Date: Sun 31 Oct 2004 - 11:22:23 CET
Some time ago there was a discussion on power-laws on this list. Power laws
are "signatures" of fractals and all we know how abundant they are...
Yes, systems are very different, although all they have some maybe vague,
idealized, oversimplified but still, similarities:
1) ...atom, cell, individual, business company, country, planet, solar
system, galaxy - all they have a common feature they are controlled from one
"strong control center"...
2) ...homogenous molecules, polymers and crystals, tissues, populations and
colonies, crowds, (con)federations, etc. - all they are functioning like
networks composed of interacting homogenous elements (sort of cellular
automata or neural network), where temporary control or activation centers
may appear and disappear...
3) ...molecules, cell organelles, organs, communities (ecological), etc -
sort of networks made of other networks with "weak control center" and also
dependent on external control...
4) ...systems of organelles, systems of organs (e.g. like cardiovascular or
nervous system), ecosystems, etc... - with stronger control center and
several such systems usually "join" into something from sep 1)
one could try to make a periodic table of nested hierarchies from this,
something like:
1)-2)-3)-4)
...
atom -molecules, polymers and crystals -macromolecular structures/cell
organelles-systems of the previous;
cell -tissue-organ-organs system;
organism-colony/population-community-ecosystem
...
solar system-...-...-...
...
galaxy-...-...-...
...
Looks like emergence of many structures of systems in this world follows
those 4 steps
Once we know similarities, we can try "doing" concilience with that...
However this is just a mental structure - a reflection of how the real world
could look like, but not necessarily what it really is. Therefore saying
fractal model of reality" does not automatically imply the reality being 100
percent fractal in a mathematical sense of that word. However it is easy to
note that self-similarity is ubiquitous. On the other hand- some geometrical
shapes of fractals indeed show different properties at different scales and
I guess that this diversity is generated by increasing combinatorial
possibilities of various self-similar combinations and transformations of
just one "something". Look at the Mandelbrot fractal, or bifurcation trees
(Feigenbaum fractal, etc...) for example - at different scales they are both
similar and different at once.
Best regards
Viktoras
-------Original Message-------
From: Stanley N. Salthe
Date: Saturday, October 30, 2004 13:27:06
To: fis@listas.unizar.es
Subject: Re: [Fis] Fractals and Concilience
My reply: OK! Good to know this! Thank you.
Well, but now I have another objection to using fractals as models of
scale hierarchies INSOFAR as they would be applied to actual world systems.
While there do appear to be isomorphic processes (which might be referred
to as laws of matter) at different levels -- like asymptotic growth
patterns, dissipation / dispersion, vortices, perhaps cognition, etc., all
abstract patterns -- it is a fact that phenomena at different scales in
the world are materially very different. This implies some informational
differences that would NOT be self-similar, and it is this self-similarity
that now appears to me as the main objection to fractals as models of scale
hierarchies. Can this problem be allayed as well?
STAN
