Surfaces and Essences

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Surfaces and Essences Page 20

by Douglas Hofstadter


  It is certainly too narrow to hear it as applying solely to acts of thievery, because the key idea seems to be some kind of slippery slope leading from small “sins” to larger sins of roughly the same type. To hear only an allusion to thievery in the proverb would be very limiting. Presumably, the proverb’s purpose is to put people on guard concerning all sorts of negative actions early in life, so that they might try to prevent those actions from growing out of control as time goes by. “Nip bad acts in the bud!” would be the crux of the advice being given.

  If, however, the scope is extended to actions without negative import, then the idea of being on guard against them no longer makes any sense. We don’t need to be on guard against good deeds, don’t need to nip them in the bud. To be sure, we can easily imagine a slippery slope leading from small good deeds to large ones — but that misses the proverb’s point. In so doing, we will be sacrificing much of the “bite” of the proverb. Such a sacrifice might be seen as a standard consequence of the nature of abstraction, since by definition, “to abstract” means to abandon the less important aspects of what one is dealing with, but if a series of acts of abstraction is carried out without any attention being paid to intent, sooner or later the gist will simply be lost. Indeed, a small sin of abstraction may lead to a large sin of abstraction.

  In the case of our proverb “He who will steal an egg will steal an ox”, we could take things one level further in abstraction, not just ignoring the idea of magnification (from egg to ox), but also ignoring the sameness of the verbs in the two clauses and even any semantic relation between them; this would lead us to conclude that the proverb means that one thing leads to another. This extreme level of abstraction includes all situations in which there are causes and effects, but what good does such an extreme leap upwards do anyone? The richness of the original proverb is lost, and in fact, when carried to this stratospheric level of abstraction, “He who will steal an egg will steal an ox” winds up being no different from “Once bitten, twice shy.”

  Although jumping up the ladder of abstraction rung by rung may in some cases be a sign of intelligence and fluid thinking, if it is taken too far, it becomes a vacuous and frivolous game, and playing such a game with a proverb reveals an impoverished and superficial understanding of it. Indeed, in the end, an excess of abstraction winds up being similar to an excess of literality, because seeing any two things as analogous is no more insightful than not being able to see any analogies at all.

  It would thus seem that there is an optimal level of abstraction, and that if we stop before reaching that level, we will exclude a host of situations that fit the proverb like a glove, such as the pint-sized swearer in nursery school who many years later turns into a volcanic spouse, and contrariwise, if we go beyond the optimal level of abstraction, we will let in a flood of irrelevant situations, such as the kid who at age six made three dollars selling lemonade at the corner and went on to become a billionaire in the soft-drink business at age sixty.

  Jumping up to such a rarefied level of abstraction as a quest for some ultimate meaning of a proverb is reminiscent of a person who would label every object in sight a “thing”, a “thingy”, a “deal”, or a “whatchamacallit”, and thus would be prone to coming out with such abstract observations as “The thingy is sitting on the deal in the whatchamacallit”, whereas most of us would find it clearer and more useful to say, “The pen is sitting on the desk in the living room.” The greater specificity of the latter sentence strikes us as obviously preferable to the ambiguity of the former, but it’s a matter of taste.

  This recalls the cartoon figures called “smurfs”, who have a highly abstract and concise lexicon, in which all nouns are covered by the super-abstract term “smurf”, and other parts of speech are treated somewhat similarly. For example, they might enthusiastically announce, “We’re off to smurf a smurf tonight!”, and even if one didn’t fully get the meaning of this utterance, it would be hard not to be caught up in the general feeling of excitement. And if the smurfs have a stock of proverbs, then it would contain such pearls of wisdom as “A smurfing smurf smurfs no smurf.” Perhaps for the smurfs themselves, this phrase would be filled with insight, but for us its meaning remains elusive.

  The problem with having only such an abstract mental lexicon — such a rarefied set of concepts — is the paucity of distinctions that it allows to be made, somewhat like the severe paucity of oxygen at rarefied altitudes. Abstraction has its virtues, which we will point out at an appropriate moment, but if one cannot draw distinctions, then thinking becomes as difficult as breathing at the top of Mount Everest.

  From Eggs to Acorns, From Oxen to Oaks

  Even if we forget about people who steal eggs and oxen, the notion that things can become bigger and better over time is everywhere to be found around us, for after all, grownups were once children; today’s multinational giants were once fledgling outfits; Steve Jobs and Steve Wozniak made the first Apple computer in a garage before going on to found their legendary firm; Sergey Brin and Larry Page incorporated Google in a humble dwelling in Menlo Park; Albert Einstein first learned to read and write before developing his theories of relativity; popes were once priests in little churches; conquerors of Everest climbed small hills before moving on to the big time; major acts of philanthropy were preceded by minuscule acts of charity; every great friendship was once just a tentative affinity; virtuoso instrumentalists were once musical novices; every chess master had to learn the rules at some point; powerful ideas gave rise to modest fruit before resulting in huge advances… All of this is far from egg-stealers turning into ox-stealers, but it nonetheless deserves a proverb or two, along with the rich category that any proverb covertly symbolizes.

  How might “He who will steal an egg will steal an ox” be converted into a more upbeat thought? The key question is to pinpoint the core idea that one wishes to capture in this category, since various possibilities, related but distinct, might be imagined. The most general version would simply be the idea that things on a large scale are the fruits, in some fashion or other, of a process of “amplification”.

  Thus, amplification can come from putting together a number of small items: a big thing is the “sum” of many little things. There are numerous proverbs that capture this idea in some form or other. For example: “Many a mickle makes a muckle” (whatever those items might be!); “Many drops make a shower”; “United we stand; divided we fall” (which paints both an optimistic and a pessimistic picture); “E pluribus unum”. All of them get across the idea that individually insignificant entities, when put together in large numbers, can give rise to entities of great magnitude and strength.

  However, in none of these is time’s flow explicitly involved. If we are looking for an optimistic counterpart to the pessimistic egg-thief-to-ox-thief metamorphosis, then our goal is a proverb highlighting the slow but steady process of evolution or growth of a single good thing over a very long time. Thus we have the famous proverb “Mighty oaks from little acorns grow”, and a more elaborated version of this thought, from eighteenth-century English writer David Everett: “Large streams from little fountains flow, tall oaks from little acorns grow.”

  A related notion of amplification over time involves putting together many small acts (or objects), one by one, over a very long period of time in order to accomplish a grand goal — in short, temporal accumulation: “A long journey starts with a single step”; “Rome wasn’t built in a day”; “Little and often fills the purse”; “Drop by drop fills the tub” (or, seeing things in a time-reversed fashion, “Drop by drop the sea is drained”, which, in French, is a genuine proverb); and finally, in a more destructive vein, “Little strokes fell great oaks”, a homily found in Poor Richard’s Almanac by Benjamin Franklin.

  A clear semantic reversal of “He who will steal an egg will steal an ox” is illustrated by the fund-raising style of American universities, which might be summarized as “A little giver will one day a grander giver be”, or,
more poetically, “Mighty donors from humble tippers grow.” Or then again, “Someone who donates a book today may donate a library tomorrow”, or even “Butter up a million, smile and snag a billion.” Finally, to give it a more antique tone, we might rephrase it thus: “A giver of eggs may one day give an ox.” Or a camel. Or a dromedary. Or a dormitory.

  In Memory Retrieval, We Are All Virtuosos

  So far in this chapter, we have been discussing acts of categorization that result in the retrieval of composite lexical entities or ready-made phrases, including compound words, idiomatic expressions, ready-made sentences, and proverbs. In particular, our discussion of people’s effortless understanding of proverbs they hear and their fluent insertion of proverbs into conversations was intended to bring to light some of the memory-access processes that we all engage in automatically and ceaselessly, processes that transpire in but fractions of a second and with truly impressive precision. This fluid fashion of tapping into deep, dormant reserves of memory is a variety of virtuosity, and far from being limited to a few gifted and highly trained individuals, it comes along free with the possession of a normal human brain.

  Telling one’s loudly protesting children in the back seat that it’s important to fasten their seat belts, one comes out spontaneously with the phrase “Better safe than sorry” without having had any prior intention of quoting a proverb. Hearing from friends who returned from a weekend vacation to find that their teen-age daughter had thrown a wild party in the house during their absence, one finds oneself thinking, “When the cat’s away, the mice will play!” Advising a friend who’s applied for several long-shot jobs of which one has suddenly come through and needs an instant reply or it will be lost forever, one blurts out, quite off the cuff, “A bird in the hand is worth two in the bush!” (We momentarily interrup the natural flow to remind readers that in Chapter 1 we announced our intention to distinguish linguistic expressions from the concepts they denote by using quotation marks or italics, respectively. In this paragraph, though, all the examples are delicately poised between the two; indeed, they are all cases of the category named by the phrase “neither fish nor fowl”. But we had to make a choice, and so, throughout the paragraph, somewhat arbitrarily, we opted for quote marks.)

  Just as words like “bottle”, “table”, and “chair” strike us as being objectively there, staring us in the face, when we are in the presence of certain visual stimuli, so the various proverbs that we have just cited above (and many others as well, needless to say) can, on occasions like those just cited, simply materialize out of thin air in our minds, as if handed to us on a silver platter — and when this kind of effortless, instantaneous retrieval happens, they simply feel right, every bit as right as calling the objects in front of us “a bottle”, “a table”, and “a chair”. On such occasions, the members of the abstract category seem to us to be objectively there and objectively real — just as real and almost as visible and tangible to us as are the material objects before our eyes, even though, of course, they are not visible or tangible in the way physical objects are. No less than there are seat belts and children in the back seat, there is a Better safe than sorry situation inside the car. No less than there is a frightful mess of half-empty beer bottles and a bevy of reveling teen-agers in the living room, there is a When the cat’s away, the mice will play situation in the house. No less than there is a job offer dangling in cyberspace and a threat of losing it forever, there is an A bird in the hand is worth two in the bush situation floating in the air. As these examples demonstrate beyond any doubt, categories go far beyond what is labeled by single words.

  Fables

  The further we’ve gone in this chapter, the longer the labels of the categories concerned have grown. First we discussed words such as “pacifier”, “understand”, “handsome”, “cockpit”, “cupboard”, “wardrobe”, “pocketbook”, and “eavesdrop”; these words are made of components that are no longer felt as such by those who use them fluently, so that the compounds have a unique flavor all their own, reminiscent of a process of sedimentation in which the initial constituents have all melted together, or of a rich, tasty sauce that is so subtle that only an expert chef can figure out what went into it. Then we looked at compounds whose components seem more transparently present, such as “bedroom”, “airport”, “bottlecap”, and “Jewish mother”. Next, we moved to prefabricated idiomatic phrases like “to drop the ball”, “to catch the drift”, “to be caught off guard”, and “to jump on the bandwagon”. Then we moved on to short ready-made sentences such as “What’s up?” and “It could be worse”, and most recently, to proverbs such as “Better safe than sorry”. At every stage of the game, our point has been firstly that such expressions are the names of categories in our minds, and secondly that, thanks to analogical perception, we feel the presence of instances of those categories no less than we feel the presence of instances of categories whose linguistic labels seem far more atomic, like “table”, “chair”, “moon”, “circle”, “office”, “study”, “think”, “spend”, “much”, “and”, “but”, and “hub” (and whose presence we also detect through analogical perception). This is a quintessential theme of this book.

  So how about fables, now — short fanciful tales that wind up stating a moral? Might those, too, be the names of categories? We shall answer in the affirmative — not just sometimes, but in all cases, as long as the fable is clearly understood. Reading a fable allows one to construct a category that is succinctly summarized by its moral; the fable itself is just one member — a very typical member — of the category, among a myriad potential members. After the fable has been understood, then, as is the case for any category, new situations will from time to time be encountered that, thanks to an analogy perceived, are seen to have a common essence with the fable, and will thus add to the category’s richness.

  From then on, a fable will act much like a word. It becomes a label that jumps to mind when someone who has incorporated it in their memory runs into a situation that “matches” or “fits” the fable — not in a word-for-word fashion, obviously (fables are seldom memorized), but by an abstract alignment with its moral, or with its title, or just with a blurry memory of its basic plot. If a flat surface comes into view off of which a person is seen eating food, this is very likely to trigger the word “table”; if a few children come into view who are playing hopscotch, this is very likely to trigger the word “jump”; in much the same way, there are certain combinations of actors and events in which they participate that are very likely to trigger the retrieval of certain fables (or of fable-labels, at least). Our claim — a very serious one — is that fables jump to mind as situation-identification labels no less than do proverbs, idioms, compound words, and “simple” words, and any situation that evokes the memory of a particular fable will be perceived as a very real member of the category that lurks behind the scenes.

  Scorning What is Out of Reach

  Æsop is remembered for the fables he wrote in the sixth century B.C., of which one of the most famous is “The Fox and the Grapes”. It was so successful that it passed down through the æons and was even adapted by a number of later authors who, despite changing its form, retained its content. The Roman fabulist Phædrus included it in his collection of Æsop’s fables in the first century A.D., and in the seventeenth century, the French poet–fabulists Isaac de Benserade and Jean de La Fontaine did the same. Here are the versions by these four authors, all translated into English:

  “The Fox and the Grapes”, by Æsop (sixth century B.C.):

  A famished fox observed some grapes dangling above him, on a very high trellis. They were ripe and the rascal would very gladly have absconded with them. But jump though he might, the trellis was simply so high that he couldn’t reach them. Seeing that all his efforts were futile, the fox strutted away with his head held high, declaring, “I could grab those grapes in a trice if I had the slightest interest in them, but they look so green that it’s simply not wort
h the trouble.”

  “The Fox and the Grapes”, by Phædrus (first century A.D.):

  Driven by hunger, a fox was lusting after some grapes on a high vine, and he jumped with all his might to reach them. But he failed, and as he walked away, he remarked, “They aren’t yet ripe, and I don’t want to eat sour grapes.”

  “The Fox and the Grapes” (after Æsop), by Isaac de Benserade (1612–1691):

  We can’t have all we seek, alas, as shows this little scene.

  A picture-perfect bunch of purple grapes was dangling high.

  To snag them, up jumped Fox, but missed, despite his valiant try;

  He jumped and jumped until he sighed, “Those grapes are far too green.”

  Our Fox, to put it frankly, felt despair and rage and pain.

  Perhaps more calmly, later, he would muse in tones forlorn,

  “Those grapes were ripe for plucking — but we mortals always scorn

  The things we strive for valiantly but never do obtain!”

  “The Fox and the Grapes” (after Æsop), by Jean de La Fontaine (1621–1695):

  A certain fox from Normandy (though others say the South)

  Was at death’s door from hunger, when he spied, upon a vine,

  A tempting bunch of grapes that he would fain place in his mouth,

 

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