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IN 1854, English mathematician George Boole published – an influential book whose topic was not psychology, as one might expect, but logic. In Boole’s day, the processes underlying human thinking were assumed to belong to the domain of logic, because everyone knew that what distinguished humans from animals is that we reason while animals do not. This was seen as the hallmark of the human mind. In the 20th century, psychologists studied children’s thinking but paid scant attention to adult thinking, since logic was clearly its key. Around 1960, however, British psychologist Peter Wason found many circumstances in which adult thinking was anything but logical. This led to much research that explored approaches other than logic.

Among the new avenues explored by psychologists was analogy. It was Aristotle who first discussed analogies, focusing on cases of the form “A is to B as C is to D”. Psychologists, recognising that analogical thought went well beyond these so-called “proportional analogies”, explored its role in problem-solving and everyday reasoning. This was certainly a marked advance, but even so, in psychology conferences today, the topic of analogy is generally covered only in sessions that deal with reasoning processes; it tends not to be seen as playing a central role in cognition but as a sophisticated reasoning tool drawn on only under special circumstances.

Yet analogies, far from being unusual cognitive gems, are mundane events, being generated several times every second, and it is through them that we manage to orient ourselves in the world. Analogical thought involves the perception of important but often hidden commonalities between two mental structures, one already existing in our brain, representing some aspect of our past experience stored in an organised fashion, and the other one freshly constructed, representing a new circumstance in our lives. In essence, an apt analogy allows a person to treat something new as if it were familiar. If one is willing to let go of surface attributes and to focus on shared properties, one can take advantage of past knowledge to deal with things never seen before.

“Analogies, far from being unusual cognitive gems, are generated every second”

If we had to deal with the world without depending on our past, we would be like perpetual newborns for whom each sensation is absolutely novel. Luckily, however, although we are forever facing brand-new situations, they are not unprecedented situations. Think of an elevator in an unfamiliar hotel. To use it, you unconsciously depend on prior experiences in many other locales. You have a non-verbal intuition for how to recognise the slightly recessed area in a corridor where an elevator will most likely be found, and for where one or more “call buttons” will be found on the wall. You expect a “ding” when an elevator car arrives and on an inner wall by the door you expect to find a panel of buttons; moreover, you know how to use buttons thanks to experience not just with elevators, but with computer keyboards, TV remotes, car dashboards. All these analogies at many scales spring unbidden to your mind. Some involve trivialities while others have serious consequences. Indeed, were you suddenly deprived of your ability to make analogies, your life would be a bewildering chaos.

If one looks out for them, analogies crop up everywhere. This holds especially for the use of words to label new situations, since labelling anything involves ignoring its details and replacing it by an abstract analogue. So, for instance, the unfamiliar creature you see in front of you is not understood by taking into account each and every one of its countless unique features; it becomes simply a dog, or perhaps a poodle. This unique structure, carefully designed by an architect and painstakingly built by a crew, is simply a bridge. And on it goes. Consider the sentences “I see the light at the end of the tunnel”, “I hear she’s back!”, “I smell a rat in their offer”, “I was touched by your gesture”, “I can taste victory!” Seeming to invoke our five senses, they are actually abstract analogies, involving anticipation, discovery, guessing, emotion and enjoyment.

Analogies pervade our discourse and reveal how we think, often unconsciously, about many situations. Consider these sentences, painting argumentation as war: “His attacks targeted her religious beliefs”; “She destroyed him in the debate”; “After much sniping, the couple finally called a truce”. But arguments are not only like battles; they are also like buildings. “He constructed a baroque argument”; “Your idea has no foundation”; “Her reasoning collapsed”; “Their conclusion was riddled with structural weaknesses”.

Every conversation is peppered with analogies, but that does not mean analogies are mostly verbal phenomena. Language may convey analogies that are not rooted in language. For example, when a bank was failing and stockholders were clamouring for its president to resign, someone said, “When a ship’s sinking, you don’t throw the captain overboard.” This was much easier to understand than an elaborate argument would have been, yet it involves numerous abstract mappings: bank as ship, financial crisis as sinking in the ocean, president as captain, and a call for resignation as throwing someone overboard. Though expressed in words, those mappings did not originate in language.

Analogy is the motor driving the build-up of concepts throughout our lives. Concepts, rather than being neat boxes into which all entities can be precisely, objectively and mechanically sorted, are fluid mental structures that, through many successive analogies, evolve continually. For example, 1-year-old Timmy’s first word is “mommy”, and he uses it to designate his own mother. However, his mother is not a static thing, but a constantly varying pattern of things, at whose core Timmy has identified something stable and invariant. Already we are dealing with abstraction and analogy-making, but Timmy’s initial concept “mommy” is merely the foundation of a future skyscraper.

Soon he will realise that other children, too, have mommies. Then he will enrich his category “mommy” by adding the mothers of cats and monkeys. However, he has not yet realised that his own parents also have mommies. A year later, he will laugh when told he once resisted this idea. At this point, “mommy” has given birth to the more abstract category “mother”, which is reaching out tentacles of abstraction to embrace mythological mothers, motherlands, motherboards and even the maternity celebrated in “Idleness is the mother of philosophy”.

Consider computers, often touted as the most revolutionary development in centuries. Ironically, though, we deal with them through analogies with pre-computer notions:

“Would you please see if you can find the ‘Bills’ folder on my desktop? In it there should be a document dated yesterday. Please copy it and put the copy in my file of urgent things to take care of, and also please send me a copy of it. Lastly, would you please tidy up my folder full of files to catalogue? Just throw away what I don’t need, and when you’ve done that, please empty the trash. When you’ve finished, don’t forget to close all the open windows. Thanks!”

Thirty years ago, this would have been unambiguous, but today one cannot tell if it is talking about objects on a physical desk or icons on a screen. Much as Timmy’s concept “mommy” yielded to incessant analogical pressures and grew, so “desktop” has also witnessed a remarkable extension in recent decades. Today’s virtual desktops are linked with older desktops through the abstract fact of being workspaces.

Naive understanding

If analogies underlie conceptual development, they must be crucial to learning. Indeed, analogies influence how we understand school subjects, and their influence often persists for decades. Take division. Schoolchildren who hear “A mother divides 20 marbles among 4 children” make the analogy to sharing. This limited view of division is called a “naive analogy”, because it relies on everyday knowledge, and because it is helpful yet in some ways misleading. For instance, it suggests that divisions always reduce the thing being divided, as that is the nature of sharing (5 is smaller than 20). Moreover, the divisor has to be a whole number, as that is also the nature of sharing (try to divide 20 marbles among π children). Lastly, the dividend has to exceed the divisor for everyone to get something (how to distribute 20 marbles to 25 kids?).

When division problems meet these implicit constraints, they are easy to solve, but when they do not, the success rate declines dramatically. Consider these problems: (1) “With 15 roses, I can make 5 bouquets. How many roses will be in each bouquet?” (2) “15 friends buy 5 kilograms of cookies and divide them up. What does each friend get?” Research shows that 93 per cent of adolescent students can solve the first, but only 28 per cent solve the second.

Most adults cannot invent a division problem that “comes out bigger” (where the answer exceeds the quantity being divided) because of the unconscious analogy they make with sharing, which is incompatible with the stipulation – yet such problems are legion. For instance, “How many ribbons half an inch long can I make from a ribbon eight inches long?” A measurement analogy is better than a sharing analogy here. It is clear that naive analogies can help or hinder: sometimes they give a ready-made recipe that works fine, but at other times they are inapplicable.

Analogical thinking operates also in abstract realms, such as scientific discovery. Many important scientists have stressed the centrality of analogies in their thought processes. The Hungarian mathematician George Pólya wrote: “Analogy pervades our thoughts, our daily talk, and our most humdrum inferences, but it also pervades artistic expression and great scientific discoveries.”

Albert Einstein’s thought was rife with analogies. In the 19th century, it was established beyond doubt that light consists of electromagnetic waves. Experiments showed that light behaved analogously to sound and water waves, and the Scottish physicist James Clerk Maxwell found a wave equation for light. The case was watertight. Yet in 1905, Einstein pondered an analogy between an ideal gas (molecules bouncing about inside a container) and a black body (a vacuum-filled container in which immaterial light waves bounce about like ripples on a pond). After some calculations, he wound up with two formulae – one for each system – that looked identical except for one exponent. For the ideal gas, the exponent was the letter N – the number of molecules – while for the black body, the analogous exponent was the total energy divided by a certain tiny energy. Einstein guessed that mother nature was whispering to him that inside the black body the energy was carried by exactly that number of molecules of light, analogous to the N gas molecules. This idea contradicted everything about light that contemporary physicists believed, yet the analogy was so compelling to Einstein that, despite universal scorn, he stuck to his guns. Finally in 1923, experiments by Arthur Compton revealed that Einstein’s idea was right. The photon was finally recognised.

If analogy is cognition’s core, does that mean we are irrational beings? Although analogical thought is not deductive, analogies constantly provide us with insightful inferences, leading us to make hypotheses about new situations on the basis of experiences with situations in our past. For instance, if we “place” a “folder” on a virtual “desktop” and walk away for a break during which no one else “touches” it, we assume it will still be sitting there when we come back. All this comes courtesy of analogy. We depend on analogical conclusions thousands of times a day – in fact, we bet our lives on them all the time. Will that man walking towards me push me into the traffic? I have no proof he won’t, but my experience with other people tells me that doesn’t happen.

“Will that man walking towards me push me? My experience with others tells me that doesn’t happen”

Underpinning rationality

Is calling analogy the core of cognition incompatible with the idea that thinking can be objective, and that there exist truths reachable by pure thought? Not at all. An analogy merely furnishes a fresh perspective, as do microscopes, telescopes and many other devices. Benjamin Franklin, one of the US’s founding figures, saw an analogy between lightning and electricity, and made predictions based on it. Former US president Lyndon Johnson thought of Vietnam as a domino that, if it fell, might cause neighbouring dominoes to topple. As it turned out, Franklin was right and Johnson was wrong. Indeed, analogies can be put to the test just as conclusions from a chain of reasoning can. The fact that many points of view can be taken on any given situation does not mean truth has gone down the drain.

Is analogy the core of cognition? Yes. Is analogy irrational, subjective and concrete? Yes indeed, but it is also the underpinning of rationality, objectivity and abstraction. Analogy is not a rare luxury of thought or an exotic, remote corner of cognition. Analogy is the entire transport system of thought, including motorways, roads and trails; it pervades thinking, from throwaway remarks to deep scientific and artistic insights. All along the spectrum, analogy lets us see the new in terms of the familiar. It guides us in learning new concepts, solving mathematical problems, dealing with interpersonal conflicts and making political decisions.

Analogy is the machinery that allows us to use our past fluidly to orient ourselves in the present. Through millions of analogies over our lives, we build vast numbers of robust, flexible categories; through analogies made in fractions of a second we retrieve apt categories based on subtle cues that reveal what counts in a situation and what doesn’t. In this way we survive in the world, understand the world and enjoy the world. It is now psychology’s turn to use analogy profoundly in order to better understand the human mind.

This article appeared in print under the headline “The forgotten fuel of our minds”