Re: Small probabilities

From: Don Nield <d.nield@auckland.ac.nz>
Date: Fri Dec 02 2005 - 16:07:24 EST

Iain:
Thank you. I now have a follow up question Are the patterns all that
improbable?
1. What is the population of transcendental numbers being considered?
For example, let rho = sqrt(pi), so that the area A of a circle of
radius r is given by A = (rho*r)^2, a nice simple formula of some
practical use. Is rho a contender for significance?
2. Since 37 is a factor of 111 it must automatically be a factor of 222
,333, 444, 555, 666, 777, 888, 999. Thus it is not surprising to me that
several multiples of 37 turn up.
3. Is the turning up of triangular numbers all that improbable? The
triangular numbers are
N*(N+1)/2 for N = 1, 2, 3, 4. ..... The probability that an arbitary
three digit integer (an integer less than 1000) is triangular is about
44/1000 or roughly 1/20, and that is not very small in this context.
Don

Iain Strachan wrote:

> 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
> <mailto: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 <mailto:d.nield@auckland.ac.nz>>
> > To: "Iain Strachan" < igd.strachan@gmail.com
> <mailto:igd.strachan@gmail.com>>
> > Cc: "Randy Isaac" <randyisaac@adelphia.net
> <mailto:randyisaac@adelphia.net>>; "Vernon Jenkins"
> > < vernon.jenkins@virgin.net <mailto:vernon.jenkins@virgin.net>>;
> <asa@calvin.edu <mailto: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>
> >>> <mailto: 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 <mailto:vernon.jenkins@virgin.net>>
> >>> *To:* Randy Isaac <mailto:randyisaac@adelphia.net
> <mailto:randyisaac@adelphia.net>> ;
> >>> asa@calvin.edu <mailto:asa@calvin.edu> <mailto:
> 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
> >>>
> >>>
>
Received on Fri Dec 2 16:09:11 2005

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