Science And Math Was: Python's Lisp heritage

[Grant Edwards]

In article <mailman.1019489191.17192.python-list at python.org>, brueckd at tbye.com wrote:

>> > 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.

Not literally, no.  I thought it obvious that since math
doesn't have a physical reference, it is pure invention, while
science due to it's ties to the physical world is a process of
discovery.

> Second, math *is* an attempt to describe the physical world

In my experience, that's a rather unique opinion, and one not
held by any of the math type people I've met.

> - that's what makes it useful.

The fact that it _can_ be used to quantify descriptions of the
physical world makes it useful.  That usefulness is not a
requirement of mathematics.

> 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.

I agree that many fields of math are useful.  That is not,
however a fundamental requirement of math.

> 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.

That's not the way I learned it.  You start with a set of
fundamental assumptions which you do not attempt to "prove".
You then build on that.

> 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.

Such hunches would imply that Euclidean geometry is an accurate
description of space...

-- 
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