[Beowulf] OS for 64 bit AMD
Kevin Ball
kball at pathscale.com
Wed Apr 6 11:12:43 PDT 2005
On Wed, 2005-04-06 at 08:36, Joe Landman wrote:
> Richard Walsh wrote:
> >We carry on with
> > it anyway
> > because the implications (all of mathematics) are so useful and
> > interesting.
>
> I suspect that it is a little more rigorous than that. We develop
> formalisms that allow us to test things reductio ad-absurdium to help
> define things better. This allows us to build up rigorous and
> (hopefully) testable hypotheses.
>
> Then again, I like the simplicity of "we do math because it is useful".
>
That math is founded upon such simple axioms is one of the beautiful
and fascinating things about math, and the fact that there actually is
no necessary connection with any sort of reality is what makes it
'pure'. By pure I mean that in mathematics, you can have statements
which you know are true, because all of the underlying assumptions (the
axioms) are a part of the system. Compare this to science, trying to
describe something where the underlying assumptions are unknowable, but
we try to model them as best we can.
Math is not testable; if it were, it would be science. Instead we
take a set of arbitrary, or if not completely arbitrary at least
entirely human-made axioms and work through increasingly complex
combinations of and abstractions from them. The idea of proving
something is unique to mathematics, because it is only possible to do
something like a 'proof' if you know all of the underlying assumptions.
Anything else is just a model of something unknowable... in the case of
physics we're getting to a pretty precise model in many cases, but we'll
never be able to go beyond models.
The fact that just about every mathematical construct or theory has
proved useful to someone in describing the actual world is evidence of
something, but whether it is just that people like to use things they
have created know to describe the world (Most languages and artforms
have been used that way too) or something deeper is unclear.
</theoretical ramble>
Kevin Ball
kball at pathscale.com
>
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