RE: Small probabilities

From: Alexanian, Moorad <alexanian@uncw.edu>
Date: Sun Nov 06 2005 - 11:59:55 EST

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.

Moorad

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.
Received on Sun Nov 6 12:02:36 2005

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