Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (7 page)

The spontaneous categorizations that are continually made by and in our brains, and that are deeply influenced not just by the language we are speaking but also by our era, our culture, and our current frame of mind, are quite different from the standard image, according to which categorization is the placing of various entities surrounding us into preexistent and sharply-defined mental categories, somewhat as one sorts items of clothing into the different drawers of a chest of drawers. Just as one can easily stick one’s shirts into a physical drawer labeled “shirts”, so one would easily assign dogs to the mental drawer labeled “dog”, cats to the nearby mental drawer labeled “cat”, and so forth. Every entity in the world would fit intrinsically into one specific mental “box” or “category”, and this would be the mental structure to which all the different entities
of the same type would be assigned. Thus all bridges in the world would be unambiguously assigned to the box labeled “bridge”, all situations involving motion would be assigned to the box labeled “move”, and all situations involving things standing still would be assigned to the box labeled “stationary”. This mechanism of “boxing” everything in the world would be both automatic and completely reliable, the
raison d’être
of mental categories being to assign entities objectively to their proper conceptual label in an objective, observer-independent fashion.

Such a vision of the nature of categorization is very far from what really goes on, and in the pages to come we will do our best to show why this is so. But hopefully, already from
Chapter 1
onwards, readers will feel persuaded that mental categories are anything but drawers into which clear-cut items are automatically sorted, and this idea will be reinforced ever more strongly as the book proceeds.

What, then, do we mean in this book by “category” and “categorization”? For us, a category is a mental structure that is created over time and that evolves, sometimes slowly and sometimes quickly, and that contains information in an organized form, allowing access to it under suitable conditions. The act of categorization is the tentative and gradated, gray-shaded linking of an entity or a situation to a prior category in one’s mind. (Incidentally, when we use the term “category”, we always mean a category in someone’s mind, as opposed to mechanical labels used in computer data bases or technical labels used in scientific taxonomies, such as lists of the names of biological species.)

The tentative and non-black-and-white nature of categorization is inevitable, and yet the act of categorization often feels perfectly definite and absolute to the categorizer, since many of our most familiar categories seem on first glance to have precise and sharp boundaries, and this naïve impression is encouraged by the fact that people’s everyday, run-of-the mill use of words is seldom questioned; in fact, every culture constantly, although tacitly, reinforces the impression that words are simply automatic labels that come naturally to mind and that belong intrinsically to things and entities. If a category has fringe members, they are made to seem extremely quirky and unnatural, suggesting that nature is really cut precisely at the joints by the categories that we know. The resulting illusory sense of the near-perfect certainty and clarity of categories gives rise to much confusion about categories and the mental processes that underlie categorization. The idea that category membership always comes in shades of gray rather than in just black and white runs strongly against ancient cultural conventions and is therefore disorienting and even disturbing; accordingly, it gets swept under the rug most of the time. Since the nature of mental categories is much subtler than the naïve impression suggests, it is well worth examining carefully.

A category pulls together many phenomena in a manner that benefits the creature in whose mind it resides. It allows invisible aspects of objects, actions, and situations to be “seen”. Categorization gives one the feeling of understanding a situation one is in by providing a clear perspective on it, allowing hidden items and qualities to be detected (by virtue of belonging to the category
person
, an entity is known to have a
stomach
and a
sense of humor
), future events to be anticipated (the glass that my dog’s tail just knocked
off the table is going to break) and the consequences of actions to be foreseen (if I press the “G” button, the elevator will go down to the ground floor). Categorization thus helps one to draw conclusions and to guess about how a situation is likely to evolve.

In short, nonstop categorization is every bit as indispensable to our survival in the world as is the nonstop beating of our hearts. Without the ceaseless pulsating heartbeat of our “categorization engine”, we would understand nothing around us, could not reason in any form whatever, could not communicate with anyone else, and would have no basis on which to take any action.

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 interdomain 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.