Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (15 page)

It might seem,
a priori
, that asking about the nature of the concept
golfer
is a minuscule question in comparison with the huge question, “What is human thought all about?”, but the fact is that it is no smaller. In any case, our modest musings about the concept
golfer
are bringing to the fore the obvious fact that concepts are densely stitched together through relationships of similarity and context. The concept of
golfer
is quite closely linked to that of
minigolfer
, and less closely to such concepts as
tennis player, runner, bicycle racer
, and so forth. Among these connections, some are very close while others are so distant that they barely exist (for example, there will be practically no relation at all between the notions of
golfer
and
sumo wrestler
in anyone’s mind, aside from the fact that both are types of athletes).

The concept of
golfer
is also connected (at various conceptual distances) to a multitude of other concepts, such as
golf course, hole, fairway, tee, wood, iron, putt, green, par,
birdie, eagle, bogey, double-bogey, hole-in-one, hook, slice, golf cart, caddie
, and
tournament
, and also, of course, to a large number of specific people (or more precisely, to the concepts one has formed that represent these people). Despite the large number of golfers of whom any fan has certainly heard the name and has very likely stored it in memory, it’s far more probable that a fan will think of Tiger Woods than of some middling player from the 1960’s. Thus the distance from the “center” of the concept
golfer
to the concept
Tiger Woods
is quite small, whereas the distance from the center out to the middling player from decades ago is very great, unless, perhaps, the particular player happens to be one’s mother or one’s uncle or something along those lines.

And thus we come to the idea of a multidimensional space in which concepts exist, somewhat like separate points; however, around each such point there is a halo that accounts for the vague, blurry, and flexible quality of the concept, and this halo becomes ever more tenuous as one moves further out from the core.

We could not make an analogy between one concept and another if those concepts had no internal structure in our mind. The very essence of an analogy is that it maps some mental structure onto another mental structure. We can only understand how a hand is analogous to a foot if we mentally recall the fingers and the toes, for instance, as well as the way the hand is physically attached to an arm and the foot to a leg. These kinds of facts are part of what “hand” means; they are integral to the concept
hand
, and they make it what it is. But how many such facts are there “inside” the concept
hand
? How detailed are the internal structures of our concepts? This is the question to which we wish to turn for a moment.

Consider a rather complex memory in the mind of a certain professor — say, the sabbatical year she spent in Aix-en-Provence. When she recalls that year, of course she doesn’t replay its 300-plus days like a movie; rather, she sees just the tiniest part of it, in its barest outlines. It’s as if she were looking down at a mountain range from an airplane, but an extensive cloud layer allowed only a handful of the chain’s highest peaks to peek through.

If someone asks her about details of the city of Aix, or about some major event that happened during the year, or about the most interesting people she met there, or about the schools that her children went to, and so on, then any of these aspects will become available upon request, but until that happens, they are all hidden under the “cloud cover”. And if she decides to shift her focus to the school that her children attended that year, then still just a handful of the school’s most salient aspects will come into view. If her focus shifts still further down onto a particular teacher, then a handful of that person’s most salient features come into view — and on it goes. The overarching memory — the sabbatical year in Aix — is never seen in its full glory; rather, just a tiny (but very salient) fraction of it is ever made available. However, pieces of it can be focused in on, and in this way, the large memory can be unpacked into its component pieces, and the same can be done to those pieces, in turn.

All our concepts, from the grandest to the humblest, have the same quality of being largely hidden from view but partially unpackable on request, and the unpacking process is repeatable, several levels down. One might at first think that concepts named by simple words, in contrast to a vast and complex event like a sabbatical year that one is recalling, don’t have much inner structure, but that’s not the case.

Consider the concept of
foot.
When you first think about a foot, you don’t think of cuticles or sweat glands or hairs on it or the fancy swirls making up its five toeprints; you think about toes and an ankle and a large vague central mass, and perhaps a sole and a heel. If you then wish to, you can mentally focus in on a toe and “see” bones and joints inside it, as well as the toenail on top and the toeprint on the bottom. And then, if you wish, you can mentally focus in on the toenail, and so it goes.

So far, our discussion might suggest that concepts are structured according to the physical parts that make them up, with unpacking always moving towards smaller and smaller pieces. Of course, that wouldn’t make sense for concepts of events or other sorts of abstractions, but even when a concept is of something physical, this needn’t be the case. We’ll now give an example that makes this very clear; it is the contemporary concept of a
hub
for a given airline. We chose this concept because the word “hub” is monosyllabic, just three letters long, and sounds very down-to-earth, at the opposite end of the spectrum from fancy technical concepts like
photon, ketone, entropy, mitochondrion, autocatalysis
, or
diffeomorphism.
And yet when one looks “inside” this concept, one finds that it, too, is complex — indeed, it has much in common with technical terms. To be concrete, what comes to your mind if we say, “Denver is a hub for Frontier Airlines”? Most people will picture in their mind a map of the United States, with a set of black lines radiating into (or out of) a dot representing Denver, as is shown below.

Perhaps they will also think, “Most of Frontier’s flights go in and out of Denver”, or else “Lots of Frontier planes and gates are found at the Denver airport”. This small set of “highest peaks” (
i.e.
, most salient facts) is pretty much all that one needs in most cases where a hub is being talked about. But in fact it leaves out nearly all of what makes up the concept
hub
, and of which most adults in our culture are perfectly aware. The stipulation “in our culture” is crucial, because hundreds of concepts that we take for granted are not part of other cultures or eras. For instance, imagine trying to explain the concept of
hub
to Johann Sebastian Bach, or to Joan of Arc, or to Archimedes, or to Nebuchadnezzar. These were all remarkable individuals in their respective cultures — but how would you go about trying to get across this “simple” concept to any one of them? It would be a rather long story.

To begin with, the word “hub” is the name of a very concrete, visual concept that we learn when we first ride a bicycle and we see the many spokes radiating out of (or into) the wheel’s center — its hub. Indeed, it’s because of wheels with spokes that airline hubs sport the name “hub”, and the concept of
bicycle wheel
is certainly more “primitive” or “elementary” than is that of
airline hub
, not only being learned far earlier in life but also being far simpler to grasp. Let’s list some other concepts that are more primitive than
hub
and that are likewise prerequisites to it. There’s
airline
, for instance, and
route
and
schedule
and
route map.
And in order to understand the concept of
airline
, you first have to be familiar with the concepts of
airplane
and
company.
And the concept of
route
depends on the concepts of
starting point, destination, leg
, and
connection.
We won’t go on forever, but let’s not forget that the
raison d’être
of hubs is economic efficiency — the relentless pressure to cut costs and to reduce the number of different flights — and thus one has to know about the concepts of
trade, gain, loss, profits, competition..
.

We have only scratched the surface of what goes into the concept
hub.
All of those ingredients are “in there”, and they could all, if and when the need arose, be unpacked and revealed. Such unpackings carry one back towards more and more basic, elementary notions — concepts involving motion, vehicles, roundness, acquisition, trading, winning and losing, large and small numbers, and on and on. And note that none of what we have so far spoken of has anything to do with the fact that airports are associated with large cities, or that airports are more than just black dots on maps — indeed, we completely skipped the internal
physical
structure of an airport, with its runways, tarmacs, concourses, gates, jetways, food courts, etc.

The image we’ve just given of a chain of concepts that depend on other concepts, moving ever downwards in complexity, is reminiscent of the nesting of Russian dolls, and might give the impression that concepts are in fact structured in this boxlike fashion. In truth, however, the phenomenon of concept-building is much subtler and more fluid than that. Concepts are not like nested boxes, with any given concept being rigidly defined in terms of a precise set of previously-acquired concepts, and with concepts always being acquired in a fixed order. Instead, when new concepts are acquired, their arrival often exerts a major impact upon the “more primitive” concepts on which they are based, a bit as if the construction of a house affected the very nature of the bricks with which it was built. Although houses that modify the nature of the
bricks of which they are made do not exactly grow on trees, we are all nonetheless familiar with this basic idea, since, for example, children are dependent upon parents in order to exist, but at the same time their existence radically transforms the lives of their parents.

This is true also for concepts. Thus the concept of
hub
depends, without any doubt, on many others, such as
airport
, but at the same time, the concept of
airport
is itself modified by the concept of
hub.
For instance, familiarity with the
hub
idea inevitably brings out the fact that airports are entities that can help airlines to become more streamlined and thus to save money; this notion is certainly not the most obvious fact about airports. Similarly, recalling that airports tend to be transit areas for travelers somewhat reduces the saliency of airports as final destinations. Even if such effects do not cause radical modifications of the concept
airport
, they are undeniably real and demonstrate that the original concept doesn’t remain unaffected by the newer one. One can imagine more radical effects of the
hub
concept on that of
airport
, such as novel kinds of architecture aimed at optimizing the design of airports to function as hubs, or the design of new kinds of airport shopping malls specially designed to serve passengers who are making rapid plane-changes and who have only twenty or thirty minutes. And the existence of hubs can change the seemingly obvious correlation between city size and airport size; that is, with hubs, it becomes perfectly conceivable for a relatively small city (such as Charlotte, North Carolina) to have an airport with an enormous volume of air traffic but very few passengers who actually disembark there. We thus see that although there cannot be a “child” concept of
hub
without the prior “parent” concept of
airport
, the child nonetheless changes the identity of the parent.

There are countless examples of this general sort. It happens particularly often in science, where a new idea depends intrinsically on previous ones, but at the same time it casts the old ones in a fresh new light, and often a deeper light. For example, non-Euclidean geometry not only came historically out of Euclidean geometry, but it also allowed a much deeper understanding of Euclidean geometry to emerge. In physics, much the same could be said for relativistic mechanics and quantum mechanics, both of which are “children” of classical mechanics, and together have yielded a far deeper understanding of it.

The same is true for concepts in everyday life. Thus, the relatively new notions of
surrogate mother, adoptive mother
, and
single mother
all come out of the concept of
mother
, as does that of a homosexual couple that adopt a child, and each of these new notions modifies the concept of
mother
, showing how a mother need not give birth to a child, need not raise a child, need not be part of a couple, and may even not be a female. In like manner, the concept of
divorce
depends on that of
marriage
, and yet it also has reverse effects on the nature of
marriage
itself (think, for instance, of the effect of prenuptial contracts, and of the fact that today everyone knows, when going into a marriage, that half of all marriages finish in divorce). The notion of
homosexual marriage
clearly depends on the prior concept of
marriage
, and the intensity of the debate over homosexual marriage is in large part due to the fact that opponents claim that the idea not only extends the concept of
marriage
but in fact does the concept serious harm. The concept
of death both depends on and modifies the concept of
life.
The concept of
fast food
both depends on and modifies the concept of
restaurant.
The concept of
credit card
both depends on and modifies the concept of
money.
The concept of
cell phone
depends on and changes that of
phone.
The concept of
traffic accident
depends on and changes that of
car.
The concept of
airplane
depends on and changes that of
distance.
The concept of
recycling
depends on and changes the concept of
garbage.
The concepts of
rape, slavery, genocide, serial killer
, and others not only depend on but change that of
human being
.