RE: Small probabilities

From: Glenn Morton <glennmorton@entouch.net>
Date: Sun Nov 06 2005 - 16:26:13 EST

One can believe in the Platonic line (or the Pythagorean line) all he wants.
The reality was that there is nothing in existence which has a infinitely
fine point with which to pick a point. And there is not an infinite time in
which to write down the digits required to specify any point. Let's say we
give you the fastest computer on earth to randomly pick a point on the
line-Let's let it go for a million years spitting out numbers after the
decimal point. When it finally runs out of resources, it stops at a number
and the result is a quantization of the line below the size of the place
held by the last digit. So, lacking the time, also quantizes the choice
and thus the probability is NOT zero for whatever point is humanly possible
to pick.

 

Sure this is an argument from practicality and reality rather than
mathematics, but I would argue that only if it is actually possible to pick
any point whatsoever is the real probability really zero for each point in
the line. To illustrate this Consider the output of the computer for that
random selection. It looks like:

 

.49292238460049- - -365

 

The five is the last digit spit out after the computer has run out of time,
resources, electricity, or the end of the universe happens just after the 5
is printed out. That then quantizes the line at

 

.00000000000000- - -001

 

Since that is a finite number the probability for points to be selected is
.00000000000000- - -001 for the points that lie at this quantization and
zero for points in between this quantization. Those points in between can
not possibly be picked and thus they are the points which have zero
probability of being picked.

 

 

  _____

From: asa-owner@lists.calvin.edu [mailto:asa-owner@lists.calvin.edu] On
Behalf Of Alexanian, Moorad
Sent: Sunday, November 06, 2005 11:00 AM
To: Glenn Morton; 'Bill Hamilton'
Cc: asa@calvin.edu
Subject: RE: Small probabilities

 

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 16:27:41 2005

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