Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (121 page)

A
NNA
: You’ve made valid and insightful points, Katy, and you’ve clearly shown why
conception
and
perception
are such closely related phenomena. As a matter of fact, they are interchangeable notions, even if common usage tends to distinguish between them, with
perception
supposedly guided by the senses and
conception
supposedly guided by the mind.

K
ATY
: All of this is well and good, but in my view, categorization must be ranked far above the making of analogies. I understand, Anna, that you hold analogies in very high esteem, and surely they merit your esteem, but nonetheless, just think for a moment: analogies are
rare
mental events, far rarer than the sorting of things into their proper categories. Analogies take place only when we are being inventive, when we are inspired to add sparkle and pizzazz to our mental life. When we make an analogy, we rock the boat, connecting two things in a way that we’d never dreamt of before. That lovely
frisson
when we spot a novel connection between ideas or objects or situations is a very gratifying feeling, but alas, it does not arise often. If we never made analogies, our mental lives would be a tad less zesty, no doubt, but our existence would not otherwise suffer in any way. Let me put it this way, Anna: if categorization is the meat and potatoes of cognition, then analogy-making is an exotic spice that one can easily do without. Coming up with an innovative analogy brings delight, that’s for sure, but doing so is a cognitive luxury; one could easily live one’s whole life without ever making a single analogy!

A
NNA
: I subscribe enthusiastically to how you have portrayed categorization, Katy. Categories are the heart and the breath, the motor and the fuel, the roads and the highways of thought, and it would take someone without an ounce of imagination to fail to recognize the utter pervasiveness and indispensability of categorization in the activity of cognition. Nonetheless, I think you delude yourself concerning analogy-making, for it is in fact ubiquitous, every bit as much as categorization.

K
ATY
: That makes no sense to me. I make an analogy only once in a blue moon!

A
NNA
: You underestimate yourself, my friend. Do you recall how in Chapter 7 of this very book several quotations were presented, all taken from writings by various specialists, some of which characterized categorization and others of which characterized analogy-making, and yet the statements were virtually identical? Specifically, there it was stated that both of these mental processes cast new and strange things in a familiar light (“categories allow us to treat new things as if they were familiar” and analogy is what allows us “to make the novel seem familiar”) — and being able to do that is an absolute necessity for survival, is it not? So you see, you make an analogy whenever you recognize the familiar in something unfamiliar.

K
ATY
: Are you suggesting that analogies are as widespread as categorizations are? I don’t see them everywhere — in fact, hardly anywhere. To be convinced, I would need some examples, because to me analogies seem as rare as hens’ teeth.

A
NNA
: In that case, Katy, think of the most ordinary moments in our lives — if you look carefully, you will see that analogies abound in them, like flowers in a spring meadow. Given that analogies allow us to understand the new in terms of the old, they are every bit as common as the assignment of things to categories. Didn’t you just point out, a few moments ago, that any new situation differs in all sorts of ways from all prior situations? Well, then, in order to make sense of a new situation, we have no choice but to relate it to things we have experienced before. This means that we have to make analogies left and right. Moreover, researchers who have studied the role of analogy in human thinking have often pointed out its ubiquity. For instance, the mathematician George Polya wrote: “Analogy pervades all our thinking, our everyday speech and our trivial conclusions as well as artistic ways of expression and the highest scientific achievements.” Along similar lines, the theoretical physicist Robert Oppenheimer declared: “When faced with something new, we cannot help but relate to it except by comparing it with what is familiar and known to us.” Psychologists who specialize in the study of analogy-making are also on the same page. Thus Dedre Gentner has written: “Analogies and metaphors are pervasive in language and thought.” And Keith Holyoak and Paul Thagard have stated: “Analogy is ubiquitous in human thinking.”

K
ATY
: So far you’ve merely given me a bunch of generalities. They are good food for thought, but I told you I want some concrete examples.

A
NNA
: All right, let me try. On what basis do you walk up a staircase that you’ve never laid eyes on before? How do you know how to use a doorbell you’ve never encountered before? How do you know how to turn the knob of a door that you’ve never seen before? How do you know how to use a shower you’ve never used before? And what about sitting on a new chair for the first time, or picking up a magazine you’ve never touched before? How do you know how to flip its pages, effortlessly telling its ads from its articles? Life is filled to the brim with rudimentary analogies like these.

K
ATY
: All these examples are not analogies; they’re just
actions
, not thoughts.

A
NNA
: I challenge you to find the borderline between acting and thinking. Mental activity lies behind every action, and the term “mental activity” is simply a fancy synonym for “thinking”. But if these examples don’t satisfy you, then take a look at Chapters 1 and 2 of this book. They show how the choice of every single word or phrase comes out of analogy-making. What could be more ubiquitous than choosing what word to say next? Then Chapter 3 shows how, through analogy, we are constantly
reminded
by one situation of prior situations, and how, when we come out with such common phrases as “me too”, “next time”, “in general”, “it won’t happen again”, “that’s what always happens”, and many others, we are relying on tacit analogies. For instance, if you say “me too”, don’t you mean “the analogous
thing holds in my case”? And if you say “next time”, what could you mean other than “as soon as an analogous event takes place”? Doesn’t “like that” mean “analogous to that”, just in more everyday language? And so, in short, analogies have no reason to feel outnumbered by categorizations; they are everywhere under foot, being neither rare luxuries nor exquisite delicacies. Analogies are not merely the icing on the cake of cognition — they are the full cake, including the icing!

Categorization is
routine;
analogy is
creative

K
ATY
(
still convinced that categorization and analogy-making are as different as day and night):
I’ve followed your argument, Anna, and I’ll withdraw my claim about the rarity of analogies. I’ll concede that we make analogies all the time, even if most of them are trivialities. It would never have occurred to me before to call such mini-thoughts “analogies”, but you’ve convinced me. Nonetheless, analogies and categorizations are very different beasts. You yourself implicitly admitted this point only moments ago, with your words “the icing on the cake of cognition”. Let me explain. To categorize is to rely on preexisting mental categories. Let’s say that a noisy, furry, four-footed entity is trotting down the street by your side and I assign it to the category
dog.
This connection to a previously acquired notion gives me instant access to many facts, such as that I’m dealing with a living entity, that it has many internal organs, that it could possibly bite and transmit rabies, that it tends to eat meat, that it enjoys being taken for walks, that it might smell bad, and so on. The moment I decide that something belongs to this category, I effortlessly retrieve all sorts of facts that I’ve accumulated over the course of my life about dogs in general or about certain breeds of dogs. But my use of all this knowledge has nothing creative to it. To the contrary, it’s entirely humdrum.

A
NNA
: I have no objection to this; calling a dog “dog” is certainly very mundane.

K
ATY
: Precisely. Whenever we categorize, we merely take advantage of facts acquired in our past. We rely on prior experiences, expecting them to repeat themselves, but we create nothing new. Although categorization pervades every moment of one’s mental life, it is neither inspired nor inspirational. By contrast, your “icing on the cake of cognition” involves originality, creativity, inspiration, and flashes of insight, all of which go way beyond bland uses of prior knowledge. In this sense, analogy deserves praise, because it’s what allows us to creatively connect things that one would tend to think are utterly unrelated. This is how analogy-making is so distinct from categorization. I admit that my observation saddens me a bit, because I would have liked categorization to play a more noble role in thought, but in any case this shows that categorizing and analogy-making are not cut from the same cloth. The former is
routine
, while the latter is
creative
.

A
NNA
(
all smiles):
Well, Katy, I’m going to disagree with you once again, but this time I hope to boost your spirits, because you seem to hold categorization in very low esteem, and I’ll show you that such a negative attitude is unjustified.

K
ATY
: Oh, really? That would make me happy! Please tell me how.

A
NNA
: To begin with, I hope you’ll agree with me that many analogies are anything but creative. In fact, I just gave you some examples — dealing with an unfamiliar staircase, doorbell, doorknob, shower, magazine, and so forth. We constantly make analogies on automatic pilot, without even noticing them, as effortlessly as we breathe. You’ll have to agree that many analogies are dull as dishwater. As this shows, categorization is far from being the gold-medal winner for blandness; analogy-making will give it a good run for its money in that department. But if I understood you rightly, it’s not in terms of dullness that you think the difference resides, but in terms of creativity.

K
ATY
: Exactly. Your examples have shown me that analogies can be flat and uninspiring, but my point is different. It’s that analogies
can
be very creative, at least now and then, whereas categorization, poor thing, is
never
creative.

A
NNA
: We agree that analogies can reach the heights of creativity; in fact, I would argue that every creative act is rooted in an analogy. One gets off the beaten track by seeing that two things are “the same thing” in a situation where their sameness has not yet been seen. Good examples are given at the end of Chapter 4, such as where Archimedes sees a crown as being “the same thing” as a human body, in that both occupy volume, or where a computer’s mouse is seen as doing “the same thing” as a human hand, in that it can manipulate virtual objects that lie behind the screen. And in Chapter 8 we saw that great discoveries in mathematics and physics are rooted in analogies. The French mathematician Alain Connes declared, “The trips we take in the world of mathematics differ from trips taken in the physical world, and the main vehicle for such trips is analogy.” And the philosopher Friedrich Nietzsche once defined intelligence as “a moving army of metaphors”.

K
ATY
: Yes, I’ve heard these ideas before, and in fact this is exactly what I’m trying to get you to see: analogies, being members of the cognitive aristocracy, have the potential to be creative, whereas humble categorization, bless its little heart, does not. And while we’re quoting authorities, let me quote the French writer Georges Courteline: “Whoever first compared a woman to a rose was a poet; whoever next did so was a fool.” That makes my point very well! The poet came up with a novel analogy between two entities, and this was a creative act; the other person merely took the category created by the poet and echoed the observation. It was a derivative act in which there wasn’t one single shred of creativity.

A
NNA
: That’s an interesting quote, but you interrupted me and didn’t let me get to
my
point, which is that categorization, too, has great potential for creativity; no law says it’s limited to the carrying-out of menial tasks. You quoted a mathematician talking about analogy, so now let me quote another mathematician talking about categorization. Henri Poincaré described mathematics as “the art of giving the same name to different things”. That is, it’s the art of discovering unusual and subtle new categories. And so, categorization should hold its head high; it should be proud of its ability to give rise to great novelty and high invention.

K
ATY
: Are you joking?

A
NNA
: Not in the least! What makes a person, an idea, an opinion, or a remark original? Surely it’s the fact that it involves a categorization that departs from the norm! For example, we think of certain architects or movie directors or novelists or fashion designers as being original because they’ve come up with an idiosyncratic universe, which means their way of categorizing things differs from those of their contemporaries. Don’t you agree? Moreover, many opinions take the form of unconventional categorizations. Thus if I declare, “The current financial situation is a mess”, I’m putting the financial situation in the category
mess.
If I say “Mathematics is a game”, “Mathematics is a language”, “Mathematics is a tool”, “Mathematics is an art”, “Mathematics is a cult”, or “Mathematics is a passion”, what am I doing if not assigning mathematics to the categories of
game, language, tool, art, cult
, and
passion
? If someone declares that my ideas are a
dead end
, or that their very voluble chatterbox friend is a
fire hose
, or that video games are a
scourge
, or that some up-and-coming young comedian is
another Woody Allen
, or that 60 is
the new 40
, or that the new tax law is
a disaster waiting to happen
, or that the president’s proposal is just a
band-aid
, or that spell checkers are a
crutch
, or that a famous politician just caught in a lurid sex scandal is
history
, or that their other car is a
bicycle
, aren’t all these just various cases of categorization, some more and some less original?