Surfaces and Essences Read online

  Two Misleading Caricatures of Analogy-making

  If categorization is central to thinking, then what mechanism carries it out? Analogy is the answer. But alas, analogy-making, like categorization, is also plagued by simplistic and misleading stereotypes. We therefore proceed straightaway to discuss those stereotypes, in the aim of quickly ridding ourselves of the contaminating and confusing visions that they give of the nature of the motor of cognition.

  The first of these stereotypes of analogy-making takes the word “analogy” as the name of a certain very narrow class of sentences, seemingly mathematical in their precision, of the following sort:

  West is to east as left is to right.

  This can be made to look even more like a mathematical statement if it is written in a quasi-formal notation:

  west : east :: left : right

  Intelligence tests often employ puzzles expressed in this kind of notation. For example, they might pose problems of this sort: “tomato : red :: broccoli : X”, or perhaps “sphere : circle :: cube : X”, or “foot : sock :: hand : X”, or “Saturn : rings :: Jupiter : X”, or “France : Paris :: United States : X” — and so forth and so on. Statements of this form are said to constitute proportional analogies, a term that is itself based on an analogy between words and numbers — namely, the idea that an equation expressing the idea that one pair of numbers has the same ratio as another pair does (A/B = C/D) can be carried over directly to the world of words and concepts. And thus one could summarize this very analogy in its own terms:

  proportionality : quantities :: analogy : concepts

  There is no scarcity of people who believe that this, no more and no less, is what the phenomenon of analogy is — namely, a template always involving exactly four lexical items (in fact, usually four words), and which has the same rigorous, austere, and precise flavor as Aristotle’s logical syllogisms (such as the classic “All men are mortal; Socrates is a man; ergo, Socrates is mortal”). And indeed it was none other than Aristotle who first studied proportional analogies. For him, analogy, understood in this narrow fashion, was a type of formal reasoning belonging to the same family as deduction, induction, and abduction. The fact that many people today understand the word “analogy” in just this narrow way therefore has genuine and valid historical roots. Nonetheless, such a restrictive vision of the faculty of analogy-making leads almost ineluctably to the conclusion that it is such a precise, focused, and specialized type of mental activity that it will crop up only in very rare circumstances (particularly in intelligence tests!).

  And yet analogy, as a natural form of human thought, is not by any means limited to this kind of case. Although each of the proportional analogies exhibited above was intended to have just one single correct response — the so-called right answer — the fact is that the world in which we live does anything but give us a long series of intelligencetest questions in the form of right-answer analogy puzzles. Thus in the case of the “Paris of the United States” puzzle given above, although we ourselves were thinking mostly of New York as “the right answer”, we have collected, in informal conversations, quite a few other perfectly defensible answers, including Washington, Boston, Los Angeles, Las Vegas, Philadelphia, and — of course! — Paris, Texas.

  Indeed, quite to the contrary, the world confronts us with a never-ending series of vague and ambiguous riddles, such as this one: “What disturbing experience in my life, or perhaps in the life of some friend of mine, is meaningfully similar to the sudden confiscation of my eight-year-old son’s bicycle by the principal of his school?” It is by searching for strong, insight-providing analogues in our memory that we try to grasp the essences of the unfamiliar situations that we face all the time — the endless stream of curve balls that life throws at us. The quest for suitable analogues is a kind of art that certainly deserves the label “vital”, and as in any other form of art, there seldom is a single right answer. For this reason, although proportional analogies may on occasion be gleaming jewels of precision and elegance, the image that they give of the nature of analogy-making is wildly misleading to anyone who would seek the crux of that mental phenomenon.

  Another widely held view of analogy (and here we come to the second stereotype) is that when people make analogies, they call on sophisticated reasoning mechanisms that, through intricate machinations, somehow manage to link together far-flung domains of knowledge, sometimes in a conscious fashion; the conclusions reached thereby may be very subtle but will also be very tentative. This vision gives rise to the image of analogies as being the fruit of strokes of genius, or at least of deep and unusual insights. And there are indeed numerous famous cases of this sort that one can cite — great scientific discoveries resulting from sudden inspirations of people who found undreamt-of links between seemingly unrelated domains. Thus the mathematician Henri Poincaré wrote, “One day… the idea came to me very concisely, very suddenly, and with great certainty, that the transformations of indeterminate ternary quadratic forms were identical to those of non-Euclidean geometry.” This flash of inspiration gave rise to much rich new mathematics. One can also admiringly recall various architects, painters, and designers who, thanks to some fresh analogy, were able to transport a concept from one domain to a distant one in such a fruitful way that people were amazed. From this perspective, the making of analogies is a cognitive activity that only a small number of extremely inventive spirits engage in; it happens only when a mind dares to explore highly unlikely connections between concepts, and it reveals relationships between things that no one had ever before thought of as being related.

  This stereotype of analogy-making does not presume that such acts are limited to scientists, artists, and designers; much the same vision of sophisticated reasoning that connects distant domains and leads to daring but tentative conclusions applies to people in everyday life. For example, it is universally accepted that analogy plays a major role in teaching. Most everyone can recall analogies from their schooldays, such as between the atom and the solar system, between an electrical circuit and a circuit in which water flows, between the heart and a pump, or between the benzene molecule and a snake biting its own tail. All of these cases feature connections that link rather remote domains (or, to be more precise, domains that seem remote when only their surface is taken into account). One can also find examples of such analogies in everyday arguments, whether someone is supporting an idea or trying to knock it down. For instance, if everyone laughs in the face of a person who dares to reveal grand ambitions, a natural retort might be, “Laugh all you want; they all laughed at Christopher Columbus!” And in political debate, analogies between far-flung situations play a key role. Thus these days, likening the leader of a foreign country to Hitler as a way to ignite patriotic fervor has become a hackneyed stratagem (for example, the elder George Bush pulled the Hitler analogy out of his hat numerous times in order to justify the first Iraq war), whereas likening a war to the Vietnam war has played precisely the opposite role in the United States (the opponents of the second Iraq war called on the Vietnam analogy over and over again). One even finds such insightful analogies, full of freshness, in childish observations, such as when the daughter of one of this book’s authors, rising to the full mental height of her seven summers, proudly declared, “School is like a staircase; each new grade is one step higher!” Such a joyous moment of enlightenment is, in its humble way, an insight comparable to Poincaré’s joyous insight into abstruse mathematical phenomena.

  To summarize, then, the first of these two stereotypes — proportional analogy — is so formally constrained that if that were all analogy-making amounted to, it would merely be the Delaware of cognition; by contrast, the second stereotype pinpoints a far more important mental phenomenon — namely, the selective exploitation of past experiences to shed light on new and unfamiliar things belonging to another domain. And thus we will spend very little time on proportional analogies in this book; however, it’s quite another matter as far as rich interd
omain analogies are concerned, and we will devote a great deal of attention to them. And yet, despite its clear relevance to our central topic, this second vision of analogy-making is still impoverished, since it vastly under-represents the wide range of mental phenomena to which analogy is connected. Indeed, it completely leaves out the idea that analogy-making is the machinery behind the pulsating heartbeat of thought: categorization.

  Analogy-making and Categorization

  Indeed, the central thesis of our book — a simple yet nonstandard idea — is that the spotting of analogies pervades every moment of our thought, thus constituting thought’s core. To put it more explicitly, analogies do not happen in our minds just once a week or once a day or once an hour or even once a minute; no, analogies spring up inside our minds numerous times every second. We swim nonstop in an ocean of small, medium-sized, and large analogies, ranging from mundane trivialities to brilliant insights. In this book, we will show how the simplest and plainest of words and phrases that we come out with in conversations (or in writing) come from rapidly, unconsciously made analogies. This incessant mental sparkling, lying somewhere below the conscious threshold, gives rise to our most basic, humdrum, low-level acts of categorization, whose purpose is to allow us to understand the situations that we encounter (or at least their most primordial elements), and to let us communicate with others about them.

  A substantial fraction of the myriads of analogies constantly being born and quickly dying in our heads are made in order to allow us to find the standard words that name mundane objects and activities, but by no means all of them are dedicated to that purpose. Many are created to try to make sense of situations that we face on a much larger scale. To pinpoint, in the form of a single previously known concept, the essence of a complex situation that has just cropped up for the first time involves a much more penetrating and global understanding of a situation than one gets from simply smacking labels on its many familiar constituents. And yet this far deeper process — the retrieval of a long-buried memory by an analogy — is so central and standard in our lives that we seldom think about it or notice it at all. It is an automatic process, and virtually no one wonders why it occurs, nor how, since it is so familiar. If asked “How come that particular memory popped to your mind right after I told you what happened to me?”, a typical person might reply, with a bemused tone at being asked such a silly question, “Well, what I remembered is very much like what you told me. That’s why I remembered it! How could it have been any other way?” It’s as if they had been asked, “Why did you fall down?” and answered, “Because I tripped!” In other words, having X, which is in some sense very similar to Y, come to mind when Y occurs and seizes our attention seems as natural and inevitable as falling down when one is tripped — there is no mystery, hence there seems to be no need whatsoever for any explanation!

  The triggering of memories by analogy lies so close to what seems to be the essence of being human that it is hard to imagine what mental life would be like without it. Asking why one idea triggers another similar one would be like asking why a stone falls if one lets go of it three feet above the ground. The phenomenon of gravity is so familiar and obvious to us, striking us as so normal and so inevitable, that no one, aside from a tiny minority of physicists obsessed with explaining what others take for granted, even sees that there is anything to ask about. For most non-physicists, it’s hard to see why gravity needs an explanation — and the same holds for the triggering of memories by analogy. And yet, how many scientific discoveries can hold a candle to general relativity, Albert Einstein’s wildly unexpected revelation of what gravity actually is?

  Categorization and Analogy-making as the Roots of Thinking

  The idea that we will here defend is that a certain mental phenomenon subsumes all the aforementioned stereotypes of categorization and analogy, but is much broader than any of them are, taken in isolation. To give a foretaste of this crucial idea, we turn once again to the theme of zeugmas, because these linguistic oddities have a great deal to do with categorization through analogy. Indeed, zeugmas provide a rich wellspring of examples running the full gamut from the most mundane to the most inspired of analogies; in their own small way, then, zeugmas perfectly reflect the ubiquity and uniformity of the mechanism of categorization by analogy.

  Suppose you heard someone say, “The asparagus tips and the potato dumplings were delicious.” Your ever-ready zeugma detector wouldn’t register a thing, because it would seem self-evident that, in this context, asparagus tips and potato dumplings simply belong to one and the same very standard category (namely, that of scrumptious edibles). But it would feel rather different if someone were to say, “The asparagus tips and the after-dinner witticisms were delicious”, because here one senses that the adjective “delicious” has been used in two quite different senses, and so the needle on one’s zeugma detector would move a bit, and as a result you would feel that a slight analogical link had been suggested between the asparagus tips and the postprandial quips. Then again, were you to hear “The asparagus tips and the expression of surprise on Anna’s face were delicious”, your zeugma detector would register a yet higher reading, meaning that the semantic distance (or interconceptual stretch) was yet greater; this would lead you to see and feel an analogy between the asparagus tips and a certain friend’s facial expression, rather than merely thinking that they both belong to the commonplace category of delicious things.

  In brief, it is misleading to insist on a clear-cut distinction between analogy-making and categorization, since each of them simply makes a connection between two mental entities in order to interpret new situations that we run into by giving us potentially useful points of view on them. As we will show, these mental acts cover a spectrum running from the humblest recognition of an object to the grandest contributions of the human mind. Thus analogy-making, far from being merely an occasional mental sport, is the very lifeblood of cognition, permeating it at all levels, ranging all the way from mundane perceptions (“That is a table”) to subtle artistic insights and abstract scientific discoveries (such as general relativity). Between these extremes lie the mental acts that we carry out all the time every day — interpreting situations, judging the quality of various things, making decisions, learning new things — and all these acts are carried out by the same fundamental mechanism.

  All of these phenomena seem quite different, but underlying them all there is just one single mechanism of nonstop categorization through analogy-making, and it operates all along the continuum we’ve described, which stretches from very mundane to very sophisticated acts of categorization. And it’s this unified mechanism that allows us to understand sentences that run the gamut of zeugmaticity, from complete non-zeugmas (requiring only mundane categorization mediated by very basic analogymaking) to extreme zeugmas (requiring unusually flexible categorization mediated by much more sophisticated analogy-making).

  But let’s take our leave of zeugmas and return to the larger picture. We claim that cognition takes place thanks to a constant flow of categorizations, and that at the base of it all is found, in contrast to classification (which aims to put all things into fixed and rigid mental boxes), the phenomenon of categorization through analogy-making, which endows human thinking with its remarkable fluidity.

  Thanks to categorization through analogy-making, we have the ability to spot similarities and to exploit these similarities in order to deal with the new and strange. By connecting a freshly encountered situation to others long ago encountered, encoded, and stored in our memory, we are able to make use of our prior experiences to orient ourselves in the present. Analogy-making is the cornerstone of this faculty of our minds, allowing us to exploit the rich storehouse of wisdom rooted in our past — not only labeled concepts such as dog, cat, joy, resignation, and contradiction, to cite just a random sample, but also unlabeled concepts such as that time I found myself locked outside my house in bitterly freezing weather because the door slammed shut by accident. S
uch concepts, be they concrete or abstract, are selectively mobilized instant by instant, and nearly always without any awareness on our part, and it is this ceaseless activity that allows us to build up mental representations of situations we are in, to have complex feelings about them, and to have run-of-the-mill as well as more exalted thoughts. No thought can be formed that isn’t informed by the past; or, more precisely, we think only thanks to analogies that link our present to our past.

  The Rapid Inferences that Categories Provide

  A term that will be useful to us in this context is inference. As is traditional in psychology, we will use the term much more broadly than it is used in the field of artificial intelligence, where it is synonymous with “formal logical deduction”, as carried out by so-called “inference engines”. By contrast, what we will mean by “making an inference” is simply the introduction of some new mental element into a situation that one is facing. Basically, this means that some facet of a currently active concept is lifted out of dormancy and brought to one’s attention. Whether this new element is right or wrong is not the point, nor does it matter whether it follows logically from prior elements. For us, “inference” will simply mean the fact that some new element has been activated in our mind.

  Thus if one sees a child crying, one infers that the child is distressed. If one sees someone shouting, one infers that the person is probably angry. If one sees that the table is set, then one infers that a meal may well soon be served. If one sees a door that is closed, one infers that it can be opened. If one sees a chair, one infers that one could sit on it. If one sees a dog, one has the ability to infer (though one does not necessarily do so) that it barks now and then, that it might bite someone, that it has a stomach, a heart, two lungs, and a brain — internal organs that one doesn’t strictly perceive but that category membership allows one to infer. Inferences of this sort are a crucial contribution to thought, and they come from categorization through analogy, for we rely ceaselessly on resemblances perceived between the present situation and ones we encountered earlier. If we did not do this at all times, we would be helpless.