Science And Math Was: Python's Lisp heritage

[Gonçalo Rodrigues]

On Mon, 22 Apr 2002 09:10:20 -0700 (PDT), <brueckd at tbye.com> wrote:

>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.

Math *is not* an attempt to describe the physical world. It may have
been so a long ago but not anymore. It is true that calculus was first
invented by the needs in physics (by Newton) but I don't think that
Cauchy, Riemann, Weierstrass and others were thinking about "reality"
(one of the few words that without "" means nothing) when making it
rigorous.

And while I cannot speak for every mathematician I can say for sure that
a large body of them strongly disagrees with "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.

I strongly disagree with this and also the modern history of
mathematics. There is a very strong connection between physics and
mathematics but many mathematicians live happily without ever thinking
of physics, or, for that matter, any applications their work might have.

>
>-Dave
>
>

best,
Gonçalo Rodrigues