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Re: bimodal ditribution form counting signs of Pi digits differences

On 11/3/04 at 1:24 AM, drbob at (DrBob) wrote:

>(a) If Pi digits ARE pseudo-random in all the ways we'd like them
>to be, there's still no proof of it -- whereas the properties of
>CA-30 are mathematically proven.

I strongly doubt that CA-30 was chosen as a pseudo random number generatore based on a mathematical argument. Instead, I very much believe the suitability of CA-30 as a pseudo random number generator have been tested thoroughly with a battery of tests used to validate pseudo random number generators. The same suite of tests could be used for the digits of Pi, if desired. 

But this would not make the digits of Pi a very good pseudo random number generator even if it passed all of the tests you could devise. The reasons include your comment below.

>(b) Computing Pi digits is MUCH less efficient than CA-30 and other
>standard generators. If we need a billion random variates, this is
>a very bad way to get them -- especially if we're not looking for
>small integers.

And since the digits of Pi are determined it would be the same sequence of numbers. Also, most problems need more than a sample from 0-9 you would obviously not be able to use the digits directly. a consequence of this is even if you knew the digits of Pi are random, it would not demonstrate the numbers you generated are adequately random.

>(c) These questions have been studied to death by experts.

Quite true.
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