John and David,
I get the strong impression that this playful diversion is being
seriously regarded in some quarters as an effective counterpoise to the
emergence of 'pi' and 'e' (and much else) from the pages of scripture;
that sensing 'a kill', 'the vultures' are gathering. So, since you
gentlemen are clearly intent on pressing the matter, let's just examine
this 'bauble' in more detail.
John wrote:
> Now the above is, I believe, true, and verifiable by anyone, at least
> in principle. The value of n is left as an exercise to the serious
> student of such things; it (the value of n) is probably "divine" also.
> Note that my little exercise is clearly "better" than that of Vernon's
> since I have no need of introducing an arbitrary mathemetical
> transformation.
I observe:
(a) You require a pre-specified string of 26 digits to occur, taken
from a stream of what you believe to be random digits; logical as this
may sound, I don't believe it has been proved mathematically, and must
therefore represent an unproven assumption.
(b) The probability of any 1 digit being right is 1/10. Hence for a
string of 26 it is 10^-26.
(c) Hence the expected order of magnitude for the number n is 10^26.
(d) On the basis that the sequence is truly random, then one would
expect the string 'johnwburgeson' (along with 'vernonjenkins' and the
rest) to turn up not just once but infinitely many times, at an average
separation of around 10^26 digits. Clearly, no significance can be
attached to this observation; it is no different from the million
monkeys producing the works of Shakespeare, ( and 'Shakespeare' will
also turn up in the digits of pi, given the randomness assumption).
(e) Hence even if the universe were 15 billion years old (as you
clearly believe), and someone started the calculation right at the
beginning, they would not have sufficient time to determine the value of
n for even the first occurrence of 'johnwburgeson'.
(f) Add the extra names immediately afterwards, and the numbers will
exceed scientists expectations of the entire lifetime of the universe
(with "georgehammond" and "georgemurphy" tacked on as well, the number n
becomes of order 10^78). Scientists believe the lifetime of the
universe from Big Bang to Heat Death to be 10^52 years - a drop in the
ocean when trying to compute 10^76 digits of pi.
(g) My mathematical transformation initially appears arbitrary, but is
verified by the same formula producing an approximation to e of similar
accuracy in John 1:1. The approximations are taken from a finite domain,
rather than an infinite one, and also occur at significant positions,
right at the beginning of the Bible, and right at the beginning of the
Gospel of John.
(h) Your "arbitrary constant" n is to all intents and purposes
incalculable. "In principle" appears to mean, "given orders of
magnitude longer than the age of the universe". My formula, on the
other hand is specified and verified independently.
John and David, if you still consider my formula to be arbitrary, then
perhaps you would like to combine forces and produce an arbitrary
formula that turns the _first_ 26 digits of pi to a representation of
"vernonjenkins". Here are the digits: 3 14159 26535 89793 23846 26433.
The formula must be of similar simplicity to mine and must derive from
the "given" order of the letters in the alphabet.
Bon voyage! I look forward to your response.
Regards,
Vernon.
John W Burgeson wrote:
>
> >>
> Much neater to represent 'pi' in a radix-26 system so that its digits
> map neatly onto the alphabet on a one-to-one basis.>>
>
> Nice idea, but I thought you'd like the conservation of the "divine
> ten" better. I still cannot believe you did not understand the point I
> was trying to make in my MOBY DICK thought problem.
>
> John Burgeson (Burgy)
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