Re: Small probabilities

From: Mervin Bitikofer <mrb22667@kansas.net>
Date: Tue Nov 08 2005 - 23:41:58 EST

Aren't terms like 'randomness' and 'probability' ultimately more a
statement of perspective than of reality? I may refer to a series of
computer generated numbers as random because they appear that way to me,
but when I become aware of the algorithms used to produce the numbers,
then I no longer view the sequence as random but as determined. In the
same way coin flips only appear 'random' to us because of the
overwhelming calculations that would be involved analyzing initial
velocity & spin vectors, air currents, micro-gravitational influences,
etc about the event. But if we had a 'God's eye' perspective where are
computational capabilities weren't limited, then each coin flip is
pre-determined, right? This, of course, assumes that the quantum
uncertainty principle is merely a measurement problem rather than an
ontological one. I.e. even though we won't ever be able to
simultaneously measure velocity & location of a particle, it would still
have these definite properties (in principle) to be known by
omniscience. Apart from this humanly inescapable ignorance, what could
the concept of 'randomness' possibly mean? If something (presumably
many things - like every electron movement) was truly ontologically
random (even to omniscience), wouldn't this require each so called
random event to be divorced from the causality that underpins science?
This would be indistinguishable from what we call 'miraculous' or
'supernatural' - except in that it would be common place, indeed always
happening, at the microscopic level.

Perhaps some of you can explain to me how it is that these quantum
uncertainties are supposed to have killed LaPlace's demon. To my
thinking, declaring that we can't know something is not the same as
concluding that it can't (in principle) be knowable. It only states
that we won't ever be able to play LaPlace's demon ourselves. Just like
the Schrödinger's cat example - which always has seemed ridiculous to
me, like some sort of philosophical solipsism disguised as science.
Can anybody enlighten me as to how it is that modern mathematicians or
scientists so neatly dismiss these century old quandaries? I'm either
missing something, or else everybody else just got tired of talking
about it & moved on to some new faddish mistress like string theory.
Until these questions are answered, I don't see how any such thing as
'randomness' could be said to even exist.

I'm certainly not a Calvinist, and I do believe in freewill though I
have no idea how that could ever be explainable. But this whole
discussion does put Dave's reference to Proverbs 16:33 in an interesting
light. (that all lots cast are decisions from the Lord). That was from
a HPS post - sorry I'm mixing subject headings, but some of this fits
together here.

--merv

Iain Strachan wrote:

> While everyone has got interested in the point-picking-from-a-line
> example, I don't believe that anyone has really addressed Bill's
> question about low probability "eliminating chance". One can get lost
> in the philosophy of picking a point from an infinite number of
> points, without seeing the real point (which was to argue against
> Dembski's notion that low probability can eliminate chance). I'd like
> to re-address this point. This is not to say that low probability can
> detect "design", which is a separate issue.
>
> Low probability by itself cannot "eliminate chance", because if every
> event is low probability, then one of them has to happen. Bill states
> that the probability of picking any point is zero yet a point is
> picked. To make it less abstract and in the realm of the real world,
> consider 200 coin tosses. You can say that the probability of any
> sequence occurring is 6.6x10^(-61) ( = 2^(-200)), which is
> exceptionally unlikely. Yet you toss a coin 200 times and lo and
> behold you've just witnessed an event with probability 6.6e-61.
> Clearly the low probability cannot eliminate chance by itself.
>
> Something like this happens with a technique I work with, called
> "Hidden Markov Models", which are used commonly in speech recognition
> (though I'm using them in a medical application). When these models
> are used to recognise speech, the speech signal is segmented into a
> number of frames, say 10ms long, and each frame is signal processed to
> produce a vector of numbers (usually some frequency domain analysis).
> Then in order to recognise a word, one constructs a probabilistic
> model that evaluates a probability for the entire sequence of these
> vectors. Now, the probability for the whole lot is simply the product
> of the probabilities for each individual one, so if there are many
> hundreds of samples, then you get incredibly small probabilities. Now
> here lies a problem: you would like to have a number of different
> models for different words that you might want to recognise, eg "one"
> "two" "three" etc. But the length of time people take to say "one"
> might vary a lot, and clearly it takes longer to say "seven" than it
> does to say "one". So because there are many more samples in the
> sequence when you say "seven", it will of necessity have a much lower
> probability, just as a sequence of 200 coin tosses has a lower
> probability than a sequence of 100. The raw probability isn't
> sufficient to discriminate between the two. But what you can compute
> is an expected value of the probability churned out by the model. If
> you say "one" into a model that is designed to recognise "seven", the
> probability will be many orders of magnitude lower than if you said
> "seven" (because the probability assigned to each of the vectors in
> the 10ms time frames will be much lower) so you can do the
> discrimination, and the confidence you have in rejecting it could be
> given by the ratio of the two probabilities.
>
> Likewise, with a sequence of coins, Dembski uses the notion of
> compressibility. Any arbitrary sequence of 200 coin tosses will on
> average require 200 "bits" to describe it. But if you describe it as
> 50 reps of HTHH, then clearly you have a much shorter description.
> Say this can be fitted into 25 bits in some specification language.
> Now the number of 25 bit strings is 2^25 and the number of 200 coin
> toss sequences is 2^200, so it follows that the probability of getting
> a 200 sequence of coin tosses describable in 25 bits is 2^(-175) =
> 2.08x10^(-53). This low probability can be used to "eliminate" chance
> - you don't expect to get that kind of repetition in a sequence of
> coin tosses.
>
> All the above is not to say that this detects design as such. There
> may be a naturalistic explanation of why you got 50 reps of HTHH. But
> it does clearly detect non-randomness.
>
> Hope this answers some of your question.
> Iain
>
> On 11/6/05, *Bill Hamilton* <williamehamiltonjr@yahoo.com
> <mailto:williamehamiltonjr@yahoo.com>> wrote:
>
> 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?
>
> I will probably unsubscribe this evening, because I don't really
> have time
> during the week to read this list. However, I will watch the
> archive for
> responses and either resubscribe or resspond offline as appropriate.
>
> 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 Tue Nov 8 23:46:56 2005

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