> 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:
[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>
>
Meets Fridays 9a-11:30 at cafe at St. John's College