Re: Small probabilities

From: Mervin Bitikofer <mrb22667@kansas.net>
Date: Sun Nov 06 2005 - 19:23:44 EST

Could you find the entire Bible in pi? Hear me out on this.

I'm fascinated by the strings of digits we find in a base ten
representation of irrational numbers like pi. Consider the following as
a very probable possibility: Any short string of digits can be found
somewhere in pi. If for example, I wish to find four sevens in a row,
an internet search program quickly informs me such a string is first
found at 1589 digits after the 3. But if I want five sevens in a row, I
have to go 162,248 digits in. Now if I understand irrational numbers
correctly, the sequence of their digits, while determined
mathematically, would still be, in a sense, 'random'. i.e. If there
were infinitely repeated patterns, then it would not be an irrational
number. So if we treat this statistically the same way we treat
randomness, then it is never a matter of 'if' but 'where' any sequence
of digits you wish to find may occur. We can easily work out the
probability of finding an X length string of digits in a Y sized field.
And that probability can never be made to go to zero as long as Y is
larger than or equal to X. Furthermore you can make the probability of
finding ANY desired string (/no matter how long/) arbitrarily close to
100% (but never quite reaching it) by simply pouring on the magnitudes
to the search range Y.

Conclusion: It is a virtual certainty of probability that the entire
coded works of Shakespeare as well as everything else are to be found
somewhere in pi. Okay - maybe I'm the only one fascinated by this,
since the magnitudes of digits required to find anything interesting
would dwarf the paltry (relatively tiny) trillions of digits now known.

So if the universe was infinite in either time or space, any
improbability becomes probable - hence the evolutionary attachment to
steady state theories with their infinite time spans or infinite #s of
'parallel' universes in which so called 'randomness' can do its tricks.
Not that I really buy any of this (or its negation either) - there are
too many assumptions in it for either creationists or their antagonists
to wield it effectively regarding probabilities. The conclusions
displayed in the eventual creationist or evolutionist pedagogy are, IMO,
more a reflection of the carefully chosen assumptions than a proof (or
even an evidence) of a reality.

--merv

by the way - I'm sure my suggestion that anything can be found in
irrational #s must be passť discussion among mathematicians, & yet I
don't remember ever hearing such a thing proposed. Does it sound
logical? I think there could be a formal proof done on this.

Don Nield wrote:

> Bill:
> The apparent paradox arises since a point has infinitely small length.
> The paradox is resolved by considerning a arbitrary small but finite
> interval in the neighborhood of the point, and talking about a
> probablity for that interval.
> Don
>
>
> Bill Hamilton wrote:
>
>> I read Dembski's response to Henry Morris
>> (http://www.calvin.edu/archive/asa/200510/0514.html)
>> and noted that it raised an old issue I've harped on before: that you
>> can
>> specify a probability below which chance is eliminated. There is a
>> counterexample given (among other places) in Davenport and Root's
>> book "Random
>> Signals and Noise" (McGraw Hill, probably sometime in the early 60's)
>> that goes
>> like this:
>> Draw a line 1 inch long. Randomly pick a single point on that line. The
>> probability of picking any point on the line is identically zero. Yet
>> a point
>> is picked. Am I missing something?
>>
>> I will probably unsubscribe this evening, because I don't really have
>> time
>> during the week to read this list. However, I will watch the archive
>> for
>> responses and either resubscribe or resspond offline as appropriate.
>>
>> Bill Hamilton
>> William E. Hamilton, Jr., Ph.D.
>> 586.986.1474 (work) 248.652.4148 (home) 248.303.8651 (mobile)
>> "...If God is for us, who is against us?" Rom 8:31
>>
>>
>>
>>
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>>
>
>
>
>
Received on Sun Nov 6 19:29:52 2005

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