Path: bga.com!news.sprintlink.net!hookup!yeshua.marcam.com!zip.eecs.umich.edu!newsxfer.itd.umich.edu!gumby!wupost!spool.mu.edu!torn!nott!cunews!freenet.carleton.ca!freenet3.scri.fsu.edu!mailer.acns.fsu.edu!not-for-mail From: jac@ds8.scri.fsu.edu (Jim Carr) Newsgroups: sci.physics Subject: Re: Real random numbers Date: 24 Jun 1994 15:56:03 -0400 Organization: Supercomputer Computations Research Institute Lines: 39 Message-ID: <2ufdoj$h69@ds8.scri.fsu.edu> References: <2u69cp$46q@asterix.uni-muenster.de> NNTP-Posting-Host: ds8.scri.fsu.edu Keywords: real random numbers , Monte Carlo simulation In article <2u69cp$46q@asterix.uni-muenster.de> hoppep@asterix.uni-muenster.de (Peter Hoppe) writes:
4-bit random numbers (0,1,...,15) have been produced from thermal noise by a complicated method. Since the production is not due to a determining algorithm (of a pseudo random generator) these numbers are 'real random numbers'. So a priori there could not be any periodicity in the number series. The equipartition has been checked by the "chi-square-test" and the correlations by the "serial-test" [1]. Both equipartition and correlations fulfill the theoretical expectations very good.
[1] D. Knuth, The Art of Computer Programming, Vol. II, Addison-Wesley, 1969
There are much tougher tests for random numbers than these, particularly if they are to be used for Monte Carlo where the numbers are used as m-tuples. The tests you really need to make are the ones George Marsaglia calls the 'monkey test' and the 'birthday test', as well as the m-tuples test. The first two are generalizations of the well known statistics problem of the monkey typing Shakespeare and of coincident birthdays in a group of people. They are tough to pass. The problem as I see it is that 4-bit numbers do not generate much variability, so you will really need m-tuples of 4-tuples of these. This increases the chance that long range correlations will catch up to you when you least want them. I am sure George would be interested in this, however, since they have been looking at ways to incorporate physical noise that is truly random into the very sophisticated generators like the combination of lagged fibonacci with congruential. The problem is that noise is seldom random enough, according to talks he has given. -- James A. Carr <jac@scri.fsu.edu> | "It's never confusing though, http://www.scri.fsu.edu | because ultimately it all fits Supercomputer Computations Res. Inst. | -- it's just cockeyed and fits Florida State, Tallahassee FL 32306 | and is fire." - Norman Maclean