<div>Yes indeed it's fascinating, and I could write all day about what I **did** do (in 92 ish?) but which was already obseleted by porting to a platform with a better ("vetted by randomness geeks") library.</div>
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<div>But I think the idea ("hmmm") was that the bit of paper fluttering down from the keypunch to the (sufficiently wide-mouthed) wastebasket might be a better source of shuffling than anything programmatic. Like, a poor-man's geiger-counter. (At the Savannah River plant, I think my dad could have wired up an actual geiger counter...). So the macroscopic but small scale aerodynamics would be the randomness generator, and I woulnd't have minded at all the problem of mapping the distribution (of letter frequency in my FORTRAN programs, say) to Uniform, programmatically, that's easily in my scope.
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<div> </div>
<div>But effectively reading from the wastebasket seemed like a stopper. Today I could do it with a vacuum hose and OCR, but at the time it seemed like too much trouble :-)</div>
<div> </div>
<div>Peter<br> </div>
<div><span class="gmail_quote">On 10/17/07, <b class="gmail_sendername">Robert G. Brown</b> <<a href="mailto:rgb@phy.duke.edu">rgb@phy.duke.edu</a>> wrote:</span>
<blockquote class="gmail_quote" style="PADDING-LEFT: 1ex; MARGIN: 0px 0px 0px 0.8ex; BORDER-LEFT: #ccc 1px solid">On Wed, 17 Oct 2007, Peter St. John wrote:<br><br>> If someone had thought of a way to queue up and read tiny bits of paper
<br>> science would have advanced a decade :-)<br><br><essay length="short"><br><br>Ahh, but but but...<br><br>Let us grant that a bucket full of such dots can be shaken to where the<br>order that they are drawn is unpredictable (note well that I don't say
<br>"random" as I'm not convinced that the word means anything beyond an<br>abstraction in this Universe). Not unlike the little bingo or lottery<br>ball machines, they get all mixed up and after enough shuffling or
<br>shaking one can attain a high degree of mixing that makes them<br>unpredictable and may make them "random" within testable resolution on<br>the source.<br><br>However, is there any guarantee that 0-9 are uniformly distributed in
<br>the original shuffled sample? There is not. If you punched out letters<br>drawn from (say) a dictionary, would they be uniformly distributed? In<br>no way. Would the results of using shuffled strings of either one be
<br>likely to produce acceptable digits in a uniform random distribution?<br>No.<br><br>And in any event, the "randomness" comes from the shuffling, not the<br>source per se. So even if one deliberated punched all the numbers out
<br>of many cards and ensured uniform populations of each digit in the<br>shuffled population (and drew from that population with replacement and<br>additional shuffling, so that one doesn't immediately introduce bias
<br>after the first digit is drawn) it is the shuffling that matters. If it<br>is good, then you don't need "a population" -- you just need one each of<br>the ten digits and a good shuffler, as you draw, replace, shuffle, draw.
<br><br>So one is then back to -- how to make a good shuffler? Physically it<br>isn't too easy, actually -- there having many balls gives one the<br>ability to average over the subtle differences between balls that might
<br>produce slight deviations from uniformity in the shuffle/draw.<br>Numerically you're right back where you started, because a good shuffle<br>requires a good random number generator (or at least a good source of<br>
unpredictability/entropy).<br><br>This is a non-trivial problem, actually. There are numerous physical<br>sources of "randomness" or "entropy" out there in the world, but many of<br>them produce not random bits with an equal probability of 0 and 1 but
<br>"random" bits with some unequal probability of 0 and 1. Some of them<br>have autocorrelation times associated with the drawing process. Some of<br>them have long term occult periodicities in the signals. Even with
<br>physical RNGs, about all one can really say is ex post facto either the<br>strings of random bits they produce pass various statistical tests for<br>randomness, or they don't.<br><br>Throw in Shannon's theorem and some of its consequences -- entropy
<br>theorems applied to code -- and "random" number generation (oxymoron<br>that it is) is one of the most interesting subjects on the planet, as is<br>testing and their various applications.<br></essay><br>
<br> rgb<br><br>--<br>Robert G. Brown<br>Duke University Dept. of Physics, Box 90305<br>Durham, N.C. 27708-0305<br>Phone(cell): 1-919-280-8443<br>Web: <a href="http://www.phy.duke.edu/~rgb">http://www.phy.duke.edu/~rgb</a>
<br>Lulu Bookstore: <a href="http://stores.lulu.com/store.php?fAcctID=877977">http://stores.lulu.com/store.php?fAcctID=877977</a><br></blockquote></div><br>
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