Re: numbers

From: Iain Strachan \(asa\) (
Date: Wed Feb 26 2003 - 19:16:00 EST

  • Next message: Iain Strachan \(asa\): "Re: Re: personal revelations"

    Dear Peter and Wayne,

    Firstly to say that I do very much appreciate that you are both prepared to
    take the time to make a thoughtful response on this subject. I realise it
    has been a matter of controversy on the list in the past, and it is good to
    be able to discuss these things in a civilised fashion.

    As I said in an earlier post, it is my tentative belief that I've been in
    some way "led" to investigate this. I won't say it's a "personal
    revelation", because that gives the idea that it's for definite and that
    would give the wrong impression. There have been many times I've wondered
    whether this is the right thing for me to do, and prayed and agonised about
    it; should I just forget it all and distance myself from the whole thing as
    a bad occult practice? The answer is, I believe, "no" to that. I genuinely
    think; and my scientific specialities lead me to believe, that there is
    something in this area, and if there is then it does have implications that
    ought to be considered about the nature of scripture, inspiration and so
    forth. I won't go as far as to say "that proves it's divinely inspired";
    but I do think there are implications that ought to be taken seriously.

    > From: Peter Ruest <>
    > To:,
    > Sorry, I'm tired of always editing out all that html stuff. Maybe I'll
    > do it again some other time...
    > Wayne, I am not a numerology buff. But I was intrigued by a question of
    > probability. Everybody just _assumes_ that these results with pi and e
    > etc. are made up artificially. My question was whether there is any
    > _evidence_ that this is possible. This question should be answerable by
    > a mathematician doing the appropriate probability calculations. But
    > since Vernon brought this up more than one and a half years ago, no one
    > has even tried to answer this question (apart from Iain, whom I
    > mentioned, and who seems to be similarly intrigued by the
    > probabilities), although there were probably dozens of posts condemning
    > such "number games" as nonsense - which is not very congenial if they
    > don't even try to answer the probability question. A solid demonstration
    > that the probabilities involved may be higher than, say, 0.001 could put
    > to rest the numerology claims once for all. But just assuming such
    > results can be made up, without any evidence, will not.

    One problem with probability calculations is that they can be made to come
    to anything you want by over-constraining or under-constraining the problem.
    One can raise the probability by saying that there are thousands of
    "interesting numbers" and one has to consider all of them.
    (under-constraining). Equally one could raise the probability to an
    insignificant level by saying there are thousands of verses to choose from.
    I guess there will always be debate here as to how the probability
    calculations are to be carried out. Someone who wants to condemn it as
    nonsense is going to say you have to allow lots of numbers and lots of
    verses. Someone dead set on proving it's genuine will insist on the exact
    numbers and the exact verses. (Overconstraining). I'll try here to do a shot
    at a "conservative" calculation, though this does insist on the two verses
    Gen 1:1 and John 1:1. This is because this was how the study originated.
    Vernon's original research was on Gen 1:1, and the natural NT companion from
    the _meaning_ had to be John 1:1. Furthermore, we had found significant
    integer patterns in Gen 1:1, and those patterns were extended in a natural
    manner in John 1:1. Therefore, meaning, and prior independent evidence
    suggested a link between the two verses.

    Given that the verses are fixed, what about "interesting numbers"? Just how
    many irrational numbers are interesting and sufficiently famous to be picked
    out as striking? The mathematicians Conway and Guy in "The Book of
    Numbers", (Copernicus, 1996) list 12 of their own "favourite numbers", and
    some of these are pretty obscure. They are:

    The Golden ratio phi (1.61803)
    gamma (0.57721) (The Euler Mascheroni constant)
    F1 = 4.669201
    F2 = 2.502907

    The last two are the Feigenbaum numbers that occur in chaos theory.

    I'd be willing to bet that most people wouldn't consider the last two to be
    suitable candidates for a "significant number" as they are so little known
    except in highly specialised areas. I've personally run into gamma a few
    times, but nothing like as many as pi. The logs are all a bit qustionable
    as inclusion. For my own criteria of significant numbers that crop up a
    _lot_ in mathematics, only the first five would really qualify. However,
    there might be others you'd want to include (e.g. phi-1, or sqrt(3)/2; an
    important geometric ratio.

    However, let's say there are about 12 on the list to be "conservative", and
    allow that either verse may come to any of them. This gives 144

    I previously figured out by sampling that the number that results from the
    formula for pi, when taken over all the verses in the OT (I know the verse
    divisions are arbitrary, but one has to take some measure to get a
    statistical sample), that the number that results is a random variable from
    a uniform distribution. Hence the pro bability of hitting any one number to
    that degree of accuracy (1 in 10^5) was around 10^-5. Since there are two
    verses, we get 10^-10. Now multiplying up by the 144 possibilities, we
    still get around 1.44e-8. While not definitive proof, the probability is
    nowhere near high enough (in my opinion), to write off as coincidence.

    Furthermore, this is all independent of the integer patterns connecting the
    two verses that pointed us in that direction in the first place. If one
    factors in all this, then the probabilities are reduced even further.

    > Wayne Dawson wrote:
    > Subject:

    (Wayne; you might be able to configure your email program to send in plain
    text rather than Japanese HTML,which comes out as gobbledegook?)

    > (JPeter Ruest wrote: (B
    > (J>Now, with respect to the actual discussion, I would assume that the
    > (B
    > (J>writer of Gen.1:1 might have known pi, but certainly not to this (B
    > (J>precision. However, I doubt that Euler's e was known at all to John.
    > So (B
    > (J>how could they just make it up, as Grattann-Guinness believes?

    As I correspond regularly with Grattann-Guinness & regard him as a useful
    contact, I'd like to clear up a possible misunderstanding here. I believe I
    made G-G aware of the pi and e approximations (he gives another, somewhat
    worse pi approx in one of his papers on maths and Christianity), but he did
    not comment on whether it was made up. It was only in response to seeing
    the integer patterns in Gen 1:1, that he made the comment "Oh! So they were
    at it in the Old Testament as well", implying that it was made up. This was
    in connection with the number 37, which carries enormous significance as an
    integer that has fascinated mathematicians since ancient times. Some other
    of G-G's papers are a little oblique in any kind of explanation as to
    whether gematria works. What is clear from the main paper on Maths and
    Christianity is his own attitude to religion, expressed in a footnote: "My
    position is: God save us from all religions, especially the aggressive

    > would (B
    > (J>certainly be even much harder to do than making up patterns of
    > integers. (B
    > (J>And how could these transcendental numbers serve as "decorations" if
    > (B
    > (J>they were not known at all, or not to the precision produced by the
    > (B
    > (J>text?

    In fact here is one point at which I would be a little cautious. One cannot
    be _sure_ that e was not known at the time of writing of John's gospel,
    simply because it was not "officially" known till the 18th Century.
    Sometime after the issue was raised initially, I came upon a web-site
    dealing with ancient Babylonian mathematics. One speculation was that they
    may have known about e, in that the constant (2,43) in their sexagesimal
    notation occurred frequently in the solution to certain equations. This
    number is 2 + 43/60 or approximately 2.716, which is close to e. Though
    this is not that accurate, it occurred sufficiently frequently for the
    author (I think it was a university maths dept web-site) to suggest they
    knew about e. Other calculations on Babylonian clay tablets (from the Yale
    Babylonian Collection YBC 7289) show a remarkable value they calculated for
    the square root of 2, correct to one part in 10^7, inscribed on a diagram of
    a right angle isosceles triangle. This indicates they had advanced
    abilities to calculate to high precision, and also that they understood
    Pythagoras's theorem, even though this was 1000 years plus before Pythagoras
    was born. The point is that knowledge gets learned and then forgotten and
    then re-discovered. I'd still say it was a pretty long shot that the author
    of John's Gospel knew e, and even if he did, I'd still say it was pretty
    well impossible to conceive of a meaningful sentence satisfying all the
    numerical constraints.

    > (JMy own concern is that it is easy to fall prey to a lot (B
    > (Jof skulduggery in this business. It has earned a bad (B
    > (Jreputation because it's a gimmick used too much by (B
    > (Jcranks in all religions to claim the superiority of (B
    > (Jtheir special brand of poison over the rest. (B

    That is certainly true, and something I try to consider all the time. In
    fact some Muslims claim a "mathematical miracle" in the Koran, based on the
    number 19. However, on examining it, the "facts" they presented didn't have
    the geometrical simplicity that is evident from a study of Vernon's
    findings. They were just a lot of twisted formulae each yielding a multiple
    of 19; never a significant multiple (e.g. to make a triangular number or
    other figurate form).

    > (JI know that all this sounds really incredulous of me. (B
    > (JWhat I am saying is that this kind of resistence (B
    > (Jis what one should expect seeing how easily it has (B
    > (Jbeen badly abused. (B

    Yes, I would certainly agree it has been badly abused. Unfortunately for
    the credibility of the subject, one of the worst offenders was Ivan Panin,
    who kind of founded the subject in modern times. He often fiddled the data,
    made changes to the text (or arbitrary choices where it was unclear), and so
    forth, in order to make the patterns come out. It's significant that
    Grattann-Guinness once told me that Panin was a "gullible jerk", but
    nonetheless G-G was convinced that other scholarly work on the incidences of
    37 in the NT was sound. Unfortunately this subject does attract cranks who
    do not do sensible maths.

    > (JProbably Vernon's observations would get more of a (B
    > (Jhearing if it didn't come with a similar package (B
    > (Jlike the rest of the cranks. (B

    I trust you are not implying that Vernon is a crank. I realise that the
    whole package, including Vernon's endorsement of YEC, is inevitably going to
    get a hostile reception on this list, but he is a personal friend of mine,
    and I believe that his approach to the maths is essentially sound. I have
    advocated a more cautious approach; let's try and determine if we have a
    genuine phenomenon here with the best science, maths and probability theory
    we can, and also have a think about the implications of it being real.

    > (JI suspect the intelligent design approach (B
    > (Jthat Dembski outlined could be applied to these codes: (B
    > (JBible, Koran etc. It is probably more useful there (B
    > (Jthan in all this wrangling over evolution. (B

    There is something to be said for this idea. I am mulling over
    possibilities that Kolmogorov complexity theory (also discussed by Dembski)
    might be applicable to the numerical structures. I think the approach
    suggested in the paper "Low complexity art", by Juergen Schmidhuber (who is
    head of a prestigious Swiss AI institute) comes closest to the kind of thing
    we want. The paper is very interesting, and may be found at .

    I'd expound on this more, but this post has already gotten way too long.

    Best wishes,
    Iain Strachan.

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