This is where I differ. A study of simple phase spaces of non-linear
differential equations shows that in the plane of solution, different areas
have the same solution. Look at the letters in this note. The same letter
is placed at different sites. Thus if you randomly walk around the page(move
up,down, left right but always stay on the page) it will be rather likely
that you will find your self on an 'a' at some time. Similarly, complex
systems have similar phase spaces. Essentially the same solution is spread
throughout the space. Thus if 'y' on this page represents the solution of
the DNA permutation for man, then it is not that unlikely that you can
randomly walk across the page and create a man-like creature. In this
fashion, God can control the probabilities and a theist can hold to
evolution. Even if God were to self limit himself to never knowing whether
you would randomly move up or down a row or left or right on the same line,
He could assure himself that as long as you randomly move, mankind would
arise!!! Eventually you will land on a 'y'.
My programs illustrate this behavior, especially the one CAMBEXPL. It runs
32? separate lineages. If you watch this for a while you will see very
similar but not identical solutions. If you printed the 'genomes' for those
solutions, you would find that the similar solutions had a very different
genome.
You wrote:
" If the program were run
again, would it develop in the same way or differently? "
If you run my program again, it develops differently but then once again
eventually you will run into some picture shape (morphology) which you are
looking for which will not be absolutely identical but quite similar. The
difference will be of the order of the differences between human races. Run
the program and look for those similar forms. They can better be seen in
EVOLVE.EXE which follows one lineage.
You wrote:
>As I understand things, all forms of Nauralistic (i.e., atheistic)
evolutionism eschew the notion of a telos or goal to evolutionary
processes (although Dawkins and others frequently use terminology that
implies or suggests that theprocess of biological change is directed
toward a goal), except the goal of survival.<
In the way I described, I can hold to teleological goals. It is perfectly
compatible with the mathematics of the phase spaces, if you are the DESIGNER
of the phase spaces. While you and I can not design such spaces, presumably
God can.
OH NO, more tough arguments with Brian again. :-)
I am going to answer one thing of Brian Harper here. Some of these systems
are not subject to initial conditions. The Mandelbrot set isn't.
Sierpinski's Gasket isn't, Ueda's chaotic attractors (in the Poincare
section) are not. Every time you run these you get the same solution. But
the best analogy I can find to what I am trying to convey is the relation
between the Julia set and the Mandelbrot set. Each point on the Mandelbrot
set is a code for the Julia sets. By randomly walking across the Mandelbrot
plane you can "evolve" the Julia sets according to the order of your walk.
So in DNA phase space, what I am envisioning is that t "domains of
attraction" are scattered in a complex fastion as can be seen in Fig. 5.11 p.
79 of NONLINEAR DYNAMICS AND CHAOS, by Thompson and Stewart, Wiley1986. For
a duffings equationof order three there are several similar solutions spread
around the plane. solutions
And Brian, the detailed workings of my program are the same as the basic code
I sent you. I just translated them into pascal to create an .exe file so
people would run them. You are welcome to the code if you want it.
glenn