Phil, There is a fundamental quality in mathematics - equality - or reversibility, if you will, that differs from nature. This means that there is a directionality in natural processes that cannot be deconstructed. Prigogine calls the lack of directional and temporal equality "far from equilibrium".
Mathematics works well at describing systems at equilibrium, and seems to get progressively worse the further from equilibrium one gets. Emergence creates an emergency, so to speak. This has been my criticism of rules centered agent based modeling, which is a theme from Wolfram, and why I have been researching compositional pattern producing networks (CPPN's) evolved by HyperNEAT. It seems to take energy to evolve. The interesting thing is a paradigmatic difference between solving problems, and recognizing solutions. Ken > -----Original Message----- > From: [EMAIL PROTECTED] > [mailto:[EMAIL PROTECTED] On Behalf Of phil henshaw > Sent: Monday, April 21, 2008 9:06 AM > To: 'The Friday Morning Applied Complexity Coffee Group' > Subject: [FRIAM] recap on Rosen > > 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 > ============================================================ 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
