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
we can invent.
the math to demonstrate the turn onto another path instead too. Live and
learn I guess.
). The general
forecasting results. In physical systems "growth runs into complications"
and nature does a lot of creative stuff with it. You just look for the
> -----Original Message-----
> From:
[hidden email] [mailto:
[hidden email]] 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>
>
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