His Masters Voice

6

From the moment I landed on the roof, through all the meetings and conversations, the feeling never left me that I was playing a scientist in a grade-B movie. The feeling was strengthened by the room — or, rather, suite — in which they put me. I cannot remember ever having at my disposal so many unnecessary things. In the study stood a desk of presidential proportions; opposite it, two television sets and a radio. The armchair had controls for being raised, turned around, and lowered, no doubt so that between bouts of mental struggling one could take a little nap on it. Near it there was a large shape beneath a white cover. At first I took this for some piece of gymnastic equipment or a rocking horse (even that would not have surprised me), but it was a brand-new, very handsome IBM cryotronic calculator, which indeed proved useful to me. Wanting to join man more closely to the machine, the engineers at IBM had him work it also with his feet. Every time I pressed the “clear” pedal I expected, by reflex, to drive into the wall — the pedal was so much like a car accelerator. In the wall cabinet behind the desk I found a dictaphone, a typewriter, and also a small, scrupulously furnished bar.

But the most peculiar thing was the reference library. Whoever had assembled it must have been absolutely convinced that the more a book cost, the more valuable it was. Thus there were encyclopedias, thick volumes on the history of mathematics and the history of science — even one on Mayan cosmogony. Perfect order reigned among the backs and bindings; and complete nonsense in the printed contents. During that whole year I did not use my library once.

The bedroom was also done up nicely. In it I found an electric heating pad, a medicine chest, and a small hearing aid. To this day I do not know whether this was a joke or a mistake. Taken together, everything expressed the careful execution of the order: “Top quarters for a top mathematician.” Glancing at the night table, I saw a Bible and was reassured — yes, they truly had my welfare at heart.

The tome that contained the stellar code, delivered over to me with great ceremony, was not especially interesting — at least not at first reading. The beginning went: “0001101010001111100110111111001010010100.” The rest was more of the same. The only additional information given me said that the code unit definitely was made up of nine elementary signs (zeros and ones).

Taking possession of this new abode, I put on my thinking cap. I reasoned more or less as follows: Civilization is a thing both necessary and accidental; like the lining of a nest, it is a shelter from the world, a tiny counterworld that the large world silently tolerates, with the toleration of indifference, because in it there is no answer to the questions of good and evil, beauty and ugliness, laws and customs. Language, the creation of civilization, is like the framework of the nest; it binds all the bits of lining and unites them into the shape that is deemed necessary by the occupants of the nest. Language is an appeal to the joint identity of the nesting beings, their common denominator, their constant of similarity, and therefore its influence must end immediately beyond the edge of that subtle structure.

The Senders had to know this. It was expected that the content of the signal from the stars would be mathematics. Great stock, as you know, was placed in the almighty Pythagorean triangles; we were going to greet, across space, other civilizations — with Euclid’s geometry. The Senders chose another way, and I believed that they were right. With ethnic language they could not break free of their planet, because every language is pinned to a local foundation. Mathematics, on the other hand, is a severance too complete. It cuts bonds not only locally; it parts with the limitations that have become parameters for villainies and virtues; it is the result of a search for a freedom that dispenses with every tangible verification. It is the act of builders whose wish is that the world should never be able, not in any way, to disturb their work. Consequently, with mathematics one can say nothing about the world — it is called “pure” for the very reason that it has been purified of all material dross, and its absolute purity is its immortality. But precisely therein lies its arbitrariness, for it can beget any sort of world, as long as that world is consistent. Out of the infinite number of possible mathematics we have chosen one; our history decided this for us with its various unique and irreversible vicissitudes.

With mathematics one may signal only that one Is, that one Exists. If one wishes to act more effectively at a distance, the sending of a “production recipe” becomes inevitable. But such a recipe presupposes a technology, and technology is a transient, mutable condition, a passing from one set of materials and methods to another. And what of a description of an “object”? But an object, too, may be described in an infinite number of ways. It was an impasse.

There was one thing that bothered me. The stellar code had been transmitted in a continuous fashion, in uninterrupted repetitions, and this made no sense, because it hindered recognition of the signal as a signal. Poor Laserowitz had not been altogether mad: zones of periodic silence indeed seemed necessary — more, imperative — as an indication of the artificial nature of the signal. Periods of quiet would have drawn the attention of any observer. Why, then, was this not done? The question haunted me. I tried turning it around: the lack of interruptions seemed a lack of information, information indicating the intelligent source of the emission. But what if actually that was additional information? What could such a thing mean? That the “beginning” and the “end” of the message were nonessential. That one could read it starting at any point.

The idea fascinated me. I understood now why my friends had been so careful not to tell me anything about the ways in which the “letter” had been attacked. I was, as they wanted me to be, entirely without preconceptions. At the same time I had to wage the battle, so to speak, on two fronts at once: the main “opponent,” of course, whose motives I tried to guess, was the unknown Sender, however, at the same time I could not help also thinking, at every step of my reasoning, about whether or not the mathematicians of the Project had taken the same path as I. All I knew about their work was that it had yielded no definitive result, not merely in the sense that they had failed to decipher the “letter,” but in the sense, too, that they remained uncertain — in other words, they had not proved — that the “letter” belonged to the category of information that had been hypothesized: the “thing-process.”

Quite like my predecessors, I felt that the code was overly laconic. It could have been supplied, after all, with an introductory part, showing, in simple statements, how one ought to read it. Or so it seemed. But the laconicism of the code was not an objective property of the code; it depended, rather, on the degree of knowledge of the receiver — or, more precisely, on the difference in knowledge possessed by sender and receiver. The same information could be found sufficient by one receiver and “too laconic” by another. Any object, the simplest object, contains, potentially, an infinite amount of information. Therefore, however much we detail a transmitted description, it will always be unnecessarily precise for some and fragmentary for others. The difficulty we were encountering only showed that the Sender was addressing parties more advanced than mankind at the given historical moment.

Information that is divorced from objects is not only incomplete; it invariably represents some kind of generalization. Its referent is never fully designated. On an everyday basis we are of another opinion, since this fuzziness in the designation of objects is, in ordinary life, barely perceptible. It is the same in science. Although we now know that speeds cannot be added arithmetically, we do not make a relativistic correction when we add the velocity of a ship to the car driving on its deck, because the correction, for speeds not near that of light, is so minuscule as to be meaningless. Now, there exists an informational equivalent to this relativistic effect: the notion of “life” is practically identical for two biologists, one of whom lives in Hawaii and the other in Norway. Yet the tremendous gulf between two alien civilizations has caused the seeming identity of many notions to fall apart. Certainly, had the Senders used, for designated objects, the set of heavenly bodies, there would not have been this problem. And if they designated atoms? Atoms as “things” to a considerable degree depend on one’s knowledge of them. Eighty years ago an atom was “very similar” to a miniature solar system. Today it no longer is.

Let us suppose that they send us a hexagon. In it one can see the plan for a chemical molecule, or for a bee’s honeycomb, or for a building. An infinite number of objects correspond to that geometrical information. One can determine what the Senders have in mind only by specifying the building material. If, say, the material is to be brick, the class of solutions will indeed be narrowed down, and yet we will still have a set of infinite magnitude, because it is possible, after all, to construct an endless number of hexagonal buildings. The transmitted blueprint ought to be provided with precise measurements. But there exists a material of which the bricks themselves determine the exact measurements. Atoms. In their bonding it is impossible to bring them closer at will, or to move them farther apart. Therefore, having before me only a hexagon, I would think that the Senders meant a molecule of a chemical compound, one constructed of six atoms or of six groups of atoms. Such a statement very significantly limits the field of further searching.

Let us assume — I said to myself — that the “letter” is a description of a thing, a description, moreover, on the molecular level. The kernel of this preliminary thinking was the consideration of the letter’s “content” as a thing having no beginning or end, and therefore circular. It could be either a “circular object” or a circular process. The distinction between the one and the other, as was pointed out, depends in part on the scale of observation. If we lived a billion times more slowly, and correspondingly longer, if a second — in this fancy — equaled an entire century, we would certainly conclude that the continents of the globe were processes, seeing with our own eyes how changeable they were, for they would be moving before us no less than waterfalls do, or ocean currents. And if, on the other hand, we lived a billion times faster, we would conclude that the waterfall was an object — because it would present itself to us as something highly immobile and immutable. The difference between “object” and “process,” therefore, gave no need for concern. It was now only necessary to prove, and not merely to speculate, that the “letter” was a “ring,” just as the molecular model of benzene is a ring. If I did not wish to send a two-dimensional image of that molecule, but chose, rather, to code it into some linear form, a series of successive signals, the place in the benzene ring from which I would begin my description would be unimportant. Every place would serve equally well.

It was from this position that I proceeded to the translation of the problem into the language of mathematics. What I did I cannot present plainly, since our everyday language lacks the required concepts and words. I can only say, in general, that I studied the purely formal properties of the “letter” — treating it as an object mathematically interpreted — for features that are of central interest in topological algebra and the algebra of groups. In doing this, I employed the transformation of transformational sets, which gives the so-called infragroups or Hogarth groups (named after me, since I was the one who discovered them). If I obtained, as a result, an “open” structure, that would still prove nothing, because it could be that I had simply introduced an error into my work, going on some false assumption (such an assumption might be, e.g., the assertion of the number of code signs in a single “unit” of the message). But it happened otherwise. The “letter” closed beautifully for me, like an object separated from the rest of the world, or like a circular process (to be more precise, like the DESCRIPTION, the MODEL of such a thing).

I spent three days setting up a program for the computer, and the computer carried out the task on the fourth. The result said that “something, in some way, closes.” The “something” was the letter — in the totality of the interrelations of its signs; but as for the “how” of that closing, I could only make certain guesses, because my proof was indirect. The proof showed only that the “described object” was NOT “topologically open.” But to reveal the “means of closure” with the aid of current mathematical methods was impossible for me; such a task was several orders of difficulty greater than the one I had managed to surmount. The proof, then, was very general — one could even say vague. On the other hand, not every text would have displayed this property. The score of a symphony, for example, or a linear coding of a television image, or an ordinary linguistic text (a story, a philosophical treatise) does not close in that fashion. But the description of a geometric solid closes, as does that of something as complex as a genotype or a living organism. The genotype, true, closes differently from the solid. But by going into such distinctions and details I fear that I will be confusing the reader rather than explaining to him what I did with the “letter.”

Let me just emphasize that from penetrating to the “sense” — or, to put it even more colloquially, to “what the letter was about” — I remained as distant as I had been before starting this work. Out of the innumerable features of the “letter,” I recognized, and recognized only indirectly, one, one that had to do with a certain general property of the structure as a whole. Because I had succeeded so well, I later tried to attack that “second problem” — the resolution of the structure in its “closure” — but during my tenure at the Project I came up with nothing. Three years later, no longer with the Project, I renewed my efforts, because the problem had been pursuing me like a stubborn ghost. I achieved only this: I proved that using the apparatus of the topological and transformational algebras would NOT enable one to solve the problem. Which, of course, I had no way of knowing when I first sat down to the task. In any case, I provided a powerful argument in support of the contention that we had indeed received from the Cosmos the sort of thing to which could be attributed — considering the degree of concentration and cohesion that produced “closure” — the qualities of an “object” (that is, of the description of an object — I am abbreviating here).

I presented my work not without apprehension. It turned out, however, that I had done something that no one else had thought of — for the reason that during the preliminary discussions the idea had won out that the letter must be an algorithm (in the mathematical sense) and therefore a general-recursive function, and the search for the values of that function had swamped all the computers. This made sense to the extent that, if the problem were solved, the solution would carry with it information pointing, like a road sign, to further stages of translational work. But the order of complexity of the letter-as-algorithm was such that the problem was not solved. Meanwhile, the “circularity” of the letter had indeed been noticed, but it was considered of no great importance, not promising — in that initial period of great hopes — any quick or appreciable success. Then, later on, everyone became so mired in the algorithm approach that they could not free themselves from it.

One might think that I had achieved no little triumph at the very beginning. I proved that the letter was the description of a phenomenon, and inasmuch as all the empirical research was going in precisely that direction, I gave it, so to speak, the blessing of a mathematical proof, guaranteeing that this was the right track. I thereby brought together those who were divided, because between the information theorists and the information engineers a breach had grown. The antagonists, finally, were referred to me. The future was to show how little I had accomplished — emerging well from an encounter with only my terrestrial rivals.