Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (36 page)

Does each of these categories exist in everyone’s mind? There’s little reason to think so. The fact that none of them has a standard lexical name is a cue that they don’t crop up very often in real life, and for that reason, it seems unlikely that these categories would be universal. On the other hand, it is probable that most people have come across, at least fleetingly, a number of these categories, although perhaps without being consciously aware of doing so.

Who among us has not, at some point or other, swiped a paper clip or a Post-it from a friend without asking, or a piece of paper, or perhaps a piece of chewing gum or a candy that was lying around? Clearly it would be unthinkable to swipe a friend’s pen or tie clip, let alone a pretty decorative item on the mantelpiece. And surely, now or then, you must have been annoyed at yourself when you realized that you forgot to pick up some salt or some napkins during the grocery store run you just got back from. How many of us feel perfectly fine about helping ourselves to French fries with our fingers, but wouldn’t dream of eating string beans that way? How often have you heard, “Hey,
somebody’s
gotta eat it, don’t let it go to waste!” in connection with the last olive in the bowl, the last slice of cheese, or the last piece of cake, which nobody dared to take for fear of looking discourteous? In some languages there is a standard phrase for this phenomenon — in Spanish, it’s “el pedazo de la vergüenza” (more often just “el de la vergüenza”), and in Italian, “il pezzo della vergogna” (both translatable as “the morsel of shame”) — but in English no such phrase seems to exist, at least as of yet.

As soon as one starts paying attention to categories of this sort, one realizes that many of them had already been created and were present in the recesses of one’s memory, ready to bubble up when needed, whereas others, though not already present, could easily be manufactured on the spot. Although such categories are usually too trifling or too esoteric to merit anointing with standard lexical labels, they nonetheless provide excellent evidence for the constant churning of categories in our minds.

We turn now to analogies of a special type that people perceive not only effortlessly but wordlessly, and that will most likely seem so elementary and simple-minded that many readers will at first probably balk at calling them analogies at all.

What could be more natural than saying “sitting right
there”
and pointing at a specific spot? To be sure, the young woman hadn’t really been
there
— far from it! In fact, it would be a good exercise to list as many differences as possible between the two
there
’s, and then to think of a number of other circumstances in which someone might have said, “sitting right
there”
, and in which his daughter would have understood
perfectly easily just what he meant. (For example, they might have been traveling in a bus or an airplane rather than a commuter train, or he might have pointed one seat ahead or two seats behind…) The chatty young woman had obviously not been sitting
there
in the strict sense of the word, but although the man was not telling his daughter the truth on a
literal
level, he was nonetheless telling her the truth on a different level — an
analogical
level — and that’s how we communicate all the time: with a minimum of effort and a maximum of very simple analogies.

This may strike you as an example of a
lexicalized
category — namely, the category denoted by the word “there”. But the word was accompanied by a gesture, which was crucial. The category that was retrieved in his daughter’s mind was triggered by the combination of a word and a gesture. Rather than the vast and vague concept that would be evoked by the word “There!” in the absence of any context, the man triggered in his daughter’s mind an infinitesimal subset of the full set of
there
’s that exist in theory — namely, just seats in a train (or perhaps a bus, a plane, a boat, etc.) that are across an aisle from where one is sitting (or across from where someone whom one knows is sitting, or was sitting, or would have been sitting, and so forth). By deploying a word–gesture combination, the man tried to indicate to his daughter the
analogous
spot, within the current frame of reference, to the spot where the chatterbox had been sitting. The spontaneous creation of this new concept — at once very general, since it could work in so many contexts, and also very specific, since it is so precise and so concrete — allowed the daughter to imagine very vividly the situation that her father had experienced during his train ride the other day: communication via finger-pointing analogies can be extremely efficient.

In a situation that is “roughly of the same sort”, a young professor has been invited to give a talk at a prestigious research institute. To her astonishment, she sees, in the middle of the front row, an elderly professor whom she has long admired, and who she would never have dreamed would come to hear her speak. During her talk, he listens with clear interest, and at the end he asks a simple but incisive question, and even does so with a sense of humor. The lecturer is thrilled. When she returns to her own university, she meets with her graduate students in her office, and says, “It was fantastic! Professor X was sitting right
there
!” And so saying, she points to the empty space between two of her students, straight in front of her. And she’s quite right, because in a sense Professor X had indeed been
there
, even
exactly
there — but in another sense of course he hadn’t in the least been
there.
Nonetheless, the implicit analogy easily wins the competition against nitpicky logic and petty-minded precision.

Someone might say that what the urban commuter and the young professor did was not merely “roughly of the same sort” but
exactly the same.
True enough — and yet, in order to see that what they did was “exactly the same thing”, one has to ignore almost all the details of the two situations in order to extract from them one single shared essence.

Here’s yet another situation of “roughly the same sort”. Two participants at the annual meeting of the Cognitive Science Society run into each other unexpectedly at a certain press’s display, and one of them exclaims, “Didn’t we run into each other right here last time?” It matters little that the event “last time” took place some five years earlier at an anthropology conference in another city on another continent, and at a rival press’s display. Even so, it was indeed “here”.

And then, returning momentarily to our meta-analogies, would it not seem that this is “exactly the same analogy” once again? In this case, the unspoken background behind the word “here” is a specific display in the publishers’ showroom at a specific meeting, but the category blurs outwards from this specific publisher and meeting to include other publishers, other rooms, other meetings, other cities, other years, and so on. The conference participant unconsciously, and perfectly reasonably, assumes that her colleague will understand the implicit context, which plays the role of the hand gesture in our previous examples. The meaning of “here” in her sentence is thus just a tiny subset of all the possible meanings of “here” that might exist in theory.

The following two anecdotes will help shed light on the subtleties of
there
situations. A music lover arrives in a great city in whose largest cemetery his favorite composer is buried. Early one morning, as a gesture of homage, he makes his way to the cemetery, but to his dismay, he finds the entrance locked. He decides to walk around the cemetery to see if there is another entry. After 45 minutes, he finds himself right back where he started, but now he happily discovers that in the meantime the main entrance has been opened, so he can make his pilgrimage. That evening, he returns to his hotel around midnight, and, to his shock, he discovers that the front door is locked, and a circuit of the building reveals that there is no other way to get in. Luckily, another client shows up just then and opens the door with a night key, letting him in as well. Tired and relieved, he goes up to his room and sits down on the bed. As he looks at the door, he notices that on it there’s a small map of the hotel showing how to escape in case of a fire. He places his finger on the map and says, “Here I am at the locked main door!” Then, sliding his finger on the map, he runs it all around the hotel, retracing in his mind the circuit he just made on foot. Right at the halfway point he smiles, for this finger-circle reminds him of his walk around the cemetery that morning. As he finishes up his circular gesture he says, “And when I’d gone all the way around the cemetery, I wound up
here
!” His single circle has done double duty for him.

And now we come to a middle-school science teacher, who starts out by drawing in the middle of the board a yellow circle, then adds some smaller objects rotating around it. All her students recognize this as the solar system, a topic that they just covered in class. Then she says, “Today you’ll see that this same picture works for atoms, too. And so
here
[so saying, she touches one of the planets and makes a large circular gesture
that applies to all the planets at once] some electrons are in orbit, and
there
[pointing at the yellow sun-dot in the middle] is what is called the nucleus.” This orbital analogy, which uses scientific terms, might seem to be more sophisticated than the tourist’s down-to-earth analogy, but is that really the case? Both analogies merely map a
large
circular gesture onto a
smaller
one using a single diagram, after all.

Far be it from us to suggest that the act of saying “Right
there
!” while pointing with one’s finger would be deserving of a Nobel Prize in physics, and yet such a banal act is remarkably close to the profound analogy that links the atom and the solar system. That discovery was made collectively, around the turn of the twentieth century, by brilliant scientists, both experimentalists and theoreticians, from many countries; among them were Hantaro Nagaoka, Jean Perrin, Arthur Haas, Ernest Rutherford, John Nicholson, and Niels Bohr. The images at the heart of this analogy were extremely elusive at that time, and it took remarkable intellectual daring, supported by a large number of empirical findings, to come up with such bold ideas. And yet only a few decades later, the educational system had fully integrated these once-revolutionary ideas, and it is in this sense that understanding the analogy between the solar system and the atom’s structure is not all that different from understanding analogies that we all make, day in and day out, totally off the cuff, when we say “here” or “there”.

It’s a common thing for people to convey their understanding of a situation that someone else just described by nodding and saying, “Exactly! That’s what always happens!”, or “I’ve often seen that before”, or else “The same thing has happened to me a bunch of times.” The blandness of such comments masks their subtlety.

Above all, these kinds of frequent and banal-sounding utterances are intended to convey the idea that in spite of the novelty, uniqueness, and complexity of the situation just described, there is nonetheless in it an essence that one is familiar with, and that although no single word or phrase that one knows captures that essence, one has already lived through such an experience, either personally or vicariously. One is saying, in effect, “Of course what you just recounted was a unique, one-of-a-kind event, but even so, I’ve been there myself. I can recall a number of events sharing the exact conceptual skeleton of your story, and so I understand deeply — in fact, perfectly — what you went through.”

We’ll now take a look at some specific examples of this phenomenon, all taken from real-life conversations, and on their surface so bland that few people would pay any attention to them, and yet much richness lurks in them.

Tom’s minimalist answer hardly seems to be overflowing with cognitive complexity. No one would believe that it harbors deep mysteries that it would take an Einstein to make sense of. And yet, Tom’s act of uttering “Me too” and Paul’s act of understanding it did in fact take considerable cognitive agility.

First of all, Tom didn’t mean he would do
exactly
the same thing as Paul — namely, pay for Paul’s beer. That idea wouldn’t occur to anyone. What he did mean, of course, was that he would do something analogous. But what? A natural thought is that Tom meant he would pay for his own beer. That’s a reasonable interpretation, but he hadn’t had a beer; actually, he’d sipped a Coke while munching some peanuts. Did his “me too” thus mean that he would pay for
those
items? Actually, no — he wasn’t intending to
pay
for anything. Since he was an invited speaker, his expenses were covered by the conference’s budget. His intent was thus to put the peanuts and Coke on his room’s account.
That’s
what Tom meant when he said, “Me too.”

Tom’s tiny remark thus turned out to be surprisingly complex, and indeed, in the “geometry” of situations, there are seldom if ever truly parallel lines. In this case, what was “parallel” to Paul’s beer was not
one
thing but a
pair
of things (provided one accepts a large number of peanuts as just “one thing”). Moreover, one item in this pair was not a beer and the other wasn’t even a drink at all. Mapping such a pair of entities onto a beer hence requires a non-negligible amount of
conceptual slippage
(letting one concept play the role of another). And the same can be said for the mapping of Tom’s hotel account onto the change in Paul’s pocket (or the bills in his wallet, or perhaps his credit card). Tom’s casual “me too” really means, if one looks closely, “I understand the intention you just described concerning the situation you’re currently in, and it’s my intention to do the analogous thing in the corresponding situation that I find myself in.”