tn er (1980), a s we have seen , emp has izes n ode re la t ions over node a t t r ibu tes ,

but O r ton y (1979) does the reverse . Thi s wo uld be a use fu l cont ras t i f i t ma de an y

contac t wi th empi r i ca l i s sues, bu t ap pare nt ly i t does not . In rev iewing the va r ious

a pproa c he s , G e n t ne r ( 1980) e mpha s i z e s t he i r c ompa t i b i l i t y despite such di fferences .

How ever , the ava i l ab i l i ty of such a reconc i l i a t ion only se rves to un dersc ore the

funda m e n t a l a rb i tr a r ine s s o f the va r i ous t he o r i e s ' f o rma l e xp re s s i on .

Leaving as ide the ques t ion of whe the r cur rent s t ruc tura l theor ies can , in fac t, p rovide

a de qu a t e a nd un i voc a l de s c r i p ti ons o f me t a pho r r e l a t ions , w e mus t f a c e t he p roc e s s i ng

p r o b l e m o f h o w t h e n o d e - n o d e a n d r e l a t i o n -r e l a t io n m a p p i n g s a r e c o m p u t e d : s t ru c -



METAPHOR COMPU TING SYSTEMS AND ACTIVE LEARNIN G 45

tura l theor ies l ike Gentner ' s ( 1980) mere ly ssume ( v ia c ove r t e r m s l ike t r a n s pa r e n c y )

t ha t t he s e m a p p i ng s o b t a i n , bu t f i nes se t he i ne v i t a b l e que s t i on o f how. W he n t he s e

c om pu t a t i o na l p r ob l e m s a r e f a c e d , howe ve r , t he y m i gh t unde r m i ne t he i n i ti a l a tt r a c ti ve -

ne ss o f t he s t r uc t u r a l t he o r i e s. W i ns t on ( 1980 ) i m p l e m e n t e d a n a na l ogy s y s te m t ha t

m a t c he s r e l a t i ons a nd a t t r i bu t es . H e f ound t ha t some c l a s si f i c at o r y p r e - p r oc e s s i ng wa s

r e qu ir e d i n o r de r t o a vo i d a c om pu t a t i ona l l y un m a na g e a b l e p r oc e s s o f b r u t e fo r c e

node m a t c h i ng . W i n s t on ' s s pe ci fi c s o l u t i on wa s t o i m po s e c a t e go r i c a l p r e - st r uc t u r i ng

o n t h e p r o g r a m ' s i n p u t :

... the examples in this paper assume a berteficient teacher who gives only relevant facts

and who does not deliberately try to confuse the system by shoveling detritus at it.

Ho wev er , th is i s no t how r ea l l ea rn ing o ccur s , an d a theo ry of r ea l l ea rn ing wi ll need

t o d i r e ct l y c on f r on t t he p r oc e s s ing p r ob l e m s o f how c o r r e s p ond i n g node s a n d r e l a t i ons

a re r ecognized as such .

A t a no t he r e x t r e m e , t he s t r uc t u r a l e n t e r p r i s e t e nds t o g r a de i n t o pu r e l y f o r m a l

c onc e r ns w i t h no t a t i ona l c onve n t i ons . Va n L e hn & B rown ( 1981 ), f o r e xa m p l e ,

de ve l op e d a r e p r e s e n t a t i on f o r p r oc e d u r e s c a l l e d p l a n n i ng ne t s s uc h t ha t t he m a x i m a l

pa r t i a l i s om or ph i s m be t we e n t wo p l a nn i ng ne t s r e c ons t r uc t s t he o r d i na r y l a ngua ge

s e ns e o f s i m i l a r i t y be t we e n t he p r oc e d u r e s the y r e p r es e n t . T he i r a pp r oa c h a bs t ra c t s

a wa y f r om i s s ues o f a c tua l l e a r ne r pe r f o r m a nc e t o a n e ve n g r e a t e r e x t e n t t ha n G e n t ne r ' s :

t he t r a ns pa r e nc y , f o r e xa m pl e , o f a m a pp i ng i s s i m p l y no t a f a c t o r i n de t e r m i n i ng t he

c om pa r i s o n r e l a t ion . On t he wa y t o de ve l op i ng t he p l a nn i ng ne t f o r m a l i s m , t hey b ri e f ly

c ons i de r a l t e r na t i ve s , f o r e xa m pl e f l ow- c ha r t i ng , bu t t he y a r gue

Since the intersection grap h (the ove rlap in structural represen tation be tween two intuitively

similar procedures) is so small relative to the ditterence subgraphs, a reasonable closeness

metric would have to report that the two procedures are not very close--a false prediction.

W ha t is a r e a s ona b l e c lo s e ne s s m e t r i c t hou gh? I s t he p r op o r t i o n o f ove r l a p p i ng

n o d e s a n d r e la t io n s t h e o n ly a p p r o p r i a t e c o n s i d e r a t i o n ? M e r e p r o p o r t i o n s c a n n o t

r e p r e s e n t t he c ogn i t i ve p roc e s s e s by wh i c h a na l og i c a l r e l a t i ons h i p s a r e u se d a nd

unde r s t ood . B u t d i vo r c e d f r om t he s e p r oc e s s e s , suc h a na l y s e s o f s i m i l a ri t y be c om e

s t ric tly fo rmal .

4. Toward an activ e learning theory of meta phor

T o s um m a r i z e t he d i s c us s i on s o f a r , t he r e i s ge ne r a l c ons e ns us t ha t s om e no t i on o f

m e t a p h o r c a n b e b r o u g h t t o b e a r o n t he q u e s t i o n o f h o w p r i o r k n o w l e d g e o r g an i z es

ne w l e a r n i ng . Ope r a t i on a l t he o r ie s ha ve f oc us e d on t he m a n i f e s t e ff ec t s o f sugge s t ing

m e t a p h o r i c c o m p a r i s o n s t o l ea rn e rs a n d h a v e p r o d u c e d a v ar i et y o f c o n c r e te d e m o n s t r a -

t i ons, bu t t he y ha ve f a i l e d t o p r ov i de i n si gh t i n t o t he m e n t a l m e c ha n i s m s o f m e t a pho r .

S t r uc tu r a l t he o r i e s a t t e m p t t o do t h is , bu t t hus f a r ha ve f a i le d t o p r ov i de non - a r b i t r a r y

a c c oun t s . W ha t i s l a c k i ng i n bo t h op e r a t i ona l a nd s t ruc t u ra l a pp r o a c h e s i s a n a c c oun t

o f t he mech nisms of m e t a p ho r i c a l unde r s t a nd i ng . S uc h a n a c c oun t wou l d t e ll u s why

one o r m or e m e t a pho r s a r e u s e f u l a nd how t he y a r e ge ne r a t e d a nd t he n u s e d t o s uppo r t

lea rn ing .

S p e c u l a ti o n a b o u t t h e m e c h a n i s m s o f m e t a p h o r i c a l u n d e r s t a n d i n g is n o t ne w .

R a t i ona l a na l y s e s c a n be t r a c e d ba c k t o A r i st o t le . T he g i st o f t he s e p r o pos a l s is t ha t

t h e u n d e r s t a n d e r s o m e h o w m a k e s i n fe r en c e s a b o u t h o w p r o p e r ti e s o f s o m e t h i n g k n o w n



METAPHOR COMP UTIN G SYSTEMS AND ACTIVE LEARN ING

47

I ns t e a d , w e ha ve f ound t ha t l e a r ne r s r e s o r t t o mor e he u r i s t i c r e a s on i ng p r oc e s s e s

f o r fi gur ing ou t how t o d o t h i ngs o r s o lv i ng p r ob l e m s o r unde r s t a nd i ng t he ope r a t i on

o f te x t - e d it o r s . T he s e p r oc e s s e s i nc l ude d a bdu c t i on ( ge ne r a t ing hy po t he s e s on ba s is

o f ve r y l i m i te d i n f o r m a t i on ; s e e L ew i s & M a c k , 1982) a nd a dd uc t i on ( ve r i fy i ng

hyp othese s wi th in these same l imi ta t ions of in fo rm at ion ; s ee Car ro l l & Mack, 1984),

r a t he r t ha n mor e p r i nc i p l e d r e a s on i ng p r oc e s s e s ( l i ke de duc t i on o r i nduc t i on ) . T he s e

p r oc e s s e s p r oduc e c onc l us i ons t ha t a r e l e s s c ons t r a i ne d t ha n de duc t i ve a nd i nduc t i ve

processes , s t ri c t ly de f ined , bu t which o pen u p the poss ib i l i ty of d i scove r ing know ledge

on t he ba si s o f i mpove r i s he d i n f o r m a t i on .

Metaphors can fac i l i t a t e ac t ive l ea rn ing in th i s s i tua t ion by provid ing c lues for

a bduc t i ve a nd a d duc t i ve i n f e r e nc e s t h r ough w h i c h l e a rne r s c ons t r uc t p r oc e du r a l know -

l e dge o f t he c om pu t e r . T he l e a r ne r be g i ns w i t h a c a non i c a l bu t ope n - e nde d c o mp a r i s on

s t a te me n t , X i s Y , w he r e Y ha s ma ny mo r e know n p r ope r t i e s t ha n X . F r om th i s,

and in t ransac t ion wi th t a sk-spec i f i c goa l s , concerns , and expec ta t ions , the l ea rner can

ge ne r a t e a nd t e s t a va r ie t y o f hypo t he s e s a bo u t X , t ha t is c a n l e a r n ctively a bou t X .

Cons ider aga in opera t iona l metaphors to ca rd f i l e s , f i l e cab ine t s , typewr i t e rs , t ape

recorde rs , et c . No t a l l p rop er t i e s o f a typewr i t e r can be ca r r i ed over to a deve lopin g

c onc e p t o f a c omp u t e r t e x t p r oce s s o r. S ome c a n ( t he l a you t a nd c ha r a c t e r - t r a ns mi s s i on

f unc t i on o f t he ke ys ) ; s ome c a nno t ( c ha r a c t e r ke ys c a nno t s t r a i gh t f o r w a r d l y be ove r -

s t ruc k u s i ng a t e x t - e d i t o r ) ; a nd s ome c a n be ma ppe d f r om t he t ype w r i t e r ba s e, bu t

s ome w ha t p r ob l e m a t i c a l l y ( e .g . w i t h r e s pe c t t o t he s t o r age o f i n f o r ma t i on , t he t a pe

r e c o r d e r p r o v i d e s a n a l t e r n a t e - - a n d i n so m e w a y s m o r e a c c u r a t e - - m e t a p h o r ) .

T he c o mp a r i s on o f a t e x t - e d i to r w i th a t ype w r i t e r c ar r ie s ll of these impl ica t ions .

The o bvious s imi la r i ti e s in func t ion and form a f ford the m eta ph or in the f ir st p lace :

t e x t e d i t o r le a r ne r s a l mos t n e ve r puz zl e ove r w ha t w i ll ha pp e n w he n t he y s t ri ke a

c ha r a c t e r key . I n t he c on t e x t o f s uc h c a non i c a l a nd s a l i e n t c o r r e s pon de nc e s , t he

dissimil rities be t w e e n t he t e x t e d i t o r a nd a t ype w r i t e r be c ome ope n que s t i ons - -

i mpe l li ng f u r t he r t houg h t a nd l e a d ing t he n t o f u r t he r l e a r n ing .

F o r e xa mpl e , ke y i ng t w o c ha r a c t e r s a t t he s a me l oc a t i on on a c onve n t i ona l t ype d

page resu l t s in an overs t r ike . How ever , tex t -ed i tors d on ' t p ro du ce overs t r ikes ( in th i s

way) . They e i the r inse r t ( i . e . p lace the new charac te r ad jacent to the o ld one , and

adjus t the t ex t line accord ing ly) or rep lace ( i .e ., p lace the new c hara c te r wher e the o ld

one w a s - - de l e t i n g t he o l d one ) . C onve n t i ona l t ype w r i t e rs , o f c ou r s e , don ' t ha ve i n s e rt

or rep lace capabi l i ty ; th i s i s a c l ea r d i s s imi la r i ty in the metaphor . But th i s l ack of

t ransparency , c l a r i ty , r i chness , e t c . i s no t func t iona l ly a l imi ta t ion on the metaphor .

S a l ie n t d i s s i mi l a r i ti e s - - i n t he c on t e x t o f s a l ie n t s i m i l a r i t ie s - - s t i mu l a t e t h ough t a nd

e nha n c e t he e f f ic a cy o f t he m e t a ph or a s a l e a r n i ng ve h ic l e.

C ons i de r a n e xa mpl e f r om a c ompu t e r s y s t e m t ha t i s ba s e d on t he me t a phor o f a

desk top . In th i s sys tem objec t s and the i r manip ula t io ns a re represented concr e te ly (a t

l eas t on the sur face ) : for example , to c rea te a new document f i l e , a use r i s p rompted

t o i ni ti a te a n a c t i on r ough l y de s c ri be d a s t e a r i ng o f f pa pe r , i n the c on t e x t o f a n i c on

r e p r e s e n t i ng a pa d o f pa pe r . O ne u s e r w e obs e r v e d t ook t he p r om pt qu i t e l it er a ll y . H e

t r i ed t o dev i se s ome a c t ion o f t e a r i ng o r s w e ep i ng t he c u r s o r a c r oss t he i c on

represent ing the paper . In fac t , the metaphor i s mis leading because ac t ions appl i ed to

objec t s l ike f i l e s (or appl i ca t ions ) m, , l s t be se lec ted in a more convent iona l fash ion ,

f r om me nus w h i c h de s c r i be t he a c t i ons .

Wa s t he me t a pho r a f a i l u r e ? I n fa c t , t he e xp e r i e nc e w as i n f o r ma t i ve be c a us e onc e

t he u s e r unde r s t ood how t o s e le c t a c t ions he c ha nge d h is r u le a bo u t h ow t o do t h i ngs .



48 JOHN M . CARROL L A ND ROBE RT L . M ACK

At t h a t p o i n t h e u n d e r s t o o d t h a t t h e m e t a p h o r wa s n o t t o b e t a k e n t o o l i t e r a l l y , b u t

m o r e i m p o r t a n t , w h e n o n e w a n t e d t o d o s o m e t h i n g , t h e a c t i o n p r o b a b l y h a d t o b e

s e l e c t e d f r o m a m e n u .

T h i s e x p e r i e n c e w i t h a m e t a p h o r ( s u p p l i e d i n p a r t b y t h e m a n u f a c t u r e r , b u t e l a b o r -

a t e d b y t h e u s e r ) wa s s u c c e ss f u l. O t h e r e x a m p l e s d e m o n s t r a t e t h a t t h e o u t c o m e o f

r e a s o n in g w i t h a m e t a p h o r c a n b e m o r e c o m p l e x . H e r e i s a m o r e c o m p l i c a t e d e x a m p l e

d e s c r i b e d b y M a c k ( 19 8 3) . A s e c r e t a r y wa s t r y in g t o u n d e r s t a n d a d e s i g n f e a t u r e o f a

tex t - ed i to r in which the en d o f a l ine i s r epres en te d by a spec ia l cha rac te r tha t can be

i n s e r te d o r d e l e t e d l i k e a n o r d i n a r y c h a r a c t e r , b u t wh i c h h a s s u r p r i s i n g a n d u n i n t u i t i v e

consequences . For example , en te r ing a l ine end break (by h i t t ing r e tu rn) sp l i t s a l ine

and pu ts ev e ry th i ng to the r igh t o f the cu r sor on a new, inse r ted l ine . De le t in g the line

break for a g iven l ine causes the nex t l ine to be conca tena ted wi th i t .

T h e s e e f f e c ts a re a c o m p l i c a t e d c o n s e q u e n c e o f h o w t e x t d a t a i s r e p r e s e n t e d i n t h i s

t e x t -e d i t o r: E v e r y t h i n g t h a t is t y p e d ( i n c lu d i n g l in e b r e a k s y m b o l s ) f o r m s a d a t a

s t r e a m . L i n e b r e a k s c a u s e t h e s t r e a m t o b e f o r m a t t e d i n t o n e w l i n e s a t l i n e b r e a k s .

M o r e o v e r , b l a n k a r e a s l y in g b e y o n d l in e e n d s a r e n o t r e p r e s e n t e d a t a ll in t h e d a t a

s t r eam.

On e p e r p l e x i n g c o n s e q u e n c e o c c u r s wh e n o n e t ri e s t o a p p e n d t e x t t o t h e e n d o f a

p a r a g r a p h , a n d i n d o i n g s o , t y p e s o v e r th e l i n e b r e a k s y m b o l : i n th i s c a se t h e n e x t

b l a n k l i n e i s c o n c a t e n a t e d t o t h e o r i g i n a l p a r a g r a p h , a s w i l l s u b s e q u e n t l i n e s a n d a n y

t e x t o n t h e m a s o n e c o n t i n u e s to t y p e . T h i s h a s t h e o d d e f f e ct o f d r a w i n g u p a n d

r e p l a c i n g m a t e r i a l o n s u b s e q u e n t l in e s. Ne e d l e s s t o sa y , wh e n a l e a r n e r wa s a s k e d t o

e x p l a i n t h e s e e ff ec t s, s h e wa s p e r p l e x e d b y t h e m , a n d wa s n o t a b l e t o i n d u c e t h e

u n d e r l y i n g p r o g r a m m o d e l . Ye t , s h e d i d f o r m u l a t e a m e t a p h o r o f t h e s t r i n g wh i c h

s e e m e d t o e x p l a i n p a r t o f wh a t wa s h a p p e n i n g .

Ac c o r d i n g t o th i s m e t a p h o r , w h a t o n e t y p e d o c c u p i e d a fi x ed n u m b e r o f s lo t s, li k e

b e a d s o n a s tr in g . T r y i n g t o t y p e o v e r e x i st i n g c h a r a c t e r s wo u l d r e p l a c e wh a t w a s

t h e r e , a n d a t t h e e n d o f l in e s , t h is s o m e h o w c a u s e d c h a r a c t e r s a f t e r wa r d s t o b e p u l l e d

u p l ik e a s t ri n g . Un f o r t u n a t e l y , t h is m e t a p h o r d id n o t e x p l a i n wh y t h e b l a n k a r e a

a f te r the l ine b r eak could no t be f i l l ed up be fore encroach ing on ex i s t ing mate r ia l .

No r d i d i t e x p l a i n wh y t y p i n g a t o r b e y o n d l i n e e n d s s h o u l d b e g i n t o e n c r o a c h o n

s u b s e q u e n t m a t e r i a l . T h e m e t a p h o r wa s i n c o m p l e t e , b u t d i d l e a d t o a p o s i t iv e o u t c o m e :

t h e l e a r n e r n o w h a d a r a ti o n a l e f o r t h e c o r r e c t p r o c e d u r e wh i c h i s t o i n s e rt n e w m a t e r i a l

( m a k e th e s t r i n g l o n g e r ) i n s t e a d o f s i m p l y i n g t r y in g t o t y p e a d d i t i o n a l t e x t s t a r ti n g

f r o m t h e e n d .

4 .2 . M E T APHOR S ARE OPE N E NDE D

W e h a v e a r g u e d t h a t m e t a p h o r s f u n c t i o n t o s t i m u l a t e p r o c e s s e s o f i n f e r e n c e t h at t ry

t o a p p l y n o t o n l y s i m il a ri t ie s b e t we e n k n o w n a n d u n k n o w n o b j e c t o f k n o wl e d g e , b u t

a l s o m a k e u s e o f

dissimilarities

a n d o m i s s i o n s i n m e t a p h o r , r e l a t i v e t o t h e n e w o b j e c t

o f k n o wl e d g e . P u t a n o t h e r wa y , m e t a p h o r s a r e o p e n - e n d e d : t h a t i s, n o t l it e ra l d e s c r ip -

t i o n s, b u t i n h e r e n t l y i n c o m p l e t e , e v e n i n d e t e r m i n a t e , n o t f o r l a c k o f w i t o r b y t h e f ia t

o f i n t e n t i o n , b u t b y definition

W h i l e t h is v i e w m a y n o t b e i n c o m p a t i b l e w i t h s t ru c t u r a l t h e o r i e s i n p r i n c ip l e , i t

d o e s n a g a t t h e a t t e m p t t o d e v e l o p e x p l i c it m a p p i n g r e p r e s e n t a t i o n s f o r m e t a p h o r s . I t

s e e m s to u s i n h e r e n t i n t h e n a t u r e o f m e t a p h o r t h a t i t s r e l a t i o n t o a m e t a p h o r i z e d



METAPHOR COMP UTIN G SYSTEMS AND ACTIVE LEARN ING 49

ob j e c t o r doma i n be no t j u s t i nc ompl e t e , bu t i nde t e r mi na te . C e r t a i n l y t h i s tr a it o f

inde te rm inacy i s t rue of expres sive and l i t e racy me tap ho r (F rye , 1966; R ichards , t925) ,

bu t w e w ou l d a r gue t ha t i t is e qua l l y t r ue o f me t a phor s i n mor e m und a ne a r e as , s uc h

as l ea rn ing to use a com put in g sys tem. It is th i s p rop er ty of meta ph or tha t a f fords

cogni t ive ly cons t ruc t ive processes which can l ead to new knowledg e . F r om the pe rspec-

t ive of ac t ive lea rn ing , the ope n-en ded ness of these ke rne l co mp ar i son s i s in t r ins ic to

the mechani sm tha t a l lows them to work . In th i s case , l ea rners a re in t roduced to

p r ope r t i e s o f t e x t e d i t o r f o r ma t t i ng a nd da t a - s t r e a m r e p r e s e n t a t i on a s p r ob l e ms they

pose to themseloes

C ons i de r , f o r e xa m pl e , w ha t a l e a r ne r g le a ns f r om t he c omp a r i s on o f a t ex t fil e a nd

a ca rd f il e. In the con tex t of t ry ing to l ea rn to ed i t co mp ute r f il es , the re is a h ighly

sa l i en t cor respondence : when one ca rd ( l ine ) i s removed (de le ted) i t s p lace in the deck

( f i l e ) i s f i l l ed by the next ca rd ( l ine ) . But having g leaned th i s cor respondence ra i ses

a l l sor t s o f fur the r ques t ions which impe l fur the r thought and l ead to fur the r l ea rn ing .

To un pack th e impl ica t ions of th is bas ic ins ight requi res d i scover ing man y prop er t i e s

of compute r t ex t f i l e s which a re e i the r l e f t ou t o f the ca rd f i l e compar i son , o r would

not be spec i f ica l ly i l lumin a ted b y it. For exa mp le , the pa r t i cu la r subpar t s of each

complex objec t (ca rd f i l e ve rsus compute r t ex t f i l e ) do not match in an obvious way.

A s ingle l ine on an index ca rd does not l i t e ra l ly match the v ideo objec t cor responding

t o a l i ne o f a f il e, bu t c o r r e s pon ds on l y in a n ope n - e n de d a nd r a t he r a bs t r a c t w a y t ha t

mus t be separa te ly spe l l ed out .

M a ny o t he r e l e me n t s o f t he c omp u t e r f i le mus t be d i s c ove r e d on t he i r ow n t e rms ,

no t t h r ough t r a c i ng ou t ma pp i ngs w i t h t he me t a phor . T o c i t e one e xa mpl e : c ompu t e r

f il e l ines a re nu mb ere d and ren um ber ed as l ines a re inse r t ed or de le ted , qu i t e un l ike

c a r ds. T he r e num be r i ng a nd a d j ust i ng o f c o mp u t e r f il e l ine s ( s c ro l l ing up w i t h de l e te d

l ines or s c ro l l ing down wi th inse r t ed l ines ) mus t be unders tood in i t s own r igh t . Our

f a mi l i a r i t y w i t h c ompu t e r f i l e s ma y ma ke i t e a s y t o p r e s uppos e t ha t t he s e ma pp i ngs

are obvious (ca rd ve rsus v ideo l ine , ca rd pos i t ion ve rsus l ine number , e t c . ) bu t th i s

ma y be t o be g i mpor t a n t que s t i ons .

T o s umm a r i z e , t he r e l a ti ons h i ps c ompr i s i ng a me t a p hor c om pa r i s on a r e no t r e a d

o f f , bu t c ons t r uc t e d by a c t ive l y w or k i ng t h r o ugh t he i mp l i ca t i ons o f t he m e t a phor .

T he r e i s o f c ou r s e a pe da gog i c a l a pp l i c a t i on o f me t a phor s i n w h i c h t he y s e rve t o c od i f y

a nd c o mm uni c a t e ne w know l e dge i n a c ompr e he ns i b l e w a y f o r ne w l e a r ne r s. H e r e

me t a phor s ma y be c a r e f u l l y c r a f t e d a nd p r e s e n t e d i n a w a y tha t he l p s t he l e a r ne r ma ke

jus t the con nec t io ns the ins t ruc tor want s the l ea rn er to make . But th i s ro le for me tap ho r

should not mis lead us in to th inking tha t a l l me taphors func t ion in th i s s eemingly

s t r a i gh t f o r w a r d w a y : t ha t i s , w he r e t he c onne c t i ons be t w e e n t he me t a phor a nd ne w

ob j e c t o f know l e dge a r e c l e a r c u t a nd s e e mi ng l y r e a d o f f .

T he t ype w r i t e r me t a ph or , i n pa r t i cu l a r , p r ov i de s a n o r i e n t ing f r a m e w or k bu t l e a ves

ma ny ope r a t i ona l de t a il s f o r the l e a r ne r t o d i s c ove r . T he me t a ph or o r i e n t s the l e a r ne r

( the com pu te r nov ice in th is exam ple ) to hyp othe s ize and ve r i fy s imi la ri t i es in s t ruc ture

a nd f unc t i on , a nd t o ha ve a f r a me w or k f o r r e c ogn i z i ng a nd a na l yz i ng d i s c r e pa nc i e s .

In th i s way, the metaphor se rves to in i t i a t e more sys temat ic processes which cons t ruc t

mor e c om pl e t e p r oc e d u r a l know l e dge r e p r e s e n t a t i ons s pe c if i ca l ly a pp r o p r i a t e t o t he

t e x t e d i to r . B u t t he me t a ph or i ts e lf s e e d s t he s e c onst r uc t ive p r oc e s s e s a nd ma y

c on t i nue t o s e rve a s a n o r i e n t i ng f r a me w or k t h r ou gh t he l e a r ne r' s i n t e r a c t i on w i th t he

spec if i c prop er t i e s o f the com pute r . A ccord ingly , we canno t enu me ra te the e f f i cac ies



50 JOHN M CARRO L L AND ROBE RT L

M CK

of a me t a ph or j u st by c oun t i ng m a ppe d r e la t ions . R a t he r , w e mus t t a ke i n to a c c o un t

the l ea rn ing process wi th in which these re la t ions have rea l meaning .

4.3. W HER E METAPHORS COM E FROM

Act ive l ea rn ing impl ies tha t e f fect ive meta pho rs wi ll be se l f -genera ted by l ea rners , and

tha t work ing out the impl ica t ions o f these meta pho rs wi l l be a pr inc ipa l p rocess of

l e a r n i ng . S e l f - ge ne r a t e d me t a phor s , be c a us e t he y a r e de ve l ope d s pon t a ne ous l y , a nd

w i t hou t a ppa r e n t e f fo r t, c ou l d be r e ga r de d s i mp l y a s g i ve ns o f t he l ea r n i ng p r oc e s s,

as in t rins ic to i t o r a s in t rins ic mot iva to rs o f it , and the re fore no t a s sources of addi t io na l

p r oc e s s i ng de ma nds . O t he r - ge ne r a t e d me t a phor s , be c a us e t he y mus t t he ms e l ve s be

expl i c i t ly comprehended by l ea rners , ra i se o the r i s sues : wha tever l ea rn ing burden i s

as soc ia ted wi th the me tap ho r i t s e l f mus t t rade of f favo urab ly wi th the sav ings in

l e a r n i ng bu r de n de r i ve d f r om e mpl oy i ng t he me t a phor s ubs e que n t l y .

There i s ind i rec t ev idence for th i s in tha t i t i s o f t en found tha t l ea rners cannot make

us e o f me t a pho r s t ha t t he y a r e ta ugh t . T he r e a r e c a s e s w he r e me t a pho r s a r e a va i la b l e

but no t recognized as such , o r no t appl i ed . Gick & Holyoak (1980, 1983) went to

grea t l engths to induce s tudent s to apply a s tory scenar io which they unders tood to

so lve a problem whose form was ana logous to the scenar io in the s tory . S tudent s were

a b l e to e xp l o i t t he a na l og i ca l c on ne c t i on w he n i n f o r me d t ha t t he r e w a s one , bu t w e re

much l es s l ike ly to see or explo i t the connec t ion spontaneous ly . I t r emains unc lea r

wha t mot iva tes a l ea rner to use a metaphor , o r even cons ide r the poss ib i l i ty tha t one

mi gh t be r e l e va n t t o und e r s t a nd i ng .

However , i t i s c l ea r tha t the re a re r i sks inherent in se l f -genera ted metaphors which

ma y no t be a pp r op r i a t e f o r unde r s t a nd i ng . G e n t ne r & G e n t ne r ( 1980) p r ov i de a n

exam ple in case of s tudent s t ry ing to unde rs tand e lec t r ica l ci rcu it s . S tudent s w ho

ge ne r a t e d me t a p hor s r e f e r ri ng t o f l ow i ng w a t e r w e r e be t t e r a bl e t o unde r s t a nd p r ope r -

t ie s of ba t t e r i e s and the i r se r i a l o r pa ra l l e l comb ina t io n than s tudent s w ho thou ght in

t e r ms o f ma s s e s o f mov i ng ob j e c t s ( e. g. c r ow ds o f pe op l e ) . C onve r s e l y , s tude n t s w h o

ge ne r a t e d m e t a ph or s i nvo l v ing t he i de a o f mov i ng ob j e c ts w e r e be t t e r a b le t o unde r s t a nd

a s pe ct s o f c i r c u it s tha t t he f l ow ing w a t e r me t a p hor c ou l d no t a de qu a t e l y de s c r ibe . N o

one me t a ph or w a s s u f fi ci en t f o r unde r s t a nd i ng a ll p r ope r t i e s o f t he c i r c u it ( o r c ha nge s

ma de i n i t ) : f a i l i ng t o c hoos e t he r i gh t one ma de i t ha r d t o unde r s t a nd one o r mor e

features .

Bot t (1979) provides an exa mp le in the dom ain of t ex t -ed i ting . Cons id e r the cont ras t

b e t w e e n t h e p i g e o n h o l e m e t a p h o r w i th t h e c a r d f il e m e t a p h o r in u n d e r s t a n d i n g

the s t ruc tu re o f a tex t fi le in a l ine ed i ting en vi ronm ent . In the fo rmer , p r in t ing cons i s t s

of fe tch ing the conten t s of a p igeon hole (a l ine of tex t ) and d i sp lay ing i t. In the l a t t e r ,

p r in t ing co ns i s t s o f fe t ch ing a ca rd f ro m a ca rd f i le and d i sp lay ing wha t i s wr i t t en on

i t (a lso a l ine of the text f ile). To this exten t , the m eta ph or s a re ident ical .

A cont ras t emerges in the case of de le t ion . De le t ing a l ine of t ex t , in the p igeo nho le

me t a p hor , a mo un t s t o f et c h i ng t he c on t e n t s o f a p i ge onho l e a nd d i s c a r d i ng

i t but the

pigeonhole itself remains (a lbe i t empty) . In the ca rd f i le me taph or , de le t ion cons i s t s in

s i mp l y r e mov i ng a c a r d f r om t he f ile . O n t he f o r m e r me t a ph or , a l e a r ne r w ou l d e xp e c t

tha t the op era t ion of de le t ing a l ine wou ld have the e f fec t o f l eav ing a b lank l ine in

the f il e. On th e l a t t e r, th i s expec ta t ion wou ld no t occur . Bot t foun d tha t the p igeo nho le

me t a pho r s p on t a ne ous l y oc c u r s t o l e ar ne r s a nd is no t g ive n up e a s i ly , how e ve r it ma ke s

the wrong pred ic t ions for de le t ion . Bot t p resumes tha t in the typ ica l case success fu l

me tapho rs wi ll be expl i c it ly t aught b y a teacher .



52 J O H N M CA RR O L L A N D RO BE RT L M A CK

observable learning behaviour (Carroll & Mack, 1983, 1984). Where the operational

theories focus chiefly on demonstrations

t h t

metaphor enhances learning, our analysis

seeks to clarify h o w that advantage becomes manifest in active learning.

This view is also compatible with the structural theories. However, it provides an

approach to the problem of arbitrary assumptions, which as we have argued threatens

to deprive the structural theories of any serious content. Recall, for example, that some

of the formal properties Gentner defined over her graph structures, seemed paradoxi-

cally related to the actual efficacy of metaphors for comprehension. Whereas Gentner

showed formally why the metaphor of interpersonal attraction ought to be a bad

account of ion bonding (because of its low base specificity), the fact is that it is a good

metaphor. What seems to be relevant is the goal of trying to understand activity directed

toward bonding. Having this goal in mind makes salient the analogy of human pair

bonding and ion bonding. Base specificity p e r s e is only a secondary consideration.

Another problematic case we considered earlier was that of relations. Gentner's

analysis arbitrarily suppressed, for example, the warms relation in her reconstruction

of the Rutherford solar system analogy. On the active learning view, it becomes

clear--and non-arbitr ary-- that the warms relation is irrelevant to the comparison

being made in this metaphor. The goal of a learner employing this metaphor is to

better understand the spatial properties of the hydrogen atom, and the manner in

which they are dictated and maintained by force relationships between the various

constituents. From the viewpoint of this goal, colour , temperatu re , and a host of

other physical dimensions are irrelevant. But the analyst discovers this by including

the learner's goals within the analysis, not by arbitrarily preselecting only the relevant

dimensions in the analysis. Active learning affords an explanation of what Gentner

was forced to merely stipulate.

Holyoak (1983) has made similar criticisms regarding purely structural definitions

of what properties of an analogy or metaphor will be relevant. He cites an example

in which an attribute of an object was critical to understanding something new about

another object. More generally, Holyoak argues that the relevance of attributes or

relationships is determined by the

c su l ro l e

that they play in some situation. Attributes

may be just as relevant as relations.

This pragmatic conception of metaphor makes it unsurprising that learners sometimes

compose two, or even more, base domains (as did the learner studied by Carroll and

Lasher, 1981). From the unembellished structural viewpoint, composite metaphors are

cases in which the mapping from the target to the base domains is formally ill-defined.

But as we have noted, these are not cases where comparisons become hopelessly

unresolvable. They are cases in which a richer basis for open-ended comparison is

accessed.

More generally, we should not expect that the description of a metaphor to be

unique. There may be multiple descriptions serving different purposes for different

goals. Holyoak (1983), for example, argues that analogical connections may be made

in terms of concrete connections between target to base domains, or they may be made

at a more abstract level in which target and base are understood as instances of more

abstract generalization. Both levels of description presumably have advantages and

disadvantages, and serve different goals. For example, abstracting a general schema

may help the learner to disentangle their understanding from the myriad irrelevant

details of the target and base, details which might otherwise obscure similarities between



METAPHOR COM PUTI NG SYSTEMS AN D ACTIVE LEAR NING

53

t he t w o doma i ns . O n t he o t he r ha nd , a ge ne r a l s c he ma ma y be t oo a bs t r a c t , s o t ha t

i t s re l evance to a spec i f i c ins tan t i a t ion obscure .

T he p r ob l e m o f me t a p ho r is i n t i ma t el y bo un d up w i t h t he t r a ns a c t i on be t w e e n a ge n t s

a nd t he i r c u r r e n t goa l s , T h i s t r a ns a c t i on i s o f t e n a dva nc e d by r e c onc e p t ua l i z i ng t he

cur ren t s i tua t ion in t e rms o f use fu l ly re la ted o the r s i tua t ions . Am on g a l l the poten t i a l

re la t ionships be tween a t a rge t and a source the re wi l l be some tha t s e rve to i l lumina te

p r ope r t i e s o f t he t a rge t t ha t a r e r e l e va n t t o c u r r e n t goa ls , a nd s ome t ha t do no t . P u r e l y

ope r a t i ona l t he o r i e s ove r l oo k t h is a nd de a l w i t h t he ou t c ome s

per se

St ruc tura l theor ies

c a n on l y de a l w i t h t h is b y pos i ti ng f u r t he r a r b i t r a r y r e l a ti ons i n o r d e r t o ge ne r a t e t he

a poster iori

app rop r ia te ma ppin g re la t ions (e .g . sys temat ic i ty pr inc ip le ) . Bu t th i s une nd-

i ng re s o r t t o a dd i t i ona l de g r e es o f f r e e dom unde r mi ne s t he e xp l a na t o r y e f fi ca c y o f

these theor ies .

T he r e s o l u t i on o f t h is , w e s ugges t, l ie s i n e l a bo r a t i ng c u r r e n t a na l y s e s o f me t a pho r

t o i nc l ude e xp l i c i t r e f e r e nc e to t he r o l e o f me t a p hor i n a c ti ve le a r n i ng a nd t o t he

pe r s ona l goa l s t ha t d r i ve th i s p roc e s s. T he r e c a n be no pu r e l y s t r uc tu r a l i nde x o f t he

us e f u lne s s o f a m e t a p ho r f o r unde r s t a nd i ng s ome nove l e n ti ty . F o r t h i s w il l al w a ys be

a j o i n t f unc t i on o f po t e n t i a l r e l a t ions h i ps be t w e e n t he t a rge t a nd me t a ph or d oma i ns ,

a nd t he goa l s a nd ne e ds o f t he l e ar ne r .

5.2. MODELS AND METAPHORS

T he a c t ive l e a r n ing p i c t u r e o f me t a ph or pe r m i t s u s t o s ha r pe n t he p r e - t he o r e t i c a l

d i s t inc t i on be t w e e n

m o d e l s

a n d

metaphors

The d i s t inc t ion we envi s ion res ides ch ie f ly

i n t he ope n - e n de dn e s s , i nc om pl e t e ne s s , a nd i nc ons i s t e n t va l i d it y o f me t a p hor i c c om -

par i sons ve rsus the expl i c i tnes s , comp rehe ns ive ness an d va l id i ty of mod e l s . Thi s

c on t r a st is no t a d i c ho t omy . M o de l s t yp i c a l ly r e l y on a ke r ne l me t a p hor , o r me t a phor s ,

a nd h e nc e s t i mu l a te m a ny o f t he s a me c om pr e h e ns i o n p r oc e s s e s w i th r e s pe c t to a c t ive

lea rn ing ( see a l so M i l l e r , 1979, for re l a ted v iews on the genera l i ty of processes fo r

c ompr e he nd i ng l i t e r a l a nd me t a phor i c a l t e x t ) .

O n t he on e ha nd , a mode l is a de s c r ip t i on o f a t a r ge t dom a i n o r ob j e c t t ha t s e e ks

to fa i th fu l ly represent the ac tua l e l ements , re l a t ions and mechani sms tha t a re cons t i tu -

t ive of ob jec t s in tha t domain . Al though mode l s a re necessa r i ly se lec t ive and abs t rac t ,

a nd a c c o r d i ng l y t o s ome e x t e n t i nc omp l e t e , t he i r i nc ompl e t e ne s s i s no t t he s a me a s

t ha t o f me t a ph or s . F o r w h i l e mode l s a r e de s i gne d t o r e p r e s e n t s ome t a r ge t doma i n ,

me t a phor s a r e c hos e n o r de s i gne d t o i nv i t e c ompa r i s ons a nd i mp l i c a t i ons w h i c h a r e

not l i teral ly true M e t a ph or s a r e no t r i gh t o r w r o ng de s c r i p t ions , a s mode l s a r e :

ra the r they a re s t im ula t i ng (or uns t im ula t ing) inv i t a t ions to see a t a rge t do ma in in

a ne w l igh t. B la c k 's (1979) i n t e r a c t i on i s t v i e w o f me t a pho r unde r s t a nd i n g de ve l ops

t h is po i n t o f v i e w i n t he c a s e o f i n t e r p r e t i ng me t a ph or i c a l e xp r e s s i ons ( se e a ls o

Tourangeau & S te rnberg , 1982) .

O n t he o t he r ha nd , a p r a c ti c a l c omp l i c a t i on e n t e rs i n t o t h is c on t r a s t w he n w e c ons i de r

a mode l a s codi f i ed in some phys ica l representa t ion . In such a case , unders tanding

t he mode l p r e s u ppos e s i n t e r p r e ti ng t he r e p r e s e n t a t i ona l f o r m a t o f i ts p r e s e n ta t i on . T he

l a tt e r c a n be i n pa r t a p r ob l e m o f me t a phor . T he p r ob l e m c a n be r e l a t i ve ly t ri v ia l, a s

w he n t he r e l a t i ons h i p be t w e e n r e p r e s e n t a t i ona l f o r ma t a n d t he mod e l i t s e l f is e xp l ic i t

a nd e ve n c onve n t i ona l ; e xa mpl e s w ou l d be f o l l ow i ng f l ow - c ha r t s o r r e c ogn i z i ng

c onve n t i ons o f pe r s pe c t i ve i n d r aw i ngs . B u t t he f a mi l ia r i ty o f t he s e r e p r e s e n t a t i ona l

f o r ma t s s hou l d no t o bs c u r e t he c ogn i ti ve me c ha n i s ms p r e s up pos e d i n i n t e r p r e ti ng t he i r



54 JOHN M CARRO LL AND ROBE RT L MACK

impl ica t ions for respec t ive t a rge t domains , a s c ross -cul tura l re sea rch has shown in the

case of p ic tor i a l repres enta t ion ( see Cole & Scr ibner , 1974) .

A pa r t f r om p re s uppos i ng t ha t l e a rne r s unde r s t a nd pa r t i c u l a r r e p r e s e n t a t i ona l f o r -

ma t s, le a rn i ng mode l s ma y s imp l y no t be pos si b le . R e c a ll t he e xa mpl e o f t he m e t a p ho r

o f the s t r i ng . T he s e c r e t ary w as pe rp l e xe d b y t he s u r f a c e e f f ec ts o f a r a t he r c o mpl e x

edi tor fea ture : the da ta s t ream. W hat w ould i t me an to pro vide a li t era l mo de l of the

da t a s t r e a m t o t h i s s e c r e ta ry? T a ke n l it e ra l ly , i t w ou l d me a n i n t roduc i ng p rog ra m mi ng

conce pt s tha t a re t echnica l a nd d i f fi cu l t to unde rs tan d in the i r ow n r ight.

T h i s v i e w o f t he d i s t inc t i on be t w e e n mode l a nd me t a ph or ha s i mm e d i a t e i mp l i c a t i ons

fo r w ha t H a l a s z & M o ra n (1982) ha ve c a l le d c on c e p t u a l mod e l s , a nd t he i r r o le i n

l e a rn i ng . H a l a s z a nd M ora n c on t r a s t c onc e p t ua l mode l s w i t h me t a phor i c , o r a na l og i ca l ,

mode l s . By the l a t t e r , they in tend sugges t ive but typ ica l ly incomple te desc r ip t ions

r e f e rr i ng to n e a r -ne i gh bor do ma i ns , o r t o c ompo s i t i ons o f t he se . I n c on t r a st , t he i r v i e w

of c onc e p t u a l mode l s is i n t e nde d t o c ov e r h i gh l y a c c u ra t e a nd a rb i tr a r il y c om pl e t e

desc r ip t ions , usua l ly in some abs t rac t format , l ike a f low-char t or a graph . They c i t e

du B ou l a y , O 'S he a & M onk (1981) , M ora n (1981) , a nd Y oung (1981) a s e xa mpl e s .

H a l a s z & M o ra n (1982) tr y t o ma ke t he a rgum e n t t ha t c onc e p t ua l m ode l s ha ve a

d i s t i nc t a dva n t a ge ove r a na l og i c a l mode l s f o r l e a rn i ng , na me l y t ha t t he y a r e t r u l y

a p p r o p r i a t e vis-a-vis the t a rge t doma in , indee d to a rb i t ra ry l imit s , by design. Analogica l

mode l s , by t he i r ve ry de f i n i t i on , c a nno t be t r u l y a pp rop r i a t e . T he y a r e a t be s t on l y

rough l y a pp rop r i a t e a s de sc r i p t ions . U nfo r t un a t e l y , th i s a rgum e n t s u ff e rs t w o s e r i ous

di f f i cu l t i e s : F i r s t , a s we have obse rved above , so-ca l l ed conceptua l mode l s a re not a t

a ll d i c h o t om ous w i t h me t a phor s . T he P l a t on i c f o rm o f a c onc e p t ua l m ode l ma y i nde e d

be s o a bs t r a c t a s t o be me t a phor - f r e e . B u t w he n t he c onc e p t ua l mode l i s c od i f i e d on

pap er as a graph or a char t , a s i t wo uld have to be in order to func t ion as an ins t ruc t iona l

t oo l , i t s i n t e rp r e t a t i on r e qu i r e s p r i o r know l e dge a bou t s uc h r e p re s e n t a t i ona l f o rma t s

and the i r charac te r i s t i c in te rpre ta t ion . To the ex tent tha t th i s process i s no t au tomat ic

a nd de t e rmi na t e , i t e nga ge s me t a phor .

The sec on d d i f f i cu l ty wi th the Ha lasz & Mo ran (1982) a rgum ent i s tha t h ighly

a c c u ra t e a nd a rb i tr a r il y c omp l e t e de s c r i p ti ons m a y s i mp l y no t be op t i ma l l e a rn i ng a i d s

(Jones , 1982) . The v iew tha t they a re presupposes a pass ive l ea rn ing theory , which

i nde e d i s p r e s uppos e d i n ma ny s t a t e -o f - t he - a r t a pp roa c he s t o i n s t ruc t i on , bu t w h i c h

we have fou nd to be incons i s t en t wi th the propen s i t i e s and capac i t i e s of ac tua l l ea rners

t ry ing to mas te r t ex t -ed i t ing sys tems (Mack, Lewis & Car ro l l , 1983) . Indeed , in our

v i e w , a me t a phor t ha t t r u l y p rov i de d a completely t r a n s p a r e n t a n d c o m p r e h e n s i v e

m a p p i n g o f t h e ta r ge t d o m a i n w o u l d b e a b a d m e t a p h o r f o r le a r n e r s - - t h e r e w o u l d b e

no t h i ng l e f t f o r t he l e a rne r t o

do.

F i na l l y , i t i s i mpor t a n t t o s t r e s s t ha t t he l e a rn i ng ou t c ome w e - - a l ong w i t h H a l a s z

& M o r a n ( 1 9 8 2 ) - - i m a g i n e ,

is

tha t a re l a t ive ly comple te , expl i c i t and va l id

model

o f

the t a rge t domain i s a t t a ined . They sugges t tha t th i s can be achieved by expl i c i t ly

present ing a represen ta t ion of the mo de l to the (pass ive ) l ea rner . In cont ras t , we sugges t

tha t me taphor can s t imula te the l ea rner to ac t ive ly se l f -genera te a mode l .

F i gu re 1 s c he ma t iz e s t he ro l e o f me t a pho r a s me d i a t o r i n t he c ons t ruc t i on o f a

k n o w l e d g e r e p r e s e n t a ti o n f o r s o m e t a r ge t d o m a i n . T h e o u t c o m e o f t he c o m p r e h e n s i o n

proc e s s is no t a n unde r s t a n d i ng o f s ome m e t a phor i c a l de s c r i p t i on o f t he ta rge t doma i n

per se

bu t ra the r a repre senta t ion of the doma in i t s e lf tha t is to say , a men ta l mode l .

T he ro l e o f me t a phor ma y va ry , bu t c ruc i a l l y , i t s e rve s t o d r a w t he c ompre he nde r ' s



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