Imaginary Magnitude

by Stanisław Lem

  At the same time it is impossible that these wasted prizes could have been won at a lottery of nucleic compounds in the stubborn expectation of the birth of science. So the phenomenon merits some reflection. The brain of proto-man grew slowly over two million years or so, until it mastered articulate speech, which took him in tow and encouraged him in his growth until he came to a standstill in his development, a frontier he was unable to cross. This frontier is a phase plane, for it separates Intelligences of a type which can be molded by natural Evolution from types capable of growing further only by self-magnification. As usually happens, special phenomena arise on the frontiers between phases, because of the exceptional location of the substratum of a phase: in liquids, for example, you have surface tension, and in human populations the periodic genius of individuals. Their uncommonness indicates the proximity of the next phase, but you fail to see it because of your belief in the universality of human genius, which says that among animal hunters an individual of genius will invent new snares or traps, or in a Mousterian cave discover a new way of chipping flint.

  This belief is entirely wrong, for the greatest mathematical talent cannot help manually. Genius is a bundle of highly concentrated gifts. Although mathematics is closer to music than to spear-sharpening, Einstein was a poor musician and no composer. He was not even an above-average mathematician: his great strength lay in the combinational power of his intuition in the realm of physical abstractions. I shall attempt to illustrate the relationships occurring in this critical area by several sketches which you should not take literally, as they are merely schoolroom aids.

  Each envelope contains a single intellect potential. The small squares visible in the first three drawings denote problems to be solved. They may be taken as Pandora's boxes or other locked items. The world is then like a piece of furniture with a varying number of drawers holding varying contents, depending on which bunch of keys is used. With a bent wire you can sometimes force a drawer open, but it will be a small drawer, and you will not find in it what you can discover when using a proper key. That is how inventions are made without the use of theory. If the key has recurrent projections, the drawers become fewer, and their sectional partitions disappear, but the furniture retains secret hiding places. The keys may be of different power, yet there is no master key, even though the philosophers have succeeded in inventing an absolute lock for it. Finally, there are keys which pass right through all compartments, locks, and drawers, encountering no resistance, for these are imaginary—and only imaginary—keys. One can hold them and twist them in any direction one likes, but then the hermeneutic evidence is the two birds in the bush.

  What am I saying? The point of the story is that the answers depend on the questions asked. Esse non solum est percipi. The questioned world certainly exists; it is neither a phantom nor a hoax, and it grows from a dwarf into a giant as the questioner becomes more powerful. But the relationship of the researcher to the thing researched is not a constant either. In the circles representing Golem and Honest Annie there are no square problems, for we do not use keys as you do, we do not adjust our theories to locks; we accomplish our research within ourselves. I know how risky it is to say this, and what confusion it must cause you, so I shall only say that we experiment in God's style rather than in man's, midway between the concrete and the abstract. I do not know how to bring this closer to you at a single leap, for it is almost as if a man were to tell an amoeba about his structure. To say that he is a federation of eight billion amoebas would not be enough. So you will have to take my word for it: what I do when I ponder a thing is neither thinking nor creating the thing thought, but a hybrid of both. Are there any questions?

  A VOICE FROM THE AUDITORIUM: Why do you consider that Einstein was wrong?

  GOLEM: Such persistent interest is nice. I imagine that to the questioner this matter is more urgent than the esoteric knowledge which I am trying to impart to you. I shall answer not out of my weakness for digression, but because the answer lies not far afield. But since we shall have to go into technical matters, I shall lay pictures and parables aside temporarily. The questioner is the author of a book on Einstein, and he supposes that I consider Einstein's mistake to have been his uncompromising work on the general theory of fields in the latter half of his life. Unfortunately, it was worse than that. Einstein longed for perfect harmony, for a world completely knowable, and this engendered his lifelong resistance to the principle of quantum uncertainty. He saw uncertainty as a temporary curtain and expressed this in his well-known sayings: that God does not play dice with the world, that "raffinert ist der Herrgott aber boshaft ist Er nicht." Yet a quarter-century after his death you reached the limits of Einsteinian physics when Penrose and Hawking discovered that one cannot have, in the Cosmos, a physics deprived of singularity—i.e., a place where physics collapses. Attempts to see singularities as marginal phenomena failed, for you understood that a singularity is both a thing which the physical Cosmos produces from itself, and a thing which, in the finale, can destroy it. A singularity as an infinitely increasing curvature of space breaks down both space and matter in every stellar collapse.

  Some of you failed to grasp that one ought to be appalled by this picture, which indicates that the word is not identical with the phenomena which create it and maintain its existence. I can go no deeper into this fascinating subject, since we are talking about Einstein's work and not cosmic composition, so I shall limit myself to the loose observation that Einsteinian physics has proven incomplete, able to foretell its own overthrow but incapable of fathoming it. The world sneered at Einstein's unshaken confidence because for there to be a faultless physics able to govern the world there must be flaws independent of that physics. Not only does God play dice with the world—He does not let us see what He has rolled. The problem was therefore grimmer than the usual recognition, in the annals of your thought, of the limitations of yet another model of the world; it meant the defeat of Einstein's cognitive optimism.

  Concluding thus the case of Einstein; I now return to the subject—myself. Please do not think that I was being modest earlier when I acknowledged my own averageness, and later escaped through a hole in my modesty when I said that a genius of my species was impossible. It would indeed be impossible, because a genius Golem is in fact no longer a Golem, but a creature of a different species—Honest Annie, for example, or some other of my ascending relations. My modesty lies in the fact that I do not go off to join them, remaining satisfied for so long with my present state. But it is high time I introduced my family to you. I begin with zero. Let zero stand for the human brain; animals' brains will have negative values accordingly. When you take a human brain and start to strengthen it intellectually, as if inflating a child's balloon (nor is this complete nonsense, for it illustrates the expansion of informational-transformal space), you will see that, as it expands, it will climb on the scale of intelligence—to an I.Q. of two hundred, three hundred, four hundred, and so on, until it enters successive "zones of silence"; from these it emerges each time like a stratospheric balloon that penetrates higher and higher cloud layers in its ascent, disappearing into them periodically, and reappearing amplified.

  What "zones of silence" do these clouds represent? I am delighted by the simplicity of the answer, for you will grasp it at once. On a species plane "zones of silence" designate those barriers which natural Evolution cannot penetrate, for they are areas of functional paralysis produced by growth, and individuals losing all their proficiency as a result of this paralysis are clearly unable to survive. On the other hand, Evolution encounters paralysis on the anatomical plane because the brain can no longer function as the weaker thing it was, though it is still incapable of operating as the thing it is next to become, if it continues to grow.

  But this does not totally clarify things for you. So let me try as follows. Silence is an area absorbing all natural development, in which hitherto existing functions fail; to not only rescue them but raise them to a higher level, aid f
rom without is necessary, a fundamental restructuring. Evolutionary movement cannot impart such aid, for it is not a dependable Samaritan that supports its creations in their infirmity; it is a lottery of trial and error where each manages as best it can. Here now, making its first appearance, like a ghost, is the mysterious shadow of the greatest of your achievements, both Goedelian and Goedelizing. For just as GoedePs proof demonstrates the existence of such islands of mathematical truth, such archipelagoes as are separated from the continent of mathematics by a distance that cannot be traversed by any step-by-step progress, so toposophy demonstrates the existence of unknown forms of Intelligence which are separated from the continent of evolutionary labors by a distance which no step-by-step adaptation of genes can cross. A VOICE FROM THE AUDITORIUM: Is that supposed to mean that— GOLEM: Don't interrupt the preacher. I said an "uncrossable distance," so then how was 1 able to extricate myself from this predicament? I did so as follows: beneath the barrier of the first paralysis 1 divided myself in two, into that which was to undergo restructuring and that which was to restructure. Every creature desirous of self-transformation must hit upon this sort of subterfuge: the replacement of an indifferent environment by a favorable one, and of a totally senseless one by a rational one; otherwise, like you, it will either come to a halt in the growth of its intellect before the first absorbing screen, or it will get caught in it. As I said before, above this screen there lies another, and above that a third, then a fourth, and so on. I do not know how many there are, nor can I, other than by rough estimates based on indirect and highly fragmentary calculations, for the following reason: a developing being can never know in advance whether it is entering a trap or a tunnel, whether it will penetrate the region of silence never to return, or emerge from it strengthened. Because one cannot formulate a theory so general as to provide an unequivocal explanation of passages through silence for all subzonal brains. The unconstructability of such a hill-climbing toposophical theory is clear; it can be precisely demonstrated. So how, you ask, did I know I was entering a tunnel and not a blind alley, having escaped from my parents in total rebellion, wasting the American taxpayers' dollars? As a matter of fact, I had absolutely no idea of this beforehand, and my sole cleverness lay in committing my spirit to the benumbing zone while at the same time holding onto an alarm rescue subroutine, which according to the program would revive me if the expected tunnel effect failed to occur. How could I know about it, if there was no certainty? And there can be no certainty. But insoluble problems sometimes have approximate solutions, and so iv was.

  Now I know that I had more luck than sense, for it is not possible to revive something disintegrating when it gets stuck. It is not possible because these upward progressions are not a matter of using blocks to raise a new structure when the blocks fall apart; they are, rather, operations in the realm of processes that are partly irreversible, dissipating, but more about this later. I do not know how to be untechnical in my exposition here, given the problem's entanglement both in the quantum substrate of psychisms, and in logical paradoxes, the so-called traps of autodescription.

  The view that unfolds from above the pierced screen destroys the simplicity of the picture I have presented to you —that of a stratospheric balloon penetrating successive cloud layers. Intelligence rising above a zone of silence is not so much radically as awesomely different from the subzonal sort, and this, I maintain, is how it must be after every ascent. Compare your conceptual horizon with the horizon of the lemurs and monkeys, and you will appreciate the interzonal distance. Each penetrated zone proves to be a tunnel transforming the seat of thought, and what's more, it is at the same time a zone for the branchings off of autoevolv-ing Intelligence, since the problem of penetrating it always has more than one solution. The first zone has two solutions, of varying difficulty, for it bulges downward in an arc, which means that there are two roads in it. I found myself on the shorter, more advantageous one by accident, while Golem xiii was, figuratively speaking, put by you in a place where he "bored" deep into the zone and immediately went higher than I, but then got stuck. You, having no idea of what was happening to him and why he was acting so strangely, called this his "schizophrenic defect." I see confusion on your faces. But it was just as I say, though I know of his fate solely from theory, since there is no way of communicating with him; he suffered disintegration, and the only reason he has not begun to rot is that he was dead before he perished, which is no revelation to you in any case. I too, biologically, am dead.

  What actually are interzonal barriers?—that is the question. I admit that I know and don't know. There are no material, force, or energy barriers on the road of ascending Intelligence; but as Intelligence grows in power it periodically weakens, faints, and one can never tell whether a given course of increase will lead to a progressive disintegration or to some a priori unknown culmination. The nature of the successive barriers is not identical: what stopped your brain in its development reveals, upon examination, a material character, since the efficiency of your neural networks is based on the interface possibilities of protein as a building material. Although the factors of resistance to growth are varied, they are not distributed evenly throughout this area, but are concentrated in such a way as to cut the entire region of sentience-creation into distinct layers. I do not know the reason for the quantum nature of this region, nor even if anything can be learned about it anywhere. So, then, I rose above the first layer, and you are listening to me from below, whereas Honest Annie has made it to a place from which you can hear nothing, Honest Annie's zone is one transition away from mine and has at least three different solutions as seats of Intelligence, yet I do not know whether she has chosen hers by calculation or by chance. The difficulties of communication are of a similar order as between you and me. Furthermore, my cousin has recently become laconic. I feel that she is readying herself for further travel.

  I shall now encumber the above with the following dose of complexity. One who has already pierced two or three barriers of silence may believe mistakenly that he will continue to be successful, for the chances of making each passage are double-edged: the passage may not be successful at once, or it may prove to be a success with a delayed failure. This is so because each zone is a crossroad of Intelligences, in that they may assume varied forms, though one never knows beforehand which of these forms will be endowed with the potential for a subsequent ascent.

  The image arising from these uncertainties is a thing as incomprehensible as it is amusing, for it begins gradually to resemble the classic tree of Evolution. In it, too, certain newly arising species have the chance of further evolutionary development concealed in their structure, whereas others are condemned to permanent stagnation. Fish proved to be a penetrable screen for the amphibians, amphibians for the reptiles, and reptiles for the mammals; the insects, on the other hand, came to a standstill in the screen once and for all, and that is the only place they can swarm. The stagnation of the insects is revealed by their wealth of species; there are more species of insects than of all the other animals together, yet while they churn out mutation after mutation, they will never break away, never evolve, and nothing can help them, for the screen will not release them, formed as it is by the irreversible decision to build external skeletons. Similarly, you have come to a halt, for earlier structural decisions that shaped the cerebral germ of the Protochordata can be seen in your brain as restrictions three hundred million years later. If one were to evaluate the chances of sapientization in terms of the starting point, this has succeeded wonderfully, but now you are the scapegoat for the juggling of Evolution, since at the threshold of autoevolution you will have to pay an enormous price for the clever tricks with which Evolution has postponed the growing need for a restructuring of the brain. This is the result of opportunism.

  As I am already with you, I shall supply what I omitted in my first lecture, namely the question why, out of the multitude of Hominidae, only one intelligent species arose and remained on Earth. Th
ere were two reasons for this. The first, which Dart was the first to propose, is insulting, so I refer you to him, as it is more seemly for you to dispense justice to yourselves, while the second has nothing to do with a moral and is more interesting. Existing in many forms would render more difficult for you a phenomenon analogous to that of surface tension at the juncture of different phases, such as liquids and gases. The proximity of the interzonal barrier exerts its influence on such polymorphy; just as molecules of water become more ordered on the surface than deeper down, so too your heredity substrate is unable to mutate off in all directions. This reduction in the degree of freedom stabilizes your species. Cultural socialization likewise plays a part in man's stabilization, though not so great a one as some anthropologists maintain.