Re: Small probabilities/detecting design

From: Bill Hamilton <williamehamiltonjr@yahoo.com>
Date: Sun Nov 13 2005 - 17:22:14 EST

This is a response to two threads to keep to the 4 post limit. After this I'm
done for the day.
In response to Cornelius's post: Yes, I believe there is evidence for design in
creation. However, I am well aware that that evidence is interpreted
differently by scientists of different faiths, or of no faith. A second issue
is, once we have acknowledged design, what can we do with it. Most of the ID
material I've read catalogues instances of design in nature. I'm currently
reading Guillermo Gonzalez' book "The privileged Planet" which assembles an
amazing array of evidcences for design. But the question for scientists is,
"Now that was have all these disparate facts, what program of investigation do
they suggest?" I think evidences of design are inspiring to Christians, and may
lead them to significant discoveries, not necessarily based on the evidences
themselves, but simply because they inspire a confidence in the rationality of
God. That's valuable to believers, but not the basis of a program of
investigation.

--- Iain Strachan <igd.strachan@gmail.com> wrote:

> 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.

Agreed. Is this what Bill Dembski means by "specified complexity"?
>
> 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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> >
>
>
>
> --
> -----------
> There are 3 types of people in the world.
> Those who can count and those who can't.
> -----------
>

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 13 17:26:05 2005

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