Science And Math Was: Python's Lisp heritage

[Tim Daneliuk]

"Gonçalo Rodrigues" wrote:
<SNIP>

> 
> You should understand that this is a philosophical viewpoint. The
> mathematical field is roughly divided in the Platonist field, those who
> believe that mathematical objects exist somewhere out there in space (to
> quote Sun Ra) in a Wonderful World of Platonic Ideas, and the formalist
> field of those who believe mathematics is essentialy a game we play on
> paper with symbols with no "real" meaning attached to it besides the
> convenience in describing natural phenomena.

Yup, I'm aware of this - I didn't want to digress more into philosophy
than absolutely necessary.  IIRC, the Enlightenment thinkers also viewed
mathematics as a branch of natural science and they were (mostly) 
Aristoteleans, right?

<SNIP>

> You should be careful when you say this. There is *virtually no*
> mathematical field that has not been applied.

True enough, but that is not a sufficient condition to argue that mathematics
is correspondent one-for-one to the natural world.  All I'm arguing here is that
mathematics embraces a problem set *larger* than just the natural world and
this cannot simply be a natural science.


<SNIP>

> This is plainly not true. String theory models live in 10 and 24
> dimensions. You would not want to disparage the biggest fad in current
> theoretical physics, would you?


Well, OK, I'll say it more formally:  Let n denote the hightest dimension
used by any of the natural sciences.  Mathematicians routinely operate
in k dimensions where k >> n.   Acceptable?

> 
> Even so let me reiterate, that almost everything that mathematicians
> have concocted is currently used in theoretical physics. To give you
> just an example, my own, I use homotopy and higher order category
> theory.
> 
> Even more when mathematics advances by theoretical physics promptings. I
> could give you numerous examples, but just remind you that quantum
> mechanics contributed a LOT (the celebrated Von Neumann, for example) to
> the growth of abstract mathematics (functional analysis, Hilbert spaces,
> operator algebras, etc.). Some of the more active work in mathematics
> today is also prompted by theoretical physics.
> 
> Somehow (I do not intend to make this more precise now) new mathematical
> formalisms and the discover of new laws in the Universe go hand in hand.


Again, my claim was not that mathematics cannot be/is not appliable, merely
that it is bigger than just its applications.

> >
> >I'm not choosing sides here on the math vs. science debate - both are important
> >artifacts of the human intellect.  I merely take umbrage with the notion that
> >mathematics is innately wired into the universe somehow.
> 
> See above to understand that what you are saying is really not that
> obvious.


Well almost nothing about epistemology is obvious.  As I said, I am willing
to be persuaded otherwise, but it sure looks to me like mathematics is the
construct I claim, not innate to the natural world...

-- 
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Tim Daneliuk
tundra at tundraware.com