Perhaps, we will come to better understanding of math if we see ***what math is not***. Here is Gregory Chaitin's Alan Turing Lecture on Computing and Philosophy, Mälardalen University, 2005:
www.youtube.com/watch?v=Rr0fOGeS7DE www.youtube.com/watch?v=3bacYDSy19Q www.youtube.com/watch?v=xaAhPo5KKUI www.youtube.com/watch?v=0sjHUuL22hQ www.youtube.com/watch?v=tW4a01hS3FU www.youtube.com/watch?v=JbwRwX1ILpc www.youtube.com/watch?v=zDl9L-_d8wk --Mikhail Gorelkin ----- Original Message ----- From: glen e. p. ropella To: The Friday Morning Applied Complexity Coffee Group Sent: Friday, July 11, 2008 6:10 PM 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
