>John Turnbull writes
>
>>In other words, systems that
>>self-organize all by themselves suggest that the end product was
>>in fact the result of a design built right into the very laws of
>>nature itself.
>>
>Agreed.
>
>However, this way of looking at the mechanisms of nature could lead to a
>very mechanistic -- deistic -- view of how nature proceeds, unless another
>aspect of chaos is duly considered. Chaos is also defined as sensitive
>dependence on initial conditions. It's fairly easy to demonstrate chaotic
>systems in which a vanishingly small variation in initial conditions, or a
>vanishingly small disturbance as the system evolves causes significant
>differences later. But by the time these differences are noted, their
>cause has quite literally become lost in the noise. Thus a mechanism
>exists whereby God can determine the behavior of objects in nature without
>His interaction with nature being seen as a disturbance.
>
It is with great trepidation that I pursue a discussion of dynamics
with someone named Hamilton ;-).
I think it's important to maintain a distinction between self-organizing
systems and chaotic systems. Both systems are very complicated, however,
self-organizing systems are, I think, much more predictable than chaotic
systems. Even so, the two systems are closely related. I'll try to get
more into this point later.
I think I muddied these waters with my earlier analogy between Goodwin's
generic forms and strange attractors. Bill is correct about sensitivity
to initial conditions, the amount of initial information required to
predict a chaotic response grows exponentially with a linear extrapolation
in time.
So, in retrospect, I don't think the analogy with a strange attractor is
particularly good. Instead, I think the idea of generic forms may actually
possess some features in common with both point attractors and strange
attractors. I would view generic forms as almost isolated islands in phase
space. If you get in their vicinity, then they suck you in very close but
not down to a single point, in other words there is great variety possible,
but variety on a common theme (the "generic form"). If one moves too far
away from the "island", the phase space becomes very "sparse" in the sense
that almost all points violate some physical principles and are thus
not allowed. In principle, I think it may actually be possible to predict
what the generic forms are. This would then be fundamentally different
from the orthodox neo-Darwinian view where the forms would arise due to
the tinkering of the blind watchmaker and then be isolated due to historical
constraints. In other words, the role of natural selection would be reduced
primarily to minor adaptatations of the generic forms.
The association with chaotic dynamics may come in the sense that predicting
precisely which generic form is attained from an arbitrary starting point
may be impossible. This is, I think, precisely Bill's point. The "orthodox"
view
of the self-organizationalists seems to be that self-organization occurs "at
the
edge of chaos" or that organized systems "crystallize" in some manner from a
chaotic system. If this is indeed the case, then the self-org systems manage
to isolate themselves from their initial conditions. In fact, I believe
that something like this *has* to happen if the term *self*-organized is
to be legitimately used, as I've discussed previously.
Here are a couple of definitions of "self-organization" which reinforce this
idea:
"For what follows it will be useful to have a suitable definition of
self-organization at hand. We shall say that a system is self-organizing
if it acquires a spatial, temporal or functional structure without
specific interference from the outside. By "specific" we mean that the
structure or functioning is not impressed on the system, but that the
system is acted on from the outside in a nonspecific fashion. For
instance,
the fluid which forms hexagons is heated from below in an entirely uniform
fashion, and it acquires its specific structure by self-organization."
-- Hermann Haken, _Information and Self-Organization_, Springer-Verlag,
1988, p.11.
=============================
"Self-organization is to be understood as the spontaneous emergence of
coherence or structure without externally applied coercion or control."
[the following is then added in a footnote]:
"Godfrey Vesey points out that in using language such as 'self-ordering'
and self-organization', we are in part returning to the Aristotelean view
that teleology is internal to matter. However, we definitely reject a
teleology that proposes organisms are shaped by adaptation to some external
purpose or function, whether it be natural selection or some omnipotent
creator that is postulated to account for it.
-- M.W. Ho and P.T. Saunders, 1986,"Evolution: Natural Selection or
Self-Organization",<Disequilibrium and Self Organization>,
C.W. Kilmister, ed., D. Reidel, 1986, pp. 231-242.
==========================
I must say that I had to smile a little on reading the above footnote. What a
tightrope these guys have to walk! First, they have to be careful to avoid the
implications of finely tuned initial conditions. Success in this regard then
leads to suspicians of vitalism ;-).
Sorry about this getting so long. I guess those not interested have already
pressed the escape key by now anyway, so I'll close by giving two more quotes
which discuss the implications of initial conditions:
=========================
Is "self-organization," the spontaneous increase of complexity, an
asymptotically qualitative phenomenon like phase transitions? In
other words, are there reasonable models whose complexity, starting
from a simple uniform initial state, not only spontaneously increases,
but does so without bound in the limit of infinite space and time?
Adopting logical depth as the criterion of complexity, this would
mean that for arbitrarily large times t most parts of the system at
time t would contain structures that could not plausibly have been
generated in time much less than t. A positive answer to this question
would not explain the history of our finite world, but would suggest
that its quantitative complexity can be legitimately viewed as an
approximation to a well-defined property of infinite systems. On the
other hand, a negative answer would suggest that our world should be
compared to chemical reaction-diffusion systems that self-organize on
a macroscopic but finite scale, or to hydrodynamic systems that
self-organize on a scale determined by their boundary conditions, and
that the observed complexity of our world may not he "spontaneous"
but rather heavily conditioned by the anthropic requirement that it
produce observers.
-- Charles H. Bennett, "How to Define Complexity in Physics, and Why,"
in _Complexity, Entropy, and the Physics of Information_, SFI Studies
in the Sciences of Complexity, vol. VIII, Ed. W. H. Zurek,
Addison-Wesley,1990, pp. 137-148.
=============================
The logic behind the inflationary explanation of the Visible
Universe's structure is to show that however the Universe began-
whether in chaos or in order-the inevitable effect of the laws of
gravitation is to deliver it to us in the form we find today.
Unfortunately, it is likely to be impossible for us to ascertain
whether inflation did occur. How could we tell whether the special
features that inflation endows upon the observable Universe were
so endowed or whether they are the reflection of very special initial
conditions? One might feel that methodologically the latter is a less
appealing 'explanation', but this anthropocentric prejudice towards
explanations that are convenient for our beliefs about the way to do
science is no argument for or against their _truth_. [...]
[...]
The wielding of laws of Nature in the manner either of the chaotic
cosmologists or of the 'inflaters' to explain the universe in a way
that puts no weight upon its structure at the beginning, can be seen
as the natural inheritance of a style of reasoning that began in
earnest with Wallace and Darwin. The pre-Darwinian explanation for
the detailed structure of the living world was an appeal to special
initial conditions: things were made that way. The result of invoking
evolution hy natural selection is to downgrade the influence of
special starting states which presuppose some element of Divine
design, and place all the responsibility for what is observed upon
the physical processes and the laws that govern their development in
time. However, there are important differences of detail. The
cosmological scenario in which appeal is made to general physical
processes to render the future state of the universe inevitable has
as its goal the predictability of that future state. Natural
selection is quite the opposite. Given a soup of chemicals in a
complex environment, its precise future evolution cannot he predicted
because the system possesses a sensitive dependence upon the precise
nature of the starting state which we shall discuss in Chapter 5.
Inflation has the opposite property that the final result is
insensitive to the starting state. A good analogy to these two
approaches to the role of starting conditions in cosmology is the
'IQ debate' between educationalists over the relatlve roles of
'nature and nurture'. There, the dichotomy is between those who
believe that intelligence is primarily genetically inherited (that
is, dependent upon 'initial conditions') and is insignificantly
influenced by environment, and those who maintain that it is
principally conditioned by environmental factors (that is, by the
'laws' of environmental development).
-- John D. Barrow, _The World Within the World_, Oxford University
Press, 1988, pp. 219-221
========================
Brian Harper |
Associate Professor | "It is not certain that all is uncertain,
Applied Mechanics | to the glory of skepticism" -- Pascal
Ohio State University |