[FRIAM] recap on Rosen

[Günther Greindl]

Hi,

I still do not see why nature should not be mathematical, or even 
(stronger) computable.

See for instance Max Tegmark's (MIT) Mathematical universe:
http://arxiv.org/abs/0704.0646

The principal claim of Rosen - that life is not mechanically emulable - 
is shown to be false by the second recursion theorem

http://en.wikipedia.org/wiki/Kleene%27s_recursion_theorem

(which shows that one can mechanically replicate; repair is then a 
matter of error correction)

Cheers,
Günther

phil henshaw wrote:
> 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                   
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-- 
Günther Greindl
Department of Philosophy of Science
University of Vienna
guenther.greindl at univie.ac.at
http://www.univie.ac.at/Wissenschaftstheorie/

Blog: http://dao.complexitystudies.org/
Site: http://www.complexitystudies.org