Science And Math Was: Python's Lisp heritage

[brueckd at tbye.com]

On Mon, 22 Apr 2002, Grant Edwards wrote:

> In article <mailman.1019483442.32389.python-list at python.org>, brueckd at tbye.com wrote:
> >
> >> > You should understand that this is a philosophical viewpoint. The
> > [snip]
> >> To put this another way, ask yourself where you stand on this
> >> question: is mathematics discovered or invented?
>
> Very well put.
>
> > Is there a difference?
>
> Yes.  Science verifies it's theories by comparing them to the
> physical world which they are attempting to describe.  It
> doesn't matter how elegant, or internally consistent Science
> is.  If it doesn't successfully describe the physical world,
> it's wrong.
>
> Science has an external reference point. Mathematics does not.
> Internal consistency is the only thing which mathematics can
> attempt to verify.  Mathematics is not an attempt to describe
> the physical world.

First, please back up, I was asking if there's a difference between
discovery and invention, which you don't mention anywhere in your
response.

Second, math *is* an attempt to describe the physical world - that's what
makes it useful. Case in point: calculus, which was invented/discovered
specifically to deal with and describe the motion of physical bodies. Had
it not been useful in describing such motion, it would have been tossed
out, or at least not so widely accepted. Math is useful because of its
relevance to the world around us.

Finally, in the more general sense, formal mathematical proofs and whatnot
might not require an external reference point, but the foundation upon
which they are built certainly does. Indeed, the fact that we've gotten as
far as something like abstract algebra is largely due to the fact that the
underlying building blocks *are* verifiable and applicable to our
experiences outside of math and many of the "advances" in mathematics have
been due to intuition or hunches provoked by real world phenomena.

-Dave