Surfaces and Essences

by Douglas Hofstadter

  Many friends and colleagues have likewise influenced Emmanuel’s ideas about thought and have enriched his intellectual, professional, and personal life. Jean-François Richard occupies a special place of honor because of his constant presence, his gift of inspiring others, and his phenomenal creative drive. Emmanuel also wishes to cite the profound influence of colleagues with whom he has had long-time interactions and who have inspired him in many ways. These include Daniel Andler, Nicolas Balacheff, Jean-Marie Barbier, Claude Bastien, Luca Bonatti, Jean-François Bonnefon, Valérie Camos, Roberto Casati, Evelyne Clément, Jacques Crépault, Karine Duvignau, Michel Fayol, Jean-Paul Fischer, Bruno Gaume, Jean-Marc Labat, Jacques Lautrey, Ahn Nguyen Xuan, Jean-François Nicaud, Ira Noveck, Pierre Pastré, Sébastien Poitrenaud, Guy Politzer, Pierre Rabardel, Sandrine Rossi, Gérard Sensevy, Catherine Thevenot, Andrée Tiberghien, André Tricot, Jean-Baptiste Van der Henst, Gérard Vergnaud, Lieven Verschaffel, and Bruno Villette. On a more personal level, Emmanuel wishes to thank so many long-time friends for their loyalty and their indescribably valuable affection: Youri Beltchenko, Florence Deluca Boutrois, Patrick Grinspan, Michaël Jasmin, Audrey Norcia, Franck Lelong, Gaëlle Le Moigne, Philippe Pétiard, Caroline Sidi, Nadine Zahoui, and Marie-Hélène Zerah.

  Our publishers on both sides of the Atlantic have been extremely cordial and helpful to us. On the American side, John Sherer was, for several years, a true believer in this book, and when he left Basic Books, T. J. Kelleher and Lara Heimert kept the enthusiastic fires warmly burning. We would also like to thank Nicole Caputo, Andrea Cardenas, Tisse Takagi, Michele Jacob, Cassie Nelson, and Sue Caulfield for their top-notch contributions to this work in its English-language incarnation. On the French side, Odile Jacob and Bernard Gotlieb welcomed us on board and made us know they would support us strongly. We owe special thanks to Jean-Luc Fidel for his meticulous reading of the manuscript and for his sensitive comments. We also wish to thank Jeanne Pérou, Cécile Andrier-Taverne, and Claudine Roth-Islert for their excellent work on the production and distribution of this book in France.

  We expresss deeepest gratitude to David Bender, Steven Willliams, and Jane Stewart Adams for scouring this book for typos and non sequiturs, and mutatis mutandis, we thank Christellle Bosc-Miné and Karine Duvignau for scouring that book. And no, certainly not to be forgotten are Greg Huber, Tom Seeber, and D. Alvin Oyzeau, all of whom tinkered most helpfully with the figures (and sometimes with the facts as well!).

  It goes without saying that many of Doug’s friends have become friends of Emmanuel’s, and vice versa, which of course blurs the borders of all these categories. Such mingling of two worlds has been one of the great side benefits of so many years of work together. Indeed, sometimes the process seemed so long it would never end, and yet here we are, putting the finishing touches on this book. We have learned a great deal about thinking, about writing, and about language from this process, and we hope our readers will take pleasure in, and hopefully inspiration from, our joint creation.

  SURFACES AND ESSENCES

  PROLOGUE

  Analogy as the Core of Cognition

  Giving Analogy its Due

  In this book about thinking, analogies and concepts will play the starring role, for without concepts there can be no thought, and without analogies there can be no concepts. This is the thesis that we will develop and support throughout the book.

  What we mean by this thesis is that each concept in our mind owes its existence to a long succession of analogies made unconsciously over many years, initially giving birth to the concept and continuing to enrich it over the course of our lifetime. Furthermore, at every moment of our lives, our concepts are selectively triggered by analogies that our brain makes without letup, in an effort to make sense of the new and unknown in terms of the old and known. The main goal of this book, then, is simply to give analogy its due — which is to say, to show how the human ability to make analogies lies at the root of all our concepts, and how concepts are selectively evoked by analogies. In a word, we wish to show that analogy is the fuel and fire of thinking.

  What Dictionaries Don’t Say about Concepts

  Before we can tackle this challenge, we need to paint a clear picture of the nature of concepts. It is easy — in fact, almost universal — to underestimate the subtlety and complexity of concepts, all the more so because the tendency to think of concepts in overly simple terms is reinforced by dictionaries, which claim to lay out the various different meanings of a given word by dividing the main entry into a number of subentries.

  Take, for example, the noun “band”. In any reasonably-sized dictionary, there will be, in the overall entry for this word, a subentry describing a band as a piece of cloth that can be wrapped around things, another subentry describing how a band can be a colored strip or stripe on a piece of cloth or other type of surface, another subentry describing a band as a smallish set of musicians who tend to play certain types of music or to use only certain types of instruments, another one for a group of people who work or play together, another one for a wedding ring, another one for a selection on a record or a compact disk, another one for a range of frequencies or energies or prices or ages (etc.), and perhaps a few others. The dictionary will clearly set out these various concepts, all fairly distinct from each other and all covered by the same word “band”, and then it will stop, as if each of these narrow meanings had been made perfectly clear and were cleanly separable from all the others. All well and good, except that this gives the impression that each of these various narrower meanings of the word is, on its own, homogeneous and not in the least problematic, and as if there were no possible risk of confusion of any one of them with any of the others. But that’s nowhere near the truth, because sub-meanings are often closely related (for instance, the colored stripe and the range of frequencies, or the wedding ring and the piece of cloth wrapped around something), and because each of these supposedly clear and separate senses of the word “band” constitutes on its own a bottomless chasm of complexity. Although dictionaries give the impression of analyzing words all the way down to their very atoms, all they do in fact is graze their surfaces.

  One could spend many years compiling a huge anthology of photographs of highly diverse wedding bands, or, for that matter, an anthology of photos of headbands, or of jazz bands, or of bands of criminals — or then again, of photos of wildly different chairs or shoes or dogs or teapots or versions of the letter “A”, and on and on — without ever coming close, in any such anthology, to exhausting the limitless possibilities implicitly inherent in the concept. Indeed, there are books of precisely this sort, such as 1000 Chairs. If the concept chair were completely straightforward, it is hard to see what interest such a book could possibly have. To appreciate the beauty, the originality, the practicality, or the style of a particular chair requires a great deal of experience and expertise, of which dictionaries cannot convey even an iota.

  One could of course make similar observations concerning the subtleties of various types of bands — thus, one could spend one’s whole life studying jazz bands, or headbands, or criminal bands, and so forth. And even concepts that seem much simpler than these are actually endless swamps of complexity. Take the concept of the capital letter “A”, for instance. One would need many pages of text in complex, quasilegal language if one were trying to pin down just what it is that we recognize in common among the countless thousands of shapes that we effortlessly perceive as members of that category — something that goes way beyond the simple notion that most people have of the concept “A” — namely, that it consists of two oppositely leaning diagonal strokes connected by a horizontal crossbar.

  Indeed, catalogues of typefaces are veritable gold mines for anyone interested in the richness of categories. In the facing figure, we have collected a sampler of capital “A” ’s designed for use in advertising, and as is clear from a moment’s observation, any a priori notion that one might have dreamt up of A-ness will be contradicted by one o
r more of these letters, and yet each of them is perfectly recognizable — if not effortlessly so when displayed all by itself, then certainly in the context of a word or sentence.

  The everyday concepts band, chair, teapot, mess, and letter ‘A’ are very different from specialized notions such as prime number or DNA. The latter also have unimaginably many members, but what is shared by all their members is expressible precisely and unambiguously. By contrast, in the mental structure underpinning a word like “band”, “chair”, “mess”, or “teapot” there lurks a boundless, blurry richness that is completely passed over by dictionaries, because spelling out such subtleties is not a dictionary’s aim. And the fact is that ordinary words don’t have just two or three but an unlimited number of meanings, which is quite a scary thought; however, the more positive side of this thought is that each concept has a limitless potential for variety. This is a rather pleasing thought, at least for people who are curious and who are stimulated by novelty.

  Zeugmas: Amusing Revealers of Conceptual Subtlety

  There is a linguistic notion called “zeugma” (also sometimes called “syllepsis”) that, although it is fairly obscure, has a good deal of charm and brings out the hidden richness of words (and thus of concepts). The zeugma or syllepsis is one of the classical figures of speech, and is often — perhaps nearly always — used to humorous effect. It is characterized by the fact that more than one meaning of a word is exploited in a sentence, although the word itself appears only once. For example:

  I’ll meet you in five minutes and the garden.

  This sentence exploits two different meanings of the preposition “in” — one temporal and the other spatial. When one imagines meeting someone in a garden, one sees in one’s mind’s eye two relatively small entities physically surrounded by a larger entity, whereas when one imagines a meeting taking place in five minutes, one thinks of the period of time that separates two specific moments from each other. Everyone understands with no trouble that these are two very different concepts associated with the same word, and the fact that the preposition “in” is used only once in the sentence despite the wide gap between the two meanings that it’s conveying is what makes us smile when we read the sentence.

  Here are a few other somewhat humorous examples of zeugmas:

  Kurt was and spoke German.

  The bartender gave me a wink and a drink.

  She restored my painting and my faith in humanity.

  I look forward to seeing you with Patrick and much joy.

  In the first, the word “German” is forced to switch rapidly, in the reader’s mind, from being an adjective denoting a nationality to being a noun denoting a language.

  The second zeugma involves two different aspects of the notion of transfer between human beings. Does one person really give a wink to another person? Is a wink a material object like a drink, which one person can hand another?

  In the third zeugma, the speaker’s faith in humanity had disappeared and was made to come back, whereas the painting had not disappeared at all. Moreover, faith in humanity is far less palpable than a painting on one’s wall. What gives this zeugma its flavor of oddness is that one of the meanings of the verb “restore” that it depends on is “to return something that has been lost”, while the other meaning used is “to make something regain its former, more ideal state”, and although these two senses of the same word are clearly related, they are just as clearly not synonymous.

  Finally, the last zeugma in our quartet plays on two sharply contrasting senses of the preposition “with”, one conjuring up the image of someone (Patrick) physically accompanying someone else (the speaker and the person being addressed), and the other communicating the emotional flavor (great pleasure) of a mental process (the anticipation of a reunion). As in the other cases, the zeugmatic use of “with” brings out the wide gap between two senses of one word, and to experience this distinction in such a crisp fashion is thought-provoking. We thus see that any well-designed zeugma will, by its very nature, automatically highlight certain semantic subtleties of the word (or phrase) around which it is built.

  For example, what does the word “book” mean? One would at first tend to say that it designates an object made of printed sheets of paper bound together in some fashion, and having a cover (and so forth and so on). This is often correct, but the following zeugma brings out a different sense of the word:

  The book was clothbound but unfortunately out of print.

  This sentence reminds us that the word “book” also denotes a more abstract concept — namely, the set of all copies available in stores or warehouses. Are we thus in the presence of one concept, or of two? And when someone says, “I’m translating this book into English”, are they using a third sense of the word? How many subtly distinct concepts secretly coexist in the innocent word “book”? It would be an instructive exercise to try to construct more zeugmas based on yet other senses of the word “book”, but we have other goals here, so we will leave that challenge to our readers.

  Instead, let’s look at a somewhat more complex zeugma:

  When they grew up, neither of those bullies ever had to pay for all the mean things that they did as, and to, younger kids.

  Here the trickiness is in the strange, lightning-fast shifting of meaning of “younger kids” as a function of whether it is seen as part of the phrase “things that they did as younger kids” or as part of the phrase “things that they did to younger kids”, since in the first case the younger kids are the ex-bullies themselves (or rather, the bullies that they once were), while in the latter case the younger kids are their victims.

  Some Revealing Zeugmas

  Although the zeugmas we’ve exhibited above are mostly quite amusing, it’s not for entertainment but for enlightenment that we’ve brought up the topic. And so let’s take a look at some cases that raise more serious issues.

  “You are always welcome in my home,” he said in English and all sincerity.

  This zeugma is clearly built around the word “in”, and the natural question here is whether we are dealing with one sense or two senses of the word. In a respectable dictionary, these two meanings would probably have distinct subentries. However, what about the following sentence?

  “You are no longer welcome in my home,” he said in anger and all sincerity.

  Are the two meanings of “in” here exactly the same? Perhaps — after all, they both apply to the mental states of a single person; but then again perhaps not — after all, one could replace “in anger” by “in an outburst of anger” but certainly one could not say “in an outburst of sincerity”. So it’s rather tricky. As a matter of fact, it would be impossible to give a definitive judgment on this issue. Indeed, we chose this example precisely because it brings out certain subtle nuances of the concept in. How does one recognize those situations that match the English word “in”? To put it another way, how does one recognize in-situations? What do all in-situations have in common, and how do some of them differ from others, and why would it be next to impossible to make a precise and sharp classification of all the types of in-situation?

  Let’s shift our attention from a preposition to a verb. Does the following sentence strike you as innocuous and perfectly acceptable (i.e., nonzeugmatic), or does it grate on your ears (thus it would be a zeugma)?

  I’m going to brush my teeth and my hair.

  Are the two types of brushing really just one thing deep down, or are they worlds apart? We might gain perspective on this question by looking at a similar example in another language. In Italian, one might easily and comfortably say:

  Voglio lavarmi la faccia e i denti.

  (In a fairly literal translation, this says, “I want to wash my face and my teeth.”) The fact that Italian speakers say things this way sheds light on how they perceive the world — namely, it shows that they perceive the act of washing one’s face and the act of brushing one’s teeth as belonging to the same category (both are types of washing),
and thus they are, in some sense, “the same act”.

  On the other hand, to speakers of English, brushing one’s teeth is not a kind of washing (washing usually involves soap of some sort, and most people would hesitate to refer to toothpaste as “soap”, though the two have much in common), so the sentence sounds zeugmatic (that is, its double application of the same word makes us smile). As for French, although occasionally one will hear “se laver les dents” (“to wash one’s teeth”), it is more common to say (and hear) “se brosser les dents” (“to brush one’s teeth”). The latter seems more natural to French speakers than the former. And thus we see that a phrase (“to wash one’s teeth and one’s face”) can be very zeugmatic in one language (English), can have a faintly zeugmatic flavor in another language (French), and can be totally nonzeugmatic in a third language (Italian).

  The preceding example shows how a zeugma can reveal a conceptual division that speakers of language A find blatantly obvious, while to speakers of language B it is difficult to spot. For instance, in English, we can say without any sense of oddness:

  Sometimes I go to work by car, and other times on foot.

  In German or Russian, however, these two forms of locomotion call for different verbs. When one takes a vehicle to arrive at one’s destination, then the verb “fahren” is used in German, whereas when one goes somewhere on foot, then the verb “gehen” is used. In Russian it’s trickier yet, because not only is there a distinction between going in a vehicle and going on foot, but also the choice of verb depends on whether this kind of motion is undertaken frequently or just one time. Thus a completely innocuous-seeming verb in English breaks up into several different verbs in Russian. In other words, what to English speakers seems to be a monolithic concept splits into four distinct concepts to Russian speakers.