Re: Can Events of Zero Probability Happen?

On Fri, 11 Jan 2008 08:32:52 -0800 (PST), Shubee <e.Shubee@xxxxxxxxx>
wrote:

On Jan 11, 9:07 am, David C. Ullrich <ullr...@xxxxxxxxxxxxxxxx> wrote:
Whether or not something can "really" "happen" is not a
mathematical question.

Ah, but that's not true in the context of my assertions. All physics
is mathematics in David Hilbert's philosophy of physics. [1][2].

Uh, right. Supposing for the sake of argument that what you
say follows from Hilbert's philosophy does indeed follow:

(i) Are you claiming that Hilbert's "philosophy" is in
fact _correct_ in some absolute sense, that any other
approach to physics is simply _wrong_?

I hope not, that would be silly. Assuming not:

(ii) How do you know that the physicist you're talking
about agrees with this "philosophy"?

I'm not going to take the time to download those pdf's
on a dialup connection. There are certainly useful
points of view according to which all physics is mathematics.
But saying that all physics is mathematics in the sense
relevant to the current discussion is simply silly.
You're claiming that mathematics itself can be used
to determine anything about the nature of the physical
world? That's obvious nonsense. Mathematics can be
used to determine what's possible _given_ certain
axioms - it can't say anything about whether the axioms
are actually true in the real world.

In particular, there's nothing implausible about saying
that "choose a real at random" is not something that
can actually "happen" in the real world - for example
there's no reason anyone has to be certain that there
is anything in the real physical universe that
actually corresponds precisely to the mathematical
notion of "real number" in the first place - it could
well be that everything is discrete.

_If_ you're interested in resolving the difference between
you and the physicist you'd ask what I suggested you
ask and see what he says. Because it's possible that
he'd have no problem with "choose a real between 0 and
1 at random", and in that case you could explain why
he's simply _wrong_ about the impossibility of events
of probability zero happening. That actually seems like
the most likely outcome. It's also possible that he'd
have some objection to the "reality" of the notion
of a random real number - if so then you'd understand
the source of your disagreements: What you're saying
is correct in a certain mathematical model, and he's
simply denying the relevance of that model to the real
world.

But suggesting that Hilbert's axiomatization contains
everything there is to know about actual physics is
just sllly - assuming that the physicist you're talking
to agrees with this, or thinking that he's simple
_wrong_ if he doesn't is even sillier. Measure theory
is not the universe.

1. The Axiomatization of Physics - Step 1 (section 2)
http://www.everythingimportant.org/relativity/special.pdf
2. The Relativity of Discovery: Hilbert's First Note on the
Foundations of Physics (sections 1.1 and 1.2)
http://arxiv.org/abs/physics/9811050

Shubee


************************

David C. Ullrich
.

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