mathematics

Persi Diaconis

Persi Diaconis is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Persi Diaconis rather than just read about it. In short: Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V.

Key takeaways

Persi Diaconis belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Persi Diaconis to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Persi Diaconis from memory before moving on to harder problems.

Reference excerpt

Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent 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.

Biography Diaconis left home at 14 to travel with magician Dai Vernon, and was awarded a high school diploma based on grades given to him by his teachers after dropping out of George Washington High School. He returned to school at age 24 to learn math, motivated to read William Feller's famous two-volume treatise on probability theory, An Introduction to Probability Theory and Its Applications. He attended the City College of New York for his undergraduate work, graduating in 1971, and then obtained a Ph.D. in mathematical statistics from Harvard University in 1974 and became a mathematical probabilist. According to Martin Gardner, at school, Diaconis supported himself by playing poker on ships between New York and South America. Gardner recalls that Diaconis had "fantastic second deal and bottom deal". Diaconis is married to Stanford statistics professor Susan Holmes.

Career Diaconis received a MacArthur Fellowship in 1982. In 1990, he published (with Dave Bayer) 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, in the Gilbert–Shannon–Reeds model of how likely it is that a riffle results in a particular riffle shuffle permutation, it takes 5 riffles before the total variation distance of a 52-card deck begins to drop significantly from the maximum value of 1.0, and 7 riffles before it drops below 0.5 very quickly (a threshold phenomenon), after which it is reduced by a factor of 2 every shuffle. When entropy is viewed as the probabilistic distance, riffle shuffling seems to take less time to mix, and the threshold phenomenon goes away (because the entropy function is subadditive). Diaconis has coauthored several more recent papers expanding on his 1992 results and relating the problem of shuffling cards to other problems in mathematics. Among other things, they showed 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. Diaconis has been hired by casino executives to search for subtle flaws in their automatic card shuffling machines. Diaconis soon found some and the horrified executives responded, "We are not pleased with your conclusions but we believe them and that's what we hired you for." He served on the Mathematical Sciences jury of the Infosys Prize in 2011 and 2012.

Recognition 1982 – Awarded a MacArthur Fellowship 1982 – Awarded the Rollo Davidson Prize 1990 – Invited Speaker of the International Congress of Mathematicians (ICM) 1995 – Elected to the National Academy of Sciences 1997 – Gibbs Lecturer, American Mathematical Society 1998 – Plenary Speaker of the ICM 2003 – Received an Honorary D. Sci. from the University of Chicago 2005 – Elected to the American Philosophical Society 2006 – Awarded the Van Wijngaarden Award 2012 – Awarded the Levi L. Conant Prize 2012 – Fellow of the American Mathematical Society 2013 – Received an Honorary Degree from the University of St Andrews 2014 – Recipient of Cahit Arf Lecture by Middle East Technical University

Works The books written or coauthored by Diaconis include:

Group Representations In Probability And Statistics (Institute of Mathematical Statistics, 1988) Magical Mathematics: The Mathematical Ideas That Animate Great Magic Tricks (with Ronald L. Graham, Princeton University Press, 2012), winner of the 2013 Euler Book Prize Ten Great Ideas about Chance (with Brian Skyrms, Princeton University Press, 2018) His other publications include:

"Theories of data analysis: from magical thinking through classical statistics", in Hoaglin, D.C., ed. (1985). Exploring Data Tables, Trends, and Shapes. Wiley. ISBN 0-471-09776-4. Diaconis, P. (1978). "Statistical problems in ESP research". Science. 201 (4351): 131–136. Bibcode:1978Sci...201..131D. doi:10.1126/science.663642. PMID 663642. Diaconis, P.; Holmes, S; Montgomery, R (2007). "Dynamical bias in the coin toss". SIAM Review. 49 (2): 211–235. Bibcode:2007SIAMR..49..211D. doi:10.1137/S0036144504446436.

See also Freedman–Diaconis rule Mathemagician Patience sorting Random walk

References

External links

Interview: Persi Diaconis discusses his life, magic and mathematics on the 7th Avenue Project radio show Persi Diaconis at the Mathematics Genealogy Project

Illustrations

Worked examples

Example 1 — a first encounter with Persi Diaconis

Start with the simplest possible case. Write down what Persi Diaconis claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Persi Diaconis before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Persi Diaconis ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Persi Diaconis

In research: Persi Diaconis appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Persi Diaconis in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Persi Diaconis is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1945 births, 20th-century American statisticians, 21st-century American statisticians, so understanding it makes those chapters shorter.
In everyday life: Look for Persi Diaconis outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Persi Diaconis in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Persi Diaconis means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Persi Diaconis out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Persi Diaconis in simple terms?

Persi Warren Diaconis (; born January 31, 1945) is an American mathematician of Greek descent and former professional magician. He is the Mary V.

Why does Persi Diaconis matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Persi Diaconis?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Persi Diaconis.