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 > ¸¸¸¸.·´ ¯ `·.¸¸¸¸ > ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ > 680 Ft. Washington Ave NY NY 10040 tel: 212-795-4844 > e-mail: [EMAIL PROTECTED] 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” > > > > > ============================================================ > FRIAM Applied Complexity Group listserv > Meets Fridays 9a-11:30 at cafe at St. John's College > lectures, archives, unsubscribe, maps at http://www.friam.org > -- Günther Greindl Department of Philosophy of Science University of Vienna [EMAIL PROTECTED] http://www.univie.ac.at/Wissenschaftstheorie/ Blog: http://dao.complexitystudies.org/ Site: http://www.complexitystudies.org ============================================================ FRIAM Applied Complexity Group listserv Meets Fridays 9a-11:30 at cafe at St. John's College lectures, archives, unsubscribe, maps at http://www.friam.org
