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What
is Beauty?
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On
the System Theory of Creation
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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 The Original is unpublished.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.
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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.
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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.
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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 MtEverest. 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.
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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.
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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?
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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 mammon.
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.
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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
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.
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