Re: Pi: Less Random Than We Thought
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 <cyphrpunk@gmail.com> wrote:
This doesn't really make sense. Either the digits are random or they are not. You can't be a little bit random. Well, you can be, but the point is that you either pass the test or you don't.
If pi's digits fail a test of randomness in a statistically significant way, that is big news. If they pass it, then there is no meaningful way to compare them with another RNG that also passes. It's just a statistical quirk due to random variation as to which will do better than another on any given test.
The bottom line is still that either an RNG passes the tests acceptably or it does not. From what they say (or don't say), pi does pass. It doesn't make sense to say that other RNGs do better.
CP
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Cypherpunk: While I respect your forthrightness you are unfortunately wrong. Read the chapters on Randon Mumber generation from "Numerical Recipes in C" and you get just a small glimpse of how sticky the issue is, particularly when it comes to computers (which are innately non-random, by the way). As a very simple example, imagine that after 10 billion digits we found that the "average" value was actually 5.000000001. This would make it, in your book, not random at all, but I suspect that for almost many uses it would be random enough. And then, imagine that the cumulative average of the digits of pi oscillated around 5 (to one part in a zillion) with a period of 100 Billion...is this random enough for you? 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." I was hoping Cordian would grumpily reply...he's a number theorist or something. -TD
From: Sarad AV <jtrjtrjtr2001@yahoo.com> To: cyphrpunk@gmail.com CC: cypherpunks@al-qaeda.net 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 some annoying subsequences of pi in it which are far from random.
Sarad.
--- cypherpunk <cyphrpunk@gmail.com> wrote:
This doesn't really make sense. Either the digits are random or they are not. You can't be a little bit random. Well, you can be, but the point is that you either pass the test or you don't.
If pi's digits fail a test of randomness in a statistically significant way, that is big news. If they pass it, then there is no meaningful way to compare them with another RNG that also passes. It's just a statistical quirk due to random variation as to which will do better than another on any given test.
The bottom line is still that either an RNG passes the tests acceptably or it does not. From what they say (or don't say), pi does pass. It doesn't make sense to say that other RNGs do better.
CP
Yahoo! Mail Stay connected, organized, and protected. Take the tour: http://tour.mail.yahoo.com/mailtour.html
participants (2)
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Sarad AV -
Tyler Durden