Steve, Good job on the defense of a reductionist position. I utilize a five phase approach to the study of complex systems. Definition - Analysis - Normalization - Synthesis - Realization (DANSR) Reductionism has its place in the analytical phase at equilibrium. Analysis is normally a study of integrable, often linear systems, but it can be accomplished on non-linear, feed-forward systems as well. The synthesis phase puts information re: complex behavior and emergence back into the integrated mix and may be "analyzed" in non-linear, recurrent networks. This is actually a probabilistic inversion of analysis as described in Inverse Theory. Bayesian refinement cycles (forward <-> inverse) are applied to new information as one progresses through the DANSR cycle. This refines the effect of new information on prior information - which I hope folks see is not simply additive - and which may be entirely disruptive (see evolution of science itself) . The fact this seems to work for complex systems is philosophically uninteresting, and may ignored - so the discussion can continue. Final point: Descartes ultimately rejected the concept of zero because of historical religious orthodoxy - so he personally never applied it to the continuum extension of negative numbers. All his original Cartesian coordinates started with 1 on a finite bottom, left-hand boundary - according to Zero, The Biography of a Dangerous Idea, by Charles Seife. Ken
_____ From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Steve Smith Sent: Sunday, September 07, 2008 6:42 PM To: The Friday Morning Applied Complexity Coffee Group Cc: Aku Subject: Re: [FRIAM] Reductionism - was: Young but distant gallaxies Orlando- You can find good references in Wikipedia <http://en.wikipedia.org/wiki/Reductionism> on this topic, including the Descartes references. _____ Reductionism >From Wikipedia, the free encyclopedia Descartes held that non-human animals could be reductively explained as automata - De homines 1662. Duck of VaucansonReductionism can either mean (a) an approach to understanding the nature of complex things by reducing them to the interactions of their parts, or to simpler or more fundamental things or (b) a philosophical position that a complex system is nothing but the sum of its parts, and that an account of it can be reduced to accounts of individual constituents.[1] This can be said of objects, phenomena, explanations, theories, and meanings. _____ All - IMO, Reductionism(a) is a highly utilitarian approach to understanding complex problems, but in some important cases insufficient. It applies well to easily observable systems of distinct elements with obvious relations operating within the regime they were designed, evolved, or selected for. It applies even better to engineered systems which were designed, built and tested using reductionist principles. I'm not sure how useful or apt it is beyond that. Some might argue, that this covers so much, who cares about what is left over?... and this might distinguish the rest of us from hard-core reductionists... we are interested in the phenomena, systems, and regimes where such does not apply. This is perhaps what defines Complexity Scientists and Practitioners. Reductionism(b) is a philosophical extension of (a) which has a nice feel to it for those who operate in the regime where (a) holds well. To the extent that most of the (non-social) problems we encounter in our man-made world tend to lie (by design) in this regime, this is not a bad approach. To the extent that much of science is done in the service of some kind of engineering (ultimately to yield a better material, process or product), it also works well. Reductionism(b) might be directly confronted by the "Halting Problem" in computability theory. Reductionism in it's strongest form would suggest that the behaviour of any given system could ultimately be predicted by studying the behaviour of it's parts. There are certainly large numbers of examples where this is at least approximately true (and useful), otherwise we wouldn't have unit-testing in our software systems, we wouldn't have interchangeable parts, we wouldn't be able to make any useful predictions whatsoever about anything. But if it were fully and literally true, it could be applied to programs in Turing-Complete systems. My own argument here leads me to ponder what (if any) range of interesting problems lie in the regime between the embarrassingly reduceable and the (non)-halting program. But to suggest (insist) that *all* systems and *all* phenomenology can be understood (and predicted) simply by reductionism seems to have been dismissed by most serious scientists some while ago. Complexity Science and those who study Emergent Phenomena implicitly leave Reductionism behind once they get into "truly" complex systems and emergent phenomena. I, myself, prefer (simple) reductionistic simplifications over (complex) handwaving ones (see Occam's Razor) most of the time, but when the going gets tough (or the systems get complex), reductionism *becomes* nothing more than handwaving in my experience. - Steve
<<Duck_of_Vaucanson.jpg>>
============================================================ 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
