Science And Math Was: Python's Lisp heritage

[brueckd at tbye.com]

On Mon, 22 Apr 2002, Grant Edwards wrote:

> >> 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.

Hmm... this sounds a lot like "invention and discovery are different
because I have defined them that way". Where does the requirement for a
physical reference come from? That seems orthogonal to invention versus
discovery.

Side note: if that were the case (that math is pure invention), then the
likelihood of two people inventing multiplication at roughly the same time
is quite small. The likelihood of them *discovering* it at the same time
is relatively much higher.

> > 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.

Perhaps, but as long as we're having a philisophical discussion, that is
completely irrelevant. :)

> > 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.

Isn't it? Without some reference point to the real world you can't even
learn enough math to theorize that it is self-contained. Yes, it's nifty
that others have shown that math *can* be completely abstract, but they
can't even get to the point of discussing such a concept without first
crossing the bridge that connects it to our existence.

> > 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.

Unless you went to a very bizarre school, you learned it by relating it to
things you could actually experience. It's not that you didn't need to
prove that one apple plus one apple makes two apples, through your own
experience you could verify it with sufficient certainty to make it a
useful and safe building block (and then later you could learn enough math
to go back and prove it from a purely mathematical perspective).

Once you're up and running, so to speak, you can move away from this
bootstrap dependency, but there's nothing to suggest that a person can
forego this process.

> > 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...

Well, an example of what might be considered a bad hunch doesn't dimish my
point in the least as there are plenty of cases where good hunches existed
too. :) And, for many purposes, Euclidean geometry *is* an accurate
description of space, and it may be nothing more than someone's hunch that
prompts us to refine our current understanding of space even further
beyond what we think of it today.  Hunch. (sorry, I desperately wanted to
reach my goal of using 'hunch' five times in single paragraph).

-Dave