From Newsgroup: sci.math

A room full of monkeys randomly entering characters at a keyboard
will, eventually, reproduce the works of Shakespeare.

Perhaps a more realistic scenario is a computer that generates a
random series of characters. In principle, given enough time,
the randon sequence will contain within it the complete works
of Shakespeare. (We assume that the random source is based on
a natural process, like radioactive decay, and not based on
an algorithm. IOW, these are true random numbers.)

Since the sequence is truly random does that imply that
the works of Shakespeare are also random?

Certainly I could not use the works of Shakespeare for encryption
purposes but the works do emerge out of a purely random process.

Within that infinite random string the works of Shakespeare will
occur an infinite number of times but so too will arbitrarily long
sequences of repeated characters.

Thus within a purely random series there will occur a great
deal of non-randomness.

What does this say about the nature of a random series?

I suspect that the resolution comes about because, in an
infinite random string, the "non-random" portions are overwhelmingly
diluted by the "random" portions.

But those "non-random" portions are still present and they
could construct rational edifices of any type.

Maybe the fact that infinity, and hence an infinite random string,
can never be actually realized is the resolution.

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From Newsgroup: sci.math

The string need not be infinite. As the length of the string increases
the probability of the works of Shakespeare being imbedded in it
increase. In the limit as the length approaches infinity the probability
of the works of Shakespeare being imbedded in it approaches being almost certain[1]. For some very long but finite string the probability will
be .99. The probability of you ever *finding* those works in that
string, however, will be quite low.


[1] https://en.wikipedia.org/wiki/Almost_surely
--
John Hasler
john@sugarbit.com
Dancing Horse Hill
Elmwood, WI USA
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