From: Iain Strachan <igd.strachan@gmail.com>

Date: Sun Nov 13 2005 - 16:37:26 EST

Date: Sun Nov 13 2005 - 16:37:26 EST

A simpler lo-tech solution than calling a random number generator is to toss

a coin 500 times, or throw a die 200 times and concatenate the values. Both

of these will generate events with probability < 10^-150. But as I said

earlier that's no big deal. It's a big deal when a pre-specified event of

very small probability occurs because then there are a limited number of

outcomes, as opposed to a vast number. Randy's example of getting the same

deal in a pack of cards twice in a row is an example of this. Or if I tossed

a coin 500 times and you tossed a coin 500 times and we compared notes later

and found we'd got exactly the same sequence. In the case of a single 500

coin toss sequence, there are 10^150 possible outcomes, each with

probability 10^-150, so there is no big deal. For the second coin-toss

sequence to match, there is only ONE outcome that achieves this, so it then

becomes remarkable that this specified event of probability 1e-150 has

occurred.

Iain

On 11/13/05, Bill Hamilton <williamehamiltonjr@yahoo.com> wrote:

*>
*

*> This problem has turned out to be quite a bit more interesting than I had
*

*> expected. Glenn's answers, and those from others point out the practical
*

*> difficulty of actually performing what I proposed as a thought experiment.
*

*> However, Glenn's digital precision answer inspired me to consider whether
*

*> I
*

*> could achieve a lesser objective: produce a random variable whose
*

*> probability
*

*> of occurrence is < 10^-150 -- the value which Dembski eliminates chance.
*

*> The
*

*> value of RAND_MAX -- the maximum value a random integer can take in a
*

*> given
*

*> environment -- is 2^31-1 for Mac OS X (probably also for Windows, but I
*

*> looked
*

*> it up at home) which is equal to 10^9.331929865. (say 10^9). A call to
*

*> ran1,
*

*> the numerical recipes uniform random number generator takes a few
*

*> microseconds
*

*> (I haven't timed it, but I have been running some simulations that make
*

*> thousands of calls to it, and the calls seem to add very little delay. So
*

*> call
*

*> ran1 17 times and concatenate the results, considering the result to be a
*

*> random number between 0 and 1 and you have produced a random variable
*

*> whose
*

*> probability is < 10^-150.
*

*>
*

*> Of course this ignores the problem of the periodicity of random number
*

*> generators, but there are ways of getting around that.
*

*>
*

*> --- Glenn Morton <glennmorton@entouch.net> wrote:
*

*>
*

*> > 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?
*

*>
*

*>
*

*> 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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*

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*

*>
*

-- ----------- There are 3 types of people in the world. Those who can count and those who can't. -----------Received on Sun Nov 13 16:41:24 2005

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