Re: Small probabilities

Don,

Sorry I didn't get to answer your query earlier - I've been rather busy at
work. Yes, clearly I would expect there to be structure embedded in the
regularities of the Hebrew language (or indeed any language). This is one
of the reasons why file compression utilities such as WinZip work so well,
because they exploit the fact that certain sequences of letters occur with
greater regularity than others. It is also this regularity in language that
enables probabilistic models to be developed for speech recognition, for
example. However, I see no reason why the linguistic regularities should
then, when mapped through the sequence you gave, and the numbers are added,
up should come to arcane mathematical objects such as triangular numbers and
pi. As a test, I applied the "pi formula" to every verse in the Torah
(having obtained a machine readable text from Vernon). The number that
results, when scaled in the same way as in Genesis 1:1 looks pretty much
like a uniformly distributed random variable & hence the probability of
getting 5 significant figure accuracy looks like 1 in 10^5. That by itself,
as I have said before, is not that remarkable - the formula is sufficiently
complex that if you searched the space of similarly complex formulae, you
might well come up with a formula that gave you that result. However, when
precisely the same formula is applied to the Greek of John 1:1 and it gives
e, the next best known transcendental number, to a similar degree of
accuracy, then you can say that this is a meaningful 1 in 10^5 probability,
as only one formula could be applied. If someone came out with an entirely
different formula that gave e from john 1:1, then it would not be
remarkable. (This relates to description length again - if it were a
different formula, you'd have to include the new formula in the description,
rather than just say it's the same one as last time).

Best,
Iain

On 12/2/05, Don Nield <d.nield@auckland.ac.nz> wrote:
>
> I did not say that a meaningful pattern must arise. I just asked Iain
> whether in assessing the probabilities he had taken into account the
> regularities in the Hebrew language -- by this I mean such things as
> the fact that some letters in a typical text occur more frequently than
> others, and the numbers in the sequence
> 1,2,3,4,5,6,7,8,9,10,20,30,40,50,60,70,80,90,100, 200,300,400 are not
> equally spaced when considered as a set --- things that provide
> contraints on the possible outcomes.
> Has Vernon searched for meaningful patterns in other parts of the Bible?
> Don
>
> Don
>
> Vernon Jenkins wrote:
>
> > Don,
> >
> > Why should one suppose that a meaningful pattern _must_ result in the
> > numbers obtained from a fair alternative reading of any portion of the
> > Hebrew text? The fact that it does so, in abundance, in respect of
> > the Bible's opening words is surely the stuff of mystery and wonder.
> >
> > Vernon
> >
> > ----- Original Message ----- From: "Don Nield" <d.nield@auckland.ac.nz>
> > To: "Iain Strachan" <igd.strachan@gmail.com>
> > Cc: "Randy Isaac" <randyisaac@adelphia.net>; "Vernon Jenkins"
> > <vernon.jenkins@virgin.net>; <asa@calvin.edu>
> > Sent: Tuesday, November 29, 2005 8:29 PM
> > Subject: Re: Small probabilities
> >
> >
> >> Has Iain taken into consideration the fact that the passage in
> >> Genesis is not a random sequence of letters but rather a Hebrew text
> >> and therefore should be expected to show some patterns if one
> >> searches for them?
> >> Don
> >>
> >> Iain Strachan wrote:
> >>
> >>>
> >>>
> >>> On 11/29/05, *Randy Isaac* <randyisaac@adelphia.net
> >>> <mailto:randyisaac@adelphia.net>> wrote:
> >>>
> >>> Yes, Vernon, I do agree that facts are facts. Can't argue with
> >>> that. The significance and meaning of those facts is the
> >>> question. Your observations are clever and perhaps even creative
> >>> and artistic.
> >>>
> >>>
> >>> Randy,
> >>>
> >>> I wonder if you could clarify what you mean by saying that Vernon's
> >>> observations are "clever" and "artistic". I may have got you wrong,
> >>> but it might appear from that that you are saying that with
> >>> sufficient ingenuity you can find a clever pattern in any sequence
> >>> of numbers.
> >>>
> >>> One of the things I've tried to do in this whole discussion about
> >>> small probabilities and description length (Kolmogorov theory etc)
> >>> is to illustrate that I think what Vernon has found is _not_ just
> >>> the product of an ingenious imagination, or a clever arbitrary bit
> >>> of mathematical manipulation - that the pattern in the integers was
> >>> indeed something that was deliberately put there, rather than just a
> >>> coincidence.
> >>>
> >>> One of the inhibiting factors of this discussion, it seems to me is
> >>> that Vernon wishes to put an interpretation on it (that the first
> >>> chapter of Genesis is literal truth), which I don't subscribe to,
> >>> and which makes the overwhelming majority of people on the ASA list
> >>> want to dismiss his observations out of hand. I think if we could
> >>> divorce the fact (of the pattern) from Vernon's interpretation, then
> >>> we might get a little further. I am of the opinion that the
> >>> pattern, which we both agree is a fact, is a piece of deliberate
> >>> design. But in general, there appear to be three interpretations of
> >>> the facts:
> >>>
> >>> (1) The pattern is a complete coincidence.
> >>> (2) The pattern is deliberate and was put there by the human authors.
> >>> (3) The pattern is deliberate and is intentional Divine action for
> >>> some purpose.
> >>>
> >>>
> >>> All of my contributions to the "small probabilities" threads (and
> >>> earlier ones on Kolmogorov) have been to the end of illustating that
> >>> I think there are sound methods for showing that (1) is not the
> >>> case. I, therefore have to deal with what are the likely
> >>> implications of (2) or (3) being the truth.
> >>>
> >>> What do you think?
> >>>
> >>> Iain
> >>>
> >>>
> >>>
> >>> Unfortunately, there is no reason to believe that there is any
> >>> philosophical or theological significance to the patterns and
> >>> relationships you have described. The verses you have quoted
> >>> previously to justify such signficance do not give carte blanche
> >>> permission to deduce meaning from arbitrary arithmetic
> >>> manipulation of numeric values of letters. As we've discussed in
> >>> this forum, the low probability of occurrence of numerical results
> >>> is not an indication of divine significance.
> >>> Randy
> >>>
> >>> ----- Original Message -----
> >>> *From:* Vernon Jenkins <mailto:vernon.jenkins@virgin.net>
> >>> *To:* Randy Isaac <mailto:randyisaac@adelphia.net> ;
> >>> asa@calvin.edu <mailto:asa@calvin.edu>
> >>> *Sent:* Sunday, November 20, 2005 7:28 PM
> >>> *Subject:* Re: Small probabilities
> >>>
> >>> Randy,
> >>> Further to the matter of the observed coordination of the
> >>> numerical geometries that derive from unbroken sequences of
> >>> the Bible's opening Hebrew words, I invite you consider some
> >>> additional data which lend considerable weight to these
> >>> incontrovertible and remarkable events. The relevant page
> >>> titled "Genesis 1:1 - The Inside Story" may be found at
> >>>
> http://homepage.virgin.net/tgvernon.jenkins/Inside_Story_SH.htm
> >>>
> >>> <http://homepage.virgin.net/tgvernon.jenkins/Inside_Story_SH.htm>.
> >>> You may remember, some time ago, Iain commenting on the fact
> >>> that these realities are 'not everyone's cup of tea'. But
> >>> facts are facts! And facts are the lifeblood of rational and
> >>> meaningful debate. Is our grasp of the eternal verities so
> >>> sure - so secure - that we, as Christians, can afford to
> >>> ignore such solid empirical data? Surely not, as I think
> >>> you must agree.
> >>> Vernon
> >>>
> >>>
> >>
> >>
> >
> >
>
>
> --
>
> Donald A. Nield
> Associate Professor, Department of Engineering Science
> University of Auckland
> Private Bag 92019
> Auckland, NEW ZEALAND
> ph +64 9 3737599 x87908
> fax +64 9 3737468
> Courier address: 70 Symonds Street, Room 235 or 305
> d.nield@auckland.ac.nz
> http://www.esc.auckland.ac.nz/People/Staff/Nield/
>
>

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After the game, the King and the pawn go back in the same box.
- Italian Proverb
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