Holding ourselves apart from nature, We are surprised when nature pays our work no mind. Were our methods unsound?
Phil Henshaw wrote: > I think what may be holding back the math is our failure to go to the next > level and consider change as a physical process. When you do that you find > what nature actually does much more interesting and inspiring than anything > we can invent. > > Using a physical systems model the process now bringing about our whole > system collapse was seen coming a long way off and it could have inspired > the math to demonstrate the turn onto another path instead too. Live and > learn I guess. > > The 2006 paper by Bettencourt is easily generalized to reach this > implication, acknowledging that for the physical growth system he considered > "achieving major innovation cycles must be generated at continually > accelerating rates"( http://www.pnas.org/content/104/17/7301.abstract). > That's remarkably close to the basis of proof for the general principle I > offered in my "Infinite Society" paper in 1979 > (http://www.synapse9.com/UnhidPatt-theInfiniteSoc.pdf). The general > principle being the theorem that I've been using ever since with excellent > forecasting results. In physical systems "growth runs into complications" > and nature does a lot of creative stuff with it. You just look for the > complications coming and then 'voila', cool new science at every turn! > > Phil > > >> -----Original Message----- >> From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On >> Behalf Of glen e. p. ropella >> Sent: Friday, July 11, 2008 6:10 PM >> To: The Friday Morning Applied Complexity Coffee Group >> Subject: Re: [FRIAM] Mathematics and Music >> >> Prof David West wrote: >> >>>> We have also talked about the lack of rigorous mathematical >>>> representation of complexity and that being a barrier to progress >>>> in the science. >>>> >>> the idea of magic raised your hackles - the above sentence raises >>> >> mine. >> >>> implicit in the sentence is some variation of "mathematics is a >>> >> better / >> >>> superior / privileged / real language compared to all other languages >>> used by humans to think and therefore we cannot really think properly >>> >> or >> >>> rigorously unless we are thinking mathematically." >>> >> I don't think that inference is implied by that sentence. I so believe >> math is a better language with which to describe reality than, say, >> English. But, that's not what the sentence above says. The sentence >> above states that a _lack_ of math rigor is a barrier to one particular >> domain: plectics. >> >> Your inference goes quite a bit further than the David's sentence. >> >> >>> this annoying attitude is expressed / believed by a majority of >>> intellectuals and academicians - not just mathematicians. We cannot >>> >> be >> >>> "scientists" unless we 'mathematize' our field of enquiry. >>> >> And although I believe that math is the best known language for >> describing reality, I don't believe that one must mathematize every >> scientific field or that one cannot be a scientist without >> mathematizing >> their field. >> >> Science is the search for truth. And truth can be sought using any >> language... any language at all. Some domains, particularly the ones >> resistant to rigor are best studied with languages that have a high >> tolerance for ambiguity... e.g. English. >> >> Some domains that are not so resistant to rigor are best studied with >> math. Often, it takes a great deal of work using ambiguity tolerant >> languages like English before an ambiguity intolerant language like >> math >> can be effectively used. >> >> If and when less ambiguous languages can be used, _then_ those >> languages >> become more effective than the more ambiguous languages. >> >> From 50,000 metaphorical feet, this can be seen as a simple case of >> specialization. A generalist uses coarse tools and a specialist uses >> fine tools. Math is a fine tool that can only be used after the >> generalists have done their upstream work in the domain. Neither is >> really "better", of course, when taking a synoptic view of the whole >> evolution of the domain. But math is definitely more refined... more >> special. >> >> >>> Interestingly enough, all advances in science stem from the uses of >>> metaphor - not mathematics. (see Quine) The premature rush to >>> >> abandon >> >>> the language of metaphor and publish using arcane squiggles is the >>> >> real >> >>> - in my not very humble opinion - barrier to progress. >>> >> I agree. Likewise, the tendency to stick with a coarse language when a >> more refined language is called for is also a real barrier to >> progress... "progress" defined as: the evolution of a domain from >> general to special, coarse to fine. >> >> -- >> glen e. p. ropella, 971-219-3846, http://tempusdictum.com >> >> >> ============================================================ >> 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 > > ============================================================ 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
