Surfaces and Essences

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Surfaces and Essences Page 42

by Douglas Hofstadter


  Yes, in part; but expertise goes considerably beyond that. Aside from certain very technical and esoteric domains, being an expert does not mean having memorized a list, even if the list is enriched with specific tidbits about each of its items. If Mr. Martin wished to become an expert on his town’s telephone directory, then memorization would suffice; he would be an expert simply by virtue of having learned many names, addresses, and phone numbers by heart. But in more conceptual domains, expertise doesn’t come from amassing knowledge of ever more species belonging to a single genus; to be sure, experts will generally have more species under their belt than will novices, but that is by no means the full story.

  Changing Category to Change Viewpoint

  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 wolf2 — note that a dog is a wolf2 but not a wolf1— 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.

  Nice Work if You Can Get 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 in
finitely 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.

  Buon appetito!

  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.

  But the world of pasta can be broken down in many ways, not just in the stereotypical fashion featuring many species underneath a single top-level genus. There are varieties that one can easily make at home, and ones that are better left to the professionals. There is fresh pasta and there is dry pasta. And most of all, there are various natural subclasses determined by shape, which profoundly affect the uses of various types of pasta in cooking, and which are, in fact, the primary reason for all the diversity that exists. Thus the smaller noodles, such as anchellini (“mini-hips”) and primaverine (“springtime noodles”), are intended mostly for soups, and then there are types with rather fanciful shapes, such as cocciolette (“potlets”), dischi (“disks”), and fusilli (“little spindles”), intended for use with salads and vegetables. The long ribbons and string-like shapes, such as linguine (“tonguelets”), tagliatelle (“little slices”) and spaghetti (“stringlets”), harmonize well with sauces. In particular, caserecce (“homemade noodles”) and conchigliette (“little shells”) go best with meat sauces, while others, such as cappelletti (“hatlets”) and ravioli, are intended to be stuffed with tasty fillings. Every cook who delights in using pasta will have a well-developed mental network of pastas and connections linking them, revealing an unconscious structuring of mental categories.

  À votre santé!

  A good plate of pasta merits a good wine, and in the world of wines, the range of categories seems to be inexhaustible. Rank beginners will make only the red/white distinction, while those who are slightly more in the know will refer to the type of vine (cabernet sauvignon or merlot, for example) and to the source country (France, Italy, Chile, Australia, the United States) or region (Bordeaux, Bourgogne, Napa Valley); however, expertise in wines involves going far beyond these kinds of facts. It can lead to distinguishing a particular vintage of a particular year of a particular grower of a particular sous-appellation of a particular appellation of a particular country — for example, a Château Beaucastel Hommage à Jacques Perrin 1998 belongs to the sous-appellation called Châteauneuf du Pape within the appellation known as Côtes du Rhône, and it comes from the prestigious vineyard Domaine Beaucastel.

  Does Château Beaucastel Hommage à Jacques Perrin 1998 constitute a typical category for a true wine connoisseur? Absolutely. It has many characteristics that people will use to describe it, such as its color, its bouquet, its taste, how it ages, its market value, the dishes it goes best with, the ideal temperature it should be served at, places where one can obtain it, ratings it has received from professional tasters, and so forth. The few thousand bottles actually produced of this exquisite elixir constitute the extension of this category — its concrete members. Of course, despite the seeming precision of this description, there are all sorts of hidden blurs at the fringes, as there are for any category: a counterfeit bottle, an unlabeled bottle, a half-consumed bottle, a poorly conserved bottle, a bottle that has been boiled or dried out, an empty bottle, a few drops spattered on a tablecloth after a glass was poured, and so forth. And no less than any other proper noun, this category lends itself to pluralization, as is illustrated by the grower of Château Beaucastel who proudly declares, “You should taste the new Jacques Perrin 1998 that I produced here in my vineyard in 2005.�
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  To give an idea of the richness of categories in this arena, we point out some of the categories that necessarily inhabit the mind of a wine lover who states, “In 1996, Dominique Laurent did a great job with Gevrey-Chambertin Premier Cru Les Cazetiers”, and which are unlikely to exist in the mind of a more modest wine lover who says, “I prefer French wines to Spanish wines.” In the former case, not only are the high-level categories wine and French wine implicitly referred to, but moreover it is taken for granted that the listener is familiar with several yet narrower categories — namely, bourgogne, Gevrey-Chambertin, Gevrey-Chambertin Premier Cru (since most members of the category Gevrey-Chambertin do not come from the first harvest), and even Gevrey-Chambertin Premier Cru Les Cazetiers (since there are quite a few other types of Gevrey-Chambertin Premier Cru aside from those called “Les Cazetiers”). To pin the wine down fully, our hypothetical commentator can be both precise and concise, saying, “Gevrey-Chambertin Premier Cru Les Cazetiers Dominique Laurent from 1996”, thereby distinguishing it from other growers who have produced related wines and from other years in which close cousins were produced. Such a fine-grained call is a clear sign of high expertise.

  Why Abstraction is Central for Expertise

  In any normal domain of expertise, even the most knowledgeable of specialists can’t come close to knowing everything about the domain. The breadth of knowledge that one would need to assimilate in order to be an expert in every nook and cranny is so vast that setting oneself such a goal makes no sense. And of course the idea of being an expert “in every nook and cranny” is in itself problematical, since when one uses a magnifying glass, every domain shatters into yet further subdomains. And yet we don’t expect experts to throw up their hands and say “I don’t know” whenever they are asked a tricky question in their domain. This is because true experts have knowledge not just about many specific cases in their domain, but also, through analogical links, a set of expectations about cases that are far less familiar to them. Thus in the domain of wine, we might imagine asking an expert, “What you do you think of the Château Vinus 1995?” Our expert might start right up and give all sorts of details learned either firsthand, through tasting, or second-hand, through conversations or reading. In this case the game is very simple, since the category relied on is precisely Château Vinus 1995. On the other hand, our expert may know nothing specific about Château Vinus 1995, and might therefore reply, “I don’t know”, which would be a perfectly truthful answer, and yet hardly useful at all, and also hardly reflective of what we think expertise is.

 

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