From: Glenn Morton <glennmorton@entouch.net>

Date: Sun Nov 06 2005 - 16:26:13 EST

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
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*> Behalf Of Bill Hamilton
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*> Sent: Sunday, November 06, 2005 8:01 AM
*

*> I read Dembski's response to Henry Morris
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*> (http://www.calvin.edu/archive/asa/200510/0514.html)
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*> and noted that it raised an old issue I've harped on before: that you can
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*> specify a probability below which chance is eliminated. There is a
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*> counterexample given (among other places) in Davenport and Root's book
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*> "Random
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*> Signals and Noise" (McGraw Hill, probably sometime in the early 60's) that
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*> goes
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*> like this:
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*> Draw a line 1 inch long. Randomly pick a single point on that line. The
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*> probability of picking any point on the line is identically zero. Yet a
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*> point
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*> is picked. Am I missing something?
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*>
*

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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