And I cherish more than anything else the Analogies, my most trustworthy masters. They know all the secrets of Nature, and they ought to be least neglected in Geometry (Johannes Kepler, quoted in *(Gentner, 1980, p. 1))
There is no word which is used more loosely, or in more variety of senses, than Analogy (John Stuart Mill)
According to David Leary, "all knowledge is ultimately rooted in metaphorical (or analogical) modes of perception and thought" *(Leary, 1990, p. 2). If he is right, then science would be no exception. Volumes have been written about analogies and metaphors in science (Edge, 1974; Gentner, 1980; Hesse, 1966), and this section could easily become larger than the rest of the book put together. In order to simplify a complex problem, we will rely heavily on a framework created by Holyoak and Thagard, in part because it relies on mental models:
Many cognitive scientists agree that people and other animals make predictions by forming mental models, internal structures that represent external reality in at least an approximate way...Analogy takes us a step beyond ordinary mental models. A mental model is a representation of some part of the environment. For example, our knowledge of water provides us with a kind of mental model of how it moves. Similarly, our knowledge of sound provides us with a kind of model of how sound is transmitted through the air. Each of these mental models links an internal representation to external reality. But when we consider the analogy between water waves and sound propagation, we are trying to build an isomorphism between two internal models. Implicitly, we are acting as if our model of water waves can be used to modify and improve our model of sound. The final validation of the attempt must be to examine whether by using analogy we can better understand how sound behaves in the external world (Holyoak & Thagard, 1995, p. 33).
Metaphors and analogies move novices', childrens' and experts' mental models into to the unknown. The use of metaphor and analogy is therefore a weak, or general heuristic, dependent on mental models of the source and target domains for its success.
What is the difference between metaphor and analogy? Let us consider an example. Experts frequently use analogies to build bridges from the known to the unknown. Historically, psychologists have used a variety of analogies to understand the mind, likening it to a telephone network and, more recently, to a computer (Leary, 1990). This analogy becomes a metaphor when the word 'like' is dropped: the mind is a computer. This metaphor is powerful, but researchers need to remember it is a metaphor. Interestingly, the study of analogy has provoked a wealth of computational models (Hofstadter, 1995)--powerful and interesting, but all reflexive uses of analogy to study analogical reasoning!
An even more common metaphor is that brain corresponds to mind. Most psychologists and biologists would not think of this as a metaphor at all--it is Truth. Metaphors are only dangerous when they are confused with Truth. Here's where metacognition plays a major role: practitioners need to realize they are creating metaphors and analogies, which may not totally capture the target. In Chapter 4, we will have more to say about distributed cognition, but the idea is simple: aspects of mind are in the world. For example, the computer I am using to write this contains portions of my memory, in the form of references, related articles, diagrams, and schedules. I could argue that important aspects of my mind are not in my brain.
Holyoak and Thagard (Holyoak & Thagard, 1995) identify three constraints that must be satisfied by a good analogy:
1. Similarity: The source of the analogy and the target must share some common properties. Both minds and computers process and store information; both can be used to solve problems.
2. Structure: Each element of the source domain should correspond to one element of the target domain, and there should be an overall correspondence in structure. Here the mind/computer analogy becomes more slippery. Because the structure of mind is unknown, experts like Herbert Simon and his colleagues look at the structure of the computer, infer that the structure of the mind could be the same, and conduct experiments to explore the parallels. So, for example, a traditional information-processing model inferred that human beings had a working memory that corresponded roughly to the RAM on a computer. Both computers and humans also have long term memory storage, parts of which can be placed in working memory and combined with inputs when solving problems. The bottleneck is working memory, which seemed to have a limited capacity in human beings. Here the structure of the analogy begins to break down--even personal computers can now have huge amounts of RAM.
Newer connectionist and neural net perspectives can also construct models of the mind consistent with the structure of their metaphors, especially since neural nets are based on an explicit analogy with the structure of the human nervous system. Here the analogy requires a further step: mind is the same as brain which is like a neural net. As we will see below, the identity of mind and brain is questionable.
3. Purpose: The creation of analogies is guided by the problem-solver's goals. Analogies are not fixed forever--as new information comes in, they can be modified. If one's goal is to understand the mind, then there is no reason not to engage in what Seifert et al. call 'opportunistic assimilation' (Seifert, Meyer, Davidson, Patalano, & Yaniv, 1995). They argue that this process occur during the incubation phase of discovery, when the problem-solver has reached an impasse; she or he stays on the alert for new information and assimilates it to achieve a solution. When an analogy reaches and impasse, it can leave a problem-solver or even an entire field primed to search for alternate mental models.
Holyoak and Thagard have applied the computer metaphor to their own work, creating a computational simulation called, ARCS, Analog Retrieval by Constraint Satisfaction. Basically, ARCS builds up a set of excitatory and inhibitory links among object and predicate pairs. The authors use as an example the analogy between Saddam Hussein's invasion of Kuwait and Hitler's occupation of Czechoslovakia. Hussein-Hitler is an example of an object pair; invade-occupy is an example of a predicate pair. These two pairs would share an excitatory link, which would have a weight associated with it. Pairs like Czechoslovakia-Kuwait and Iraq-Kuwait would share a negative weight. Given these similarities, ARCS should settle onto an analogical structure which resembles the one used by President Bush, if the initial weights and links are set up in the right way. As with Thagard's ECHO, one could also set up the links from another perspective, say that of one of the critics of Bush's invasion.
ARCS allows one to model almost any analogical structure. It is a reflexive application of the computational metaphor to the study of metaphors. ARCS can mimic the performance of human participants in experiments, allowing us to construct hypotheses to account for their performance. It would be useful to see ARCS applied to a detailed case.
In the next chapter, we will consider Bell's use of the ear as an analogy for a telephone; perhaps a future version of ARCS will be able to take on this or a similar case, although the notion of a mental model may be hard to reduce to computational form. Ippolito & Tweney clarify that mental models are "dynamic representations of dynamic systems rather than static replications of real-world objects. The emphasis on the dynamic is intended to convey a conception of mental models as more akin to organisms than to devices that can be reduced to the enumeration of structures or translated into machine language" (Ippolito & Tweney, 1995, p. 234). There are certainly computational frameworks that can accommodate organic evolutionary structures--genetic algorithms, for example--but the point is it will take a very sophisticated, dynamic structure to simulate the development of mental models, especially if we include metacognition as an important component.
In Section 1.1, we discussed the role of analogies in Kepler's discovery of his three laws. Holyoak and Thagard include a list of additional analogies that have been used in science (Holyoak & Thagard, 1995), including:
1. Sound and water waves, proposed by the Greek Chrysippus in the second century B.C. and the Roman Vitruvius in the first century A.D.
2. Light and sound: Huygens proposed this analogy in 1678. Newton's particle theory eclipsed it until experiments by Thomas Young and Augustin Fresnel established that light could behave like a wave. Bohr later argued that the particle and wave views of light should be argued as complementary, and explicitly made an analogy to the yin-yang sign (Holton, 1973).
3. Bacterial mutation and a slot machine: In 1943, Salvador Luria "reasoned that if bacteria become resistant because of gene mutations, then the numbers of resistant bacteria in different bacterial cultures should vary like the expected returns from different kinds of slot machines" (Holyoak & Thagard, 1995).
4. The atom as a solar system: Gentner (Gentner & Clement, 1988) has used this particular analogy to illustrate her structure-mapping theory:
The basic intuition is that an analogy is a mapping of knowledge from one domain (the base) into another (the target), which conveys that a system of relations that holds among the base objects also holds among the target objects. Thus, an analogy is a way of noticing relational commonalties independently of the objects in which those relations are embedded....To take a familiar example, in the Rutherford analogy between the solar system and the hydrogen atom, the intended interpretation consists of a set of common relations: that the nucleus is more massive than the electron (just as the sun is more massive than the planet), that the nucleus attracts the electron, that this plus the mass relation causes the electron to revolve around the nucleus, and so on. Object descriptions are disregarded; there is no attempt to match the nucleus with the sun in color, size or temperature (Gentner & Clement, 1988, p. 313).
This analogy created a new mental model of the atom, one my generation of science students carried in their heads for years. Unfortunately, it is misleading in certain respects. Nils Bohr proposed a new model in 1912 in which electron orbits were not like planetary ones; they were more like rungs of a ladder, with the electrons only at the rungs and not in between. Electrons could switch between rungs by absorbing or giving off a photon. He also proposed that the atomic nucleus was more like a drop of water than a body like the sun. "The force that stuck the nucleus together was the nuclear strong force. Counteracting that strong force was the common electrical repulsion of the positively charged nuclear protons. The delicate balance between the two fundamental forces made the nucleus liquid-like. Energy added from the outside by particle bombardment deformed it; it wobbled like a liquid drop, oscillating complexly just as the braided streams of water Bohr had studied for his dissertation had oscillated" (Rhodes, 1986, p. 228).
Meitner and Frisch were able to use this mental model to explain a paradoxical result obtained by their colleague, Otto Hahn. When uranium was bombarded by neutrons, it appeared to leave a residue of Barium, an element far down the periodic table. As Hahn said in a letter to Meitner, "We understand that (uranium) really can't break up into barium...So try to think of some other possibility" (Rhodes, 1986, p. 253). Meitner and Frisch used Bohr's water drop analogy. The electrical repulsion of the 92 protons in the Uranium nucleus was almost great enough to counteract the strong force that created the surface tension holding the nucleus together. In effect, the Uranium nucleus was a wobbly drop; when it was hit by a neutron, it could oscillate into an elongated drop that contained two bulbs; electrical repulsion could drive the bulbs so far apart they would split into two separate nuclei of elements well down the periodic table (Rhodes, 1986, pp. 258-9).
Based on his studies of molecular biology laboratories, Dunbar speculates that most of the scientfic analogies that cross domains may be used more for explanation than in discovery. Of 99 analogies proposed by the scientists in his study, only two were outside of biology. Kepler's analogy between a ferryman and a planet circling the sun clearly crosses domains and therefore is distant (see 1.1). Kepler claims this analogy had an important role in his thinking. Bohr's water drop is probably distant also, although both atomic nuclei and the behavior of water drops can fall under physics. Again, Meitner and Frisch claim this analogy was important. Dunbar might counter that scientists retrospective accounts of their discoveries are unreliable; in interviews conducted months after the laboratory meetings, Dunbar's scientists did not remember that they had made extensive use of analogies. In contrast to authors like Boden (Boden, 1990)who argue that analogies are used to resturcutre and transform scientific knowledge, Dunbar found that they were used as scaffolding to make a series of small changes in problem representation. After a new representation was adopted by the group, the scaffolding was thrown away to the point where the scientists could not even remember using it (Dunbar, 1997).
This apparent discrepancy would probably not surprise Thomas Kuhn. Dunbar's laboratories illustrate normal science at its best--small, incremental changes in the structure of knowledge, contained within a paradigm. Distant analogies are probably most useful in times of scientific revolution, when it is necessary to think 'out of the box'. It would be interesting to do a fine-grained study like Dunbar's of a laboratory during a period of reovolutionary science and see if there was a switch to more remote analogies.
How do expert and novice scientists differ in their use of analogies? Clement (1991) asked ten PhDs or advanced doctoral students in physics, mathematics or computer science to solve problems like determining what happens when the width of the coils on a spring are doubled and the suspended weight is held constant. The participants used local analogies to solve these sorts of problems, for example, imagining what would happen if the coils were replaced by a U-shaped spring of the same length. Here once again we see the experts trying to strip away what is irrelevant, to create a simpler problem that falls into a familiar category. They also used heuristics like counterfactual reasoning that were employed by participants working on abstract tasks, but only when pressed to justify their solutions more thoroughly. This move was consistent with Popper's notion that reasoning is most useful during the justification phase of scientific inference.
Clement concluded that novices should be taught the heuristic value of analogical reasoning, which could help them form the kinds of mental models used by experts. For example, Clement showed how novices could gradually learn that static objects can exert forces. Clement used a series of bridging analogies--first, a hand pressing on a spring, then a book on a foam pad and then finally a book on a table (Clement, 1991).
We need more expert-novice comparisons under controlled conditions on problems that encourage spontaneous analogy generation. Furthermore, these comparisons, and the resulting educational applications, should focus more on the issue of metacognition. How do we turn novices into reflective practitioners (Bredo, 1994) that can use expert techniques effortlessly on familiar problems, but also adapt, modify or even abandon approaches in their quest for discovery? Earlier in this chapter, we discussed reflexivity: the idea that social scientists should apply their methods to themselves as well as the objects of their study. In order to be reflexive, you have to be reflective--you have to be able to distance yourself from your problem-solving activity and evaluate it, especially when an approach isn't working. As we will see in Chapter 5, this kind of reflection ought to involve ethical considerations.
This page was last edited: Wednesday, July 14, 1999