Surfaces and Essences

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by Douglas Hofstadter


  We are not the only thinkers, we hasten to add, to have posed such far-reaching questions. A bold web site called “The Sandwich Manifesto” addresses head-on the fundamental question “What is a sandwich?” One issue raised there is whether anything that has the form “A–B–A” is a sandwich. For example, do the books on a shelf, sandwiched between two identical bookends roughly a yard apart, form a sandwich? Or is the name “Einstein” a sandwich, given that it is spelled “Ein-st-ein”? Is America a sandwich, with the Atlantic and Pacific Oceans being the slices of bread? The non-identicality of those two great bodies of water, not to mention the non-identicality of “Ein” and “ein” (after all, the first boasts a capital “E” while the second does not), brings up the more general issue of the identicality, or lack thereof, of the two “slices of bread”.

  On one memorable occasion in Paris, the métro station Odéon was described by a fairly bored métro rider as being “sandwiched” in between two métro stations bearing the names of saints (Saint-Michel and Saint-Germain-des-Prés). This trio of stations might thus, with good reason, be called a “subway sandwich”. In a (somewhat) similar fashion, car-borne criminals are sometimes said to be “caught in a sandwich” if two police cars manage to maneuver into a position such that one of them is behind the criminals and the other is ahead of them. Another flesh/flesh/flesh configuration is the sexual position known as “The Sandwich”. But leaving the body behind and moving on to the mind, we have rhyme sandwiches: consider a rhyming quatrain whose rhyme scheme is “ABBA”, where the “A” rhymes play a bread role to the “B” rhymes’ meat. And surely we would not want to overlook the crucial role of inedible sandwiches in the realm of solid-state physics. Specifically, there are important types of semiconductors called “P” (for “positive”) and “N” (“negative”), and from them are formed three-layer structures of the form “PNP” and also of the complementary form “NPN”. These are both standardly called “sandwiches” in academic papers by physicists — and such sandwiches are incidentally also members of the category transistor (hardly a concept to be sneezed at).

  The bold interchange of the meat and bread roles in solid-state physics raises another fundamental question of sandwichology — namely, whether there are certain categories of things that are more eligible to play the bread role in a sandwich, with other categories being more eligible to play the meat role. For example, we all know that peanut butter and jelly constitutes a fine member of the meat category (at least in the context of sandwich-making), but would it ever be able to serve in the role of bread ? Let us pose this question in a more point-blank fashion. One can envision, without the least difficulty, an “NPN” sandwich in which the “N” stands for a delicious Indian naan and the “P” stands for peanut butter and jelly — but what about an inside-out “PNP” sandwich? Or is this simply going too far? Have the ultimate limits of the sandwich category been transcended, or could it be that our era is simply not yet ready for such bold new visions?

  Arguably the most burning conundrum in sandwichology is under what conditions an entity that has the form “A–B–C” should be counted as a sandwich. For instance, if one’s Bostonian bosom buddy Bradley (“B”, for short) happened to be fast asleep on his comfortable Chesterfield couch (“C”, for short), and if Bradley’s Abyssinian feline friend Adele (“A”, for short) were suddenly to leap atop dormant Bradley, might the resulting A–B–C configuration count as a sandwich? And if A had been an armchair rather than an Abyssinian? Armchairs being presumably a bit more couch-like than Abyssinians, would one not be ever so slightly closer to the canonical A–B–A form?

  The last few paragraphs have been rather fanciful, but it is worth noting that the word “sandwich” is routinely used in colloquial speech and even in formal contexts, sometimes as a noun and sometimes as a verb, to denote abstract and definitely non-edible patterns. How many times, for instance, have you casually remarked, “My meeting with the dean this morning was sandwiched right between my dermatologist’s appointment and my dentist appointment”? You probably can’t even remember! Yes, in an era when using the word “sandwich” to describe all sorts of inedible things has become a routine worldwide phenomenon, we are no longer talking about wild, self-indulgent flights of fancy. We are talking popular culture.

  As you can no doubt sense by now, the questions of shadowology, wavology, and sandwichology open up vast conceptual horizons without an abstraction ceiling lurking anywhere in sight.

  The Downfall of Proud Capitals

  As we have just seen, the extension of concepts by analogy seems limitless. It allows us to see one’s homeland as one’s mother, to see a snow-free area under a tree as a shadow, to see a pattern of sequential brakings by drivers along a stretch of freeway as a kind of wave, a sequence of three appointments as a sandwich, and also to see the story of a person who finds reasons for satisfaction in their failure to purchase tickets for a concert they had dearly hoped to attend as just a differently dressed retelling of the sour grapes fable. Sometimes leading to extending the boundaries of a category, such as bird or book, moon or marriage, eat or undress, much or but, or to the construction of a new and more abstract category, such as lump or desk, or even a whole range of new concepts, as in the case of shadow and wave, the process is simply part and parcel of the human condition, and as such is unstoppable. Indeed, almost as if to show off its irresistibility, the process of category extension survives even in extremely austere environments where one would suspect it could not — namely, in the world of proper nouns, a world where everything comes in ones, and thus a world that, by its very definition, would seem to prohibit the extension of categories.

  In contrast to common nouns, which are obviously the names of categories, proper nouns, which are singled out by the capital letters with which they start, might seem to be of a completely different nature. Although they are certainly definable through language, proper nouns aren’t supposed to need definitions because the set of entities that they refer to seems to be unambiguously defined. Often, they designate one and only one entity: a planet, a continent, a country, a city, a monument, a human being, a work, and so forth — and when they designate more than one entity, as does a first name, a last name, a commercial brand, a nationality, and so forth, the set of entities to which they apply seems nonetheless so sharp and clearly defined that one might have a hard time imagining that there is anything about them that resembles the “halos” that surround the cores of all typical categories, as we have been describing them all through our book so far.

  Indeed, one might well go so far as to question the use of the word “category” when there is just one member. What kind of sense does it make to speak of categories such as Paris, Galileo, Earth, and Moon, when each of those exists (or at least once existed) in but a single case? But upon analysis, this kind of argument is quickly seen to hold no water. Our irrepressible human tendency to extend categories by the making of analogies applies in the case of proper nouns no less than it does for all other nouns (and other words, for that matter).

  Chapter 1 recounted the story of Galileo, the Moon, and the many moons that subsequently came along. That story may have seemed like a very unusual case, but leaps such as that from “Moon” to “moons” (or from “Sun” to “suns”) take place all the time around us, far removed from the specialized world of scientific discoveries. In particular, they take place whenever categories are extended by an act of marking, in which a proper noun loosens its belt a bit and in so doing becomes the label of a more general category.

  For instance, brand names have often become generic words, thanks to the popularity of the products they name. Thus the old-time General Motors brand of refrigerator called “Frigidaire” became, in the 1920s, an uncapitalized noun in American English (and also in French), just as the brand name “Hoover” for vacuum cleaners became an ordinary uncapitalized noun in British English. Essentially the same story can be told about the brand names “Kleenex”, “Coke”,
“Xerox”, “Saran Wrap”, “Dustbuster”, “Scotch Tape”, “Teflon”, “Q-Tips”, “Jacuzzi”, “Frisbee”, and so on (and thus we could as easily have decapitalized these words as left them with capital initial letters).

  In all these cases, first there is a small category whose members are the products of the specific brand name — and then new products are made that are different enough from the original ones that they seem to call for a new word, yet at the same time, they aren’t fundamentally different from the original products, since they all share the key characteristics that created the need for the original products. When people want to give a name to these new copycat products that form a halo around the original ones, they will often spontaneously borrow the original brand name but will decapitalize it in order to indicate that this is an extended sense of the original word (much as “Moon” became “moon”). The new members and the old members of the original category now all belong to this new category. Thus the word “kleenex”, when decapitalized, stands for all tissue papers, but when capitalized, it stands only for tissue papers of the Kleenex brand.

  Now this phenomenon might seem like a desirable thing from the point of view of a popular brand, a demonstration that it is collectively recognized as the most canonical item of its sort. However, although a few companies might welcome such genericizing of their names, more often the shareholders of the genericized companies do not see things this way at all. Indeed, major brand names tend to combat this process very actively, since it tends to dilute the meaning of their name, in the sense that people soon come to hear the word that once was a brand name simply as a bland name without any identity at all.

  Brands want to be recognized for their uniqueness, not for their genericity. Who would appreciate it if, within a few years of their naming their very popular dog “Oliver”, bandwagon-jumping families in the neighborhood had given every single new dog the name “Oliver”?

  The turning of a proper noun into a common noun transforms a once-special term into a commonplace. Who would ever proudly boast of owning “an authentic jacuzzi” or “a genuine frisbee”? In the case of these two brands (and both are indeed brands), the unmarked sense has long since eclipsed the marked sense, and as a result the first letter has been demoted to lowercase status. This type of slide, which entails the loss of legal protection of the brand name, has been dubbed “genericide”. This explains why, when the verb “to google” first appeared in the 2006 editions of the Oxford English Dictionary and the Merriam-Webster Collegiate Dictionary, the Silicon Valley giant instantly launched an intense campaign to restrict the usage of its name, particularly focusing on preventing the proper name “Google” (or rather, the non-proper-name “google”) from being used as a verb denoting Web searches regardless of what software is carrying them out.

  In the above examples, in which a single word comes to occupy two levels of abstraction, we recognize the telltale signature of the phenomenon of marking. And by coincidence, the noun “mark” is occasionally used in English to mean “label” or “brand name”, as in “What mark is your shirt?” Actually, this unexpectedly close relationship between the ordinary word “mark” and the technical term “marking” is not a coincidence, since a commercial brand or logo or mark is a visual identifier, allowing potential customers to distinguish similar-looking products from each other. And the adjective “marked”, whose origins have to do with the idea of stamping something with a distinguishing symbol (a “mark”), is used to describe subcategories, much as a commercial mark designates a subcategory of products that all belong to one single overarching category.

  Commercial marks (i.e., brand names) such as we’ve been discussing make up but the tip of the iceberg of the phenomenon of lexical labels that fluidly swivel back and forth between denoting just one single entity and denoting a far vaster category. There are in fact cases where the name of a unique individual, place, or object can, despite its uniqueness, be naturally applied to dozens, hundreds, or thousands of entities.

  Sacred Categories

  The worldwide unity of the Catholic church is due to the existence of a single spiritual leader, the head of the Vatican: the Pope. Aside from a few historical upheavals that led, at the end of the fourteenth century, to the simultaneous naming of two popes — Urban VI and Clement VII — Catholics have always been able to look to their unique Pope for leadership. He is the Pope, and that’s all there is to it. However, if the current Pope enjoys the distinction of being the unique terrestrian member of this exalted category (previous members enjoying eternal repose), his title is extremely sought after when it comes to the broader sense of the term, which is to say, the unmarked category.

  If one goes to the Web, the papal harvest is rich. Pop Art has its uncontested pope: Andy Warhol. The pope of the personal computer industry is heralded as Bill Gates or Steve Jobs. John Waters is pronounced the pope of bad taste, Robert Parker the pope of wine, Paul Bocuse the pope of gastronomy, etc. Indeed, popes with a lowercase “p” proliferate like flies. Picasso has been called the pope of Cubism, André Breton that of surrealism. Bob Marley has been declared to be Reggae’s pope, Ray Charles jazz’s pope, and Frankie Ruiz the pope of salsa music. Celtic music, too, finds its pope in Alan Stivell, and contemporary abstract music, not to be left out, has Pierre Boulez for its pope. While the Dalai Lama is anointed the pope of Buddhism, Richard Dawkins is acclaimed the pope of atheism, and lastly — surely to no one’s surprise — Pierce’s Pitt is proclaimed the pope of pulled pork (where? in Williamsburg, Virginia).

  But why quit when you’re on a roll? If you persevere in your Web search, you can find popes of positivism, football, Japanese trash cinema, neoconservatism, boxing, free software, haiku, contemporary design, multimedia, management, documentary, TV news, underground cinema, the harpsichord, Scandinavian rock music, manga, rap, tennis, Italian jeans, dog biscuits, coaching, bio-art, broccoli, business calendars, and on and on. Indeed, the list of popes can be extended pretty much without end, and so it makes sense to declare a state of “papal hyper-inflation”, meaning that there are so many popes of this, that, and the other thing that at this point the title has lost much of its punch. No matter how narrow some human activity might be, there is always some practitioner of it who is perceived by somebody or other as having sufficient prestige and sway as to merit a nomination to the pantheon of “generalized popes”.

  And while we’re talking about pantheons, they, too, form an interesting case, hovering blurrily somewhere between proper noun and common noun, somewhere between singular uniqueness — “The Pantheon” — and plural (“many pantheons”). Indeed, even when doubly capitalized, as just shown, the name is not unambiguous, there being good reasons to think it designates Il Pantheon (in Rome) and other good reasons to think it designates Le Panthéon (in Paris). In any case, pantheons were originally conceived of as monuments erected to honor a civilization’s gods (or perhaps its Gods). The Pantheons in Rome and Paris both represent the highest honor that their respective nations can bestow on individuals of great achievement, serving them as a kind of exalted cemetery. But the category of pantheons is far wider than this, since a pantheon can be a kind of “software temple”, or a “temple of the imagination”, requiring neither a building nor burials — just a listing of names of a number of important individuals. Accordingly, Albert Einstein is clearly in the pantheon of physicists, and Henri Poincaré, though not buried in the Panthéon in Paris, certainly figures very high in the pantheon of mathematicians.

  Various sacred sites and books serve to keep religion on people’s minds. Thus the name of Mecca, a destination for millions of pilgrims each year from all around the world, has become, in its decapitalized version, a word that captures the idea of a venerated place — indeed, a cult place — for a particular activity. Below are listed a few dozen meccas that we came across using, shall we say, the pope of search engines. We found meccas of:

  automobile styling, basketball, catamarans, cigars, cinema, cricke
t, cross-country skiing, entertainment, faded jeans, golf, granite, hang-gliding, hip-hop, hockey, hot-air balloons, 100-kilometer runs, jazz, “made in China”, motorcycle racing, mountain biking, 1950’s furniture, nudism, obstacle courses, parachuting, petroleum products, piano-playing, psychedelics, rap, rock, rollerblading, rugby, sandwiches, shopping, soccer balls, socialism, sound effects, speed skating, surfing, swing, tea, tennis, terrorism, tourism, the triathlon, videogames, volcanology, voodoo, and wind-surfing.

  What is constant in all these meccas — what constitutes the “essence of mecca-ness” — is the idea of a place of supreme importance, the idea of uniqueness (even though for some of the activities two or three would-be meccas vie for the title of the mecca), and even the idea of some kind of sacredness (even though, for most of these meccas, the activity in question has nothing to do with religion).

  The Book of Books — that is, the Bible for some, and the Coran for others — has also been deemed worthy of becoming an abstract category. The category of “Book of Books”, representing just one book, gets stretched so that it becomes applicable to all sorts of different books in different domains (but presumably just one per domain). Thus there exists a bible of Thai cooking, a bible of ribbon embroidery, and a bible of body-building. And the most reliable book about gardening in an Islamic country might well be called “the coran of gardening”, since of course the Bible of Islam is the Coran, and the reverse holds equally well, the Coran of Christianity being the Bible.

  To be sure, religion isn’t the only field in which this kind of pluralization of proper nouns takes place; the phenomenon occurs in the most mundane of activities no less than in the most otherworldly ones, as we shall see. Indeed, capital letters fall by the wayside left and right on Earth as they do in Heaven.

 

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