Re: [Fis] Fractals and Concilience

Terry said:

>Stan said:
>> Well, not all hierarches refer to nested entities. Scale
>>hierarchies
>>are more or less nested when we realize that they are not only spatial, but
>>spatiotemporal. Yet, even here it cannot be the case that fractals are
>>appropriate models. Fractals are more or less continuous, but scale
>>hierarchies have breaks at scale differences of about order of magnitude.
>>There is not yet a full understanding of what forces or constraints result
>>in breaks between levels in such a hierarchy, or what establishes their
>>distances apart. Without such breaks there would be no "room" for
>>dynamics at any level.
>
>Physical fractals are mostly continuous, but there are plenty of fractals
>based on discrete phenomena. For example the kind of temporal dynamics in
>the form of power laws that underlie earthquakes. These are fractals as
>well. In fact I think the beauty of fractals for modeling is that they
>provide a continuum from the purely material level, e.g, physical fractals
>such as shorelines or branching patterns, to the purely abstract level,
>e.g., mathematical patterns underneath surface chaos. My own work is to use
>fractals to model self-similar and self-referential dynamics evident at the
>edge of psychological boundaries. ln some ways I can see the full range from
>physical to mathematical to psychological as a versatile approach to the
>problem of conscilience.

And Victoras said:
>Stanley said: Yet, even here it cannot be the case that fractals are
>appropriate models. Fractals are more or less continuous, but scale
>hierarchies have breaks at scale differences of about order of magnitude.

I would think they could be... Fractals are not necessarily continuous.
There are many discontinuous or discrete fractals. Some examples: Cantor's
dust, Sierpinski's gasket, Koch's curve and many fractals produced using
affine, polynomial or other transformations of spaces and geometric
primitives, other IFS methods, etc... However I would tend to think that
the most of natural phenomena are neither truly continuous nor discrete.
Most likely if one looks at a distant complex Something it may seem
continuous, but when it is zoomed in - one sees jumps, discontinuous
patterns made of seemingly continuous smaller ones. It is still possible to
zoom in again and to discover that those seemingly continuous smaller
patterns are also made of yet smaller discontinuities, thus one could zoom
probably down to Plank's constant looking at how every continuum turns to
discontinuum at smaller scales made of other continuums that zoom into yet
smaller discontinuities again...

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

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Received on Sat Oct 30 22:22:47 2004