chaos and order

Let us imagine that Mr. Smith, a bank clerk, is living with his puritanical aunt—who has a female lodger—in a multistorey house whose front wall is made of glass. As a result, the learned observer on the other side of the street is able to see everything that goes on inside. Let the interior of the house represent the “universe” we are supposed to examine. The number of “systems” that can be distinguished within this universe is practically infinite. We can approach it, for example, on an atomic level. We will then have groups of molecules from which chairs, tables, and the bodies of the three persons are made. The persons move; we want to be able to predict their future states. Since each body consists of around 25 molecules, we would have to outline 3 x 1025 trajectories of those molecules, that is, their spatiotemporal paths. This is not the best approach, as before we manage to establish just the initial molecular states of Mr. Smith, the female lodger, and the aunt, around fifteen billion years will have passed, those people will have fallen into their graves, while we shall not have even managed to provide an analytic representation of their breakfast. The number of variables under consideration depends on what it is that we actually want to examine. When the aunt goes down to the cellar to fetch some vegetables, Mr. Smith kisses the lodger. In theory, we could arrive at who kissed whom just on the basis of the analysis of molecular behavior, but in practice, as we have demonstrated earlier, the Sun is likely to go out first. We would be unnecessarily diligent because it is enough to treat our Universe as a system that consists of three bodies. Conjugations of two bodies periodically occur within it when the third body goes down to the cellar. Ptolemy is the first one to appear in our Universe. He can see that the two bodies conjoin while the third one moves away. He thus develops a purely descriptive theory: he draws some cycles and epicycles, thanks to which one can know in advance which position will be taken by the two upper bodies when the lower one finds itself in the lowest position. Since in the very middle of his circles, there happens to be a kitchen sink, he declares it the center of the Universe, with all the significance this carries. Everything then revolves around the sink.

Astronomy is developing slowly. Copernicus arrives and invalidates the sinkocentric theory. After him, Keppler sketches out far simpler trajectories of the three bodies than the Ptolemaic ones. Then Newton comes. He declares that the bodies’ behavior depends on their mutual attraction, that is, on the attractive force of gravity. Mr. Smith is attracted to the lodger, while she is attracted to him. When the aunt is nearby, they both revolve around her, because the aunt’s force of gravity is correspondingly stronger. Now we are finally able to predict everything well. Yet suddenly the Einstein of our Universe arrives and subjects Newton’s theory to a critique. He claims that it is completely unnecessary to postulate the existence of any forces. He creates a theory of relativity, in which the system’s behavior is determined by the geometry of four-dimensional space. “Erotic attraction” disappears, just as attraction does in the theory of relativity itself. It is replaced by the curvature of the space around the gravitating masses (in our case—erotic masses). Then the coincidence of Mr. Smith’s and the lodger’s trajectories is designated by special curves, which are known as erotodesic. The aunt’s presence causes a deformation of the erotodesic curves, as a result of which the coincidence between Mr. Smith and the lodger does not take place. The new theory is simpler, as it does not postulate the existence of any “forces.” Everything is reduced to the geometry of space. Its general formula (that the energy of kissing equals erotic mass times the velocity of sound squared, since, as soon as the door closes loudly behind the aunt and this sound reaches Mr. Smith and the lodger, they throw themselves into each other’s arms) is particularly beautiful.

Yet some new physicists then arrive—such as Heisenberg. They conclude that while Einstein has correctly predicted the system’s dynamic states (the state of kissing, nonkissing, etc.), more precise observations involving large optical devices that allow us to see individual shadows of the arms, legs, and head demonstrate that it is possible to identify certain variables that the theory of erotic relativity overlooked. Those physicists do not question the existence of erotic gravitation, yet in observing the tiny elements from which cosmic bodies are constructed (i.e., those arms, legs, and heads), they notice the indeterminacy of their behavior. For instance, during the state of kissing, Mr. Smith’s arms do not always occupy the same position. In this way, a new discipline starts to emerge, which is known as the micromechanics of Mr. Smith, the lodger, and the aunt. It is a statistical and probabilistic theory. Large parts of the system behave in a deterministic manner (immediately after the door has closed behind the aunt, Mr. Smith, and the lodger…, etc.), yet this is a consequence of indeterministic regularities coming together. At this point, real difficulties begin, because one cannot move from Heisenberg’s micromechanics to Einstein’s macromechanics. Bodies seen as fixed entities behave in a deterministic manner, yet erotic advances happen in a variety of ways. Erotic gravitation does not explain everything. Why does Smith sometimes hold the girl’s chin and sometimes not? More and more statistics are produced. Suddenly a bombshell drops: arms and legs are not fixed entities; they can be divided into shoulders, forearms, thighs, calves, fingers, palms, and so on. The number of “elementary particles” is growing at an astounding rate. There is no unified theory of their behavior anymore. Between the general theory of erotic relativity and quantum micromechanics (the quantum of caressing has been discovered) lies an unbridgeable abyss.

Indeed, an attempt to reconcile gravitational theory with quantum theory (one that applies to the actual Universe, not to the one from our anecdote) has been impossible to achieve so far. Generally speaking, every system can be redefined so that it consists of any number of parts, which is in turn followed by looking for relations between those parts. If we only want to predict some general states, we can do so with a theory that contains a small number of variables. If we examine systems that are more and more subordinate to the original ones, the issue gets more complicated. Nature isolates stars from one another, but we have to isolate individual atomic particles ourselves: this is one of the many problems. We have to choose the kinds of representations that will reconcile the minimum number of variables considered with as high precision as possible for the prediction. Our anecdote was a joke, since the behavior of those three persons cannot be represented deterministically. They lack the necessary regularity of behavior for us to do this. This approach is nevertheless possible and actually imposes itself when a system shows great regularity and a great degree of isolation. Such conditions occur high in the skies, but not in an apartment. Yet when the number of variables increases, even astronomy has difficulties with using differential equations. These difficulties are already brought on by the attempt to outline the trajectory of the three gravitating bodies, while for six bodies such equations are impossible to solve.

Science exists owing to the fact that it creates simplified models of phenomena, ignoring less significant variables (e.g., by assuming that masses of smaller bodies within a system equal zero) and searching for constants. The speed of light is one such constant. It is easier to find constants in the actual Universe than in the aunt’s apartment. If, rightly so, we are unwilling to consider kissing to be a phenomenon as universal as gravitation, but we want to find out why Smith engages in kissing, then we are at a loss. With all its limitations, mathematical mechanics is so universal that it allows us to calculate the position of cosmic bodies thousands and millions of years ahead. But how should we calculate the trajectories of Mr. Smith’s brain impulses to predict his “oral coincidences”—or, to put it less academically, kisses—with the lodger? Even if that were possible, the symbolic representation of the subsequent brain states would turn out to be more complicated than the phenomenon itself (i.e., impulses traversing the neural network). In a situation like this, a neural equivalent of an act of sneezing would be a volume whose cover would have to be lifted with a crane. In practice, the mathematical apparatus will have got stuck in the ensuing complexity long before we actually get around to filling such volumes. What are we left with then? With considering the phenomenon itself its most perfect representation, and with replacing analytical with creative activity. In other words—with imitological practice.

Stanisław Lem “Summa Technologiae”, translated by Joanna Zylinska, University of Minnesota Press, Minneapolis 2013, p. 161-164

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