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Gentner, D. and Gentner, D.R Generative Analogies as Mental Models Dedre Gentner Subject explaining electric current: If you in- to predict the set of inferences that should follow crease resistance in the circuit, the current slows from use of a given analogy; (2) contrast two analogi- down. Now thats like a high--cars on a highway cal models for the domain and show that they lead to where you--if you notice as you close down a lane, different indirect inferences; (3) to show that peoples you have cars moving along. Okay, as you go down inferences concerning simple circuits vary according to into the thing, the cars move slower through that which of these models they use; and finally (4) to narrow point. discuss the general issue of analogical models and structure-mapping. When people are reasoning about an unfamiliar do- main, they often appear to use analogies, as in the A structure-mapping theory of analogy. The claim above example from a protocol. Analogies are also used here is that analogies select certain aspects of exist- in teaching, as in the following excerpt: ing knowledge, and that this selected knowledge can be The idea that electricity flows as water does is a structurally characterized. First, lets consider what Picture the wires as pipes carrying good analogy. an analogy is not. An analogy such as water (electrons). Your wall plug is a high-pres- (1) An electric circuit with a battery and resistor sure source which you can tap simply by inserting much like a plumbing system with a reservoir a plug. The plug has two prongs--one to take the and a constricted section of pipe. flow to the lamp, radio, or air conditioner, the clearly does not convey that all of ones knowledge second to conduct the flow back to the wall. A about the plumbing system should be attributes! to the valve (switch) is used to start or stop flow. circuit. The inheritance of characteristics is only If implicit or explicit analogies are an important partial. This might suggest that an analogy is a weak determinant of the way people think about complex sys- similarity statement, conveying that some but not tems, then it becomes crucial to know exactly how such all of the characteristics of the base system apply to analogies work. This paper considers the psychological the target system. But this weak characterization fails role of these analogies in structuring the target to capture the distinction between literal similarity domain. and analogical relatedness. Contrast statement (1) with The first question that must be posed is whether a literal similarity statement like such seeming analogical models do in fact strongly (2) A hose is like a pipe. affect the persons conceptualization of the target The literal domain (the Generative Analogy hypothesis), or whether similarity statement (2) conveys that the pipe and they are merely convenient ways of talking about the the hose share object attributes--e.g. cylindrical domain (the Mere Terminology hypothesis). The mere use shape--as well as sharing similar relationships with of terms borrowed from a given domain--as, for example, other objects--e.g. CONVEY (hose, water)/CONVEY (pipe, when electricity is discussed in terms of moving vehi- water). Statement (1) also conveys considerable overlap cles or flowing water--is not in itself proof that the in functional relations: e.g. I MPEDE (resistor, current) speaker is conceiving of electricity as deeply analo- /IMPEDE (constriction, water). However, it does not gous to traffic or to water flow. convey overlap of objects and their attributes. The To demonstrate that an analogy has generative con- resistor as a separ to object need not have any quali- ceptual power, we must show that nontrivial inferences ties in common with A constriction. The analogy, in specific to the base occur in the target. These infer- short, conveys overlap in the system of relations ences must be such that they cannot be attributed to among objects, but no particular overlap in the charac- shallow lexical associations; e.g. it is not enough to teristics of the objects themselves. The literal find that the person who speaks of electricity as similarity statement conveys overlap both in relations "flowing" also uses terms such as "capacity" or among the objects and in the attributes of the indivi- "pressure". Such usage is certainly suggestive of a dual objects. Generative Analogy, but it could also occur under the The analogical models used in science can be Mere Terminology hypothesis. characterized as structure-mappings between complex The goal here is to show that, at least some of systems. In these analogies, the objects of the known the time, the Generative Analogy hypothesis holds: domain, the base domain, are mapped onto the objects of that deep, indirect inferences in the target follow the domain of inquiry, the target domain; the predicates from use of a given base domain as an analogical model. of the base domain--particularly the relations that hold To do this, we must first decide what inferences should among the nodes--are then applied in the target domain. follow from use of a given analogy, and then observe Structure-mapping analogy asserts that identical opera- whether the analogies people adopt appear to affect the tions and relationships hold among nonidentical things. set of inferences they readily make. The relational structure is preserved, but not the The plan of this paper is (1) to propose a objects. structure-mapping theory of analogy that will allow us Given a particular propositional representation of knowledge we can proceed with an explicit charac- terization of analogical mapping. A structure-mapping analogy between a target system T and a base system B This research was supported by the Office of Naval Re- search and was carried out at Bolt Beranek and Newman and at U.C.S.D. Donald Gentner collaborated on all aspects of this work, but particularly in developing the two analogical models of electricity. I thank Allan Collins, Ken Forbus, Ed Smith and Al Stevens for many insightful comments on this research. Please address correspondence to Dedre Gentner, Bolt Beranek Newman, 50 Moulton Street, Cambridge, MA 02138. 9 7 To model of imple elecic cici. One common analog ed o each imple elecici i baed on plmbing em. Fige 1 ho he ce-mapping coneed b hi analog. The objec-node of he hdalic bae domain (e.g. he eeoi and conic- ion) ae mapped ono he objec-node (he bae and eio) of he cici. Gien hi coepondence of node, he analog cone ha he elaionhip ha hold beeen he objec and objec-aibe of he hdalic em alo hold beeen he node of he elecic em: fo eample, ha cen inceae ih olage j a ae of ae flo inceae ih Combinaional poblem. One a o obee deep pee; and ha cen deceae ih eiance indiec infeence in he age domain i o ak j a he ae of ae flo deceae ih degee abo diffeen combinaion of componen. Fo eample, of conicion. e can ak ho he cen in a cici ih o ei- A econd kind of analog fo elecic cici i o in eie o in paallel compae ih ha in a baed on objec moing hogh che. Cen i imple one-eio cici. The ane ae no ob- een a a moing cod of mall objec: olage i he io. The fo cici geneaed b eie and paa- foad pee o phine of he objec. Like he llel combinaion of baeie and eio ae non- plmbing model, he moing-objec model poide ela- anpaen. The poide an ecellen a o obee ion ha map efll ino he elecical em: If e infeence, a oppoed o hallo ebal aocia- e imagine a oce of phine coeponding o he ion. To dedce he cen in hee fo cici, bae, and gae in he che coeponding o he he peon m moe beond he fi-age naie model eio, hen he moe phine, he highe he ae of cici (hon in Fige 1). Thi fi leel of of aggegae moion; he naoe he gae, he loe i nigh i ha baeie make fo moe cen, ei- he ae of aggegae moion. o make fo le cen. Thee le hold fo baeie and eio in eie, b no fo paallel combinaion, a hon in Fige 2. Paallel baeie Alhogh hee o analogie cone man of he gie he ame cen a a ingle em, no moe; ame elaion, in ome epec he diffe in he hile paallel eio allo moe cen han in a apne of he elaional mach ih he age domain, imple cici, no le. paiclal if e conide lighl moe comple cici (ee Genne and Genne, in pe.) 98 Figure 2. CROWD MODEL Current and voltage in simple serial and parallel Again I have all these people coming along configuration circuits. here. I have this big area here where people are milling around. I think it is crucial SIMPLE CIRCUIT CURRENT VOLTAGE that I separate them though before they get x At x At x to the gates . I can model the two gate system by just putting the two gates right into the arena just like that. So this is one possible model of the two gate system. There are two gates instead of one which seems to imply that the resistance would be y I V half as great if there were only one gate R for all those people. SERIAL' BATTERIES This protocol suggests that models do affect infer- x ences. The following study tests this possibility more on a larger scale.
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