>Glenn, a question for you (since I'm not an expert in nonlinear
> dynamics):
>While chaos theory describes the way a system's time-evolution is quite
>sensitive to initial conditions, aren't there also mathematical
> equations of motion which lead to very similar time evolution no matter
>what the initial conditions? (Is this a "strange attractor"?) The
>existence of such systems could be appealed to by those who seek to
>blunt the force of an anthropic principle which depends on "fine-tuning"
>of initial conditions.
>
>What do you think? And you, Brian?
>
Attractors, strange and otherwise are a common phenomenon in complex,
iterative systems. And yes, Sierpinski's Gasket is an example of an
attractor which produces the same pattern regardless of the initial
conditions (Examined in infinite detail different initial conditions
yields different details, but the macroscopic effect is always the same.
It looks like an infinite regression of inscribed, alternating inverted
triangles
The Henon-Heiles attractor (which is derived from stellar orbits around a
galaxy) have a set sequence of patterns for certain initial conditions
which are quite predictable and stable. Stable orbits are like this. But
other conditions lead to absolute chaos. (see Stephen Koonin,
Computational Physics, pp 235-246 There is also a wonderful article from
Astrophysics (I think) by Henon but I can't find it)
Now to the philosophical question. Can these attractors blunt the
anthropic principle which indicates design? I don't think so but I am
going into a area of philosophy in which I am a babe in the woods. There
is no a priori reason that I can see for why a given numerical methods
equation should yield a given solution. Before a mathematician chides me,
I need to explain that somehow, in some way, the very logic we use must be
a creation itself. If I recall John Archibald Wheeler's discussion in
_Gravitation_ (by Thorne, Misener and Wheeler) Chapter 44; of his
pre-geometry, he views the laws of nature and logic to be created at the
time of the Big Bang. Thus there is no logical necessity for us to have
the logic we have.
Under this condition, one must ask why do we have the logic system we
have? Is this the only logic system possible? For us maybe but not
necessarily for the Creator. He could have chosen another logic if He had
so chosen. I would view our formal logic as one of the initial conditions
of the universe.
>Stan Zygmunt
> ^
> |
> |
>(note the spelling, Glenn! :) )
I wish I could say it was a typo. My most profound apologies. I really
am embarrassed about that 'cause I should have known better. :-(
glenn
Foundation,Fall and Flood
http://members.gnn.com/GRMorton/dmd.htm