[Fis] Fractals and Concilience

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
>dynamicsat 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.

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Received on Sat Oct 30 06:46:04 2004