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Mental Leaps: Analogy in Creative Thought
Analogy—recalling familiar past situations to deal with novel ones—is a mental tool that everyone uses. Analogy can provide invaluable creative insights, but it can also lead to dangerous errors. In Mental Leaps two leading cognitive scientists show how analogy works and how it can be used most effectively. Keith Holyoak and Paul Thagard provide a unified, comprehensive account of the diverse operations and applications of analogy, including problem solving, decision making, explanation, and communication. Holyoak and Thagard present their own theory of analogy, considering its implications for cognitive science in general, and survey examples from many other domains. These include animal cognition, developmental and social psychology, political science, philosophy, history of science, anthropology, and literature. Understanding how we draw analogies is important for people interested in the evolution of thinking in animals and in children; for those whose focus is on either creative thinking or errors of everyday reasoning; for those concerned with how decisions are made in law, business, and politics; and for those striving to improve education. Mental Leaps covers all of this ground, emphasizing the principles that govern the use of analogy and keeping technical matters to a minimum. A Bradford Book
336 pages, Paperback
First published December 7, 1994
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November 28, 2021
The topic of "analogy" is important in numerous, diverse areas, including psychology, artificial intelligence, philosophy, history, politics, law, art, and science. In fact, it's difficult to think of any important type of human activity where analogy can't play a significant role. The discovery and use of analogies seem to be a core function of human cognition. It's important even in non-intellectual activities like "sports", such as soccer and tennis. Certain "patterns" can be recognized repeatedly in all of these areas, and these patterns influence many or even most decisions made by humans. More recently, patterns are detectable by digital computers and devices incorporating them, such as "self-driving" vehicles.
The key question in all cases is: What is it that makes some object, event, or circumstance "like" or "similar to" a different object, event, or circumstance? Answering the question is often very important, because likeness or similarity can be the principal influence on decisions made by an animal, human, or computer.
The book under discussion doesn't treat analogy in quite this much generality. But it still covers a great deal of ground, and a level of abstraction that may be, at times, difficult for general readers to follow. The first two chapters lay the groundwork by presenting in abstract terms what analogies consist of. At the most basic level, an analogy involves some sort of "similarity" between objects, concepts, or events. Most animals with at least some sort of rudimentary brain can detect similarities between different stimuli they can perceive through their sensory organs. For instance, even the simplest animals can distinguish "food" from "non-food" via chemical, auditory, or visual stimuli.
But there's a lot more to analogy than "similarity". At higher levels, "structure" is also important. In the simplest form, such structure could be merely the order of letters in a group of letters: "abc" has a different structure than "cba". Most objects, events, or situations have a number of constituent parts among which there are specific relationships. These relationships determine structure and can make significant differences between things even if they have similar parts. As a young child may have remarked, a dog is recognizable because all of its parts are dog parts, and they're put together in a doggy way.
The third and fourth chapters of the book discuss scientific studies done on the abilities of animals from apes up to young children to recognize increasingly complex analogies. Even human babies in their first year can discern simple patterns, such as favorite toys. A stuffed bear doesn't look quite like a stuffed cat, yet each may appeal to the child for similar reasons. But by preschool or kindergarten age children can perceive patterns far beyond the abilities of even well-trained chimpanzees. That's why formal schooling starts around the same age for most children.
The fifth and sixth chapters cover the use of analogies by adults, especially sophisticated and highly-intelligent adults. In these cases, the purpose of recognizing the "best" analogies among a number of possibilities is considered. The purpose is, typically, problem-solving or decision making. One example is how an army can conquer an enemy fortification. The "best" approach may not be for the attackers to approach the fortification from a single direction, because that enables the defenders to train all their weapons on the entire group of attackers. A better strategy may be for the attackers to divide their forces into several groups and attack from several different directions.
A very different sort of problem is how trained physicians can use radiation to attack a patient's cancerous tumor. In this case, directing the radiation from one fixed source is a bad idea, because that will also harm healthy tissue near the tumor. Instead, such radiation therapy is now done from a source that moves continuously around the patient, so that only the tumor itself is always the main target. The analogy of this case with the previous one is obvious. In fact, this is a pattern that's been used so often and in so many situations that it has a name: "divide and conquer". Strangely, the book doesn't point this out.
Also not mentioned is that the divide-and-conquer technique can be applied in the opposite way. For instance, a software programmer can analyze a problem into different sub-problems that can be handled more easily in known ways. And this can be done recursively, to further divide each sub-problem into smaller units. That's a strategy used by almost all competent programmers. In this case, it's the target problem itself that's being divided. Unscrupulous politicians and their supporters also use this technique to divide and fragment their opposition into quarreling factions.
There's an important point to be made about the use of analogies in dealing with difficult problems or decisions. The point is that several or even many analogies may suggest themselves for the same problem or decision. In that case, among the different analogies, some will prove to be much more successful or cost-effective than others in dealing with the problem or decision. Some, in fact, could be quite disastrous. Choosing the "best" analogy could be a matter of life or death for a patient being treated for disease. Or between victory and defeat in a military battle.
The seventh, eighth, and ninth chapters consider the role of analogies in three different but important areas. The seventh chapter deals with the use of analogies in philosophy. "Plato's Cave" is a noteworthy example. In such cases, analogy is used for explanation, teaching, persuasion, or - perhaps - deliberate deception. The analogies often take specific traditional forms, such as metaphor, symbolism, or mythology. Often such things are used by individuals or groups that want to persuade others to adopt the persuaders' beliefs, doctrines, or ideologies. Many religions, for example, use mythological analogies - such as "Heaven" or the "Garden of Eden" - to deceive their followers into accepting their dogmas. Many politicians and political parties, especially of the authoritarian sort, are similarly duplicitous. (The book under discussion doesn't use these particular examples.)
The eighth chapter is about the use of analogies in scientific study and research. Darwin, for instance, conceived his ideas about evolution partly from a consideration of Thomas Malthus' explanation of how human population growth eventually leads to conflict and strife among people when their numbers rendered available resources inadequate. Evolutionary psychologists have extended this idea to explain not just physical characteristics but also some aspects of human psychology. Hypotheses arrived at by such analogies may prove to be incorrect, because analogies are inexact by their very nature. So analogy is a good technique for formulating hypotheses. But once a hypothesis has successfully been tested rigorously, analogies can be used for explaining the results to others or to extend the conclusions to more general situations.
The ninth chapter deals with the role of analogies in what the authors refer to as the "web of culture". That is, beliefs and feelings shared among people in a particular culture - which may eventually spread to other cultures. Poets, writers of fiction, artists, and creators in other domains (photography, dance, drama, cinema, music, etc.) almost universally use analogies to natural phenomena, social traditions, or previous work in their domain as a source of new ideas. These creative products, which may have been developed by specific individuals or from the general culture are usually the result of adapting analogies to new situations or circumstances. The audience for such creative products is able to appreciate them by analogy to things or experiences they're already familiar with. The products typically involve the use of symbols, metaphors, or similies. Shakespeare, for example, is quite explicit about what he's doing in his Sonnet 18, which begins "Shall I compare thee to a summer’s day?" The Bard points out not only similarities, but also differences, between the one he addresses and a day in summer.
The tenth, and last, chapter discusses attempts to use computers to formulate good, or at least plausible, analogies in a way that emulates how humans analogize. Since the book was published in 1995, and is based on work up to that time, the use of computers in formulating and understanding analogies has evolved in additional directions. The computer model they developed was based on three aspects the authors identify as "similarity", "structure", and "purpose". The last of these, purpose, refers to the intended use of an analogy. These things are called "constraints" on proposed analogies - that is, conditions that a "good" analogy needs to meet in order to be useful. The objective was to emulate on a computer the process by which humans formulate and understand analogies.
One way to think of analogies is as a form of pattern recognition, where what is to be recognized consists of objects, concepts, physical phenomena, etc. Presumably, there are discoverable ways in which humans recognize such patterns. But it's not clear that emulating humans is the only practical (or even possible) way for a computer to recognize patterns. Since 1995, "connectionist" and other techniques for "machine learning" have been developed that can identify patterns entirely from digitized data about whatever is being studied. Obvious examples include recognition of human faces, animal species, weather patterns, social trends, etc. Typically, the data involved is so voluminous that no human could possibly see patterns in the digital data - even in cases (like species or faces), where recognition by human brains may be almost instantaneous.
However, for things of great concern to humans, such as problem-solving or decision making, it's quite unclear how the relevant data could be digitized, or even collected. So the approaches discussed in the book to finding and understanding analogies, or doing almost any creative work, are still very important. The book's subtitle, after all, is "Analogy in Creative Thought".
The key question in all cases is: What is it that makes some object, event, or circumstance "like" or "similar to" a different object, event, or circumstance? Answering the question is often very important, because likeness or similarity can be the principal influence on decisions made by an animal, human, or computer.
The book under discussion doesn't treat analogy in quite this much generality. But it still covers a great deal of ground, and a level of abstraction that may be, at times, difficult for general readers to follow. The first two chapters lay the groundwork by presenting in abstract terms what analogies consist of. At the most basic level, an analogy involves some sort of "similarity" between objects, concepts, or events. Most animals with at least some sort of rudimentary brain can detect similarities between different stimuli they can perceive through their sensory organs. For instance, even the simplest animals can distinguish "food" from "non-food" via chemical, auditory, or visual stimuli.
But there's a lot more to analogy than "similarity". At higher levels, "structure" is also important. In the simplest form, such structure could be merely the order of letters in a group of letters: "abc" has a different structure than "cba". Most objects, events, or situations have a number of constituent parts among which there are specific relationships. These relationships determine structure and can make significant differences between things even if they have similar parts. As a young child may have remarked, a dog is recognizable because all of its parts are dog parts, and they're put together in a doggy way.
The third and fourth chapters of the book discuss scientific studies done on the abilities of animals from apes up to young children to recognize increasingly complex analogies. Even human babies in their first year can discern simple patterns, such as favorite toys. A stuffed bear doesn't look quite like a stuffed cat, yet each may appeal to the child for similar reasons. But by preschool or kindergarten age children can perceive patterns far beyond the abilities of even well-trained chimpanzees. That's why formal schooling starts around the same age for most children.
The fifth and sixth chapters cover the use of analogies by adults, especially sophisticated and highly-intelligent adults. In these cases, the purpose of recognizing the "best" analogies among a number of possibilities is considered. The purpose is, typically, problem-solving or decision making. One example is how an army can conquer an enemy fortification. The "best" approach may not be for the attackers to approach the fortification from a single direction, because that enables the defenders to train all their weapons on the entire group of attackers. A better strategy may be for the attackers to divide their forces into several groups and attack from several different directions.
A very different sort of problem is how trained physicians can use radiation to attack a patient's cancerous tumor. In this case, directing the radiation from one fixed source is a bad idea, because that will also harm healthy tissue near the tumor. Instead, such radiation therapy is now done from a source that moves continuously around the patient, so that only the tumor itself is always the main target. The analogy of this case with the previous one is obvious. In fact, this is a pattern that's been used so often and in so many situations that it has a name: "divide and conquer". Strangely, the book doesn't point this out.
Also not mentioned is that the divide-and-conquer technique can be applied in the opposite way. For instance, a software programmer can analyze a problem into different sub-problems that can be handled more easily in known ways. And this can be done recursively, to further divide each sub-problem into smaller units. That's a strategy used by almost all competent programmers. In this case, it's the target problem itself that's being divided. Unscrupulous politicians and their supporters also use this technique to divide and fragment their opposition into quarreling factions.
There's an important point to be made about the use of analogies in dealing with difficult problems or decisions. The point is that several or even many analogies may suggest themselves for the same problem or decision. In that case, among the different analogies, some will prove to be much more successful or cost-effective than others in dealing with the problem or decision. Some, in fact, could be quite disastrous. Choosing the "best" analogy could be a matter of life or death for a patient being treated for disease. Or between victory and defeat in a military battle.
The seventh, eighth, and ninth chapters consider the role of analogies in three different but important areas. The seventh chapter deals with the use of analogies in philosophy. "Plato's Cave" is a noteworthy example. In such cases, analogy is used for explanation, teaching, persuasion, or - perhaps - deliberate deception. The analogies often take specific traditional forms, such as metaphor, symbolism, or mythology. Often such things are used by individuals or groups that want to persuade others to adopt the persuaders' beliefs, doctrines, or ideologies. Many religions, for example, use mythological analogies - such as "Heaven" or the "Garden of Eden" - to deceive their followers into accepting their dogmas. Many politicians and political parties, especially of the authoritarian sort, are similarly duplicitous. (The book under discussion doesn't use these particular examples.)
The eighth chapter is about the use of analogies in scientific study and research. Darwin, for instance, conceived his ideas about evolution partly from a consideration of Thomas Malthus' explanation of how human population growth eventually leads to conflict and strife among people when their numbers rendered available resources inadequate. Evolutionary psychologists have extended this idea to explain not just physical characteristics but also some aspects of human psychology. Hypotheses arrived at by such analogies may prove to be incorrect, because analogies are inexact by their very nature. So analogy is a good technique for formulating hypotheses. But once a hypothesis has successfully been tested rigorously, analogies can be used for explaining the results to others or to extend the conclusions to more general situations.
The ninth chapter deals with the role of analogies in what the authors refer to as the "web of culture". That is, beliefs and feelings shared among people in a particular culture - which may eventually spread to other cultures. Poets, writers of fiction, artists, and creators in other domains (photography, dance, drama, cinema, music, etc.) almost universally use analogies to natural phenomena, social traditions, or previous work in their domain as a source of new ideas. These creative products, which may have been developed by specific individuals or from the general culture are usually the result of adapting analogies to new situations or circumstances. The audience for such creative products is able to appreciate them by analogy to things or experiences they're already familiar with. The products typically involve the use of symbols, metaphors, or similies. Shakespeare, for example, is quite explicit about what he's doing in his Sonnet 18, which begins "Shall I compare thee to a summer’s day?" The Bard points out not only similarities, but also differences, between the one he addresses and a day in summer.
The tenth, and last, chapter discusses attempts to use computers to formulate good, or at least plausible, analogies in a way that emulates how humans analogize. Since the book was published in 1995, and is based on work up to that time, the use of computers in formulating and understanding analogies has evolved in additional directions. The computer model they developed was based on three aspects the authors identify as "similarity", "structure", and "purpose". The last of these, purpose, refers to the intended use of an analogy. These things are called "constraints" on proposed analogies - that is, conditions that a "good" analogy needs to meet in order to be useful. The objective was to emulate on a computer the process by which humans formulate and understand analogies.
One way to think of analogies is as a form of pattern recognition, where what is to be recognized consists of objects, concepts, physical phenomena, etc. Presumably, there are discoverable ways in which humans recognize such patterns. But it's not clear that emulating humans is the only practical (or even possible) way for a computer to recognize patterns. Since 1995, "connectionist" and other techniques for "machine learning" have been developed that can identify patterns entirely from digitized data about whatever is being studied. Obvious examples include recognition of human faces, animal species, weather patterns, social trends, etc. Typically, the data involved is so voluminous that no human could possibly see patterns in the digital data - even in cases (like species or faces), where recognition by human brains may be almost instantaneous.
However, for things of great concern to humans, such as problem-solving or decision making, it's quite unclear how the relevant data could be digitized, or even collected. So the approaches discussed in the book to finding and understanding analogies, or doing almost any creative work, are still very important. The book's subtitle, after all, is "Analogy in Creative Thought".
July 16, 2024
Having read it almost 30 years after its publication, I can confidently say it's a foundational book for anyone interested in critical thinking. The authors give an excellent overview of what an analogy is, its three key elements, and how analogical reasoning can be used well. Includes pitfalls. Can skip the last chapter, since computational reasoning has moved way beyond what the authors outline.
August 22, 2025
Kinda dated but not in a particularly bad way since I have deep unearned nostalgia for the time before the bitter lesson…
September 14, 2008
320 pages. A quirky book about the science of analogy. I liked the logical progression of it, what animals can use analogy, how do human children use it, how do adults use it. What roles does it play in science, art, religion. How do we use it to trigger memories of similar situations. They conclude with a chapter on the computer program they’ve developed that derives analogies. It’s a fine book, a bit tedious.
I expected it to be more about how to use analogies to increase creativity. It was more about how and why analogies work. I’m a wiser human, but I’m not sure I would recommend it to anyone who didn't already know about it.
I expected it to be more about how to use analogies to increase creativity. It was more about how and why analogies work. I’m a wiser human, but I’m not sure I would recommend it to anyone who didn't already know about it.
Displaying 1 - 4 of 4 reviews