At 03:55 PM 5/6/05 -0400, Tyler Durden wrote:
Yes, but only provided the universe lasts long enough for those digits
to be
computed!
-TD
Actually, a few years ago someone discovered an algorithm for the Nth
(hex) digit of Pi
which doesn't require computing all the previous digits. Mind blowing.
http://cypherpunks.venona.com/date/1993/05/msg00213.html
Back in the old days, Tim May would occasionally talk about the
Kolmogorov-Chaitin theories about randomness - Kolmogorov complexity gives
you a lot of deep explanations about this sort of problem. Alas, I never
actually *read* those
http://cypherpunks.venona.com/date/1993/05/msg00213.html
Back in the old days, Tim May would occasionally talk about the
Kolmogorov-Chaitin theories about randomness - Kolmogorov complexity gives
you a lot of deep explanations about this sort of problem. Alas, I never
actually *read* those
--- Tyler Durden [EMAIL PROTECTED] wrote:
Let us remember, of course, that the digits of pi
are not random
whatsoever: they are the digits of pi! Random is in
the eye of the
beholder.
-TD
Exactly. What an algorithm gives out is always
deterministic. We try to see if there is some
hi,
--- Gil Hamilton [EMAIL PROTECTED] wrote:
For example, is this sequence
of bits random:
01100100010? How about this one: 00? From
a true random number
generator, both are completely possible and equally
valid.
Random as in the sense guessable and thus posing a
problem to the
From: Sarad AV [EMAIL PROTECTED]
Sent: May 5, 2005 8:43 AM
To: [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Subject: Re: Pi: Less Random Than We Thought
Well, if it were generated by a random process, we'd expect to see every
n-bit substring in there somewhere, sooner or later, since the sequence
Yes, but only provided the universe lasts long enough for those digits to be
computed!
-TD
From: John Kelsey [EMAIL PROTECTED]
To: Sarad AV [EMAIL PROTECTED], [EMAIL PROTECTED]
CC: [EMAIL PROTECTED]
Subject: Re: Pi: Less Random Than We Thought
Date: Fri, 6 May 2005 09:42:09 -0400 (GMT-04:00
--- Tyler Durden [EMAIL PROTECTED] wrote:
Let us remember, of course, that the digits of pi
are not random
whatsoever: they are the digits of pi! Random is in
the eye of the
beholder.
-TD
Exactly. What an algorithm gives out is always
deterministic. We try to see if there is some
From: Sarad AV [EMAIL PROTECTED]
Sent: May 5, 2005 8:43 AM
To: [EMAIL PROTECTED]
Cc: [EMAIL PROTECTED]
Subject: Re: Pi: Less Random Than We Thought
Well, if it were generated by a random process, we'd expect to see every
n-bit substring in there somewhere, sooner or later, since the sequence
hi,
--- Gil Hamilton [EMAIL PROTECTED] wrote:
For example, is this sequence
of bits random:
01100100010? How about this one: 00? From
a true random number
generator, both are completely possible and equally
valid.
Random as in the sense guessable and thus posing a
problem to the
Yes, but only provided the universe lasts long enough for those digits to be
computed!
-TD
From: John Kelsey [EMAIL PROTECTED]
To: Sarad AV [EMAIL PROTECTED], [EMAIL PROTECTED]
CC: [EMAIL PROTECTED]
Subject: Re: Pi: Less Random Than We Thought
Date: Fri, 6 May 2005 09:42:09 -0400 (GMT-04:00
hi,
If you remember D.E Knuth's book on Semi-Numerical
Algorithms he shows some annoying subsequences of pi
in it which are far from random.
Sarad.
--- cypherpunk [EMAIL PROTECTED] wrote:
This doesn't really make sense. Either the digits
are random or they
are not. You can't be a little
Sarad writes:
If you remember D.E Knuth's book on Semi-Numerical
Algorithms he shows some annoying subsequences of pi
in it which are far from random.
I don't have Knuth's book handy to look at, but it's not really correct
to speak of a particular sequence or subsequence of digits as being
random
grumpily reply...he's a number theorist or
something.
-TD
From: Sarad AV [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
CC: [EMAIL PROTECTED]
Subject: Re: Pi: Less Random Than We Thought
Date: Thu, 5 May 2005 05:43:35 -0700 (PDT)
hi,
If you remember D.E Knuth's book on Semi-Numerical
Algorithms he shows
grumpily reply...he's a number theorist or
something.
-TD
From: Sarad AV [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
CC: [EMAIL PROTECTED]
Subject: Re: Pi: Less Random Than We Thought
Date: Thu, 5 May 2005 05:43:35 -0700 (PDT)
hi,
If you remember D.E Knuth's book on Semi-Numerical
Algorithms he shows
[1]Autoversicherung writes Physicists including Purdue's Ephraim
Fischbach have completed a study [2]comparing the 'randomness' in pi
to that produced by 30 software random-number generators and one
chaos-generating physical machine. After conducting several tests,
they have
[1]Autoversicherung writes Physicists including Purdue's Ephraim
Fischbach have completed a study [2]comparing the 'randomness' in pi
to that produced by 30 software random-number generators and one
chaos-generating physical machine. After conducting several tests,
they have
Link: http://slashdot.org/article.pl?sid=05/05/01/1759240
Posted by: timothy, on 2005-05-01 18:26:00
from the at-least-statistically dept.
[1]Autoversicherung writes Physicists including Purdue's Ephraim
Fischbach have completed a study [2]comparing the 'randomness' in pi
to that
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