Re: Small probabilities

On 11/29/05, Randy Isaac <randyisaac@adelphia.net> wrote:
>
> Yes, Iain, you got it precisely right. With sufficient ingenuity you can
> find a clever pattern in any sequence of numbers. But not an *a priori*prescribed pattern. Remember the days of "The Bible Code" in the late
> 90's? A bit different but similar principles. Following a few links from
> our ASA website, we find http://cs.anu.edu.au/~bdm/dilugim/diana.html<http://cs.anu.edu.au/%7Ebdm/dilugim/diana.html> where
> Lady Diana's death and the names of her boyfriend and driver are found in
> Moby Dick. Perhaps Herman Melville was a prophet for our times. Strange
> how these predictions are always found after the fact.
>
> Net: Option 1) without a doubt. I read your posts on this thread and I
> thought you were ending up here as well. I'm not sure why you moved away
> from it.
>

Randy,

You got precisely the wrong impression from my posts on the thread, and I am
mystified as to why you should think I was heading for option (1). However,
Vernon has also written privately indicating that I'm undermining his
position with all the stuff about Kolmogorov etc, when the opposite was the
case. I've never moved away from the position of thinking (with, I believe
perfectly defensible scientific reasons) that the patterns Vernon has found
were put there deliberately by some agency or other (option (2) or (3)).
What I do not subscribe to is the conclusion that Vernon wants to draw, that
it means that Genesis 1 is literal historical truth. Although, for a time
in my life ( a difficult time when I was under a lot of stress), I did
consider myself a creationist, careful thinking about the scientific
evidence, and indeed a reading of the more considerate expositions on this
list, trying to ignore the ruder ones, I came to the conclusion that my
original position of accepting both evolution and God was perfectly
consistent. This shift in my position towards a TE position is one that has
saddened Vernon, but there is not much I can do about that.

I'll summarise what I said about small probabilities, and try to illustrate
better why I consider there to be good evidence that Vernon's patterns are
not coincidence and products of a fanciful imagination (there is plenty of
numerology on the web for which this is the case).

We were agreed that if you dealt a hand of bridge, and then followed it by
another deal with shuffling, that resulted in exactly the same deal, that
this would be a truly remarkable happening, evidence of cheating. Though
the two deals have the same miniscule probability, the second one is
constrained to being only one outcome, whereas the first one could have been
any.

I take it we're agreed on that?

Would you also agree that I can use a description length/compressibility of
data argument to describe this. ie to describe a sequence of 104 card I
only need to describe 52 of them and then say "same repeated"? That the
number of possible descriptions of 104 cards in just over half the length it
takes to describe 52 is vastly less than the total number of 104 card
sequences?

I next gave the story of Laura Buxton, the girl who let off a helium balloon
with her name on it from her back garden, which then travelled 110 miles,
and landed in someone else's back garden, where it was found by another
girl, who happened to be called Laura Buxton as well.

I said that although it might have appeared a remarkable coincidence to the
girls it happened to (who subsequently got in touch and became friends),
that in the long run it wasn't at all a remarkable coincidence, considering
the vast number of possible strange coincidences that could happen ( one of
my favourites being three people who were executed at Brackenberry Hill who
were called Bracken, Berry, and Hill). But there is nothing remarkable
about these - we expect them to happen.

However, I then went on to say that if the next week in the paper, there was
an identical incident to the Laura Buxton story, except the girls were
called Sarah Harding, and the balloon travelled 130 miles. Would you agree
that in this case, there is something going on - I would suspect the second
story as being made up - the coincidence is too remarkable, because now it
has to follow a specified pattern (the Laura Buxton scenario).

Would you agree that you also would suspect the second story?

Now we return to Vernon's "pi" approximation (which, if I recall, you
brought up initially, so this is my response, which you don't seem to have
understood if you thought I was arguing for a coincidence).

What I said was that by itself, the fact that a seemingly arbitrary
mathematical formula applied to the numerical values of the letters of Gen
1:1 gives a reasonable approximation to pi is nothing remarkable in itself,
because of the vast choice of possible formulae that could be applied.
However, just as in the Laura Buxton scenario, what made me sit up and take
notice, was that precisely the same formula was applied to the letters of
John 1:1 to give an equally good approximation to e, the other well-known
transcendental number in mathematics. The description length the second
time is much shorter, because you don't need to re-specify the formula.

Does that now make it clear what my position is, and why I don't accept
option (1)?

As for the "Bible code" phenomenon, I am skeptical of that, and for the same
reason - it can be analysed in terms of description length. The problem is
that these "codes" are found from a truly huge search space, and it
therefore requires a large number of bits to specify where the code is
located, almost certainly longer than the codeword itself. To specify an
ELS, you need to specify the start letter, and the skip distance. There
seem to be examples of huge skip distances, e.g. over 30,000. So lets say
you need 16 bits to specify the skip distance, and let's say there are a
million characters in the Old Testament. So you need 20 bits to specify the
start position. 36 bits in total, which could be used to encode 7
letters. Now, some of the proponents have claimed to find really long
sequences, but if you read them they are quasi meaningless gibberish, and
the search space of possible quasi meaningless gibberish sentences is vast.

Regards,
Iain
Received on Thu Dec 1 03:45:28 2005