Drunkard's Tennis and the Advice of Winners

Writing grants and teaching, not to mention trying to get some actual research done, has taken up a considerable amount of my time this quarter. I mean, sheesh, I’ve barely had any time to read! This has, of course, made me grumpy. So when the publisher of The Drunkard’s Walk: How Randomness Rules Our Lives by Leonard Mlodinow offered me a review copy of the book, I was very happy. I mean, I love probability and I love, um, well….you know 🙂
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School's Out For Summer…Almost

Today is the final exam for the course I’ve been teaching this summer. So I need some reading material for when I’m not watching the students take their exam. Here are two fun ones I just downloaded (one via Alea):

The Reverse of The Law of Large Numbers
Authors: Kieran Kelly, Przemyslaw Repetowicz, Seosamh macReamoinn
Abstract:The Law of Large Numbers tells us that as the sample size (N) is increased, the sample mean converges on the population mean, provided that the latter exists. In this paper, we investigate the opposite effect: keeping the sample size fixed while increasing the number of outcomes (M) available to a discrete random variable. We establish sufficient conditions for the variance of the sample mean to increase monotonically with the number of outcomes, such that the sample mean “diverges” from the population mean, acting like an “reverse” to the law of large numbers. These results, we believe, are relevant to many situations which require sampling of statistics of certain finite discrete random variables.


Complex and Unpredictable Cardano
Aurthor: Artur Ekert
Abstract: This purely recreational paper is about one of the most colorful characters of the Italian Renaissance, Girolamo Cardano, and the discovery of two basic ingredients of quantum theory, probability and complex numbers. The paper is dedicated to Giuseppe Castagnoli on the occasion of his 65th birthday. Back in the early 1990s, Giuseppe instigated a series of meetings at Villa Gualino, in Torino, which brought together few scattered individuals interested in the physics of computation. By doing so he effectively created and consolidated a vibrant and friendly community of researchers devoted to quantum information science. Many thanks for that!

Fun with Linda

For fun, answer the following in the comment section, without reading what others have left in the comment section:

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations.
Which is more likely?
1. Linda is a bank teller.
2. Linda is a bank teller and is active in the feminist movement.

Then read this.

Der Took Our Science N Engineering Jerbs!

Whatever you do, Mr. and Mrs. Joe and Mary America, make sure to tell everyone you know not to go into science and engineering! You see those who major in science and engineering are certain to not get jobs, because, as many commenters love to point out, all those jobs are being exported overseas! But wait, what is this:

The overall unemployment rate of scientists and engineers in the United States dropped from 3.2% in 2003 to 2.5% in 2006…according to data from the National Science Foundation (NSF) Scientists and Engineers Statistical Data System (SESTAT). This is the lowest unemployment rate measured by SESTAT since the early 1990s. It continues a trend of lower unemployment rates for scientists and engineers compared with unemployment rates in the rest of the U.S. economy.

Who knew? A degree in science and engineering actually appears to help your employment chances 🙂

Probability Intuition

Last quarter I taught discrete math. One component of the class was to cover some basic probability theory. On one of the homeworks we asked the following two questions about random five card poker hands:

  • Given that the hand contains an ace, what is the probability that the hand contains another ace?
  • Given that the hand contains the ace of diamonds, what is the probability that the hand contains another ace?

Without doing any explicit calculations, which of the above probabilities do you think will be larger?
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Is This a Mathematica Bug?

Miguel Pais points to an interesting behavior of Mathematica, where he plots the function which is the square of the square root of x. Now, if the domain of x is taken to be complex numbers, Mathematica’s behavior seems to me to be fine. But can anyone explain this behavior
as anything other than a bug?
Update: Oops. That wasn’t the one I was trying to paste. See what happens when I disconnect from the intertubes for a few days. How about this one: