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 cant 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 isnt 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]: 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
