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Time and Complexity

This text was presented in a workshop which had been organized at the Ringberg-Castle, Tegernsee, May 28-31, 1989 in honour of the 60th birthdays of Friedrich Meyer and Jürgen Ehlers, members of the Max-Planck-Institute for Astrophysics, to which the author is affiliated, too. It appeared originally in: Proceedings of the Workshop on Gravitation, Magneto-Convection and Accretion (B. Schmidt, H.-U. Schmidt, H.-C. Thomas eds.), MPI für Astrophysik, Karl-Schwarzschild-Straße 1, D - 85704 Garching bei München.

I shall use this “after-dinner-talk” (presented before supper) to smuggle some “soft” considerations about science and scientists into the “hard” scientific program of this birthday celebration. It seems worth while reflecting on our own position as producers or even dealers in science, since this stuff has taken over the role of “opium for the people” and as mankind’s addiction may be reaching a final state of destruction.

Of course, neither of our two “celebrants”, and none of the contributors to this celebration should be blamed. Everyone in this room deals with things untouchable, though we are still of basically two different types. Let me classify them as types I and II. (I am really aiming at type III, but this will appear later.)

A type-I astrophysicist is mainly interested in the patterns of selforganization observed anywhere between the sun and our cosmological horizon. He finds it quite natural that underlying fundamental laws exist, but he is much more fascinated by the complex structures built on them, and he wants to model them, indulging in re-creation. The type-II scientist, on the other hand, is not at all surprised that the real world has grown complexity if the fundamental laws allow for it. Rather, he is fascinated by those laws themselves, especially by the question of how far they are arbitrary or necessary.

As usual, extreme representatives of the types can be expected to tend towards degeneracy: The one may become a collector of eye-catching real phenomena, or even just of data – the other may, in an attempt to create concepts about the real world, lose all contact with it and get lost in homemade artistic worlds of rigorous mathematical beauty. In a way, the extremes touch each other again: Unrealistic art finds its collectors, too – especially since computers provide a wealth of unpredictable artistic prodigy.

Anyway – what is reality? To quote from Helmut Friedrich’s talk: “Now we have got rid of all the physics, but all the difficulties are still there”. You see: Science may emancipate itself from so-called nature, but not from complexity. It has still not reached its great aim, simplification of the world, reduction of everything to graphs in a plane, i.e. what we call explanation. In fact, this aim may turn out to be a strange attractor: The sequence of questions and answers which generate each other may form a kind of infinite Mandelbrot set – not in spatial but in logical structure, and perhaps with dwindling self-similarity of the concepts as magnification runs on. So, the attempts to unify amd simplify the understanding of the world may in fact contribute to the growth of its complexity.

This reminds us that we don’t have proper measures of complexity. There is even a sort of relativity involved in its judgement. The point of view of an observer will influence the measure. An old dispute with Bernd Schmidt comes to my mind: A non-rotating lump of viscous fluid, alone in an otherwise empty world, will take the shape of a ball, won’t it? Is this a trivial or a deep theorem? A simple or a complex statement? Well, Bernd told me, there is still no rigorous proof for it in General Relativity. So, why not make it an axiom? But, of course, other simple things would then appear as highly complex. Remember: One must not apply the term “complex” to parts of a system. The complexity is in the whole. Even complexity-theorists have now started to realize that a “measure of complexity” cannot be based merely on internal relations within a subsystem but must somehow include the whole process of its creation. (Cf. Rolf Landauer’s recent commentary in Nature 336, 306 on the proposals by Bennett and by Lloyd and Pagels, and the literature quoted there.)

“Relativity of complexity” also shows up in physical cosmology. We may now observe or conceive extreme simplicity for the origin of what we call our universe: Just the laws of physics, and no detailed ordered structure except the extremely well-ordered primeval expansion, i.e. some initial condition of “low entropy”. But in order to discover its own basic simplicity, this universe had to evolve complexity up to our level, including mathematical geniuses and giant accelerators and telescopes. And why has all that happened? Because it was more likely than other possibilities? Obviously, the meaning of time is to let more likely things happen – the becoming of complexity, the realization of possibilities, the selection of things realized, among the things possible. You know it: The evolution of elementary particles, of galaxies, stars, living planets, neural networks, cultural networks – it all follows the same principle: The state of the world explores its neighbourhood in the “space of possibilities” by accidental fluctuations, discovers more long-lived structures, which are therefore more likely to survive longer. (The “accidents” involved are either quantum fluctuations or accidental encounters with a long history – back to the beginning, with many other accidents along the way.)

The concept of a “space of possibilities” which I often use in the formulation of this Darwinian tautology may remain vague. Only one line in this space is definitely known to have been possible: The realized past. The possible is only found by trial and error. Whether something compatible with the laws of nature “could have been realized” is usually an undecidable question, and whether something will be realized has to be waited for. On the other hand, thinking and even dreaming are certainly real processes connected with matter in space and time – e.g. in neuronal networks and libraries. In this sense, our ideas belong to that one line, are realized, even materialized possibilities. Who says, what we see is more real than what we think? Thinking is a very real phenomenon of self-organization, still more highly developed than seeing! The idea of reality becomes quite fuzzy when you realize that. We don’t even have to discuss the EPR-paradox to shatter our confidence in concepts of “objective existence here and now” …

However, I don’t want to get lost in extreme type-II reflections. If you know me, you know that I only speak here in order to excite thinking and action against a third type of scientists: Those do-gooders who not only dream of effecting all things possible, but who have really started doing it – with fatal consequences. These type-III scientists outnumber by far the ones of types I and II, and their Baconian megalomania is sweeping aside Darwinian modesty. They claim that they can improve the world because they have understood the laws of nature.

What’s wrong with this idea? Aren’t we scientists clearly the tools by which the world here and now gropes its way further into the space of possibilities? Why should more scientific knowledge be harmful in this latest version of the evolutionary process? Why do I call it “opium for the people”? Well, of course, you know: The harm is not in the “opium” as such but in its misuse. And the parallel goes quite far: The drug is applied to solve a problem, but it creates a new and bigger problem. More of the drug has to be used, and more quickly. The new problems thus created are even bigger, need still higher dose, stronger drugs, faster application. . . Sounds like an instability, doesn’t it? How can the evolutionary path of the world (or of its subsystem Gaia) into the space of possibilities become unstable? Isn’t this just a matter of value-judgement?

Exactly! “How to judge values?” is the fundamental question. Evolutionary selection in dissipative open systems has answered it: If more and “better” relations between all subsystems can be found by fluctuations (where better relative isolation of some parts may often also be a better relation), they will probably be realized. And what is “better”? The more likely under the circumstances! As we saw: “Very likely, the more probable is going to happen” – and in a complex dissipative system this is the growth of complexity as far as possible. So, the better, the more valuable, arises without any value-judgement! Or, rather, the selection process is the valuejudgement! No God seems to be necessary to discriminate between good and evil. More valuable possibilities, i.e. more complex ones, where things fit together in a more viable way, are just more likely to be realized. All is well, isn’t it?

Just one little dark spot in all this enlightenment remains to be cleared up, the role of time in the growth of complexity. And here, I must shock you, we meet the Devil. A theorem may be proved in system theory: In a spatially finite system with unbounded evolution, the devil (“dia-bolos”, i.e. he who “throws things into disorder”) must at some stage appear at the front of evolution and cause a singular crisis. The mechanism is easily understood – you find hints at it already in the myths of Lucifer/Prometheus or of the Tower of Babel – but a constructive proof of the theorem lies at hand only now: One of the successes of evolution must be an increasing speed of the evolutionary process itself, because more and more efficient “languages” are found and realized in the space of possibilities. The beings at the front of evolution will, due to their own complexity, need some time to develop individually. This is their own life-time or generation-time. If they try to judge values (i.e. select new possibilities for realization) on a shorter time-scale than this, adaptation of the new and the old cannot work by definition. Hence, most likely, complexity will not grow but decrease. Under these circumstances, the worse is the more likely! Complex diversity will be quickly and globally replaced by universal simplicity. Reduction of diversity, however, allows for still faster global decisions, and the next decisions will be even more likely wrong in the same sense.

You see, evolution itself defines and creates a critical time-scale, which it then tries to surpass. But thereby it must destroy its own logical pre-condition. The leading figures at the front of evolution don’t give themselves enough time to judge values in the process of exploring the neighbourhood in the space of possibilities. Of course, the tautology remains valid that “more likely things will probably be realized” via the accidental fluctuations (including their more recent form of appearance, called planning) – but with a lack of time for selective adaptation, i.e. adaptive selection, the more likely is no longer a growth of complexity but rather its decomposition. In a very sophisticated way the entropy-law seems to have conquered the Earth, an open dissipative system in which we thought it wouldn’t be valid. While everybody was still worrying and quarreling about the resources, we have been filling up and blocking the sinks …

Now, the news and the science-journals are full of the symptoms of this crisis. But the understanding of its origins remains poor. Most doctors recommend faster innovation and unification as the proper drug. This means that the ailment itself is offered as its only promising remedy. We cannot expect the dealers of the drug to promote much insight. Those type-III scientists, the do-gooders who promise to improve the world by ever more contraptions conjured up ever more quickly from ever more matter and energy, have to be discredited. Perhaps the scientists assembled here are sufficiently remote from the complications of reality to be able to reflect on the role of time in the growth of complexity. Thinking about general principles of evolutionary creation of values you will discover that “deviltheorem”, and you will immediately recognize that evolution toward higher complexity can only go on if we guarantee its pre-conditions at the front: Conservation of old complexity must become a kind of holy rule, and the speed of change must be bounded by the “human measure” (and, of course, still more tightly where our biological or even climatological roots are threatened).

I cannot discuss here the role of occasional revolutions which arise from hot spots in the system, where dissipation is not organized in a sufficiently complex way. But it is obvious that we are approaching one. Our mental capabilities which inevitably had to lead into this crisis also have to evolve the insight that further evolution will need self-restriction. The “preconditions of evolution” which had been automatically fulfilled in the past, will have to be fulfilled by social “constitutions”. Those conditions, which we will have to try and re-establish, I have often characterized by the slogans “Vielfalt und Gemächlichkeit”, which is roughly (and clumsily) “manifoldness and leisureliness”. It means that the selection procedure, trial and error at the front in the space of possibilities, has to be left to many individuals and groups (implying very de-centralized structures) – and it means a deliberate, institutionalized suppression of the speed of innovation ( – except in purely mental fields like music, poetry or mathematics). Consequences for a new organization of politics, economy, science and technology are indeed manifold. In a book which I have just written, I could only rather accidentally touch on a few of them (Das Grundgesetz vom Aufstieg, Carl-Hanser-Verlag, München 1989).

Perhaps some of you will spare a little time from research about the last billions of years and help think about how the laws of logic and probability will influence your own remaining life-time, and all of the future. We must not leave this to the “experts” who want to sell their products. Too long, scientists have misunderstood the last sentence of Wittgenstein’s Tractatus: “Whereof one cannot speak thereof one must be silent”. We are still misusing it in pleading for irresponsibility. But surely, Wittgenstein didn’t learn speaking by being silent. The word should be changed: “Whereof we cannot speak thereof we must stammer”.