Re: math, is it just physics?

On 1/29/2025 5:46 AM, joes wrote:

Am Wed, 29 Jan 2025 09:48:47 +0100 schrieb WM:

On 28.01.2025 21:56, sobriquet wrote:

So in a way one could claim that concepts like
integers and their properties and relationships
can be more or less empirically observed
in the behavior and properties of things like
elementary particles such as electrons or fields.

>
Or bricks, marbles, people etc.
The natural numbers have been abstracted from reality.
The laws like
"the existence of n implies the existence of n+1"
were so evident, that no axioms appeared necessary
before Dedekind, Peano, Schmidt etc.
Only Cantor's assumption of
an actual set with |ℕ| being a fixed quantity
greater than all numbers
is not abstracted from reality.

>
Oh PLEASE show me something physically infinite.

I can't show it to you, but
what if physical evidence showed that
something physically infinite might exist?
That strikes me as just.as.good.as showing you,
for the purpose of deciding whether
mathematicians should be allowed to speak of
infinite things.
Consider the cosmos,
of which our observable universe is
a small and possibly.infinitesimal part.
Our observations to date are best explained by
a cosmological curvature with a value in
a narrow range around 0.
If our local patch is typical,
and what we observe locally holds throughout,
then
an observed curvature > 0 indicates
a finite cosmos much bigger than the observable,
and
an observed curvature ≤ 0 indicates
a infinite cosmos.
The latest I've heard,
the finite/infinite question is still up in the air.
I consider that to be where it should be
until we have good reasons which bring it down.
Math, is it just physics?
Mathematicians will do what mathematicians do,
but some of what they do will be encouraged,
if it is found to be useful elsewhere.
Including, but not limited to, in physics.
The idea (suggested in other threads) that
mathematicians should only do useful.elsewhere math
has the way this works exactly backwards.
Mathematicians can't limit themselves to
what will some day find a use elsewhere.
How could they possibly know that?
Physicists, faced with a new problem,
look at what math has already been done
for help in describing and reasoning about it.
Bernhard Riemann (1826 -- 1866)
did not work on differential geometry
_for general relativity_ (1915)
He couldn't have.
Einstein couldn't know someone else's work
was useful before that work was done.
He couldn't have.