The Analogical Animal
The key to human cognition may well be the
ability to compare one thing to another.
By DOUGLAS HOFSTADTER And EMMANUEL SANDER
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
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
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
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
—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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