# Re: Small probabilities

From: George Murphy <gmurphy@raex.com>
Date: Sun Nov 06 2005 - 22:12:18 EST

----- Original Message -----
From: "Bill Hamilton" <williamehamiltonjr@yahoo.com>
To: "Alexanian, Moorad" <alexanian@uncw.edu>; "Glenn Morton"
<glennmorton@entouch.net>
Cc: <asa@calvin.edu>
Sent: Sunday, November 06, 2005 9:49 PM
Subject: RE: Small probabilities

> Thanks, folks. I'm still convinced that it is improper to say that the
> probability of an event is so small it can't happen, but Glenn, Moorad and
> Don
> bring up a very real point: in the real world it is not possible to deal
> with
> infinitesimal points. Probably I'm just too nitpicky: I want anyone who
> says
> the probability of an event is too small for that event to occur to give a
> statement of the relative sizes of the sets involved, or to estimate the
> mean
> time between events. If the mean time between events is say 100 billion
> years,
> then we could conclude teh event in question is very unlikely. It should
> be
> pointed out that Borel, when he stated that an event whose probability is
> less
> than 10^-50 could not happen, made that statement in a book that was
> intended
> to be an introduction to probability theory for nonmathematicians. So he
> wasn't
> wearing his "eminent mathematician" hat when he made the statement.

I don't want to take a stance on the probability question but shopuld say
aomthing about the Planck length that Glenn introduced. There are theories
of quantum gravity in which space-time is discrete, & in which there simply
are no space or time intervals smaller than, respectively, (hG/c^3)^(1/2) ~
10^-33 cm &
(hG/c^5)^1/2 ~ 10^-43 sec. But what a combination of quantum theory &
general relativity says is that lengths & time intervals smaller than these
amounts can't be measured. That's not exactly the same thing, unless one is
a convinced positivist.

Shalom
George
http://web.raex.com/~gmurphy/
Received on Sun Nov 6 22:13:42 2005

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