Gödel, Escher, Bach: An Eternal Golden Braid (66 page)

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Authors: Douglas R. Hofstadter

Tags: #Computers, #Art, #Classical, #Symmetry, #Bach; Johann Sebastian, #Individual Artists, #Science, #Science & Technology, #Philosophy, #General, #Metamathematics, #Intelligence (AI) & Semantics, #G'odel; Kurt, #Music, #Logic, #Biography & Autobiography, #Mathematics, #Genres & Styles, #Artificial Intelligence, #Escher; M. C

BOOK: Gödel, Escher, Bach: An Eternal Golden Braid
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ing paths in the same way. These core symbols are like the large cities, to which everyone can make reference without ambiguity. (Incidentally, the fact that cities are localized entities should in no way be taken as indicative that symbols in a brain are small, almost point-like entities. They are merely symbolized in that manner in a network.) The fact is that a large proportion of every human's network of symbols is universal. We simply take what is common to all of us so much for granted that it is hard to see how much we have in common with other people. It takes the conscious effort of imagining how much-or how little-we have in common with other types of entities, such as stones, cars, restaurants, ants, and so forth, to make evident the large amount of overlap that we have with randomly chosen people. What we notice about another person immediately is not the standard overlap, because that is taken for granted as soon as we recognize the humanity of the other person; rather, we look beyond the standard overlap and generally find some major differences, as well as some unexpected, additional overlap.

Occasionally, you find that another person is missing some of what you thought was the standard, minimal core-as if Chicago were missing from their ASU, which is almost unimaginable. For instance, someone might not know what an elephant is, or who is President, or that the earth is round. In such cases, their symbolic network is likely to be so fundamentally different from your own that significant communication will be difficult. On the other hand, perhaps this same person will share some specialized kind of knowledge with you-such as expertise in the game of dominoes-so that you can communicate well in a limited domain. This would be like meeting someone who comes from the very same rural area of North Dakota as you do, so that your two ASU's coincide in great detail over a very small region, which allows you to describe how to get from one place to another very fluently.

How Much Do Language and Culture Channel Thought?

If we now go back to comparing our own symbol network with those of a Frenchman and a German, we can say that we expect them to have the standard core of class symbols, despite the fact of different native languages. We do not expect to share highly specialized networks with them, but we do not expect such sharing with a randomly chosen person who shares our native language, either. The triggering patterns of people with other languages will be somewhat different from our own, but still the major class symbols, and the major routes between them, will be universally available, so that more minor routes can be described with reference to them.

Now each of our three people may in addition have some command of the languages of the other two. What is it that marks the difference between true fluency, and a mere ability to communicate? First of all, someone fluent in English uses most words at roughly their- regular frequencies. A non-native speaker will have picked up some words from

dictionaries, novels, or classes-words which at some time may have been prevalent or preferable, but which are now far down in frequency-for example, "fetch" instead of

"get", "quite" instead of "very", etc. Though the meaning usually comes through, there is an alien quality transmitted by the unusual choice of words.

But suppose that a foreigner learns to use all words at roughly the normal frequencies. Will that make his speech truly fluent? Probably not. Higher than the word level, there is an association level, which is attached to the culture as a whole-its history, geography, religion, children's stories, literature, technological level, and so on. For instance, to be able to speak modern Hebrew absolutely fluently, you need to know the Bible quite well in Hebrew, because the language draws on a stock of biblical phrases and their connotations. Such an association level permeates each language very deeply.

Yet there is room for all sorts of variety inside fluency-otherwise the only truly fluent speakers would be people whose thoughts were the most stereotyped possible!

Although we should recognize the depth to which culture affects thought, we should not overstress the role of language in molding thoughts. For instance, what we might call two "chairs" might be perceived by a speaker of French as objects belonging to two distinct types: "chaise" and "fauteuil" ("chair" and "armchair"). People whose native language is French are more aware of that difference than we are-but then people who grow up in a rural area are more aware of, say, the difference between a pickup and a truck, than a city dweller is. A city dweller may call them both "trucks". It is not the difference in native language, but the difference in culture (or subculture), that gives rise to this perceptual difference.

The relationships between the symbols of people with different native languages have every reason to be quite similar, as far as the core is concerned, because everyone lives in the same world. When you come down to more detailed aspects of the triggering patterns, you will find that there is less in common. It would he like comparing rural areas in Wisconsin in ASU's which had been made up by people who had never lived in Wisconsin. This will be quite irrelevant, however, as long as there is sufficient agreement on the major cities and major routes, so that there are common points of reference all over the map.

Trips and Itineraries in ASU's

Without making it explicit, I have been using an image of what a "thought" is in the ASU-analogy-namely, I have been implying that a thought corresponds to a trip. The towns which are passed through represent the symbols which are excited. This is not a perfect analogy, but it is quite strong. One problem with it is that when a thought recurs in someone's mind sufficiently often, it can get chunked into a single concept. This would correspond to quite a strange event in an ASU: a commonly taken trip would become, in some strange fashion, a new town or city! If one is to continue to use the ASU-metaphor, then, it is important to remember that

the cities represent not only the elementary symbols, such as those for "grass", "house", and "car", but also symbols which get created as a result of the chunking ability of a brain-symbols for such sophisticated concepts as "crab canon", "palindrome", or "ASU".

Now if it is granted that the notion of taking a trip is a fair counterpart to the notion of having a thought. then the following difficult issue comes up: virtually any route leading from one city to a second, then to a third, and so on, can be imagined, as long as one remembers that some intervening cities are also passed through. This would correspond to the activation of an arbitrary sequence of symbols, one after another, making allowance for some extra symbols-those which lie en route. Now if virtually any sequence of symbols can be activated in any desired order, it may seem that a brain is an indiscriminate system, which can absorb or produce any thought whatsoever. But we all know that that is not so. In fact, there are certain kinds of thoughts which we call knowledge, or beliefs, which play quite a different role from random fancies, or humorously entertained absurdities. How can we characterize the difference between dreams, passing thoughts, beliefs, and pieces of knowledge?

Possible, Potential, and Preposterous Pathways

There are some pathways-you can think of them as pathways either in an ASU or in a brain-which are taken routinely in going from one place to another. There are other pathways which can only be followed if one is led through them by the hand. These pathways are "potential pathways", which would be followed only if special external circumstances arose. The pathways which one relies on over and over again are pathways which incorporate knowledge-and here I mean not only knowledge of facts (declarative knowledge), but also knowledge of how-to's (procedural knowledge). These stable, reliable pathways are what constitute knowledge. Pieces of knowledge merge gradually with beliefs, which are also represented by reliable pathways, but perhaps ones which are more susceptible to replacement if, so to speak, a bridge goes out, or there is heavy fog.

This leaves us with fancies, lies, falsities, absurdities, and other variants. These would correspond to peculiar routes such as: New York City to Newark via Bangor, Maine and Lubbock, Texas. They are indeed possible pathways, but ones which are not likely to be stock routes, used in everyday voyages.

A curious, and amusing, implication of this model is that all of the "aberrant"

kinds of thoughts listed above are composed, at rock bottom, completely out of beliefs or pieces of knowledge. That is, any weird and snaky indirect route breaks up into a number of non-weird, non-snaky direct stretches, and these short, straightforward symbol-connecting routes represent simple thoughts that one can rely on-beliefs and pieces of knowledge. On reflection, this is hardly surprising, however, since it is quite reasonable that we should only be able to imagine fictitious things that are somehow grounded in the realities we have experienced, no matter how

wildly they deviate from them. Dreams are perhaps just such random meanderings about the ASU's of our minds. Locally, they make sense-but globally ...

Different Styles of Translating Novels

A poem likèJabberwocky" is like an unreal journey around an ASU, hopping from one state to another very quickly, following very curious routes. The translations convey this aspect of the poem, rather than the precise sequence of symbols which are triggered, although they do their best in that respect. In ordinary prose, such leaps and bounds are not so common. However, similar problems of translation do occur. Suppose you are translating a novel from Russian to English, and come across a sentence whose literal translation is, "She had a bowl of borscht." Now perhaps many of your readers will have no idea what borscht is. You could attempt to replace it by the "corresponding" item in their culture-thus, your translation might run, "She had a bowl of Campbell's soup." Now if you think this is a silly exaggeration, take a look at the first sentence of Dostoevsky's novel Crime and Punishment in Russian and then in a few different English translations. I happened to look at three different English paperback translations, and found the following curious situation.

The first sentence employs the street name "S. Pereulok" (as transliterated). What is the meaning of this? A careful reader of Dostoevsky's work who knows Leningrad (which used to be called "St. Petersburg"-or should I say "Petrograd"?) can discover by doing some careful checking of the rest of the geography in the book (which incidentally is also given only by its initials) that the street must be "Stoliarny Pereulok". Dostoevsky probably wished to tell his story in a realistic way, yet not so realistically that people would take literally the addresses at which crimes and other events were supposed to have occurred. In any case, we have a translation problem; or to be more precise, we have several translation problems, on several different levels.

First of all, should we keep the initial so as to reproduce the aura of semi-mystery which appears already in this first sentence of the book? We would get "S. Lane" ("lane"

being the standard translation of "pereulok"). None of the three translators took this tack.

However, one chose to write "S. Place". The translation of Crime and Punishment which I read in high school took a similar option. I will never forget the disoriented feeling I experienced when I began reading the novel and encountered those streets with only letters for names. I had some sort of intangible malaise about the beginning of the book; I was sure that I was missing something essential, and yet I didn't know what it was ... I decided that all Russian novels were very weird.

Now we could be frank with the reader (who, it may be assumed, probably won't have the slightest idea whether the street is real or fictitious anyway!) and give him the advantage of our modern scholarship, writing

"Stoliarny Lane" (or "Place"). This was the choice of translator number 2, who gave the translation as "Stoliarny Place".

What about number 3? This is the most interesting of all. This translation says

"Carpenter's Lane". And why not, indeed? After all, "stoliar" means "carpenter" and "ny"

is an adjectival ending. So now we might imagine ourselves in London, not Petrograd, and in the midst of a situation invented by Dickens, not Dostoevsky. Is that what we want-, Perhaps we should just read a novel by Dickens instead, with the justification that it is "the corresponding work in English". When viewed on a sufficiently high level, it is a "translation" of the Dostoevsky novel-in fact, the best possible one! Who needs Dostoevsky?

We have come all the way from attempts at great literal fidelity to the author's style, to high-level translations of flavor. Now if this happens already in the first sentence, can you imagine how it must go on in the rest of the book? What about the point where a German landlady begins shouting in her German-style Russian% How do you translate broken Russian spoken with a German accent, into English?

Then one may also consider the problems of how to translate slang and colloquial modes of expression. Should one search for an "analogous" phrase, or should one settle for a word-by-word translation? If you search for an analogous phrase, then you run the risk of committing a "Campbell's soup" type of blunder; but if you translate every idiomatic phrase word by word, then the English will sound alien. Perhaps this is desirable, since the Russian culture is an alien one to speakers of English. But a speaker of English who reads such a translation will constantly be experiencing, thanks to the unusual turns of phrase, a sense-an artificial sense-of strangeness, which was not intended by the author, and which is not experienced by readers of the Russian original.

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