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From: George Van Treeck <treeck>
Subject: Re: Can NeuralNets Forecast the Digits of Pi?
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If you read the original problem: given a sequence of digits, then predict the
next digit.  This not the same generating Pi to N decimal places.

For rational numbers there is always a repeating sequence (a pattern).
Given a piece of the pattern, a net could certainly predict the next
part. However, transendental numbers like Pi, seems to have no
repeating sequence (no pattern to learn).  Mathematicians have tried for
many years to find a pattern and failed.  The binary digits of Pi make one
of the best random number generators.

If you do come up with a net that can learn to spot patterns in such
an apparently random sequence, then don't tell anyone but me!!!  I'll make
us both rich applying it to learn to predict the next numbers in computerized
lotto systems based on the previous numbers!  :-)

-George

adamnet@ix.netcom.com (Jared Shope ) wrote:
>In <488li0$f6i@st-james.comp.vuw.ac.nz> russell robinson
><R.Robinson@gns.cri.nz> writes: 
>>
>> One Friday afternoon I got sick of work and, just for fun, tried
>> to see if a neural-network could forecast the next digit in
>> Pi (3.14159..... in decimal; I worked with binary digits) from 
>> the preceeding N digits.  These digits appear to be random to the 
>> ususal tests for randomness (at least the ones I tried). So it would
>> be interesting if a network could find some determinism. I tried some
>> simple back-propagation nets, and various values of N, but could 
>> never get any significant predictability.  The program I used was
>> able to forecast the usual simple chaotic time series examples, so
>> I am fairly sure it works OK. 
>>
>> The question is: does anyone else want to try, just out of 
>> curiousity? Or is it a completely dumb thing to try? Or has somebody
>> already done this?  Or is there a mathematical proof that it must 
>> fail?  I can send you about 4800 digits in whatever radix you like,
>> calculated by the methods in "Numerical Recipes" by Press et al.
>>
>> Cheers, R. Robinson
>
>There are some very fast methods for generating as many digits of pi as
>you like. Yes, this is a dumb thing to do.
>-- 
>Dale Smith, Ph.D.	Phone: 800-753-2326
>Quantitative Analyst	Email: adamnet@ix.netcom.com
>ADAM Investment Svcs	(Put my name in the Subject field!)
>Atlanta GA		Home Email: dtsmith@mindspring.com
>  Opinions I express here are my own and not my employer's.

