And new math should be more like Computational Intelligence than Lie groups and algebras. --Mikhail
----- Original Message -----From: [hidden email]To: [hidden email]Sent: Sunday, July 13, 2008 11:55 PMSubject: Re: [FRIAM] Mathematics and Music - missed opportunityPhil, I totally agree with it:
>>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.<<And perhaps first we need to understand quantum mechanic. I think Chaitin and maybe Wolfram are close to it.
--Mikhail
----- Original Message -----From: [hidden email]To: [hidden email]Sent: Sunday, July 13, 2008 10:21 PMSubject: Re: [FRIAM] Mathematics and Music - missed opportunityI 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.pnasorg/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: [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
>
>
> ============================================================
> 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
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