On Wed, 17 Oct 2007, Peter St. John wrote:
If someone had thought of a way to queue up and read tiny bits of paper science would have advanced a decade :-)
<essay length="short"> Ahh, but but but... Let us grant that a bucket full of such dots can be shaken to where the order that they are drawn is unpredictable (note well that I don't say "random" as I'm not convinced that the word means anything beyond an abstraction in this Universe). Not unlike the little bingo or lottery ball machines, they get all mixed up and after enough shuffling or shaking one can attain a high degree of mixing that makes them unpredictable and may make them "random" within testable resolution on the source. However, is there any guarantee that 0-9 are uniformly distributed in the original shuffled sample? There is not. If you punched out letters drawn from (say) a dictionary, would they be uniformly distributed? In no way. Would the results of using shuffled strings of either one be likely to produce acceptable digits in a uniform random distribution? No. And in any event, the "randomness" comes from the shuffling, not the source per se. So even if one deliberated punched all the numbers out of many cards and ensured uniform populations of each digit in the shuffled population (and drew from that population with replacement and additional shuffling, so that one doesn't immediately introduce bias after the first digit is drawn) it is the shuffling that matters. If it is good, then you don't need "a population" -- you just need one each of the ten digits and a good shuffler, as you draw, replace, shuffle, draw. So one is then back to -- how to make a good shuffler? Physically it isn't too easy, actually -- there having many balls gives one the ability to average over the subtle differences between balls that might produce slight deviations from uniformity in the shuffle/draw. Numerically you're right back where you started, because a good shuffle requires a good random number generator (or at least a good source of unpredictability/entropy). This is a non-trivial problem, actually. There are numerous physical sources of "randomness" or "entropy" out there in the world, but many of them produce not random bits with an equal probability of 0 and 1 but "random" bits with some unequal probability of 0 and 1. Some of them have autocorrelation times associated with the drawing process. Some of them have long term occult periodicities in the signals. Even with physical RNGs, about all one can really say is ex post facto either the strings of random bits they produce pass various statistical tests for randomness, or they don't. Throw in Shannon's theorem and some of its consequences -- entropy theorems applied to code -- and "random" number generation (oxymoron that it is) is one of the most interesting subjects on the planet, as is testing and their various applications. </essay> rgb -- Robert G. Brown Duke University Dept. of Physics, Box 90305 Durham, N.C. 27708-0305 Phone(cell): 1-919-280-8443 Web: http://www.phy.duke.edu/~rgb Lulu Bookstore: http://stores.lulu.com/store.php?fAcctID=877977 _______________________________________________ Beowulf mailing list, Beowulf@beowulf.org To change your subscription (digest mode or unsubscribe) visit http://www.beowulf.org/mailman/listinfo/beowulf
