The Analogical Animal

The key to human cognition may well be the ability to compare one thing to another.


At (one of his) White House Correspondents Dinner, resident Barack Obama got some laughs when he said that his advisers had suggested he start his speech "with some jokes at my own expense, just take myself down a peg. I was like, 'Guys, after 4½ years, how many pegs are there left?' "

In this remark, few of us would immediately think of "take myself down a peg" as an analogy, but that's what it is: a comparison between two things, in this case, between the president's standing and pegs on a board. Mr. Obama did it again later in his speech, complimenting journalists "who took the time to wade upstream through the torrent of digital rumors to chase down leads and verify facts." "Wade upstream" and "torrent" qualify as analogies, too.

In fact, once you start to look for analogies, you find them everywhere, not just in the metaphors and other figures of speech used by politicians. It is by way of analogy that human beings negotiate and manage the world's endless variety. We would make an even grander claim: that analogies lie at the very center of human cognition, from the humblest of everyday activities to the most exalted discoveries of science.

When you use the elevator in an unfamiliar hotel, for instance, you tacitly depend on the analogy with countless elevators you have used before. You know that you are most likely to find the elevator by looking for a recessed area in the wall of a corridor, and when you reach that area you expect (and find) a button at a standard height. You expect doors that slide open sideways.

Once inside the elevator, you have to choose a small button you have never seen before, and you must press it with a certain force. You do all of this without thinking about it. You unconsciously depend on prior experiences with thousands of buttons in hundreds of elevators, and you seek the best way to deal with this new button by relying on an analogy between it and your personal category button.

Much the same could be said for when you wash your hands in a sink you've never seen before with a piece of soap you've never touched before, and of course it's also thanks to analogy that you deal successfully with the never-before-seen bathroom door, doorknob, electric switch, faucet and towel.

Consider the 2-year-old child who delightedly states, "I undressed the banana!"; or the 8-year-old who asks his mother, "How do you cook water?"; or the adult who inadvertently blurts out, "My house was born in the 1930s." Each of these spontaneous utterances reveals an unconsciously-made analogy that contains a deep rightness despite a surface wrongness.

In short, we all depend on a never-ending stream of very simple analogies between everyday things, and these mini-analogies follow on the heels of one another all day long, day in, day out. A common piece of folk wisdom says that analogies, by their very nature, cannot be relied on—yet in order to survive, we all depend on this incessant stream of mundane analogies. If the myriad analogies pervading and defining our daily life were intrinsically unreliable, no one would be here to tell the tale or to hear it.

What is true at the prosaic level is just as true at the level of profound scientific insight. In physics, for instance, the greatest breakthroughs by the most creative minds—-Newton, Maxwell, Heisenberg, Einstein—were all the fruit of analogies. An excellent example is Einstein's 1905 hypothesis of a deep parallel between an ideal gas (a container filled with molecules) and a black body (a container filled with electromagnetic radiation but nothing material). He was led to this guess because he had noticed a curious mathematical similarity linking the formulas giving the energy spectra of these systems.

This initially spotted similarity suggested to him that the connection between the two systems might well extend far below the surface. Following this intuition, Einstein carefully calculated each system's entropy (the disorder present in it), manipulating the two formulas until they looked almost identical. In the formula for the ideal gas's entropy, the letter N appeared, standing for the number of molecules in the gas; in "the same spot" in the formula for the black body's entropy, there was an expression that could be interpreted as counting the number of times a certain very small energy would "fit" into the total energy in the black body.

Einstein had compressed the distinction between these two physical systems down into a tiny but telling contrast. He took this hint seriously, interpreting it as telling him that a black body itself contains a vast number of immaterial "molecules of radiation"—particles analogous to the N material molecules in the ideal gas. Even for its finder, this was a profoundly radical idea, because electromagnetic radiation included light.

Einstein's analogy had suggested to him that light might well consist of small packets of energy analogous to molecules, but this idea flew in the face of the most solidly established facts about light. Looking back, Einstein declared his "light-quantum" hypothesis, based on but one intuitively felt analogy, to be the most daring idea of his life. Indeed, it unleashed among his colleagues an incredibly intense barrage of hostility that lasted many years.

And yet in 1923, Arthur Holley Compton discovered that when an electromagnetic wave "collides" with an electrically charged particle, what ensues doesn't obey Maxwell's equations for light waves but the rules of collisions between particles. To the astonishment of physicists, the behavior Compton reported agreed exactly with Einstein's 1905 predictions. Thus light, at long last, became particulate! Einstein's little-known analogy constitutes an example of human intelligence at its very finest.

The making of analogies allows us to act reasonably in situations never before encountered, furnishes us with new categories, enriches those categories while ceaselessly extending them over the course of our lives, guides our understanding of future situations by recording what happened to us just now, and enables us to make unpredictable, powerful mental leaps. The attempt to put our finger on what counts in any given situation leads us at times to seeing hidden links between situations despite enormous differences on their surface, and at other times to drawing crucial distinctions between situations that on first glance seem nearly identical.

Analogy, one can say without exaggeration, is the very fabric of our mental life. —Messrs. Hofstadter and Sander are the co-authors of "Surfaces and Essences: Analogy as the Fuel and Fire of Thinking," which has just been published by Basic Books.

A version of this article appeared May 4, 2013, on page C3 in the U.S. edition of The Wall Street Journal.

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