Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (120 page)

In this regard, it is interesting to read what Henri Poincaré, whom we cited earlier concerning the way mathematicians are guided by analogies, had to say about Einstein. In a letter of reference for the young man who had applied for a position as professor in 1911, he wrote:

A contemporary of Johann Sebastian Bach once said that “as soon as Bach heard a theme, he was very quickly able to imagine all of its consequences”. That sounds very much like the quality in Einstein that Poincaré praises so highly! It would thus seem that this ability to “imagine all the possibilities” in a very short time lies close to the core of human creativity at its highest levels.

If we examine the pathway that Einstein took to reach the extended principle of equivalence (which applies to all phenomena of physics, not just to those of mechanics), we see that he re-exploited, in a new context, an analogy that he had already exploited once. More specifically, he carried out the same conceptual extension in two different contexts, each time starting with the concept of
mechanical experiment
and ending up with the more abstract concept of
physical experiment.
Each of these extensions was of course due to an analogy — namely, the vertical analogical leap that amounts to the thought: “Physics is
analogous
to mechanics; it’s just that it includes more.” (Recall the similar vertical analogical leap of Doctor Gelenk, who thought, “Joints are analogous to knees, only they are a more general biological notion.”) And Einstein used this analogical leap in two situations that were themselves analogous (first in extending the principle of Galilean relativity to yield special relativity, and later in extending the restricted principle of equivalence to yield the founding ideas of general relativity). Thus, the most advanced breakthrough of Einstein’s life came out of an analogical leap that was analogous to another analogical leap — thus an analogy between analogies, or, if you will, a meta-analogy.

This recalls a remark once made by the Polish mathematician Stefan Banach, as recounted by his friend Stanislaw Ulam: “Good mathematicians see analogies between theorems or theories, but the very best ones see analogies between analogies.” And along the same lines, Einstein’s Scottish predecessor James Clerk Maxwell once observed that rather than being attracted by parallels between different principles of physics, he was attracted by parallels between parallels, which would certainly seem to be the quintessence of abstraction.

To sum things up, what Einstein’s creative life illustrates so clearly is that the perception of profound and abstract analogies in the vast tree of science has the effect of shaking not just a twig or a branch, but the trunk itself. If ever anything made the earth tremble, it was the analogies discovered by Albert Einstein.

Our book ends with a dialogue in which two friends, Katy and Anna, argue about what lies at the core of cognition. Katy sees categorization as playing that role, and she is persuaded that it differs in many ways from analogy-making. Anna sees analogy-making as lying at cognition’s core, though she agrees with Katy about categorization’s importance; indeed, she does her best to show that analogy-making and categorization are one and the same thing by finding weaknesses, point by point, in Katy’s arguments.

The following table summarizes the nine dimensions along which Katy claims that categorization and analogy-making differ significantly.

A careful examination of these potential distinctions leads, as will shortly be seen, into territory lying well beyond the question as to whether analogy-making and categorization constitute just one thing or different things. It raises issues concerning how we perceive the world, how we form concepts, how we understand, and how we communicate. In short, it opens up the entire question of the nature of thought.

But our two protagonists, in their spirited exchange, will surely make all this far clearer than we could, and so, without further ado, we’ll give them the floor.

The telephone rings
.

K
ATY
: Hello! Who is it?

A
NNA
: Hello, Katy, it’s Anna. I hope I’m not waking you, at this early hour.

K
ATY
: Oh, no — not at all. As a matter of fact, just a few minutes ago I woke up from a strange dream in which you and I were having a lively telephone call. Actually, it wasn’t an ordinary phone call — it was a heated argument! And it was taking place in Chinese, of all things. How
that
was possible, I don’t have the foggiest idea (or the cloudiest, for that matter), since I don’t speak a single word of Chinese!

A
NNA
: Are you serious? Exactly the same thing just happened to me!

K
ATY
: How odd! But
exactly
the same?

A
NNA
: Well, sort of — you know what I mean. Something very similar —
almost
exactly the same. To be specific, I too just woke up from a strange dream, and in
my
dream, just as in yours, you and I were having a heated argument on the telephone! But in mine, our debate was all taking place in Russian — and as to how
that
could have happened, well, I don’t have any concept (not even the tiniest one), since, as you well know, I couldn’t utter a word in Russian to save my life!

K
ATY
: What a weird coincidence! One dream, dreamt simultanously by two different people! It sounds like a fairy tale! What was the nature of our heated argument in your dream?

A
NNA
: To tell the truth, I don’t recall at all. I guess that makes sense, since I literally didn’t know what I was talking about, speaking as I was in Russian! And in
your
dream, what was our argument about, Katy?

K
ATY
: Well, I have to admit that I don’t remember a single word of it either, since everything I said was in Chinese, of which, as you well know, I am totally ignorant. Is truth not stranger than fiction?

A
NNA
: Well, I wouldn’t know, but dreaming is certainly a strange phenomenon. The mind leaps about in such fantastic ways.

K
ATY
: The human mind is profoundly mysterious, I agree. Thinking is the most elusive phenomenon under the sun, even though we do it all the time. Shouldn’t its nature be crystal-clear to us, since it’s the medium in which we swim? Or perhaps it is murky and miraculous precisely because it’s so ubiquitous.

A
NNA
: I fully agree with you, Katy, and actually, this brings me right around to the reason that I phoned you so early in the morning. Lately, you see, I have been thinking a great deal about thinking, and I’ve come to the surprising conclusion that there is one special type of mental process that lies at the very core of it all. I wonder if you can guess what it is.

K
ATY
: What a coincidence! I, too, have been thinking about thinking, Anna, and I, too, have identified a special mental process that I believe lies at thought’s very core. Would it not be astonishing and wonderful if both of us had independently stumbled on the very same idea?

A
NNA
: Oh, yes — that would be a delightful surprise. So let me tell you straight off what my candidate mental process is. For me, the key mechanism underlying all of thinking is
the making of analogies
— the spotting of a link between something one is just experiencing now and something one has experienced before. An analogy can summon up any aspect of our past, and thus, when we face a new situation, we can bring to bear the closest experiences we have ever had. In a word, analogy-making is the mechanism at the basis of all thought.

K
ATY
: Analogy-making, eh? Now there’s an off-the-wall candidate! It’s certainly not what I would have proposed. I see we have rather divergent views on the topic. So let me come straight out as well, and put my cards on the table:
categorization
, not analogy-making, is where I think the secret of our minds lies. Categories grow out of our experiences and they organize our mental libraries; categories are the building blocks of thought, and categorization is the magical key to all of thinking.

A
NNA
: Oh, really? So you would say that categorization is more important than analogy-making in the life of the mind? Tell me how you see things, Katy.

Categorization is a
constant necessity;
analogy is a
rare luxury

K
ATY
: Gladly! In the process of thinking, nothing is more pervasive or essential than the assignment of things and situations to known categories. To simplify the world, we constantly have to carve it up into standard, familiar pieces; otherwise, we would find ourselves overwhelmed by a tidal wave of constant novelty. After all, each moment and each situation that we face is different from all other ones we have already experienced, even if only slightly so. Each time you blink, shift your gaze, breathe in or breathe out, move your lips or nostrils or eyebrows, your face is a little different from how it was a hundredth of a second earlier. And each of these micro-movements you make changes, even if only infinitesimally, the perspective from which you see the table in front of us. And as our surroundings change from moment to moment, the only way for us to orient ourselves is to sort the incoming stimuli into familiar, reliable categories, such as
table
, even if we have never seen that specific table before. What is around us is always changing, and if we didn’t continually categorize it all, thus simplifying it into stable regularities, our environment would seem to us like utter chaos. Everything would be novel and
unknown, and our heads would forever be spinning. My ability to recognize a novel thing as being, say, a
chair
, a
table
, a
breeze
, a
look of surprise
, or a
thinly veiled threat
, is due to the fact that I have already developed these categories, and I have a huge repertoire of them. Without that storehouse, I would be unable to recognize any of the recurrent features of the world around me. So it’s categorization that allows me to survive in this unpredictable world. That’s my view, my dear Anna.