Carl, Well, It depends on whether you're the kind of person who, when finding that nature has a habit of changing the title of the course and the text shortly before her exams, continues to study the wrong text because that's the course they signed up for... [ph]
> > 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
