> There's a curious reversal that occurred to me in reading an article by
> Boschetti on the computability of nature in relation to Rosen's "Evolution
> of life is not the construction of a machine", the deep problems of why math
> "can't do nature". I'm writing a piece on how self-consistent models don't
> make good operating manuals because they omit the independent parts that
> make environments work. It's as a stating point for discussing how our
> models fit their subjects and what to do about the radical lack of fit in
> many cases.
>
> Computability is usually discussed in terms of ?chaos? in which small
> differences can have large mathematical consequences or the inability to
> define boundary conditions clearly or that models can?t properly represent
> the multiple scales of organization that natural systems have. There's
> also an incomputability of mathematical models that comes directly from our
> means of doing it, the physical process of doing it. Calculation has an
> easily perceived ?grain? that comes from its being built from the assemblies
> of individual parts in computers, the 1's and 0's. Self-consistent sets of
> equations do not have any grain. The implied continuities of mathematics,
> therefore, can not be represented with the integer calculations required for
> digital processing. Mathematical rules imply shades of difference and
> dynamical derivative rates of change without limit. Perhaps how our
> mathematical tools necessarily operate then shows that the problem isn?t
> just that how math is built it can't successfully emulate nature. Maybe it
> also shows that the way nature is built it can't successfully emulate math.
> If nature "can't do math", that may have different implications.
>
>
>
> Phil Henshaw
> ????.?? ? `?.????
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
> 680 Ft. Washington Ave NY NY 10040 tel: 212-795-4844
> e-mail: pfh at synapse9.com explorations: www.synapse9.com
> ?in the last 200 years the amount of change that once needed a century of
> thought now takes just five weeks?
>
>
>
>
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