Glen E. P. Ropella wrote > Sent: Wednesday, June 27, 2007 2:38 PM > > > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA1 > > Phil Henshaw wrote: > > Na, I think even the most sophisticated math misses all the truly > > supple shape of natural form, and it it's of huge > signifiance in our > > missunderstanding of natural phenomena. > > I _strongly_ disagree with that. I talk to many people who > say things like "I'm not good at math" or "I don't understand > math". And I can't help thinking that they must not be > talking about the same thing I'm talking about when I say > "math". It seems impossible for a person to not understand > math because math is pervasive in human activity. oh for sure, people almost universally are quite confident that what they imagine is what any person they listened to was intending to say, and it mostly ain't so.
> For example, all musicians are mathematicians. All brick > layers are mathematicians. All lawyers are at least > logicians if not mathematicians. Architects, nurses, truck > drivers, corporate bureaucrats, and some skate punks are > mathematicians. Well, normal intuitions do in fact often appear to emulate the juggling of exceedingly sophisticated differential equations, which we then display little or no ability to trace and confirm.. etc. It's part of the 'fun'. > Now, it's true that most of these people don't know how to > _describe_ what it is that they do. They just _do_ it > without trying to formalize what they're doing. But, as > Wittgenstein, Tarski, Goedel, and many others have shown us, > math is _more_ than formalization. The working mathematician > doesn't spend her days trying to demonstrate the differences > between ZF and PA. The working mathematician spends her days > thinking about the world and trying to _intervene_ in the > world to make something happen (or to explain, predict, > describe some thing). but a secondary reason for that phenomenon, it appears to me, is that nature isn't 'doing' math either, exactly, but making up altogether new math continually to fool us into thinking there must be some kind of formula. That provides a fairly concrete behavioral reason for why intelligent life is quite inexplicable. It's 'inexplicable' because explanation is actually not how it works! Neither nature, nor normal intelligence, follow explanations. That's got he cart before the horse. > > Hence, math doesn't _miss_ the "supple shape of natural > form", it is derived directly from such natural form. > When/if it misses some element, it is because the > mathematician failed to capture that element, usually on purpose. Perhaps you'll allow that there may be a 'grey' area created if the mathematician creates such a good illusion of reality that an observer has a hard time telling the difference. Is there a difference then or not? Well, "can't tell" is the correct answer. Then the question is whether that difference ever makes a difference, and whether one might be better watching what's really happening and ignoring the model of the mathematician (every third wink at least) which would lead you far astray if you were not to pay attention to the widening discrepancy of things "going wrong with the model"... QED "You just gotta pay attention" is the one rule that one necessarily always needs to fall back on. > > p.s. My argument above does not make the word "mathematician" > useless by ascribing it to _everyone_ (as Bristol did when > implying that every thing is emergent). well, I too think there is a very non-trivial understanding of 'every thing is emergent', since in fact all physical phenomena do individually emerge as evolving complex systems, whether our information makes that entirely predictable or not. Our information may miss it, and not appear to be, but close observation demonstrates quite conclusively that the physical stuff is. > It is only ascribed > to those who attempt to form rigorous conceptions of the > things around them and use those conceptions to interact with > the world. not in the sense I used above. It's a practical operational, productivity improving sense, of learning how to watch what's happening to get better kinds of clues kind of 'everything emerges'. > There are some (Paul Feyerabend comes to > mind) who make the case that such strict adherence to method > can impede understanding. And that may be true. (I believe > it is.) As such, there are plenty of people out there who > actively resist the development of and application of > rigorous method. Those are not (always) mathematicians. > > - -- > glen e. p. ropella, 971-219-3846, http://tempusdictum.com > ... given any rule, however "fundamental" or "necessary" for > science, there are always circumstances when it is advisable > not only to ignore the rule, but to adopt its opposite. -- > Paul Feyerabend Ah well, play is good, particularly good, but not always to take entirely seriously itself, perhaps.... Phil ============================================================ 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
