Re: Small probabilities

From: Iain Strachan <igd.strachan@gmail.com>
Date: Wed Nov 09 2005 - 08:19:53 EST

Randy,

Thanks for the thoughtful reply.

Your example of the repeat-deal with a pack of cards is of course
susceptible to the same analysis within the description-length framework -
to transmit the information relating to two deals of a pack of cards
requires in general for you to send 104 card descriptors in the message. But
if the second deal was the same as the first, then you'd only have to send
52, plus an indicator that the same sequence would then be repeated. Hence
the description length of the repeat-deal case is about half that of the
general case & can therefore by the same token be treated as a meaningful
low probability.

Regarding the "pi in Gen 1:1" phenomenon. I agree that it would be no more
than a curiosity if that were all there was to it. The internet has many
peculiar people who do tortuous mathematical calculations to prove something
(often the date of the "rapture", which to my knowledge no one has got right
yet! ;-). So if you get pi to 5 sig figures from Gen 1:1 using an apparently
arbitrarily concocted mathematical formula, then so what? From the vast
range of mathematical formulae you could apply it would be easy to find one
that gave you any answer you wanted. What makes it more interesting is that
Vernon reported that the value of e to a similar accuracy could be obtained
from the related NT "beginnings" verse, John 1:1, _by applying exactly the
same formula_ . It's the fact that it is the same formula that makes it
noteworthy. In description length terms, you have to transmit the model as
well as the parameters. In this case, the model only has to be transmitted
once (as the 52-card sequence has to be transmitted once), thus reducing the
description length. I don't think this example is capable of being used to
derive a formal probability, however, but it reminds me of the story,
printed in the UK newspapers a year or so ago, of a little girl called Laura
Buxton. Laura Buxton was a girl who released a helium balloon from her back
garden at a party. The balloon travelled 150 kms and then came down in
another back garden, where it was picked up by another little girl whose
name was also Laura Buxton. If that sort of thing happens to you, then you
immediately think it's an amazing coincidence, or something special has
happened and it gets reported in the local press. But when you consider the
vast range of amazing coincidences that could happen, then it's not
surprising that such things happen, and when they do, get reported. But
consider this; suppose next week you read in the newspaper that exactly the
same thing had happened to two girls called Sarah Harding who lived 135 Km
apart. Now that really would be amazing; note how much shorter my
description was the second time, because the basic model ( one girl releases
a balloon that travels a large distance to be found by another girl of the
same name) is taken as read the second time, and only the parameters of the
model ( girls' name, distance travelled) need to be described. In the same
way, it takes Vernon's web-page some considerable space to show how pi can
be derived from Gen 1:1, but very little to say that the same formula yields
e from John 1:1.

However, I think the geometric features of Vernon's work are more
susceptible to this kind of formal analysis than the pi/e derivations.

Best,
Iain

On 11/9/05, Randy Isaac <randyisaac@adelphia.net> wrote:
>
> Iain,
> Thanks for getting the discussion back to the original key point and for
> the good analysis. There isn't a probability so low that it eliminates
> chance simply because it isn't the whole story We have to consider the
> bigger picture and the span of possible events. This is also an area where
> one must differentiate between the past and the future. Events in the past
> can have extremely low probabilities of occurrence but they nevertheless
> occurred because of the large number of possible outcomes. That same event
> predicted for the future is virtually guaranteed not to occur by chance.
> Dealing a deck of cards is still a good example. Deal a hand of bridge and
> the result has an infinitesimally small probability of occurring, namely
> 1/52!, if you also count the sequence of cards in each hand. But there are
> also 52! possibilities so the probability of getting one of them is unity.
> But put that same sequence in the future, and predict a particular sequence
> and the probability reverts to exactly 1/52! which is essentially zero.
> Similarly, in evolution the "design space" is indeed vast but so is the
> set of possibilities. Net: calculation of probabilities of what has been
> observed is not only impossible to do because of our lack of knowledge, but
> it is also meaningless because of the range of possibilities. On the other
> hand, predicting a specific result in the future has a near zero chance of
> occurring.
> That's why I keep saying that finding numerical or geometrical
> curiosities in a text is fun but not meaningful. Pi to 5 significant digits
> in Gen. 1:1 is simply that, a curious observation. (on the other hand, if we
> were to find Hubble's constant in Gen. 1:1 to 5 significant figures, now
> THAT would be fascinating!)
> Randy
> ----- Original Message -----
>
> *From:* Iain Strachan <igd.strachan@gmail.com>
> *To:* Bill Hamilton <williamehamiltonjr@yahoo.com>
> *Cc:* asa@lists.calvin.edu
> *Sent:* Tuesday, November 08, 2005 11:08 AM
> *Subject:* Re: Small probabilities
>
> 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. .......
>
>

--
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There are 3 types of people in the world.
Those who can count and those who can't.
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Received on Wed Nov 9 08:22:47 2005

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