What is Beauty?
On the System Theory of Creation

A presentation of the following ideas had been planned for a Conference of physicists, philosophers and theologians in Venice (December 17/18, 1993) which took place under the title
The Beauty of the Universe within the series Venice Conferences on Cosmology and Philosophy. I could not participate because of illness, but nearly a year later I wrote this version for the proceedings. The Original is unpublished. – An Italian translation by Alberto Bragaglia appeared as: “CHE COS’È LA BELLEZZA? – SULLA TEORIA SISTEMICA DELLA CREAZIONE” in: La bellezza dell’Universo (Eds. F. Bertola, M. Calvani, U. Curi, M. Donà). Il Poligrafo, Padova 1996 (ISBN 88-7115-057-0), pp. 43-83.

1. A preposterous approach

Pulchritudo splendor veritatis. Beauty is the splendour of truth. These words are attributed to Augustine. We might stop here, if we were satisfied with a contemplative life – but scientists have to go on and ask: What is truth? They are searching for it, they say. What have they found, so far?

When we look into the world, we find reality. We find it beautiful if it stirs emotions related to happiness or awe. Considering the natural history of feeling, this may seem natural with lovely faces and friendly landscapes – but why does a regular spiral galaxy appear more beautiful than a very disturbed one and, on the other hand, the pattern of a snow flake more beautiful than a regular hexagon? Would Augustine have seen more truth in one than in the other? Are our aesthetic value judgments related to any “objectively true” features of reality? Can we find some general principle behind attraction and repulsion of real or possible structures?

Scientists often confuse truth with reality. They claim they are striving for truth when, actually, they want to introduce a new marketable gadget into reality. Dazzled by the glittering of the money which springs from this kind of creativity, they may feel tempted to speak of
the splendour of reality. On the other hand, even “observational” scientists and engineers usually agree that the concept of truth should be reserved for something less transitory than the phenomena realized by matter in space and time – especially now when, sub specie aeternitatis, even the proton is suspected to be ephemeral.

Asked for an example of what he means by the word
truth, a scientist will certainly mention the Laws of Nature. Those are cast or forged in mathematical formulae, after a proper mapping between observable phenomena and quantitative theoretical concepts has been found. A particularly fascinating experience has been that some kind of truth often sparkles in wrong theories: Phenomena seem to follow mathematical formalisms even if there are obvious internal contradictions in the underlying conceptual and mathematical systems. As “the laws” are discovered piece by piece, they may never be “the truth” – and still they seem to approximate it in some sense. Obviously, before we can speak about beauty, we must think once more about the relation between truth and reality. Unavoidably, this will take most of the space for this article which isn’t about phenomena but about ideas.

By definition, or by arrogation, the true laws of nature govern everything which might be realized in material processes – from the formation of elementary particles in the early universe to the neuronal activity of my cerebral cortex while I write this sentence. However, realizability is a difficult concept even if you don’t believe in miracles which transgress or “transcend” the laws. Just now, the discussion about the interpretation of quantum mechanics is receiving fresh impetus from physicists quarreling about “the nature of reality”, but there are still no generally accepted scientific ideas of what it means when we say that something “is there” or “is happening” or “is possible”.

Of course, my own wrestling with such questions over five decades was accompanied by similar processes in many other heads, which occasionally came to my attention, and my terminology has developed in contact with many older ideas. But I have never been interested in the question when and where a thought was first thought or spoken out or printed. The evolution of human ideas cannot reasonably be viewed as the spreading of discrete “memes”, which might be traced to a specific article in some journal. The obsession with “originality” is a disease to which we will eventually come back, because it has even infected the idea of beauty. The process of mutual adaptation across the borders of “expertise” seems more important to me. If I would quote anybody in this “article about everything”, this would only tell something about my memory, but nothing reliable about the history of ideas. So, I shall rather not quote at all, and leave the book-keeping to others.

* * *

Mathematical truth may be defined in a rather clear sense. Reality is fuzzy. Rigorous physical theories do not pertain to reality but to abstractions of it which are called truths as long as no contradictions have been discovered. As the physicists of our century struggled down to ever deeper levels of abstraction, the idea of a “history of the real world” as a sequence of “events” has become more and more blurred. For decades it has even been fashionable in quantum mechanics to reserve the concept of an event for “observations” in which that metaphysical “collapse of the wave function” should take place. Thus, oddly enough, observers were thought to take care that something “real” happens at all. This way of splitting the world into material and mental reality still resembled traditional divisions into res extensa and res cogitans or “outside and inside”. If we want to draw ethical or aesthetical conclusions from a scientific world view, we should perhaps first try and reach some
re-unification of mind and matter. Can’t we see ourselves as parts of “natural” reality? Everybody does this in front of a mirror. Only when it comes to feelings and consciousness, many people are in doubt how those could belong to the material world in space and time.

Occam’s razor is a proper tool to cut out such dubitations at this point. If soul and mind appear as infinitely more complex than all other experiences, this is no reason to shift them into “another world”. In order to strengthen your belief in the possible riches of complexity in a material world, let me ask a simple question: How many points do we need in order to let the number of their different relation structures (via straight lines) surpass the number of atoms in the observable universe? The answer: Twenty-four! This trivial example shows that there must be a practically infinite potential for complexity in the activity patterns of ten to hundred billion neurons, when each of them is connected to many thousands of others – and even more so, when many brains cooperate in the form of societies. Obviously, there is enough
res extensa to house every imaginable reality, including the res cogitans and all its activity. The problem is not one of capacity but one of organization, that is creation.

So, doesn’t the question suggest itself, whether the known laws of nature and the findings about the evolution of the universe from big bang to consciousness teach us something about the process of self-organization in people, too? Haven’t we learnt a lot about how matter, stars, life and brains came into existence, even though we know that the laws used in all that “understanding” are not yet really fundamental ones? Newton’s theory is not obsolete for the use in a planetary system, and the results about the structure of atomic nuclei or molecules will not stop making sense if we find a deeper “unified theory of everything”. Let me assume that our present ideas about mental processes as physical phenomena do not critically depend on further progress at the front of theoretical physics. Of course, it remains an open question whether the “wrong” laws of nature, which we have to deal with on the present level of theoretical concepts, are near enough the truth which is steering the organization of soul and mind in our cerebral activity. But this question must not divert us from a more urgent one: What follows from what we have understood already? What follows for ourselves if we assume that the creation of man, and all subsequent human creativity, obeys the same laws as pre-human creation?

Let us see what happens if we, with that crude reduction to incomplete scientific terms, dare to approach the idea of beauty. Is this a preposterous approach? Well, remember the episode from Heisenberg’s biography, when some of the most brilliant theoreticians washing the dishes in an Alpine refuge were startled about the result: With dirty water and dirty towels they produced beautifully shining glasses! This may encourage us to try and reapproach the realm of ideas and the system theory of God and Devil in terms of more modern language. In spite of the unsatisfactory conceptual basis, let me offer some thoughts about the process of creation and about conditions under which its results are likely to be beautiful or ugly.

2. Is there a universe?

We shall now put on quasi-classical spectacles to look at the “obvious” reality of cosmic structure, of the earth, of its biosphere, of human brains and of their interaction in society. We neglect the vexations which quantum mechanics has generated for the concepts of history and reality. And if we really live in a “universe”, we neither have to worry about the relativity of time, if the overall uniformity is sufficient to introduce a global cosmological time coordinate. Then, we may talk about universal “moments” and a universal history in our fuzzy image of an evolution of physical reality.

Cosmology and fundamental physics have now reached a stage where speculations about “the nature of the laws of nature” are not quite meaningless, even though no fundamental theory has yet been found. The laws themselves may be looked at as a “part of reality” – in the sense that they are perhaps not given as “absolute truth” but that they are consequences of the early history of our universe. Among the thinkers who have started brooding over “the egg of the universe” – i.e. the very beginning where the concepts of space, time and matter start making sense – there are basically two species, which tend to prefer different answers to Einstein's question, whether “God could have made the world different”. There are those who expect that proper concepts can and will be found from which the laws governing our universe follow inevitably – including the “constants of nature”. In this case, the laws of physics would be determined by pure logic. There are, however, others who suspect that the ultimate logical foundation of our world lies much deeper and would allow for universes with very different laws. Then, the details found in modern physics would not have more “necessity” than the phenotype of the elephant or the wording of this article. The principle of evolutionary self-organization would then govern the rise of complex structures not only on the “six days of creation” but in the very first idea of our universe.

Fortunately, for the choice of our own will between good and evil, nothing depends on a decision of such questions. It does not matter, whether our universe is the only possible one or one among infinitely many others – if only the concept of a universe makes some sense at all. And the belief in a universe is well supported by observational hints: Wherever we can look in space and time, matter obeys the same laws and seems to have come from that common early state of extreme uniformity, that we call the “big bang”. All subsequent creation seems compatible with the notion that our world started without any detailed structure and came out of just one idea: The greatest possible density and uniformity with the fastest possible expansion. Indeed, our most important cosmological experience is:
There is a universe – defined by common laws and a common early phase, perhaps with a common “point of origin”. The “age of the universe”, around 15 billion years, is still uncertain. Even with a more reliable measurement of the “Hubble-constant” (the speed of global expansion) it will not yet be fixed because there seems to be a lot of invisible but gravitationally active material, and also the so-called vacuum might influence the spatial expansion via some unknown force, like Einstein’s “cosmological constant”.

This beginning is extremely “special” in the set of all imaginable configurations. Without deeper insight from some more fundamental theory it appears as infinitesimally likely, i.e. practically impossible. We can only speculate whether this special choice is logically unavoidable or rather the consequence of some early evolutionary selection process. Uniformity could have been immensely amplified when our universe was “inflated” from a tiny bubble in an infinite chaos. Anyway, it has turned out that the appearance of man in our universe sets quite narrow limits to the laws and the order of its early stages: “Our world must have allowed for human evolution in order to let such questions come to our minds”. This truism is called the “anthropic principle”. However, it is probably not sufficient to enforce the extreme order of the early universe which finds its expression in the low entropy of only a few billion photons per baryon in the cosmic radiation background. That number may not sound small, but it appears as extremely unlikely in the immense number of possible more disorderly states if one includes gravitation. Roger Penrose has made this evident in his book
The Emperor’s New Mind.

In a deeper theory, though, space, time and matter might “spring from nothing” in a single “fluctuation of the vacuum”. Then, there might not be any other possibilities to be counted in the beginning. Isn’t it “new-born” space which is coming into our view in the course of time as we “see” the origin at our cosmic horizon with infinite redshift? Isn’t it tempting to speculate that after a re-formulation of the fundamental concepts, the extreme initial symmetry might turn out to be a necessary consequence of the fact that “everything came out of one”? In a way, this hope has always resonated in the word “universe”. If it came true, one might say: “Fundamental laws, perhaps even the laws of logic, enforce the absolute uniformity of the egg of the universe”, or “God as the creator does not yet have properties but only possibilities”.

On the other hand, many theorists suspect that at least some features of the laws of nature may be the outcome of an early selection from a wider range of possibilities. The observed universality of our laws, or at least that of some numerical constants contained in them, should then be due to some process like inflation. A whole “multiverse” of other worlds might then be thought to “exist” beyond our range of possible observations. To be sure, the concept of existence would become quite fuzzy at this point: Should we grant a higher ontological status to such “other universes” than to unrealized possibilities like, say, the history of the earth without that cosmic accident which killed the dinosaurs – or, say, the history of my family if my mother had died as a baby?

* * *

Obviously, for a tiny fraction of a second after the origin, our present knowledge of the true laws is still insufficient. But, as physicists know, we can already calculate what must have happened a few minutes later, when the first nuclei formed – and the results compare well with observations! Thus, the quasi-classical view on the “history of reality” as an evolution process of matter in space and time seems to make good sense. The “quasi”, however, has to be added in order to incorporate the most important new experience of our century which has lead to quantum mechanics: There is a stochastic element in all history! Reality is not strictly determined but influenced by accidents. For instance, if we keep a hundred atoms of the radioactive Cesium-137 in a box, the laws of nature and all past and present realized structures do not determine how many of those atoms there will be after one year. At any time, there is only a probability distribution given for that number, such that after roughly 30 years the “expectation value” is half the original number. This kind of reality is not uniquely determined but selected “accidentally” among the more or less likely possibilities lying within reach of unavoidable fluctuations.

In the conventional interpretation of quantum mechanics, the stochastic selection was thought to take place in the “collapse of the wave function” due to an observation. The wave function itself, which defines the probability distribution, behaves deterministically. As I said, we shall avoid this conventional split between mind and matter, because we want to consider the observer’s consciousness itself as a part of the material process in space and time. So, we cannot clearly say where and when the “quantum mechanical events”, the “acts of realization” happen. However, this is probably not a shortcoming of reality but rather one of present physical concepts. Like the concept of an empty space-time with test bodies, that of an isolated system and its observables does not tell the full story. Such ideas formulate important features of certain processes of measurement, but they are not “the truth” pertaining to reality. In fact, in spite of quantummechanical dogma, most physicists are inclined to call the decay of a radioactive nucleus a real event, even if no observer is there to register it. For our present purposes, without better fundamental concepts, we can hope that our rather naive realism is a reasonable approximation to the truth – with the implicit assumption that “there is” some truth about “process and reality”.

The world-view within which we now want to discover beauty is that of naï ve cosmologists, geologists, biologists or historians. In this approximation we say: There really is a universe, and its reality evolves through events, which it creates itself in its intrinsic spontaneous fluctuations and encounters. In each event the new reality is chosen within the set of available possibilities. This choice is not arbitrary, but accidental within a given momentary probability distribution. Probabilities are determined by the present and past reality, and by the available possibilities. Of course, both reality and possibility are assumed to be subject to logic and to the laws of nature. With the events, however, “pure chance” is coming in. One might be tempted to call those stochastic events the “acts of creation” but we shall see that this would be misleading.

From “chaos theory” we have learnt that even strictly deterministic laws of nature would not make the behaviour of most systems predictable in practice. Tiny “non-linearities” in the equations governing the processes can produce an exponentially increasing divergence of histories which started with arbitrarily small initial differences. You know that “butterfly-wingeffect” from long-range weather forecast. As a simpler quantitative example, mathematicians have calculated how sensitive the balls in an idealized frictionless billiard game would be to minute external influences. If one computes the paths of a few balls which collide with each other and with the cushions, it turns out that after a surprisingly small number of collisions the motion-picture on the table might be totally different if one explicitly included the gravitational action of a single electron at the edge of our milky way! I think I remember that the resulting number of collisions was smaller than the 24 in our former example – and again this throws some light on the number of possibilities of quite simple systems. Clearly, the state of my mind when I have finished this sentence would not be predictable in any sense, even if the momentary firing rate of every single neuron in my brain and all underlying molecular and atomic activity had been continuously registered in some huge, “super-universally” huge, library – and if their evolution were governed by absolutely deterministic fundamental laws.

Scientists and philosophers used to think that the difference between strictly deterministic and stochastic events must be essential for our ideas about freedom. However, in our present picture of the universe, even this difference becomes fuzzy: As the billiard example shows, what happens in my brain, must be influenced by microscopic events near our cosmic horizon, that is near the “original act of creation”. So, even if there were no local spontaneous fluctuations at all, and if even the decay of radioactive nuclei were somehow “determined”, there would be infinitely many tiny influences which could by no means be distinguished from purely spontaneous accidents. For the practical way in which we look at the history of our universe and at our own history, and for the perception of our own freedom, it does not make much difference whether the selection of reality within the realm of possibilities is influenced by “initial fluctuations” near the actual cosmic horizon or in infinitely many spontaneous local accidents during the whole long history and in the pattering and flaring of our present brain activity.

Our experience with microscopic phenomena suggests the latter picture – but we don’t have to be dogmatic about it. The essence of creative freedom is not to be found in the detailed character of the wriggling but in its sheer presence. Random initial conditions which enter any region in space and time at its momentary horizon would be as effective in the process of “trial and error” as spontaneous fluctuations at many space-time points. Creativity is due to the principle of evolutionary self-organization, which means: Wriggling among a lot of possibilities makes it likely to find more attractive ones. If there is or if there ever was a stochastic element in the history of the universe, creation is going on incessantly. It has now reached the level of our “freedom of will” – the source in which (as even the etymological roots suggest) a chaotic “welling-up” organizes itself along the attractors of mind and culture.

3. Attractors in the space of possibilities

The larger realm within which reality is being selected I like to call the “space of possibilities”. Of course, philosophers and theologians of all times have given many different names to closely related and similarly vague concepts. “Heaven”, “the realm of ideas”, “the spiritual world”, “eternity”, “eternal truth”, “the beyond” are some of the words used in our western tradition for a larger province, of which reality is a part or a shadow and from which it seems to be being steered or receiving creative power.

When I consider the realm of possibilities, I obviously include at least all material structures and processes which might in principle be realizable because they do not contradict the laws of nature. When I call this set a “space”, I must think of some concept of neighbourhood for its “points”. We may imagine a picture quite similar to that of the phase-space for a classical system. There, any momentary state is specified by the positions and velocities of all particles or, if those are restricted, of the “degrees of freedom”. As a point-like particle in three-dimensional space is free to move in three spatial directions, its phase-space is already 6-dimensional. The momentary state of a gas with N such particles would have to be specified in at least 6N dimensions. Clearly, if such ideas can be applied to the real world or any part of it, this dimension is practically infinite. Still, theoreticians liked the phase-space picture because every possible momentary state of a system corresponds to a single point, and deterministic laws of nature define one single line through each point as its past and future history. So, the “dynamics” of a system could be visualized by the properties of bundles of lines in its phase space – that is by all its possible histories.

In this classical picture, the “freedom” of a system lies only in the choice of initial conditions. For a given state, i.e. a point in phase space, the whole preceding and subsequent history is a single fixed path, connecting all the state points which become realized according to the supposedly deterministic laws of nature. In principle, those laws allow the exact calculation of the path into the future as well as into the past of each state. All the other possible states and histories of the system, namely all points in phase space which do not lie on that one single line, will not become realized. In this type of classical physics, there is really no “freedom” of a system, except in the free will of an experimenter who chooses and fixes initial conditions. (“Initial” they are only in the sense that they pick a path from the bundle of possible histories; usually, there is no beginning or end of lines in phase space, unless they run into a point-like attractor …)

If we dare to think of something like “the space of possibilities of our universe”, any real or possible momentary state of the whole world, including all brains, books and computer-storages, is considered as a point in this space. With all the complexity and beauty of the world, this may appear as a huge step beyond the classical phase-space picture. This step does, however, not lie in the larger number of dimensions. “Nearly infinite” as it is, the number of particles in a brain is not larger than in the same volume of water. So, it cannot simply be the “size” of the phase space, its practically infinite number of dimensions, which is responsible for the appearance of all that beautiful complexity in the world. It is the organization of correlations, which seems so incredibly unlikely to be found and kept and evolved further – whether by “planning” or by “accident”. Still, it is obvious that all this is possible.
There it is – really: this one single line in the space of possibilities, the real history of our world, from big bang to the state at this moment. And your reading of this text is a tiny filament of this history in a sub-space which is infinitesimally small in comparison with the whole, and still practically infinitely large. Isn’t that stupefying? But our stupefaction is not due to the fact that this is possible but to the fact that it has been found among the immensely many other possibilities in the course of history. Somehow, this line seems to have been more attractive than others.

Everybody must have seen by now some of those surprisingly beautiful coloured computer graphics in which phase-space attractors of simple nonlinear dynamic systems are projected into planes or sub-spaces. One of the most impressive features of such pictures is how basins of attraction which are well separated in certain regions of phase space can be interwoven in other regions in incredibly sophisticated ways. Like the infinitely filigreed edge of the Mandelbrot set, such patterns are usually produced from extremely simple iteration processes with just a few mathematical symbols. So, we shouldn’t be surprised that the space of possibilities is full of attractors. They are lines (or, generally, manifolds of relatively low dimension) near which real processes tend to accumulate when they have somehow got into their basin of attraction.

Relatively simple ideas of that kind we find everywhere as elementary particles and atoms. Progressing to higher complexity we find galaxies and stars, organic molecules, all forms of life, the whole biosphere, human brains and cultures. Some features of the simpler ones we can represent by formulae and simulate in computers, but when we think of the number of possibilities with our “24 points” we see why this becomes impossible higher up in the “great chain of being”. Still, we have our eyes, our telescopes and microscopes, our thoughts and dreams, to find out what is there! All those beautiful structures and processes – and some ugly ones, too. It has turned out that everything in the universe, and the universe itself, is a dissipative structure – i.e. some arrangement of matter exchanging energy and matter with similar and other structures such that the pattern stays near the same idea, i.e. near the same attractor in the space of possibilities. The basic attractors are of a cyclic nature, and reality runs through them again and again for such a long time that even Einstein loved to think of a stationary universe – although he knew about evolution of everything else and certainly realized transitions to more attractive ideas in his own mind.

What makes an attractor attractive? Obviously its mathematical structure, its embedding in the bundles of all paths in phase space – but even for quite simple systems this is usually so complex that it can only be discovered by trying. In the deterministic picture of classical phase space one has to try a large number of points, distributed over a wide range of phase space, and use them as initial conditions for computer calculations. The corresponding bundles of histories may then accumulate in certain regions and make you suspicious that there is an attractor. With more trial and error you may then confirm or refute this assumption. This is why there was so little mathematical thinking about “deterministic chaos” and attractive structures “between order and chaos”, before we had fast computers – although in principle the insight into such phenomena had been around long before.

* * *

What about the “existence” of reality and possibilities? Let us contemplate the example of the Mandelbrot set a bit more thoroughly.
Is it there? Does this structure exist in any sense? Penrose said it is there like Mt Everest. But mountains are very short-lived phenomena, whereas mathematical structure is there beyond time, in the “realm of ideas”. Isn’t it obvious that we should, in some sense, include the Mandelbrot set in what I call the “space of possibilities”? It has been approached by material space-time structures in the course of the history of our universe, though only lately – perhaps first in activity patterns of Benoit Mandelbrot’s brain, and then in computer print-outs and on millions of colourful book pages. True, it has not been “realized”. Not only because of its infinity this is for ever impossible. Thus, it makes good sense to extend our concept of “heaven” and include not only what might in principle be realized by matter in space and time but also all possible “limit points”. For mathematicians this is a very natural procedure (like introducing the “real numbers”), but engineers will accept it, too, since they have always known that machines are not identical with their blueprints and, still, in some sense quite near them. To be sure, it isn’t the realization of a blueprint in ink on paper, or in the memories of computers or people, to which the realization of the machine is near; it is the idea – an attractor in the space of possibilities, beyond the reality of space-time, i.e. a spiritual “gestalt”.

Will not, at this point, philosophers and theologians also become interested in the mathematical trick of attributing “existence” to accumulation points? I don’t ask them to resume the old dispute about the “reality of universals” – but I think it makes some sense to say that the unrealizable attractors of reality “are there”! They pervade the space of possibilities everywhere densely. Heaven and earth touch each other in infinitely many points. Our reality comes quite close to the “impossible” idea of a Newtonian planetary system, and our thinking and longing is really quite near the philosophical and spiritual ideas of our ancestors. Not even scientists can deny that God and the angels are back in Heaven, and quite near reality, when so much cerebral activity and culture has been wriggling about those attractive ideas!

Do I really have an immortal soul? Does God exist? Are the angels real? Perhaps these are the wrong questions, when not even the “gestalt” of a proton is real – although the realization of all protons in the world is wriggling very close to this idea (the mathematical structure of which has still not been fully discovered, though). Man, of course, the most complex phenomenon so far realized by matter in space and time, follows more complex attractors than elementary particles. But this does not make soul and mind or the whole history of philosophy and religion less real than such more primitive phenomena. Here I am – and I don’t mean the cells or the molecules in my body and brain! I mean reality as it is organized by my own attractors in the space of possibilities. The process of finding them is the self-organization of my freedom along my individual “gestalt” which I experience as my soul and mind, embedded in the ideas of our culture. “Praying” is an old word for my wriggling in this process. God and the angels help by being around, and attractive.

4. The logic of creation

You know many attractors which govern our present reality. Just look at “Gaia”, the idea of the earth and its biosphere – that immensely complex dissipative structure in the stream of sunlight. The earth’s reality is near all sorts of more or less cyclical sub-attractors with very different cycles. There are the elementary particles, nuclei and atoms with their extremely short internal periods and very long lifetimes. They cooperate by weaker interactions to follow the attractive ideas of certain molecules, which again cooperate with still weaker interactions via the exchange of energy and matter to follow the ideas of the genetic code, the living cell, the organ, the organism, the society. Among all possible chaotic histories of our atmosphere, the earth’s climate attracts the weather, our health attracts the activity of all our organs, ethics attracts our thinking and behaviour. No two individual cells are identical, no man is like any other, and still everything seems to be near its attractors in the realm of ideas. However, considering how fast man is changing life and even climate, we recognize that the recent front of Gaia’s evolution in the space of possibilities lies in the wriggling of our minds. Thus, with my present attempt to re-unify the split world, let me include in the figure of “Gaia” not only the human bio-mass but also our mental and cultural activity, that is the earth’s “noosphere”.

Although in classical physics attractiveness is a consequence of the laws of nature, this “consequence” must mean a sequence of trial and error, when we look at the path of real history with its infinitely many decisions between possibilities. (And remember: Even the laws of nature might be the result of a process of evolutionary self-organization under more fundamental laws of logic.) The full structure of the attractors, the underlying truth, can scarcely ever be reconstructed when something shows its attractivity. We just have to admit: It works! In spite of infinitely many deviations, in immensely many sub-spaces corresponding to local reality, the projections of the phase-space path run through similar cycles again and again without leaving the old basins of attraction. Evidently, the attractors of local reality are
viable, and their viability means repetition, reproduction – in atoms, cells and people. The Greek ethos, from which ethics is derived, means custom – i.e. what has proven its value in generations, i.e. in the repetition of cycles.

When we look more closely, we see that viability is not just a matter of local internal organization, but that the global and even universal context is essential. For instance, terrestrial life and climate take care of each other’s viability. And the global structure of the universe is essential for the viability of all its complex dissipative sub-structures. All free energy used by them is in fact “fossil energy” from the big bang. Why? Expansion creates gravitational potential energy which is later partially regained in the formation of lumps; and the stream of energy from stars, which helps create complex molecules and life around them, is due to the fact that the early universal expansion was too fast to allow all possibilities of the nuclide chart to be realized; this could be achieved only later in the centres of stars. Thus, the ultimate source of all free energy is the origin of the universe with its very low or even zero entropy – and the ultimate sink of entropy (for all practical purposes) is the dark night-sky, i.e. the cosmic horizon, i.e. the simple origin again.

* * *

We still haven’t explicitly answered the question how reality is selected among the inexhaustible filigrees of heavenly possibilities. Don’t expect the revelation of a secret, please! The answer is trivial, and it is contained in what I have said so far. It is the tautology that “probably something likely is going to happen”. We saw that the stochastic element in all history, that “wriggling of reality”, introduces fuzziness into the phase-space picture. Perhaps, in a future fundamental theory, the “state-points” themselves will be described as fuzzy, but anyway, at any point, the continuation of history is not strictly determined but subject to “accidents” which make a choice within probability distributions. This means that there are transition probabilities between attractors in the space of possibilities. Now we understand more clearly what the “viability” of an attractor is: It means that due to its internal and external organization the usual accidents are unlikely to lead out of its basin of attraction. In other words: The probability distribution is sufficiently sharp to make the continuation along that attractor very likely. But now it is also clear that with a large number of accidents in a neighbourhood where the basins of attraction of many different attractors are near each other, there is a chance – and with enough trial and error even the logical necessity – that local reality leaves this region and follows a still more viable attractor. “The more viable is more likely to survive”. Again a tautology. The principle of creation, from the origin of space, time and matter to the co-evolution of our biosphere and noosphere, is nothing but Darwin’s tautology.

It is obvious that there are two general features of viability which seem to contradict each other: Isolation and connectivity. Physical isolation of local systems is attractive, because it helps to prevent strong fluctuations caused by external interactions, under which the transition to other attractors would be likely. For example, matter which has collapsed into a black hole forms a very attractive island. No outside activity will be able to pull out anything again, and the time-scale of its dissipation through quantum-fluctuations is practically infinite. This is an example of an instability which finds the simplest possible attractor, completely defined by just three numerical values: mass, angular momentum and charge. But also the more complex dissipative structures, an atom, a galaxy, a living cell, an organ in an organism, an individual in a species or a person in a society have features of an island: External influences are not likely to critically disturb and totally destroy the internal organization. – On the other hand, interconnection, i.e. manifold interaction with the whole surrounding, is also attractive if it is organized with sufficient complexity. Complexity means that “things fit together” such that the interactions are likely to increase the viability of both the parts and the whole instead of disturbing it. I usually discriminate the terms “complex” and “complicated”: Complexity is meant to include viability; complicatedness arises when viability is disturbed or destroyed through excessive interactions. Then, history tumbles through the space of possibilities, along complicated unstable attractors, towards less complexity or even ultimate simplicity. With sufficient diversity this isn’t harmful to the whole – but there is a problem to which we have to come back …

In a sufficiently rich space of possibilities, like that of our universe with its streams of energy and entropy, competition between the two tendencies of isolation and interconnection takes care that hierarchically organized complexity is most attractive. In the evolution of matter, this has to do with the fact that there is a hierarchy of elementary physical interactions. In a deeper theory, though, this fact might itself be attributed to the process of evolutionary self-organization. After all, on higher levels of complexity, the ways of interactions are themselves discovered in this process. As reality in various regions of physical space follows its sub-attractors, the local histories are more likely to “fit together” if their basins of attraction are adapted to the probable sizes of internal fluctuations and external accidents. Viability for the parts and the whole is closely linked with “evolvability”, since disturbances which lead to further transitions must be rare but not totally excluded along the “best” attractors likely to be found.

The delicate balance between permanence and fluctuation favours specialized “species” of structures with a hierarchy of rising internal and external complexity and a hierarchy of interactions with decreasing strength. In a sufficiently rich space of possibilities, attractors of this kind are likely to be selected by reality if there is enough space and time for trial and error. The reality of our biosphere and noosphere illustrates this perfectly. (I don’t know, whether general theorems of this kind have been proven in a mathematical system theory of evolution, but it seems intuitively clear and I would be surprised if this tendency towards hierarchical discretization, diversification and specialization would not be found in expensive numerical simulations of evolution in sufficiently rich artificial spaces of possibilities.)

If this is what we find in ourselves and around us, it does not mean that there are no other lines in the space of possibilities. “There are” infinitely many possible histories with different patterns of organization, and many may be closely approached occasionally, but nearly all of them are not likely to be continued in the process of accidental wriggling. If reality tries them in some spatial region, they turn out to be “errors”. This means that they are soon abandoned again – usually because they lead into instability and local collapse. Although most transitions to other attractors will turn out as errors, with enough trials in many different regions of physical space-time, there is a very good chance (as good as necessity) to find still more viable and evolvable ones. Via “auto-catalytic” spatial interactions this increases the chance of finding the same ones in other places. Good ideas spread in space. Near the simple beginning of the world, the “legal structure” of the attractors may determine reality to a large degree. That is why the same types of nuclei, astrophysical structures and molecules are realized in space-time regions which scarcely interact. (As we saw, the riddle of the universality of laws is still unsolved.) With rising complexity, however, the choice of viable attractors becomes so large that the realized ones appear as accidental in immensely many aspects. In most evolutionary transition steps the realized forms of higher life or culture have probably not been much more attractive than many other possible ones. Various “good choices” must be available, but realization of one of them often makes the others practically unreachable. E.g., if different possibilities of evolvable chemical codes for life may “exist”, and may even have been within reach after the formation of the earth, only one was likely to be realized globally in the end. How likely “it was in the beginning” that our level of complexity is reached, with the realization of what we experience as soul and mind, we cannot say. Do just a few planets have to try? Or a whole universe? Or even a “multiverse” … ?

* * *

As I have tried to picture the space of possibilities in close analogy to classical phase space, one may have been tempted to think that the attractivity of an attractor should be fully determined by the laws of nature. However, since the probability distribution for “what is going to happen” is influenced in a different way by reality and its neighbouring possibilities, the actual attractivity of lines in the space of possibilities in any present moment also depends on the past real history and, therefore, on immensely many past accidents. This suggests a bold assertion: Not even in this sense “is God almighty”. Viable and evolvable attractivity is not fully determined by the “heavenly truth” of attractors. Hasn’t this been understood in all myths of creation? What else do the words at the end of each day in Genesis mean: “And God saw that it was good”? He didn’t know beforehand! And he didn’t always know for sure while he was kneading and moulding in the tohu-wa-bohu and in the clay. He needed a lot of time. Viability, the beauty of reality, was tested all the time but became particularly obvious at the end of a day, when adaptation had been achieved on one of the hierarchical levels of complexity and had proven its value – that is its viability. (Sorry, the tautology lies in the principle of creation …)

Now we see why it wouldn’t be fair to call the
accidents “acts of creation”. If one likes this word, it should rather be reserved for the processes of transition between relatively durable attractors. Locally, it may often make sense to speak of those as single successful acts, because many types of transitions between sub-attractors (e.g. typical phase-transitions described by physicists and chemists, or even some revolutions in societies) appear as straightforward on some “macroscopic” scale. But such acts of “spontaneous self-organization” are always accompanied by wriggling on smaller scales, and spatial spreading may happen with a lot of “fighting” for adaptation. The value judgment is contained in the whole process of wriggling and finding. – To summarize: Creation is the evolutionary self-organization of reality, the process in which the “freedom” of the accidents is organized by the attractors in the space of possibilities. However, as we saw, not only the finding of attractive histories, but even the very definition of their attractivity occurs only in the course of history. Reality and the “spiritual world” are inseparably intertwined.

5. What is truth?

Have we gained more insight into the connection of truth and reality? At a first glance, the word “truth” seems to suggest itself for all structures in the space of possibilities. However, reality also belongs to this space; it is the line connecting all momentarily realized state-points. We know that reality doesn’t always and everywhere shine with beauty. To count it as a part of truth might not fit with Augustine’s idea of beauty. Lies and ugliness would also be true in this sense. In a way, we would be confronted with all the frustrations of the “theodicy”. Can we avoid this problem if we don’t use the word truth for the structural ideas of arbitrary assemblies of “points” in the space of possibilities, but reserve it for attractors? Well, even this turns out to be quite unsatisfying. Isn’t a black hole particularly attractive – not to talk about the devil? Since we identify the space of possibilities with the “realm of ideas” and the “spiritual world”, doesn’t the attractivity of evil belong there, too? Should we, perhaps, include viability in the definition of truth, in order to exclude evil? But this would immensely complicate the concept, since we have just seen that evolutionary viability is not a purely intrinsic feature of attractors in the space of possibilities or its sub-spaces. The actual viability of an attractor does not only depend on its internal structure and its embedding between the basins of other attractors; it cannot even be defined without relation to reality. If reality had chosen a different path, the truth of a chosen attractor might be different, perhaps depending on intricate real details due to historical accidents. Shouldn’t truth rather be something “eternal”, i.e. something exclusively defined within “heaven”, i.e. by intrinsic properties of the attractors in that realm of ideas?

If we try and keep reality outside the definition of truth, we seem to be quite close to what Augustine meant. Can’t we say: “Truth is a property of any cyclic attractor in the space of possibilities”? Isn’t it exactly the property of being cyclical? Doesn’t this include a kind of “abstract viability” which we experience as beautiful? If some part of reality would follow such an attractor, undisturbed by any fluctuations, it would live forever. In a sense, this kind of truth would be “beyond time”. To be sure, the cycle is meant to be “run through in time”, but time is only a mathematical parameter here, and there is no discrimination between future and past. The cycle could be run through in both directions. This kind of time, like that in the phase-space picture of classical mechanics, doesn’t have an “arrow”. It is, so to say, the “time of being”, not the “real time”, which is the “time of becoming”. Reality, which is inevitably suffering from fluctuations, cannot stay on such permanent “reversible” attractors. Reality must be creative. Not even elementary particles and black holes are eternal, although some of them live long compared to the age of our universe. But for a theoretical physicist their beauty does not depend on that lifetime. It lies in the joy which he feels when he is able to “understand” how complex attractors can be “explained” (i.e. flattened out, made flat, on a sheet of paper, or a viewgraph). So, isn’t beauty just the splendour of the eternal mathematical truth of cyclic attractors, which can be approximated in the evolutionary wriggling of material space-time structures, including that of our cerebral ctivity?

Very disappointing! It looks as though we haven’t at all come nearer an answer to our initial question: What is beauty? Didn’t physicists know beforehand that the fascination with cyclic phenomena and their spatial patterns in atoms or galaxies is of the same kind as the fascination with mathematical structure? Similarly, for a modern biologist the fascination with the cycles of genes and proteins in a living cell may be of that nature. For a scientist, something is sufficiently “explained” when it has been reduced to tautologies – that is what all mathematical truth is, in the end. No mathematical theorem is more true than any other. If there is no truth but tautologies, however, the various degrees of beauty which we perceive cannot be due to different degrees of truth. The beauty of a rose, the beauty of a face, the beauty of a poem – what makes the different splendour of their truths? What about the aesthetic difference between the beautiful simplicity of a black hole and the beautiful complexity of Bach’s “art of the fugue”? And why do most of us find the rose so disgusting when we are told that it is made of plastic? There must be an intuitive perception of something like a “complexity index” which determines the splendour of truths and leads us to value judgments.

True, complexity is itself a complex concept, and when you start thinking about it, you discover a kind of “relativity of complexity”. Is the Mandelbrot set complex like its representation, or utterly simple like the algorithm for its generation? More generally: Whether a mathematical theorem appears as complex or as simple, depends on the starting point. You may choose a theorem, which needed a long proof, as an axiom, and one of the old axioms may then become a complex theorem. In a way, complexity is never the property of a part but always of the whole. Still, if beauty lies in the eye of the beholder, we may ask: Which axioms lie behind our intuition? The plastic rose is far more complex than a Kerr black hole, and the process leading to its production includes not only the evolution of complex flowers but even that of still more complex
people. On the other hand, the discovery of the Kerr black hole involved a lot of people, too – maybe people of higher mental complexity. Thus, the complexity (– however defined –) of mathematical truth in an attractor doesn’t seem to be a sufficient measure for its splendour. We seem to sense some other kind of truth behind the beauty of an axiom or a theorem, a black hole or a galaxy, a rose or a face, a cathedral or a poem. What is it? It seems to have to do with the viability of our own attractors in the real process of creation.

We had just tried to discard such a connection of truth with reality, in order to avoid conceptual complications. But this was a mistake. Obviously, we assign values to truths, even though truth is tautological, and the value judgment doesn’t seem to be just a matter of counting possibilities or bits of information in eternal mathematical structures. What is it, then? We forgot that our individual and collective mental activity is part of the process of creation. Our aesthetic value judgment is part of that selection process in the wriggling of evolutionary self-organization. It must have to do with the discovery of viability, which happens in this process. As reality is groping its way through the space of possibilities, it “feels” rewarded when it finds a viable attractor. For the reality of a human mind this re-ward is re-cognition. Clearly, this already plays a role in the “psychology” of higher animals, e.g. when they feel comfortable “at home”, and restless otherwise. So, a disposition for the recognition of viability is guaranteed by the bio-psychological realization of human mind. The beauty of the universe, as perceived in a starry night and with the cycles of the sun, the moon and the planets, the beauty of the biosphere and one’s homeland, and the beauty of one’s kinsmen and their language – as the consciousness of mankind awakened, all this was unquestionable, like it still is for every awakening child. Any healthy mind realized that the universe was the mother’s womb, that the biosphere was paradise.

Then, further biological organization of cerebral attractors, i.e. their discovery in the space of possibilities via the wriggling of reality, brought a new front within reach of the fluctuations. On these roots more and more attractive ideas of culture and civilization have been found, very slowly over a million years, much more rapidly over the last few thousand years, and like in an explosion during the last few decades. For most of the time, nobody would have asked what beauty is, like nobody asked why customs were good and right. Habits were usual, beauty was beautiful. Nothing mysterious. Just the rewarding recognition of viable attractors. Why, then, should at last such questions have come up: What is truth? What is beauty?

6. The devil-theorem

There is a conflict built into the very principle of creation. Evolutionary self-organization through accidental wriggling of reality along its attractors does not necessarily favour the discovery of complex viability. There are those powerful “unstable” attractors which find a viable cycle only after an essential reduction of complexity. In fact, this kind of collapse must often happen locally, but (except in the extreme case of a black hole) that devastated region will soon serve as fertile experimental ground for further trial and error, starting from attractors still realized in the spatial neighbourhood. Their ideas survive and expand, unless they also come too near a more attractive unstable one. However, spatial expansion is necessarily accompanied by contact with new possibilities. (Not “new” in the realm of ideas, of course, but new in real time.) Adaptive wriggling must then lead to other reachable attractors.

In the competition between various regions in real space, more evolvable attractors, the organization of which allows for faster and wider “wriggling”, have a selective advantage. As an old example, remember the invention of sexuality: Via accidental combination the number of trials in each reproduction cycle is immensely larger than in the old procedure of sheer division and mutation. Therefore, this new principle quickly conquered the front in the space of possibilities. More recent examples are the invention of neural networks in the brain and, at last, of language and conscious thinking in the cerebrum accompanied by the development of cultures and their mythologies and systems of slavery, which still brake the free expansion of mind. At last, there comes that explosion of civilization with writing, longdistance weapons and long-distance traffic, scientific enlightenment with more and more technical gadgets and “media”, and economic enlightenment with globally convertible currencies and with terms of trade and property rights which permit and, therefore, enforce the buying-up of the livelihood of ones fellow-citizens and whole nations – with total liberation from the old kind of slavery and the organization of much more powerful enslaving ideas which take care that everybody follows the same attractor, once called

We see: For purely logical reasons, there must be an “evolution of evolvability”, i.e. an increase of the speed of innovation. Simultaneously, the “faster” ideas must spread to increasingly larger scales in real space. In an isolated spatial region, like on a planet, this ongoing evolutionary progress must approach a global unstable attractor – again for purely logical reasons: There are upper limits to the organizational scale and to the speed of innovation. As they are approached, a decomposition of viable complexity must set in. Globalization reduces the diversity of trial and, together with the increasing speed of innovation, diminishes the chance of finding “better” attractors. And the faster an attractor is left for a new one, the less likely is it that it has been sufficiently tested for viability. So, there is no reliable basis for the next trials. The creation process becomes globally unstable. Acceleration and globalization amplify each other, until essential global features change on the critical time scale. When even Gaia’a oldest and most reliable attractors are being left, the crisis reaches its climax. As that singular epoch in planetary evolution, the tumbling of biosphere and noosphere near a catastrophic instability, must inevitably be reached for system-theoretical reasons, it deserves a scientific name. I call it “the global acceleration crisis”. We start realizing that we have reached its climax. Why? What is the critical speed of innovation?

Mind has long realized that it is in danger of falling sacrifice to attractive ideas which are not viable. Etymology suggests that “evil” is related to “uppishness”. The uppishness of scientific enlightenment lies in the belief that progress leads upwards if it is produced in good will. But this isn’t enough! While scientists are looking for the intrinsic truths of all kinds of attractors, they have neglected that other kind of truth which lies in the very principle of creation. Like all truth, it is of a tautological nature: A cyclic ttractor in a rich neighbourhood of possibilities cannot even be suspected to be viable, before reality has run through it at least once. Scientists claim that their business is to discover more attractive structures and to offer them as “new options” to everybody. Society is then supposed to make a reasonable selection. However, there is a problem: At what pace of innovation is evolutionary progress likely to find viable attractors? With how many new options can people, individually and collectively, be confronted within a year and make reasonable decisions? or within a second? or a picosecond, with faster computers?

In the general obsession with the successful acceleration of progress, it has been overlooked that there is an intrinsic time-scale in the problem! What is the cycle of reproduction of the highest value which has been realized so far? Which attractor of reality am I talking about? Of course, it is the attractor of a viable person, God’s image. That this is “the crown of creation” has been understood not only in Western culture. It does not seem to be an error that the idea of “human rights” is becoming one of the leading ideas on the whole planet. One might be tempted to assign an even higher value to viable cultures and to the whole system of biosphere and noosphere. But this would only strengthen my argument. The cycles of cultural attractors, in which the individual ones must be embedded, are necessarily much longer – not to talk about global biospherical cycles. But man is able not only to destroy himself by his own wriggling – he can even introduce global innovations on very short time-scales. This is why we say he can be trapped by the devil. He is able “to sell his soul”, and jump on to unstable attractors. This isn’t new. The new development – with the global acceleration crisis – is that nearly everybody does it, and has to do it. The leading idea of global civilization has become that we can and must improve everything within one generation and even faster, before even one cycle of the relevant attractors has been completed.

That this should be logically impossible, contradicts the most attractive ideas of our time, but it follows from what I have tried to explain here. After we have understood it, we shall grope for different attractors – and not in arbitrary directions, with the hope that “anything goes”. What we have found out about the process of creation, will allow us a clearer vision of good and evil, of beauty and ugliness, of essential values which used to appear as indiscernible to “value-free” science. A closer look at spatial and temporal scales of evolutionary processes will introduce value judgment as a scientific argument. The arbitrariness, which up to now seemed to result from the enlightened world view, from the tautological truths of science, will become transparent. Behind it, we shall discover not only the seductive attractivity of the devil’s haste, but also a more consolatory “transcendental certainty”, namely the fact that system-theoretical logic provides commandments which may help us to put the devil in chains.

Lo and behold: There are logical conditions for “successful” creation, which define the difference between good and evil, between beauty and ugliness. Our wriggling between the ideas of truth and reality wasn’t useless. Scientific enlightenment is, at last, going to bear fruit in the fields of ethics and aesthetics. Considering the “tautological” self-evidence of our findings, though, we must not be surprised if we find similarities with images and imaginations from older myths of creation.

* * *

We have understood that in the course of evolution nearly all trials must have been errors. Failure is the most essential constituent in the creative process and can’t be “devilish”. Why, then, does the figure of the devil play such an important role in nearly all myths of creation? Clearly, this has to do with the fact that man is capable of more than the usual kind of mistakes. He can destroy himself, his society, and even his roots in the earth’s biosphere. This is recognized, e.g., in the stories of Prometheus, the
fore-thinker who brought fire from heaven, and of Lucifer, the lightbringer. That angel had watched creation and seen how it worked. He had understood the functioning of elementary particles, of nuclei, atoms and molecules, of the genetic code and the living cell, of organs, organisms and species, of brains, societies and markets … Why, then, should he not be able to improve the world much more quickly? We know: He tried, and he fell, and he received a new name, diabolos, which means “he who throws things into disorder” – though all was done in good will, with the best intentions, which still pave the road to hell.

One might think that in our “reductionist” phase-space picture the Devil cannot be an attractor, like the idea of the proton is, or the idea of “Gaia”, or that of a man and his individual soul. Isn’t the truth of God and the angels of a different nature? It lies in the logical principle of creation, and not in a specific “gestalt”. Isn’t this why it is forbidden to make an “image of God”? But this would be a misunderstanding. In conscious human cerebral activity the logical principles of creation can be understood, and this means that God and Devil are actually approached by material reality! On our level of mental complexity, they do represent very effective attractors. This is why they have been around for at least several thousand years, probably since the evolution of free thinking started in gifted individuals. The truth of those attractors is essential in our own creativity, i.e. at the present front of evolution, in the self-organization of human freedom. After our re-unification of mind and matter we can even try and talk about them in scientific language. What I am presenting here, is the sketch of a “system theory of God and Devil”. And the statement about the inevitability of the global acceleration crisis I have occasionally called the “devil theorem”.

Why does our creation myth allow the devil to become active only on the last day, when man had appeared? Because all the previous beings were not yet able to destroy the highest values, i.e. the most complex viable cycles, which had been reached so far. An animal can make a mistake and die, but this is a negligible accident in the co-evolutionary wriggling of the whole biosphere. A species may develop abilities which are harmful to many others, but the diffusion of profitable genetic mutations or sexual combinations into the whole population necessarily takes many generations. Before a dangerous innovation can spread over the whole earth, other species have had time to adapt through frequency-shifts in their own gene-pools. And although higher life forms necessarily have much longer generation times than the micro-organisms, they have been able to cope with them through their own diversity and via an “immune system” which is able to evolve counter-forces on similarly short time-scales as the potential enemies. Therefore, fatal large-scale accidents which could have critically reduced the complex diversity of the whole, were extremely unlikely to happen as a consequence of biological evolution itself. They could only occur “from outside”, e.g. when a stone the size of
Mont Blanc hit the earth 65 million years ago – and more often in the early history of our planetary system. If this had been likely to occur much more frequently, the biosphere might not have been able to reach noospheric attractors. On the other hand, the death of the dinosaurs created more evolutionary freedom for the mammals with their brains …

Only the human brain has reached a level of internal complexity on which the self-organization of speed and size of innovations must become the basic problem. Whereas in biological evolution the necessary steps of mutation, reproductive mixing and phenotypic selection set a limit to the speed of innovation, such that essential global changes can take place only within many generations, the biological limits to the inventiveness in mental processes do not forbid us to change the world within a few years. Of course, this needed time to become obvious. For most of the time of human evolution and the early history of culture, the groping of individual minds couldn’t reach very far in the realm of ideas. Viability demanded that the cultural attractors sufficiently constrained the individual ones. Only culturally accepted truth or beauty was true or beautiful. If exceptionally gifted people stepped too far in their individual wriggling, the organization of social attractors probably took care that they were soon eliminated. However, with very attractive ideas it was also likely that some disciples were already trying them. Mind was such a successful invention, that its freedom could not be suppressed indefinitely. It started groping in more and more new areas in the space of its possibilities – very slowly at first, but accelerating – and more and more quickly after globalization of the fastest leading ideas had been achieved – until it was by no means clear anymore, what was beautiful or ugly, good or evil.

* * *

We cannot go into details about the system theory of leading ideas in the history of mankind. It is, of course, fascinating to look for branching points in the past, because they may give us hints to viable attractors which are still near. Just one more question: Why did the idea of “equality of all people in front of God”, and the corresponding idea of democracy become attractive just before the climax of the crisis? This is not an accident! There is a very powerful “wrong” attractor next to both ideas, a devilish trap, a very probable “misunderstanding” which is self-accelerating. Along the old viable attractors of culture, nearly everybody had the same opinions, formulated in taboos, myths, proverbs, poetry, laws. So, majority was usually “right” in judgments about good and evil or beauty and ugliness. As the individual mind becomes more and more liberated, this is unfortunately no longer true – if we want to uphold the notion that “goodness” and beauty are associated with complex viability. As social reality reaches unstable attractors, the more deeply rooted attractors of our time-tested psychological heritage take care that the majority thinks it is right because it is the majority. So strong is this idea rooted in us, that even some political philosophers still believe in its truth. But clearly, near the climax of the global acceleration crisis, majority must be wrong in nearly every respect. We see again that the truth of attractive ideas cannot be judged without reference to their embedding in the whole neighbourhood in the space of possibilities, including reality. On unstable attractors political “conservatism” may lead into collapse, whereas “revolutionary” wriggling towards a few selected old ideas may bring the rescue.

Faster change has become the main attraction of the conservatives. The only generally accepted custom is innovation, the replacement of all the usual habits by more useful ones – in world-wide competition, which means world-wide collaboration towards the same aims, of course. Newly discovered ideas attract more and more quickly every spot on the earth – from the centers of the Western world to the people of the last hidden islands and valleys. At last even the biosphere has to adapt to new attractors. We set free more heavy metals than all weathering processes; about every hour we invent a molecule which may not have been realized before in our whole universe; also about every hour a living species is disappearing, perhaps even up to ten; this means an essential reduction of the biosphere within one human life time; we change the climate of the earth on that same time scale, and the ozone layer, which was built up by life within the last billion years and which brought more complex attractors into the reach of life, is being decomposed still more quickly. Right now, as those problems have become obvious even to conservative scientists, they have started to discuss the possibilities of “geo-engineering”. There are so incredibly many attractive ideas within reach!

Now, however, with that speed of global innovation, the “solution” of a problem is likely to produce several new problems which are felt on a larger scale and which need a solution still more urgently. A larger scale and a higher speed of innovation still have a selective advantage in this process of evolutionary self-organization called progress. This is a euphemism for the kind of system behaviour that scientists would call an
instability in any other context. It is exactly the selective advantage of size and speed, which made it likely, practically necessary, that we ran into this crisis. And still, it must not mean final decline and fall. Crisis means decision. The choice is between further tumbling down, perhaps back to Precambrian attractors, and the successful self-organization of human freedom. Of course, this is just a sophisticated wording for what one used to call culture. – Why should there be a chance of viable self-organization, when all present tendencies promote the instability? But this is the essence of an instability! This is how we recognize it! And therefore, there is still the chance that the majority understands it, too, if the symptoms become even more visible. Then, new attractors may strengthen different interactions.

I used to say that I didn’t recognize the world any more when I reached the middle of my life. For our children this experience came at the end of childhood. People of our time may find it “unjust” that the crisis becomes manifest while it is our turn to live. Many sulkily refuse to look at it. But it had to be reached sometime, unavoidably. Now, here it is. Soon nobody can deny any more that man is changing not only his social environment and his culture on the critical time-scale, but even the earth’s climate and other essential features of the biosphere. It is becoming incontestable that within two generations all that would collapse if we go on with what we call our civilization. In this situation, more and more individuals start searching for remnants of viable ideas. Trends which are right now scarcely recognizable in the rapid stream of the instability will suddenly lead to the self-organization of patterns which dissipate and break its impetus. Reduction strategies for unsustainable customs will be developed. Many majorities on smaller scales will suddenly start following similar attractors because their truth is practically self-evident under the conditions of the crisis. This will happen on the level of conscious mind, the leading structure – as the instability is not a biological but a mental disease.

After we have understood the principle of creation, including the devil theorem, we shall be able to work for the self-organization of our freedom. It is immediately obvious where more viable attractors are to be found, and if this insight spreads fast enough – i.e. also on the critical time-scale of a generation – viability may still be achieved. It does not represent an internal contradiction, but lies in the logic of instability, that we must try and constrain speed as quickly as possible, and that we must co-operate globally to restrict global power. It is self-evident that the new attractors of society must organize constraints to nearly everything “big and fast”. This will become constitutionalized as the governing principle in politics, technology and economy. So-called realists call this “utopia”, because they lack the sense for all neighbouring attractive possibilities except the smooth, broad road to hell.

7. The beauty of the seventh day

Wasn’t this supposed to be an essay about beauty? I am sorry, we had to take that long deviation to clear up the relation between reality and possibilities, and between realism and idealism. And now, space, time and everybody are exhausted. Anyway, of course, we are still not able to say what beauty is. No surprise! The essential feature of complexity is that it cannot be analyzed quantitatively. (To defend this statement against naï ve optimism, let me again remind you that the number of different possible relation structures with straight lines between 24 points surpasses the number of atoms within our cosmic horizon.) Insofar, scientists were right to refrain from value judgment about details of the filigrees in reality and its attractors. However, if they accept a single proposition, they will be able to make quite general judgments about the relative “survival value” of attractive ideas in technology, economy and other social activities. That single proposition is: The front of terrestrial evolution in the space of possibilities should not fall back to pre-noospheric or even pre-biospheric attractors. This demand certainly deserves to be called “ethical”. If human mind accepts it, it will continue the “ethos” of our universe, its custom to find viable attractors of beautiful complexity.

Of course, the creation myth which I have sketched here, is not “proven” – it is a proposal, an offer especially to scientists, meant to encourage value judgment. In this framework, scientifically correct judgments about necessary constraints of human freedom – namely my general statements about spatial and temporal scales of viable social attractors – are unavoidable, of a tautological nature, like the principle of creation itself. No doubt, the majority accepts our “ethical” proposition. In the imagery of our myths, we may say: This shows that the devil has not won yet.

Where are we in the process of creation? Which day is it? A genetic engineer announced the morning of the eighth day, recently. A beautiful day it might become, he hoped, because he wasn’t able to judge the probabilities of seeing beauty or ugliness at the end of the day. In fact, he thought he would make the weather himself, with his best will. After we have understood the conditions for successful creation, we can tell him: If mind would try to improve its own biological roots within a few generations, chaos would be the probable result, with a probability extremely near one. The beauty which we can imagine in the realm of ideas, if we allow for arbitrary combinations of genes from the pools of all species, is overwhelming. Marvelous children, men and women, beautiful, healthy and joyful for more than a century, living in a world full of sophisticated gadgets and a moderate selection of fantastically useful and cheaply produced other creatures … For fun, we may even make animals which Hieronymus Bosch might have painted! Why should all this be devilish?

We have understood now: With too many trials at a front near the old time-tested attractors of our material roots, the probability of reaching new viable attractors is practically zero, whereas the probability of losing the old attractors and of starting to tumble and become unstable, is nearly one. The example makes it perfectly obvious where human creativity is likely to succeed, and where not. In our imagination, in poems, novels and pictures, we are certainly allowed to try other worlds – if their interaction with the real one is sufficiently weak. Our creativity must concentrate in our purely mental activity, which leaves the old world intact. We are still on the seventh day! God’s rest does not mean that creation has stopped. This is impossible, as we have seen. The front of creativity has moved to our mental abilities. But our main task on the seventh day is “to praise God”. In the clumsy language of this article that is: “Let your mind come near the truth of complex attractors which it can reach”. This includes the attractors of pre-mental reality, God’s creation of six days – which must not be abandoned, of course – and it includes all human ideas and works of art which are not in destructive conflict with those. We are back with Augustine. As mind wriggles near this kind of truth, it perceives beauty.

Creation and perception of beauty are both creative processes. In a first step, some part of reality has been created by the organization of accidents near complex viable attractors in the space of possibilities, i.e. in heaven. This may be part of the “outside” world, produced by the cosmos, the biosphere or by people in the form of works of art and craft or as communicable ideas, like poetry or music. In perception, the other creative step, a human brain interacts with this reality, and its neural activity, the mind, wriggles about the resulting patterns. If the fluctuations between newly excited patterns and the memory reach cycles in this process, this does not necessarily lead to the perception of beauty. If such “recognition” is reached too fast, it may even cause boredom.

The perception of beauty only arises when the wriggling goes on for some time and touches many neighbouring attractors in the memory. This is accompanied by a feeling of continuing surprise, and even excitation. It is, so to say, the sparkling of the complex truth of all the attractors touched in that trial and error of mental activity. In the end, though, this sparkling may give way to a steady splendour, when more adaptation has been reached and mind follows the complex attractor with reduced fluctuation rate. This is accompanied by a feeling of satisfaction. As far as I am concerned, after my long wrestling with the text of this article, my excitation about Augustine’s words has given way to a kind of satisfaction, but I still find them beautiful, not boring. Some wriggling is going on. Creation is not finished around this idea.

A complex mental process in productive and perceptive creation is not necessarily connected with a complex structure of the motive. Simplicity and symmetry often excite the mind to higher receptivity for its own internal beauty, its own viable complexity. Even simple geometrical patterns, and “monochromes” or extremely monotonous music may, therefore, cause long-lasting sparkling – as in a theoretical physicist – or inexhaustible splendour – as in a meditating monk.

In the history of art and music, which is part of the general progress towards the climax of the global acceleration crisis, we can see how the very concept of beauty changes. More creative minds wriggle faster and faster, and abandon the traditional ideas more and more quickly. In those purely mental activities innovation on our critical time scale, defined by a generation, must not yet mean decline. Here, the new can add to the old without fully destroying it, as it now often does in the biosphere and in many traditional cultural ideas which need more “hardware” for their expression. In the perception of art and music, some people may even follow the old attractors more often than new ones – e.g. in museums and concerts. Near the climax of the crisis, though, innovation in the production of art has long passed the critical pace and has reached the time scale of the most short-lived fashions. The very concept of beauty disappears. Worldwide success of the fastest possible innovation, called originality, becomes the main selection criterion. Eventually, sparkling and satisfaction are no longer correlated with the “motives” and the skills in a work of art, but exclusively with the money involved.

Since the search for attractive structure takes time, thus hampering faster innovation, two tendencies must evolve naturally: For the invention one may use computers. They can do certain things in fractions of a second, which a human mind cannot do in a lifetime. Clearly, due to the selection criteria in the instability, the aesthetic value of such things is likely to rise, even more so, if the computer is very expensive. On the other hand, particularly modern people will become accustomed to finding chaos beautiful. Chaos seems to allow perfect freedom of the mind in its perceptive wriggling. However, this is an illusion. If mind finds complex ideas from chaos, they must in fact have been very near subconsciously. Only the chaos near proven complex attractors is likely to be fertile in the creative process.

I do not want to insinuate that computer-produced pictures, like bits of the Mandelbrot set and many other fractals, cannot be extremely beautiful. They can stimulate mental activity in quite unexpected ways. Haven’t we just used the Mandelbrot set as a guide in the discussion of what “existence” and “being there” might mean? The very language of this essay, admittedly still clumsy in its wriggling for a combination of exactness and freedom, would not have evolved without the acquaintance with the theory of deterministic chaos and the complex filigree structures of attractors and their basins of attraction in the phase space of simple dynamic systems.

Though, in a way, intuitively gifted minds must long have known that complex order can only exist near the “edge of chaos”, and that selforganization of viable complex structures is impossible without accidental fluctuations around the attractors near that border, the consequences for human self-constraint could scarcely be made accessible to most people in a culture moulded by science, technology and “materialism”. Now, with the popularization of chaos theory and ideas of modern physics and biology, there is a chance that the principles of creativity become familiar to many – and, eventually, to a majority. Perhaps my attempt of a “re-unification of mind and matter”, of “earth and heaven”, in the space of possibilities can help to find a language, in which scientists, theologians, economists, artists, and maybe even politicians and people in the “media” can talk to each other about the logical roots of the global crisis.

There is no reason to lose hope. The fundamental structures of our brain and of its drives are not changed by the evolutionary instability. Man isn’t a failure in the process of trial and error. Children still enjoy beauty and abhor ugliness and evil. We must not be blinded by exceptions. And the adaptability of societies to changing circumstances is obvious from the history of culture. The only difference is that now the new constraints will not come from outside, but will be consciously created by the majority of all people after they have understood the principle of creation. The world has really become “man’s age” – i.e. what the old English
werelt for world means originally. The necessary self-organization of human freedom on viable attractors is certainly possible, and it will become likely as soon as more people start talking about the phenomenology and the logical roots of the global acceleration crisis. Of course, this cannot happen if most gifted people run after more money, or want to solve the problems of mind with more material gadgets, or lean back peacefully or cynically to watch what evolution or God are going to achieve. But as we approach the climax of the crisis, more and more people will not feel satisfied. The wriggling will increase as more and more of the ugliness of our age becomes visible and felt. We can be sure that beautiful attractors are near.