Surfaces and Essences: Analogy as the Fuel and Fire of Thinking (59 page)

Thus Mr. Martin, in order to slake his thirst for knowledge about dogs, will construct new categories at various levels of abstraction, and will create links among them. His way of understanding dogs will go beyond just knowing many breeds; it will include different ways of categorizing them, thus allowing him to glide back and forth from one viewpoint to another.

Thus, for instance, there is a standard distinction among four main subcategories of
dog
: the
molossoids
, which have massive heads, short muzzles, small floppy ears, and heavy bones (
e.g.
, bulldogs); the
lupoids
, which have triangular heads and pricked-up ears (
e.g.
, German shepherds); the
braccoids
, which have wide muzzles and floppy ears (
e.g.
, Dalmatians); and the
graioids
, which have wide fine heads, thin limbs, and small ears facing backwards (
e.g.
, greyhounds). Yet further refinements are possible, including such subcategories as
pointers, hunting dogs, retrievers, water dogs, sheep dogs, terriers, dachshunds, sled dogs
, and so on. The process of refinement can also take place within a single breed; thus the
smooth-haired Catalan sheepdog
and the
Czechoslovakian wolfdog
are two types of sheepdog among perhaps fifty, and in certain elite circles, it would be a terrible
faux pas
not to know the difference between Afghan, Scottish, and Hungarian greyhounds.

The gradual enrichment of one’s personal repertoire of categories will necessarily involve the creation of a number of different levels of abstraction, since categories are always interrelated in many ways. Thus a
Bohemian wirehaired
is a kind of
griffon
; a
griffon
is a kind of
pointer;
a
pointer
is a kind of
hunting dog;
a
hunting dog
is a kind of
braccoid;
a
braccoid
is a kind of
dog
.

One can of course pursue links very far upwards, leading towards abstraction heaven. How many levels, for instance, would you suppose there are between
dog
and
animal
? Two or three, perhaps, such as
carnivores, mammals
, and
vertebrates
? It’s true that these are three of the rungs on the ladder, but they are by no means the only ones. For a Latin-oriented zoologist, a dog is a
canis lupus familiaris.
This is part of the broader category of
canis lupus
(which means
wolf
₂
— note that a dog is a
wolf
₂
but not a
wolf
₁
— we’re back to marking once again), of which the
gray wolf is
a different example. Then a
canis lupus
is part of the family of
canidæ
, like its cousins the fox and the jackal (at this level, claws are not retractable). And the
canidæ
belong, in turn, to the
caniformia
, a level of classification that they share with (among others) otters, walruses, bears, skunks, and raccoons. Above that there are the
fissipedia
, and at this level dog meets cat, or more technically put,
caniformia
and
feliformia
find themselves united. These are in turn subsumed by the great order of
carnivora.
From there we gradually ascend to the
placentalia
(where we humans join dogs, cats, and skunks, our common link being that our embryos grow inside the mother’s body and are fed by a placenta), then the
theria
(which reach out to include kangaroos), then the
mammalia
(a familiar landmark in a strange landscape), then the
gnathostomata
, the
vertebrata
(having a skeleton and a spinal column), the
chordata
(having the nervous system above the alimentary canal), the
deuterostomes
(characterized by certain processes that take place during embryogenesis), the
eumetazoa
(many-celled animals), and finally, at long last, one level up, we hit the
animalia
(which is to say,
animals
!). Although some of these levels are debatable today (taxonomy being a field in constant flux and filled with controversy), let’s say that there are at least a dozen vertical steps, if not more, between
dog
and
animal
.

This ascent in the world of biological categories, so sheer that it might make one dizzy, wasn’t meant to imply that expertise always involves so many different levels of abstraction. Usually abstraction hierarchies are far more modest than this. However, the fact that one can find a case where so many levels are stacked one on top of the other shows that abstraction hierarchies are not just a far-fetched fantasy; to the contrary, whether they have many or few levels, hierarchies of this sort are inevitable ingredients in the human process of acquiring knowledge.

Consider the world of typefaces, for instance. There are book faces and advertising faces, there are sans-serif faces and faces with serifs, there are “old style”, “transitional”, and “modern” faces, and many other ways of classifying typefaces exist. For any standard typeface, there are roman and italic varieties, and each one comes in many different point sizes and weights, and specialists can add shadings of various types.

In most domains, familiarity with even three or four levels can be a quite telling sign of knowledge. Novices often remain stuck at only two levels — a genus and some species within it — and the construction of just one more level may be a crucial conceptual leap ahead. As we will see later in this chapter, and even more clearly in the final chapter, the leap upwards to a new general category — a vertical slippage, so to speak — can open up important perspectives, whether in the simplest activities of everyday life or in the most exalted of scientific discoveries.

It would be wrong to suppose that one particular way of cutting up a domain into categories is “the right one”. Any nontrivial domain is going to admit of rival category systems that allow it to be sliced along different sets of axes. Take the world of dogs, for instance. Many other ways of categorizing dogs exist than those that are considered “official”, and each different breakdown comes from a particular way of dealing with dogs. Hunters have one, veterinarians have another, dog-show organizers yet another, not to mention pet-store sales clerks or directors of zoos — and each of these people will have built up an expert-style organization of categories in their head, made by creating new categories and by inserting new levels where useful. It’s almost certain that they will have different systems of categories and will organize them differently, and none of the systems will coincide with the official zoological set of categories.

To take just one more among innumerable other domains, for an aficionado of rock music,
classical music
might well be just one single tiny little category, blurring together a few dimly familiar but esoteric names such as Beethoven and Mozart, maybe even Bach, but
classical music
will be nearly invisible in the rock-music fan’s richly interlinked network of subcategories of
music.
Of course the reverse could easily hold for a lover of classical music, who has a giant and complex network of subcategories of
classical music
(including rich subnetworks for the works of many specific composers), but who, in symmetric fashion, casually lumps a huge variety of types of modern popular music under the single bland and monolithic-sounding label “rock music”, thus betraying an ignorance that would mortally offend the rock-music lover.

In sum, we all build up our knowledge by constructing categories, linking them together, and structuring them by abstraction. In general, neither novices nor experts do this consciously, but if one examines any domain at all carefully, one finds that it is filled to the brim with categories and interconnections among them, and that such links form such a complex pattern that it would astonish an outsider, who would have been tempted to see the domain in the simplest possible way: as just one main overarching genus with a few species one level below it.

Any domain, no matter how limited it might seem from afar, can be refined forever not only horizontally (the number of categories) but also vertically (the levels of abstraction). The quest to mirror reality perfectly would require an infinitely fine-grained set of categories, but each of us is capable of only so much refinement. How far to go in this quest? The answer is not theoretical but practical, depending on what goal one has set for oneself with respect to the chosen domain.

Take, for example, the domain of professions, seen from the viewpoint of people who specialize in thinking about them. Everyone is familiar with such distinctions as that between
employees
and
free-lance workers
, or between
blue-collar
and
white-collar workers
, or between
management
and
labor
, or between jobs in the
industrial sector
and in the
service sector.
But this set of coarse-grained distinctions is as nothing compared to the variety that exists in the charts of professions created by the aforementioned specialists in types of jobs. For example, in the construction sector, there are
waterproofing and insulation workers
as well as
pipelaying fitters
and
wood-fastener installers
, not to mention
plywood-panel assemblers, disk flange operators
, and
metal-fabrication duplicator-punch operators.
Among textile workers, one finds such jobs as
fur garments patternmaker
.

Hierarchical listings of jobs include such general categories as
manufacturing and processing
, below which one finds, for example,
central control and process operators
, and one level further down there is the category of
petroleum, gas, and chemical process operators
, and in that category a sample job is
pipeline compressor-station operator.
Following down other branches of this same tree whose highest-level abstraction is
manufacturing and processing
, one runs across such professions as
crayon-making machine tender
and
paper-bag-making machine operator
, and even that of
tennis-ball-maker operator.
Last but not least, if one starts at the top level of
logging and forestry workers
and descends to
chainsaw and skidder operators
, one encounters such exotic-sounding professions as
grapple skidder operator
.

In Web sites specializing in job searches there are typically on the order of twenty high-level nodes, such as
fabrication and construction industries
, below which one will find hundreds of more detailed nodes, such as
metal-forming, -shaping, and -erecting occupations.
Then below that level, one may find all sorts of more specialized nodes, such as
structural metal and platework fabricators and fitters
, and below that a seemingly endless list of specific kinds of professions. Such complexity may seem surprising, but this is merely an overview, and within each sub-area there are yet further specializations. No matter where one turns, be it the medical profession, the publishing profession, the fashion
industry, or whatever, there are several layers in the classification and hundreds if not thousands of job types. One gets the sense that one could zoom in almost forever.

Let’s look at a profession usually listed at the lowest, most specific level of such a hierarchy — namely, that of
university teachers and researchers.
For people who work in that world, however, the phrase “university teachers and researchers” isn’t specific at all; it stands instead for a huge high-level rag-bag. Their world of jobs is richly structured, distinguishing among
full professor, associate professor
, and
assistant professor
, as well as
instructor
and
lecturer.
It includes
visiting professors, visiting researchers
, and
visiting scholars.
And let’s not forget
teaching assistants
and
research assistants
(both
graduate
and
undergraduate
) — and so far we haven’t even breathed a word about specific disciplines here!

In sum, if one wanted to make a “complete” chart of professions, it would involve a diagram with hundreds of thousands of categories, if not more. To be sure, no one has such a diagram in their head, so making such a diagram is not crucial for somebody whose goal is expertise, but being a specialist in some domain inevitably means that one has internalized some local portion of this complexly structured knowledge.

We now shift to a very different domain from that of professions — a most concrete and everyday domain, which at first glance would seem far removed from subtle considerations of categories. We are speaking about food, and in particular about the world of pasta, which offhand seems far simpler than the world of jobs. It might seem unlikely that there could be too much diversity when it comes to products made solely from semolina and water, perhaps eggs. And to be sure, in many countries, “pasta” means little more than “spaghetti” and perhaps “macaroni”; however, if one goes to Italy one will find an impressive variety of products in the pasta section of any grocery store. In fact, there are at least 80 types of pasta — 200, if one allows synonyms — including such little-known ones as
creste di gallo
(“rooster combs”), which are small-sized noodles (if one dares use such a crass-sounding term for such a delicacy) that are especially suited for soups and salads,
strangolapreti
(“priest-stranglers”), which, as their name suggests, are rather heavy, and are often made with spinach, and
torchi
(“torches”), especially suited for thick sauces.