# RE: Small probabilities

From: Bill Hamilton <williamehamiltonjr@yahoo.com>
Date: Sun Nov 06 2005 - 21:49:19 EST

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.

> There are indeed an infinite number of points in a line and so strictly
> speaking the probability is zero to find any particular point. The latter is
> mathematics and the real question has to be based on experiments. One always
> deals with a large, but finite number of outcomes---a die with a large number
> of sides, say. Note also that when one measures lengths---which, presumably,
> have an infinite number of mathematical points---one uses smaller lengths
> that also have an infinite number of mathematical points. Any measuring
> device deals with finite lengths. One has to distinguish mathematics that
> deal with infinities with reality, which deals with finiteness.
>
>
>
>
> From: Glenn Morton
> Sent: Sun 11/6/2005 10:32 AM
> To: 'Bill Hamilton'
> Cc: asa@calvin.edu
> Subject: RE: Small probabilities
>
>
> > -----Original Message-----
> > From: asa-owner@lists.calvin.edu [mailto:asa-owner@lists.calvin.edu] On
> > Behalf Of Bill Hamilton
> > Sent: Sunday, November 06, 2005 8:01 AM
>
>
> > I read Dembski's response to Henry Morris
> > (http://www.calvin.edu/archive/asa/200510/0514.html)
> > and noted that it raised an old issue I've harped on before: that you can
> > specify a probability below which chance is eliminated. There is a
> > counterexample given (among other places) in Davenport and Root's book
> > "Random
> > Signals and Noise" (McGraw Hill, probably sometime in the early 60's) that
> > goes
> > like this:
> > Draw a line 1 inch long. Randomly pick a single point on that line. The
> > probability of picking any point on the line is identically zero. Yet a
> > point
> > is picked. Am I missing something?
> >
> Hi Bill, I was intrigued by your math example. The answer is related, IMO
> to Zeno's paradox, whose solution hints at the quantization of space. In
> reality there are not an infinity of points on the line. The Planck length
> is the shortest link and that is 10^-35 m (or something like that I am not
> going to look it up). Thus the chance of the point being picked is 1 inch
> divided by planck's length (using the same units which this sentence isn't.)
> When I get the units right, I come up with something like each "point"
> having a chance of 10^-37 or so and thus the chance is not zero and thus it
> is possible to pick a point.
>

Bill Hamilton
William E. Hamilton, Jr., Ph.D.
586.986.1474 (work) 248.652.4148 (home) 248.303.8651 (mobile)
"...If God is for us, who is against us?" Rom 8:31

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Received on Sun Nov 6 21:52:04 2005

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