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Re: Simple random number generator?
Posted:
Nov 27, 2012 12:09 PM
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"Clark Smith" <noaddress@nowhere.net> wrote in message
news:k90pcp$udq$1@news.albasani.net...
> On Mon, 26 Nov 2012 15:08:17 -0500, Existential Angst wrote:
>
>> Would be the digits of e, pi, et al?
>> If that's the case, no need for fancy pyooter algorithms?
>>
>> Inneresting article on pi, randomness, chaos.
>> http://www.lbl.gov/Science-Articles/Archive/pi-random.html
>
> Is it not the case that the digits of e, pi et al. can't strictly
> be random, if it is only because they are highly compressible? I.e.
> because there small, compact formulas that spit out as many digits as you
> want in a completely deterministic way?
Deterministic?? y = mx + b is deterministic..... Any curve you can graph
is deterministic, but I think Bailey and Crandall would certainly not use
the word dterministic here, as in "predictive". Yeah, the formula or
whatever "determines" the next digit, but the user of the formula doesn't
know what that next digit will be, formula or no formula. To wit:
"This result derives directly from the discovery of an ingenious formula for
pi that Bailey, together with Canadian mathematicians Peter Borwein and
Simon Plouffe, found with a computer program in 1996. Named the BBP formula
for its authors, it has the remarkable property that it permits one to
calculate an arbitrary digit in the binary expansion of pi without needing
to calculate any of the preceding digits. Prior to 1996, mathematicians did
not believe this could be done."
Which, apropos of your point, is an even worse scenario, formula-wise, for
randomness, yet Bailey/Crandall don't think "formula-ization" of randomness
precludes true randomness.
"The digit-calculation algorithm of the BBP formula yields just the kind of
chaotic sequences described in Hypothesis A. Says Bailey, "These constant
formulas give rise to sequences that we conjecture are uniformly distributed
between 0 and 1 -- and if so, the constants are normal."
In addition, pi et al meet "casino-type" tests of randomness, which of
course are not proofs of randomness.
My point was:
Even random number generators can be suspect, from what I read some time
ago. I just thought it mildly interesting -- esp in light of Hypothesis
A -- that if true randomness is *intrinsic* to the mathematical fabric of
irrationals like e, pi etc, then generators are semi-moot, from a true
"need" pov. But still innersting and perhaps important from a "how do they
do it" pov.
This randomness thing may be a kind of consequence of going from analog to
digital, ie, altho you can graph y = sinx, AND you can graph random numbers,
one is predictive while the other is essentially an ad-hoc descriptive, with
no notions of derivatives or integrals applying to the curve whatsoever --
except for the trivial case of a random plot (y = the random value, x = the
trial "count"), that dYavg/dX = 0.
Anyway, I always thought e, pi et al were random sequences. Apparently
others do, as well.
But proly it will never be proven, one way or the other.
--
EA
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