Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (11 page)

Chapter 5
is devoted to the role of analogy in very ordinary, everyday situations. It deals with analogies that, because they are essentially invisible, manipulate us. We are unaware of being taken over by an analogical interpretation of a situation. In this sense, the invisible analogy manipulates us because it has simply imposed itself on us, willy-nilly. And it manipulates us also in another sense — namely, it foists new ideas on us, pushing us around. Unsatisfied with being merely an agent that enriches our comprehension of a situation we are facing, the analogy rushes in and structures our entire view of the situation, trying to make us align the newly encountered situation with the familiar old one. For instance, when a small private plane crashed into a building in Manhattan on October 11, 2006, the analogy with the events of September 11, 2001 was irrepressible, leading instantly to speculations of terrorism, even though the building was not seriously damaged; the Dow Jones average even took a noticeable nosedive for a short while. And thus analogies just jump in uninvitedly, thinking and making decisions for us, without our being aware of what is going on.

In
Chapter 6
, by contrast, we deal with analogies that, in some sense, we ourselves manipulate — analogies that we freshly and deliberately construct when we run into a situation that arouses our interest, sometimes in order to explain it to ourselves or to others, sometimes to argue for our own point of view. This is especially the case for what we have dubbed
caricature analogies.
These are analogies that one dreams up on the spur of the moment in order to convince someone else of an idea in which one believes. They transpose a situation into a new domain while exaggerating it. For instance, a scientist seeking a job abroad wrote to a colleague: “I love my native land, but trying to get research done here is like trying to play soccer with a bowling ball!” Also discussed in this chapter is the way in which political decisions at all levels flow from analogies perceived by decision-makers between current situations and historical events, our main case study being some of the key analogies that shaped the Vietnam war. A few studies of inter-language translation conclude this chapter, focusing on the analogies used by skilled people in order to create coordinated parallelisms between two languages and two cultures on many scales, ranging from the very small to the very large.

Chapters 7
and
8
deal with analogy in scientific thinking.
Chapter 7
is concerned with what we call “naïve analogies” — in particular, the kinds of analogies on which nonspecialists tend to base their notions of scientific concepts. We show that notions
that one picks up in school, whether in mathematics, physics, or biology, are acquired thanks to appealing and helpful but often overly simple analogies to concepts with which one is already familiar. Thus an elementary arithmetical operation such as division, which supposedly is totally under one’s belt by the time one starts middle school, is generally still rooted (even in the case of most university students) in a naïve analogy with the down-to-earth operation of
sharing
(as in the act of distributing 24 candies evenly to 3 children). To be sure, sharing is quite often a perfectly good way to look at division, but the view that it affords of the phenomenon is overly narrow. For example, this naïve view of division makes it very hard for people to devise a word problem that involves a division whose answer is
larger
, rather than
smaller
, than the quantity being divided. This chapter analyzes the implications, both positive and negative, of naïve analogies for education.

Chapter 8
then looks at the extreme other end of the spectrum — namely, how great discoveries are made by insightful scientists. We show how the history of mathematics and physics consists of a series of snowballing analogies. By examining from up close certain great moments in the history of these disciplines, we reveal the crucial role played over and over again by analogies — sometimes very obvious ones, sometimes very hidden ones. In particular, the deep analogies of Albert Einstein play a starring role in this chapter, including a little-known analogy that led to his hypothesis in 1905 that light consists of particles, an idea that was mightily resisted by the entire physics community for nearly two decades. The most carefully examined historical episode is that of Einstein’s own slow and gradual process of coming to understand the various levels of meaning of his celebrated equation “E =
mc
²
”.

The epilogue to our book is a dialogue — thus it is entitled “Epidialogue” — in which categorization and analogy-making are compared and contrasted along many dimensions, and although at first the two processes may seem very different, at the end of this careful comparison, the spirited debaters conclude that there is no difference between them, and they realize that in fact they are one and the same.

At every moment we are faced with a new situation. Actually, the truth is much more complicated than that. The truth is that, at every moment, we are simultaneously faced with an indefinite number of overlapping and intermingling situations.

In the airport, we are surrounded by strangers whom we casually observe. Some seem interesting to us, others less so. We see ads everywhere. We think vaguely about the cities whose names come blaring out through loudspeakers, yet at the same time we are absorbed in our private thoughts. We wonder if there’s time enough to go get a frozen yogurt, we worry about the health problems of an old friend, we are troubled by the headline we read in someone’s newspaper about a terrorist attack in the Middle East, we smile to ourselves at a clever piece of wordplay in an ad on a television screen, we are puzzled as to how the little birds flying around and scavenging food survive in such a weird environment… In short, far from being faced with
one
situation, we are faced with a seething multitude of ill-defined situations, none of which comes with a sharp frame delineating it, either spatially or temporally. Our poor besieged brain is constantly grappling with this unpredictable chaos, always trying to make sense of what surrounds it and swarms into it willy-nilly.

And what does “to make sense of” mean? It means the automatic triggering, or unconscious evocation, of certain familiar categories, which, once retrieved from dormancy, help us to find some order in this chaos. To a large extent, this means the spontaneous coming to mind of all sorts of
words.
Without any effort, one finds oneself thinking, “cute little girl”, “funny-looking coot”, “same dumb ad as at the airport I was at yesterday”, “an Amish family”, “sandals”, “what’s she reading?”, “who’s whistling?”, “where is their nest?”, “when are we going to board?”, “what an annoying ring tone”, “how could I have left my cell-phone charger at home?”, “and I did it last time, too”, “the air-conditioning is on too high in here”, and so on.

All these words! No experience is more familiar to us than this ceaseless barrage of words popping up in our mind extremely efficiently and without ever being invited. But where do these words come from, and what kind of invisible mechanism makes them bubble up? What is going on when one merely thinks silently to oneself, “a mother and her daughter”?

To be able to attach the label “mother” to some entity without thinking about it, one has to be intimately familiar with the concept
mother
, which is denoted by the word. For most of us, this intimacy with the concept goes all the way back to our earliest childhood, to our first encounters with the notion. For one-year-old Tim, the core of the concept is clearly his own mother — a person who is much bigger than he is, who feeds him, comforts him when he cries, sings him lullabies, picks him up, plays with him in the park, and so forth. Once this first mental category bearing the name “Mommy” has a toehold, Tim will be able to see that in the world around him there are similar phenomena, or as we prefer to put it, analogous phenomena.

We take a momentary break here to explain a typographical convention of our book. When speaking about a word, we will put it in quotation marks (“table”), whereas when speaking about a concept, we will use italics (
table).
This is an important distinction, because whereas a word is a sequence of sounds, a set of printed letters, or a chunk of silent inner language, a concept is an abstract pattern in the brain that stands for some regular, recurrent aspect of the world, and to which any number of different words — for instance, its names in English, French, and so forth, or sometimes no word at all — can be attached. Words and concepts are different things. Although the distinction between them is crucial and often very clear, there will unavoidably be cases in our text where it will be ambiguous and blurry, and in such cases, we’ll make a choice between italics and quotation marks that might seem a bit arbitrary. Another source of ambiguity is the fact that here and there we’ll use italics for emphasis, just as we’ll use quotation marks to suggest a sense of doubt or approximation (which could sometimes be conveyed equally well by the word “so-called”), and of course we will use quotation marks when we are making a quotation. Alas, the world is simply filled with traps, but we hope that the ambiguities are more theoretical than actual. And with that said, we return to our main story.

One day in the park, Tim, aged eighteen months, sees a tot playing in the sandbox and then notices a grown-up near her who is taking care of her. In a flash, Tim makes a little mental leap and thinks to himself more or less the following (although it’s far from being fully verbalized): “That person is taking care of
her
just like Mommy takes care of me.” That key moment marks the birth of the concept
mommy
with a small “m”. The lowercase letter is because there are two members of this new category now (and of course using uppercase and lowercase letters is just
our
way of hinting at what’s going on in Tim’s head, not
his
way). From this point on, it won’t take Tim long to notice yet other instances of this concept.

At the outset, Tim’s concept of
mommy
still floats between singular and plural, and the analogies in his head will be quite concrete, a comparison always being made to the
first
mommy, which is to say, with Mommy (the one with the capital “M”), but as new instances of the concept
mommy
are superimposed and start to blur in his memory, the mental mapping that Tim will automatically carry out, each time he spots a new grown-up in the park, will start to be made not onto Mommy, but onto the nascent and growing concept of
mommy
— that is, onto a generalized, stereotyped, and even slightly abstract situation, centered on a generic grown-up (
i.e.
, stripped of specific details) and involving a generic child who is near the grown-up and whom the grown-up talks to, smiles at, picks up, comforts, watches out for, and so on.

It’s not our goal here to lay out a definitive theory of the growth of the specific concept
mommy
, as our purpose is more general than that. What we are proposing is that the birth of
any
concept takes place more or less as described above. At the outset, there is a concrete situation with concrete components, and thus it is perceived as something unique and cleanly separable from the rest of the world. After a while, though — perhaps a day later, perhaps a year — one runs into another situation that one finds to be similar, and a link is made. From that moment onward, the mental representations of the two situations begin to be connected up, to be blurred together, thus giving rise to a new mental structure that, although it is less specific than either of its two sources (
i.e.
, less detailed), is not fundamentally different from them.