Mathematics
jrosenhouse | August 27, 2008The big Monty Hall book is working its way through production. Just received the proposed catalog copy on my destined for a Pulitzer masterpiece. Seems my book is, among other things, “light-hearted yet ultimately serious.” Why yes, come to think of it, I suppose it is!
But we're having a little trouble coming up with a mutually agreeable subtitle. My editor suggested, "Mathematics's Most Perplexing Brain Teaser.” I'm not so sure. “Perplexing” is not my favorite word in the world. Doesn't exactly roll off the tongue. And I don't like making nouns that end in s possessive. How do you…
edyong | August 22, 2008
On 14 January 2005, Lawrence Summers (right), president of Harvard University spoke of the reasons behind the disproportionate lack of women in top-end science and engineering jobs. Avoiding suggestions of discrimination, he offered two explanations - unwillingness to commit to the 80-hour weeks needed for top level positions and, more controversially, a lower "intrinsic aptitude" for the fields. According to Summers, research showed that genetic differences between the sexes led to a "different availability of aptitude at the high end".
For years, scientists have battled over the…
jrosenhouse | August 21, 2008As the Beijing Olympics comes to a close, let us take a moment to congratulate the United States Team for their third place finish in the recently completed International Mathematical Olympiad, held in Madrid. The U.S. Team included Alex Zhai, who obtained one of only three perfect scores in the entire competition.
China placed first, Russia took second. If you're feeling ambitious, go have a look at the problems (PDF format). Congratulations to the team!
jrosenhouse | August 20, 2008My account of the big creationism conference will resume shortly, but I really must take time out to discuss this article by Brian Hayes of American Scientist. He is discussing the Monty Hall problem, you see.
The story begins with this earlier article by Hayes. He was reviewing the recent book Digital Dice: Computational Solutions to Practical Probability Problems, by Paul Nahin. Having enjoyed Nahin's previous book Duelling Idiots and Other Probability Puzzlers, I suspect this new one is worth reading as well.
Hayes writes:
The Monty Hall affair was a sobering episode for probabilists.…
mikethemadbiologist | August 12, 2008As Jesse at Pandagon notes, even though the presidential race is stagnant in that the numbers aren't shifting much, that's not the same as the race being in a dead heat. This would be obvious, if your typical political reporter wasn't a mathematically illiterate moron.
Yes, I know that there's only one poll that matters and it's in November, blah, blah, blah. But based on the available poll data, there's no way this is a dead heat. Why? Because, in 40 out of 41 polls since Clinton dropped out of the race, Obama has led McCain. If they truly were in a dead heat (i.e., 50/50), the…
pontiff | August 1, 2008John Baez points to a remarkable mathematician (having being lead there by Alissa Crans):
You may have heard of the Mathematics Genealogy Project. This is a wonderful database that lets you look up the Ph.D. advisor and students of almost any mathematician. This is how I traced back my genealogy to Gauss back in week166.
I was feeling pretty proud of myself, too -- until I found someone who had two Ph.D. students before he was even born!
Yes indeed: our friend and café regular Tom Leinster is listed as having two Ph.D. students: Jose Cruz in 1959, and Steven Sample in 1965. At the time…
jstemwedel | July 30, 2008You've probably already heard the news last week that a study published in Science indicates that the gender gap between girls and boys in mathematical performance may be melting faster than the polar ice caps. The study, "Gender Similarities Characterize Math Performance" by Janet S. Hyde et al., appears in the July 25, 2008 issue of Science (behind a paywall). [1]
Hyde et al. revisit results of a meta-analysis published in 1990 (J. S. Hyde, E. Fennema, S. Lamon, Psychol. Bull. 107, 139 (1990).) that found negligible gender differences in math ability in the general population but…
jrosenhouse | July 29, 2008Continuing my perusal of the new Notices of the American Mathematical Society, I came across this review (PDF format) of John Allen Paulos recent book Irreligion: A Mathematician Explains Why the Arguments for God Just Don't Add Up. The review is by mathematician Olle Haggstrom. Paulos' book has been sitting on my shelf for a while, but I have not yet gotten around to reading it. My impression from flipping through it is that it will provide nothing new to people familiar with these arguments, but provides a decent overview for people only vaguely familiar with them.
Haggstrom's review…
jrosenhouse | July 28, 2008Via Mark Chu-Carroll, I just finished reading this article by mathematician Keith Devlin. He writes:
Let's start with the underlying fact. Multiplication simply is not repeated addition, and telling young pupils it is inevitably leads to problems when they subsequently learn that it is not. Multiplication of natural numbers certainly gives the same result as repeated addition, but that does not make it the same. Riding my bicycle gets me to my office in about the same time as taking my car, but the two processes are very different. Telling students falsehoods on the assumption that they can…
mikethemadbiologist | July 28, 2008Who woulda thunk it? A recent paper in PLoS One argues that the NIH review process uses far too few reviewers to claim the level of scoring precision that the NIH provides.
NIH grants are scored on a scale from 1.0 to 5.0, with 1.0 being the best; reviewers can grade in tenths of a point (i.e., 1.1, 2.3, etc.). The authors, using some very straightforward statistics, demonstrate that four reviewers could accurately assign whole integer scores (1, 2, 3...), but to obtain reliable scores with a precision of 0.01, a proposal would require 38,416 reviewers.
Not going to happen. Keep in mind…
jstemwedel | July 26, 2008Today Chad has an interesting post about attitudes among academics toward math and science versus the humanities and arts. The general attitude Chad sees on display in his academic milieu is that a gappy knowledge of art history or music or literature is something to be embarrassed about, but when it comes to innumeracy or scientific ignorance, intellectuals have no shame.
Chad writes:
Intellectuals and academics are just assumed to have some background knowledge of the arts, and not knowing those things can count against you. Ignorance of math and science is no obstacle, though. I have…
jrosenhouse | July 21, 2008The new issue of the Notices of the American Mathematical Society turned up in my mailbox today. It features an interesting, if slightly disturbing, editorial (PDF format) by CUNY mathematician Melvyn Nathanson. He wonders about how confident we can really be regarding the proofs that appear in our research journals:
But why the delay? Surely, any competent person can check a proof. It's either right or wrong. Why wait two years?
The reason is that many great and important theorems don't actually have proofs. They have sketches of proofs, outlines of arguments, hints and intuitions…
mikethemadbiologist | July 1, 2008Consider this a public service announcement. The NY Times has a very good op-ed piece explaining how mathematical epidemiology can be used to better understand bee colony collapse. The good news is (right now anyway) that it doesn't look like all of the colonies will die off.
pontiff | July 1, 2008One of the subjects of great debate in physics goes under the moniker of "the arrow of time." The basic debate here is (very) roughly to try to understand why time goes it's merry way seemingly in one direction, especially given that the many of the laws of physics appear to behave the same going backwards as forwards in time. But aren't we forgetting our most basic science when we debate at great philosophical lengths about the arrow of time? Aren't we forgetting about...experiment? Here, for your pleasure, then, are some of my personal observations about the direction of time which I've…
jrosenhouse | June 21, 2008Thanks to David Killoren for directing me to this excerpt from Bloggingheads. Science writers John Horgan and George Johnson spend a few minutes disucssing the Monty Hall problem. Johnson recently reviewed Leonard Mlodinow's book The Drunkard's Walk: How Randomness Rules Our Lives, which contains an explanation of te problem. After Johnson gets frustrated trying to explain the problem to Horgan, the following exchange takes place:
Johnson: I thought I understood this when I wrote the review. It's already eluded me again.
Horgan: This is like explaining the two-slit experiment in quantum…
pontiff | June 18, 2008David Brooks, has an op-ed in the New York Times about Tiger Woods and his astonishing string of triumphs in the golfing world (including last weekends U.S. Open which I watched the end of on both Saturday and Sunday: my wife was right he did make that last put.) Brooks piece waxes on and on about the Tiger's ability to concentrateAnd for that, in this day and age, he stands out. As I've been trying to write this column, I've toggled over to check my e-mail a few times. I've looked out the window. I've jotted down random thoughts for the paragraphs ahead. But Woods seems able to mute the…
pontiff | June 13, 2008Writing 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 :)
First of all, let me say that Mlodinow's book is preaching to the converted! A large portion of his book is devoted to showing how randomness…
pontiff | June 9, 2008Today 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):
arXiv:0803.3913: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…
pontiff | May 27, 2008For 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.
pontiff | May 8, 2008Two fans in Dodger stadium caught back to back fouls during a Mets game (and, almost as importantly, the Dodgers lost, woohoo!)
From the article:
But USC mathematics professor Kenneth Alexander used Wednesday's Dodger Stadium crowd size and game statistics -- 40,696 in attendance and a foul ball count of 48 -- to postulate the odds against Walker and Castro catching back-to-back fouls.
Calculating that only one of 18 pitches were fouled into the stands (other fouls stayed on the playing field) and factoring in the six fans sitting close by the pair, Alexander fielded the problem.
"One in 10…