Analogy

analogyimagesThis post is long in coming.  It is surprising that analogy has not come up before in over 70 posts.  I can certainly recall times when someone convinced me with a clever analogy, and then it turned out to be dead wrong.  Nevertheless,  we need analogy and we are vulnerable to analogy. It seems to me that we try to turn our love of stories, anecdotal evidence, into analogies sometimes to generally bad results.  Keith Holyoak is one of the leaders in trying to understand how humans use analogy.  This post and the next two posts will use his work in an article:  “Thinking, Broad and Deep” a review of Surfaces and Essences, Analogy as the Fuel and Fire of Thinking by Douglas Hofstadter and Emmanuel Sander, May 2013, and his chapter in the Oxford Handbook of thinking and reasoning, 2012.

Holyoak in his review asks what makes human thinking special?  He notes that in addressing the American Psychological Association in 1955, physicist Robert Oppenheimer made the case for the centrality of analogy: “Whether or not we talk of discovery or of invention, analogy is inevitable in human thought, because we come to new things in science with what equipment we have, which is how we have learned to think, and above all how we have learned to think about the relatedness of things.”

Holyoak suggests that Hofstadter and Sander’s thesis—analogy is the core of cognition—is less (or more) radical than it might sound, as they extend analogy to include “categorization through analogy- making.” Categories are not fixed and final products but are endlessly extensible by analogy. Waves on water come to embrace sound waves, then light waves, then spin waves, and then probability waves, as the concept wave becomes increasingly abstract. Holyoak believes that the authors convincingly refute those enthusiasts of embodied cognition who assume that because concepts are typically grounded in human perception and action, abstraction has been explained away. No: “abstraction is key, and to leave it out of one’s theory of thinking is to miss the boat by a wide margin.” Holyoak enjoys the examples in the book:  lofty scientific analogies are foreshadowed by the “banalogies” of everyday cognition. An elderly father driving by a cemetery baffles his adult son with the remark, “This is where all four of your grandkids were born”—the intended “all four of your grandparents are buried” fell victim to analogical slippage. As a child analogizes a toy truck to a real one, so Galileo analogized from Earth’s one-of-a kind Moon to hypothesize the moons of Jupiter (exemplifying “meta-analogy”).  As Oppenheimer observed, “We cannot learn that we have made a mistake unless we can make a mistake; and our mistake is almost always in the form of an analogy to some other piece of experience”.

Holyoak in his chapter explains that two situations are analogous if they share a common pattern of relationships among their constituent elements, even though the elements themselves differ across the two situations. Identifying such a common pattern requires comparison of the situations. Analogy involves some of the same processes as do judgments of similarity . Typically one analog, termed the source or base, is more familiar or better understood than the second analog, termed the target. By “better understood,” we mean that the reasoner has prior knowledge about functional relations within the source analog—beliefs that certain aspects of the source have causal, explanatory, or logical connections to other aspects. This asymmetry in initial knowledge provides the basis for analogical transfer—using the source to generate inferences about the target. For example, the earliest major scientific analogy, dating from the era of imperial Rome, led to a deeper understanding of sound (the target) in terms of water waves (the source). Sound is analogous to water waves in that sound exhibits a pattern of behavior corresponding to that of water waves: propagating across space with diminishing intensity, passing around small barriers, rebounding off of large barriers, and so on. The perceptual features are very different (water is wet, air is not), but the underlying pattern of relations among the elements is similar. In this example, like most analogies involving empirical phenomena, the key functional relations involve causes and their effects. By transferring knowledge about causal relations, the analogy provides a new explanation of why various phenomena occur. Analogy is an inductive process, and hence analogical inferences are inevitably uncertain. The wave analogy for sound proved  successful; an alternative “particle” analogy did not.

Holyoak looks at analogy as a key example of the broader concept of role-based relational reasoning and looks at the history of research on analogy.  Analogies have  figured prominently in science and mathematics, and they are often used in everyday problem solving as well as creative cognition. In legal reasoning, the use of legal precedents (relevant past cases) to help decide a new case is a special case of analogical reasoning. Analogies can function to sway emotions, to influence political views, to guide consumer decisions, and to teach mathematics. Analogy is sometimes used as part of a rational argument, using systematic connections between the source and target to generate and support plausible (though fallible) inferences
about the latter.

Figure 13.1 from Holyoak’s chapter sketches the major component processes in analogical transfer. Typically, a target situation serves as a retrieval cue for a potentially useful source analog. It is then possible to establish a mapping—a set of systematic correspondences that serve to align the elements of the source and target. Based on the mapping, coupled with the relevance relations within the source, it is possible to elaborate the representation of the target and derive new inferences. In the aftermath of analogical reasoning about a pair of cases, some form of relational generalization may take place yielding a more abstract schema for a category of situations (as in the case of the evolving “wave” concept), of which the source and target are both instances.

The history of the study of analogy includes three interwoven streams of research, which respectively emphasize analogy in relation to psychometric measurement of intelligence, to metaphor and language, and to the representation of knowledge.  Metaphor and the representation of knowledge will be included in future posts.

Work in the psychometric tradition focuses on four-term or “proportional” analogies, in the form A:B::C:D, such as HAND:FINGER::FOOT:?, where the problem is to infer the missing D term (TOE) that is related to C in the same way B is related to A. The pair A:B thus plays the role of source analog, and C:D that of target. Proportional analogies were discussed by Aristotle, and in the early decades of modern psychology became a centerpiece of efforts to define and measure intelligence. Charles Spearman argued that the best account of observed individual differences in cognitive performance was based on a general or g factor, with the remaining variance being unique to the particular task. He reviewed several studies that revealed high
correlations between performance in solving analogy problems and the g factor.

Holyoak concludes that analogy is an important special case of role-based relational reasoning, a psychological process that generates inferences based on patterns of relational roles. At its core, analogy depends on comparison of situations,  but analogical reasoning is a complex process of retrieving structured knowledge from long-term memory, representing and manipulating role-filler bindings in working memory, generating new inferences, and finding structured intersections between analogs to form new abstract schemas.  Holyoak believes that symbolic-connectionist models have the greatest promise in relating relational reasoning to its neural substrate.

Holyoak, K. J. (2012). Analogy and relational reasoning.  In K. J. Holyoak & R. G. Morrison (eds.).  The Oxford handbook of thinking and reasoning (pp 234-259).  New York: Oxford University Press.

Holyoak, K. J. (2013). “Thinking, Broad and Deep.”  Science, May 3, 2013, Vol 340, pages 550-551.

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