Science After Babel, page 12
Under the Astrologer’s Tent
As the ruler of the soul, Ptolemy wrote in the Tetrabiblos, Saturn has the power to make men sordid, petty, mean-spirited, indifferent, mean-minded, malignant, cowardly, diffident, evil-speaking, solitary, fearful, shameless, superstitious, fond of toil, unfeeling, devisors of plots against their friends, gloomy, taking no care of their body. We know the type. Some men are just rotten.27 Brian Greene is under the astrologer’s tent. Ptolemy’s heavy arm is draped in friendship over his own frail shoulder. From Democritus to Steven Weinberg, a great many physicists and philosophers find themselves there. Einstein, too. They disagree about the particulars of planets and particles, but not about the chief thing, the idea that something must account for everything.
The astrologers know perfectly well that everything encompasses a lot. They know, too, that as astrologers, they are obliged to trace a connection in nature between something and everything, a form of force or influence, a tangible, if tentative, line. They have not been reticent. They are full of ideas. Ptolemy appealed to a radiation of sorts proceeding from Saturn, and Al-Kindi, writing in the rosy springtime of Islamic philosophy, to stellar rays. Troubled by action at a distance, Albert the Great knew better. A lighthouse in Italy, he remarked, cannot influence a lighthouse in England. Brian Greene has made his appeal; he has pitched his case. The elementary particles are fundamental. They are the something that explain everything. If his own discipline of theoretical physics happens to have a prominence denied Assyriology, he may be forgiven a shiver of satisfaction. But what is the connection between something and everything? It is an obvious question. Beyond saying that the laws of physics govern the elementary particles and everything made of the elementary particles, Greene has nothing more to say and says nothing more about it. No wonder. Greene was born under the sign of Aquarius. We are like that, we Aquarians, taciturn.
It requires a certain coldness to pick all this apart. Nothing in nature is fundamental to everything. If one is doing particle physics, the elementary particles are more fundamental than contracts; in drafting a contract, it is the other way around. Quantum fields are the cynosure of quantum field theory; they do not count in physiology. Philosophers hoped that it would be otherwise and that some set of objects would flaunt proudly their fundamental character, but what is fundamental is inevitably a relative judgment, partial, incomplete, and always changing. If a set of objects is fundamental, it cannot explain everything; if it explains everything, it cannot explain anything. This is not a paradox. It is the way things are.
In the world as it is, there is no relationship in nature answering to causality. Thus al-Ghazali and thus David Hume. Neither is there a relationship in nature between the elementary particles and the world or worlds in which they are embedded.28 These metaphysical imputations have all dwindled and disappeared. What remains is a relationship between theories and their models, and not between elementary particles and things—bags or otherwise. Inference is the source of influence, and beyond inference, there is nothing. Is there a relationship in nature that corresponds to the inferential relationship between theories? Not obviously. Hardly ever. To have discovered this is among the great achievements of Western science, but it has come at a price, a profound withdrawal from the world. Under the astrologer’s tent, a sense of gregarious gaiety yet prevails. Ptolemy’s arm is not yet heavy on Brian Greene’s shoulders; but deep down the astrologers know that the gaiety will not last. The world in which they could cast spells and conjure with action at a distance has disappeared. What remains is the logician’s cold light, cold comfort, I suppose, but better than no comfort at all:
But this rough magic
I here abjure, and, when I have required
Some heavenly music, which even now I do,
To work mine end upon their senses that
This airy charm is for, I’ll break my staff,
Bury it certain fathoms in the earth,
And deeper than did ever plummet sound
I’ll drown my book.29
18. BLIND AMBITION
I BELIEVE. I WANT. I DO. WHAT COULD BE SIMPLER? INTELLIGENCE IS the overflow of the mind in action. In dreaming or desiring, on the other hand, I occupy a world bounded entirely by memory, meaning, and belief: I need do nothing. That overflow is entirely internal. In either case, our intelligence is directed toward specific objects or states of affairs. I believe—what? That Clearasil Starves Pimples or that Pepsi Is the Choice of a New Generation; I desire—what? That the young Sophia Loren might step smoldering from the television set for perhaps an hour or that I might win a MacArthur Fellowship (the academic equivalent of the Irish Sweepstakes). What I believe (or desire) and what is believed (or desired) are connected by something very much like an intentional arrow, a kind of miraculous metaphysical instrument. The relationship between my thoughts and their objects is thus strange from the first. But this relationship between what I think and what I think about is duplicated in language itself: like the thoughts that they express, the sentences of a natural language transcend themselves in meaning.
In seeing things from a first-person stance, with the entire world revolving around my own ego—a kind of Ptolemaic system in psychology—I direct the arrow of intentionality from the inside out, infusing the objects and properties of the external world with all of the significance that they ever possess. I assume, of course, that others do as much. Read forward, the arrow of intentionality goes from what I feel to what I do; read backward, from what is done to what is felt. The sense that we are all in this together arises only as the result of a supremely imaginative kind of back-pedaling; the interpenetration of two human souls, when it occurs, is wordless.
There is more. Each of us acts in the world as both subject and object: we do, and things are done to us. In moving away from the lunatic solipsism in which my ego exists in the absence of all others, I endow those human beings in my own perceptual ken with more or less the same cognitive states that I myself enjoy. This is the basis for a sense of sympathy. The endowment itself, I presume, may be reversed, as when I myself figure in someone else’s awareness as an imaginatively constructed subject of experience. But here is a queer, artful point. The inferences that I make about others, others make about me. My inferences about others I cannot verify, but their inferences about me represent something like the backward wash of a familiar wave. A subject acting simultaneously as a psychological object enjoys a unique Archimedean perspective on the system of inferences by which mental life in the large is constructed.
This confluence of circumstance suggested to the American philosopher John Searle a very deft argumentative maneuver, something akin, really, to a movement in judo. His arguments were prompted by work undertaken at Yale by the psychologist Roger Schank. Like many other American theorists, Schank has approached the problem of artificial intelligence with a kind of bluff, no-nonsense sense that getting a machine to understand something is a matter of attending to the details in a patient, straightforward way. In a photograph at the back of his book, The Cognitive Computer, he stands with his arms folded over his ample belly, scowling directly into the camera, an expression of earnest ferocity on his face, as if to suggest that by the time he got through with them, those computers of his would either shape up or ship out. His aim, as he explains things, is to teach the digital computer to comprehend simple stories of the sort that might be told to children.
The exercise is set out without irony. The education of the digital computer in this regard commences with what Schank calls a script—a kind of running, rambling background account in which the saliencies of various stories are set out and explained. With the scripts in hand, the computers are prepared to make sense of what they read. They are then interrogated with a fine eye directed toward telling whether they have understood what they have absorbed. In fact, Schank’s machines do get quite a bit right; the record of their conversation is admirable, and the unbiased reader often has the feeling that just possibly he is reading something strange and remarkable.
It is against this conclusion that Searle has set his face. It is a simple fact, Searle begins, that he is utterly ignorant of the Chinese language. Suppose that he were to be locked in a room with a large sample of Chinese script—the samples, say, arranged on cardboard sheets. Now imagine that Searle were to be given “a second batch of Chinese script together with a set of rules for correlating the first batch with the second.” The rules are in English. A third collection of scripts is presented Searle. And another set of rules. This makes for three separate sets of Chinese symbols and two sets of English rules.
From Searle’s point of view, the material he confronts is an incomprehensible jumble. From the outside, where sense is made of all this, those Chinese symbols have a specific meaning. The first corresponds to a general script—the sort of thing that a computer would need in Schank’s setup to make sense of a story. The second is actually a story in Chinese. The third represents a list of Chinese questions. From time to time, those questions are presented to Searle with a nudge and a wink and a tacit request that he say something. In answering, Searle consults his set of rules. The two sets enable Searle to match the questions to the story by means of the background script. In this respect, Searle remarks, he is precisely in the position of the digital computer.
But (a very excited, explosive but!) under such circumstances would there be any inclination to say that a subject so situated understands the meaning of the symbols he is manipulating? An observer might come to this conclusion. Put a question in Chinese to this character, after all, and he answers in Chinese. Yet this is not at all how Searle himself sees things. Whatever he may be able to say in Chinese, he remains confident that he understands nothing of what he has said and is prepared to champion his ignorance defiantly. Some great notable aspect of what it means to understand a language has simply been overlooked.
For the most part, computer scientists have tended to ignore Searle’s argument and the point of view that it represents. It had long been known in science that you cannot beat something (a research grant) with nothing (a destructive argument), and what Searle had to offer them was nothing at all. Analytic philosophers responded promptly to Searle. The results are confusing. A great many superbly confident rebuttals appear to contradict one another. As for myself? When pressed on the point, I tend to run my hands through my hair or tug mournfully at my ears, gestures I am convinced that suggest that I have something tack-sharp to say were I willing only to say it.
19. KOLMOGOROV COMPLEXITY
THE AIM OF SCIENCE, RENÉ THOM ONCE REMARKED AS WE SIPPED espresso in a café near the Opéra, is to reduce the arbitrariness of description. I nodded my head and fixed my face in an expression that I thought conveyed a sense of alert but sophisticated appreciation. On the view of things that I had been taught at Princeton, the aim of science, insofar as science has any aims whatsoever, is a matter either of explanation or prediction. Going further, explanation involves seeing in the particular (this swan is white) intimations of the general (all swans are white) in such a way that the particular, when properly described, follows deductively from the general. In moving upward (past the swans, at any rate), the scientist ascends toward the laws of nature.
I thought to ask Thom what he meant, but by the time I had posed my question in a way that suggested I knew the answer, Thom was industriously applying himself to an apple tart.
Science is pursued, I think, for many reasons, not the least of which is to fill up the time. In this regard, it is always successful. Insofar as science is purely an abstract activity, like mathematics, chess, or nuclear strategy, it is undertaken chiefly for the acquisition of that magical moment in which things that formerly stood distinct and separate fall together in a limpid whole. Such is intellectual bliss—paler by far than physical bliss, but nothing to sneeze at either.
Blisswise, certain concepts form a tight circle in the sense that each may be used to define and justify the other. Complexity, information, randomness, order, and pattern (or form) are connected like the members of a family of cheeses: Gruyère, Brie, Port Salut, Camembert, but not Velveeta. This suggests that they may all flourish, or fall, together. Shady characters of all sorts—semioticians, anthropologists, linguists, sociologists, communication theorists—are especially partial to concepts of just this kind, perhaps because of the way that their names fill the mouth when uttered. This is no reason to reject these concepts out of hand, but no cause for congratulation either.
The technician, or the astrologer, no less than the rest of us, is pattern intoxicated. Reading the charts or the stars, he sees the subtle seams by which nature is constructed—the pattern at the bottom (or top) of things. A pattern is peculiar in that knowing part (moving in) one is likely to guess correctly at the rest (moving out). The patterns scouted by the stock market technician are especially plain: if they are there at all, they are there on the surface of things. On the other hand, consider the numbers 1, 4, 1, 5, 9, 2, 6, 5, 3, .... There is not much by way of pattern here; still less when the sequence is extended: 5, 8, 9, 7, 9, 3,.... A cursory examination might suggest that these numbers are quite without significance. Not so. They represent the decimal expansion of pi, to use an example that, like Mexican food, keeps coming up. Here the pattern is a matter of the way in which the sequence is generated and lies hidden from the surface.
There is pattern, then, and generative pattern. Suppose the world contracted to a pair of symbols: 0 and 1, say. A binary sequence is a system of such symbols in a distinct order—0, 1, 1, 0, 1, 1, for example—and of a specified length—six in the present case. Six binary symbols may be arranged in 64 separate sequences. In the general case, a sequence of length n (there are n symbols) may be recast in 2n separate ways as 2n separate sequences. Sixty-four is just 26, where 26 is 2 multiplied by itself 6 times.
Imagine now that binary sequences are being produced at random—by the action of a roulette wheel, for example. Of the two sequences
the first seems distinctly less likely than the second: a man idly flipping coins does not expect to come up with a run of six heads. Yet in point of probability, the two sequences are reckoned alike. There are sixty-four possible sequences in all. Each has a l-in-64 chance of occurring. The most natural probability distribution over the space of n-place binary strings assigns to each string the same probability—2−n. It goes against the grain, mine, at any rate, to accept this conclusion, especially when n is large; but nothing in the sequences themselves indicates obviously that one is less (or more) likely to occur than any other.
Sometime in the 1960s, Russian mathematician Andrey Kolmogorov thought to argue that the degree to which a given binary string is random might be measured by the answer to a simple question: to what extent can the string be re-described? Kolmogorov thought of the possible re-descriptions of a given string as instructions to a fixed computer. Now if S is a binary string its length is measured in bits. An n-place binary string is n bits long. The most obvious re-description of S is S itself—the sort of thing I might send you to make sure that you get what I mean. In the case of sequences such as 2, nothing less will do. 1, on the other hand, may be expressed by a single terse command: Print 0 six times. A simpler description of binary string is thus a shorter description of the string. Sequences that cannot be generated by shorter sequences, Kolmogorov argued, are complex or random. This is a definition. But random sequences are precisely those that are rich in information. The definition thus ties together four concepts loitering casually at the margins of this discussion: randomness, compactness, complexity, and information. Playing an unusually inconspicuous role is the notion of probability.
Kolmogorov first spoke on this subject in a brief note published in 1967. His work was duplicated by the American mathematician Gregory Chaitin, who experienced a flash of intellectual lightning while an undergraduate at the City University of New York, sitting among students baffled by long division. The subject is known now as algorithmic information theory. Those algorithms are a reminder that Kolmogorov thought of descriptions in terms of inputs to a fixed computer.
Quite surprisingly, the problem of decisively determining whether a given string is random turns out to be unsolvable. If a shorter description of the string may actually be produced, well and good. If not, all bets are off. A shorter description may exist; then again, it may not. There is no demonstrative telling. The decision problem for complexity is recursively unsolvable. Like truth, randomness is a property that remains ineluctably resistant to recursive specification.
Kolmogorov’s elegant and simple idea—a little jewel, a diamonoid—achieves its startling effects by means of an especially simple series of inferences. If all else fails, a binary sequence of length n may be re-described by a binary sequence of just the same length. There are 2n such sequences, and 2n − 2 sequences shorter than this. But on any reasonable interpretation of complexity, sequences within a fixed integer k of n itself must be reckoned random or complex if the n - place sequences are themselves reckoned random or complex. It follows that only 2n − k − 2 sequences are less complex than n − k. If k = 10, the ratio of 2n − 10 to 2n is precisely 1 in 1,024; the ratio of simple to complex sequences is thus on the order of 1 in 1,000. This means that of 1,000 sequences of length n, only one can be compressed into a program more than 10 bits shorter than itself. The number of purely random sequences grows exponentially with n, of course, and this implies that randomness and complexity are the norm in the general scheme of things. But if most sequences are random, the appearance of 1 should prompt a natural sense of surprise; sequences like 2 are what one expects and what one generally gets.
This line of argument, of course, resolves one problem only by embedding it within another—resolution by delayed dismay.
