Persi Diaconis
From Wikipedia, the free encyclopedia
Persi Warren Diaconis (born January 31, 1945) is an American mathematician and former professional magician. He is the Mary V. Sunseri Professor of Statistics and Mathematics at Stanford University. He is particularly known for tackling mathematical problems involving randomness and randomization, such as coin flipping and shuffling playing cards.
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[edit] Card shuffling
Professor Diaconis achieved brief national fame when he received a MacArthur Fellowship in 1982, and again in 1992 after the publication (with Dave Bayer) of a paper entitled "Trailing the Dovetail Shuffle to Its Lair" (a term coined by magician Charles Jordan in the early 1900s) which established rigorous results on how many times a deck of playing cards must be riffle shuffled before it can be considered random according to the mathematical measure total variation distance. Diaconis is often cited for the simplified proposition that it takes seven shuffles to randomize a deck. More precisely, Diaconis showed that it takes 5 shuffles before the total variation distance of a 52-card deck begins to drop from the maximum value of 1.0, and 7 shuffles before it drops below 0.5, after which it is reduced by a factor of 2 every shuffle.
Diaconis has coauthored several more recent papers expanding on his 1992 results and relating the problem of shuffling cards to other problems in mathematics.
More recently, some have questioned this result, arguing that the measure of randomness is too demanding, and that six shuffles are enough (Trefethen et al., 2000).[1]
Diaconis and colleagues have published follow-up papers, showing that the separation distance of an ordered blackjack deck (that is, aces on top, followed by 2's, followed by 3's, etc.) drops below .5 after 7 shuffles. Separation distance is an upper bound for variation distance.[2][3].
[edit] Biography
Diaconis left home at 14[4] to travel with sleight-of-hand legend Dai Vernon, and dropped out of high school, promising himself that he would return one day so that he could learn all of the math necessary to read William Feller's famous two-volume treatise on probability theory, An Introduction to Probability Theory and Its Applications. He returned to school (City College of New York for his undergraduate work graduating in 1971 and then a Ph.D. in Mathematical Statistics from Harvard University in 1974), learned Feller, and became a mathematical probabilist. He was awarded the Rollo Davidson Prize in 1982. In 2003 he received an honorary D. Sci. degree from the University of Chicago.[5]
[edit] Works
- Group representations in probability and statistics, Institute of Mathematical Statistics, Hayward, CA, 1988. vi+198 pp. ISBN 0-940600-14-5.
- "Theories of data analysis: from magical thinking through classical statistics", in Hoaglin, D.C et al. (eds) (1985). Exploring Data Tables Trends and Shapes. Wiley. ISBN 0-471-09776-4.
- D. Bayer and P. Diaconis (1992), "Trailing the Dovetail Shuffle to Its Lair", Annals of Applied Probability, volume 2, page 294–313.
- "Statistical problems in ESP research", Science, 201, p. 131-136
[edit] See also
[edit] Notes
- ^ Trefethen, L. N.; Trefethen, L. M. (2000), "How many shuffles to randomize a deck of cards?", Proceedings of the Royal Society, Series A 456 (2002): 2561–2568, doi:, ISSN 1364-5021
- ^ "Shuffling the cards: Math does the trick". Science News. Friday, November 7th, 2008. http://www.sciencenews.org/view/generic/id/38434/title/Shuffling_the_cards_Math_does_the_trick. Retrieved 14 November 2008. "Diaconis and his colleagues are issuing an update. When dealing many gambling games, like blackjack, about four shuffles are enough"
- ^ Assaf, Sami; Persi Diaconis, and K. Soundararajan. "A Rule of Thumb for Riffle Shuffling" (PDF). t.b.a.. http://www-stat.stanford.edu/~cgates/PERSI/papers/redblack.pdf. Retrieved 14 November 2008.
- ^ Lifelong debunker takes on arbiter of neutral choices
- ^ Salsburg, David, "The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century", Macmillan, 2002. ISBN 0805071342. Cf. p.224
[edit] External links
- Personal web site
- Profile from Indiana University
- Persi Diaconis at the Mathematics Genealogy Project
