Mathematics
cevans | March 10, 2010
A couple of years ago, I was poking around in a European art museum and came across an exhibit of exquisitely beautiful Eastern Orthodox religious paintings, "icons." Beyond being visually striking -- they have an austere, hieratic, distant quality -- they are also, I realized at the time, in a way, scientific.
Alright, I know, that's a wild statement. But hear me out.
A religious icon is more than a painting. It has a semiotic value that's highly codified, a language and practical purpose of its own that sets it apart from all the other representational art preceding our modern era of…
jrosenhouse | March 5, 2010From Yahoo News:
To shed light on why humans often fall short of the best strategy with this kind of problem, scientists investigated pigeons, which often perform quite impressively on tasks requiring them to estimate relative probabilities, in some cases eclipsing human performance. Other animals do not always share the same biases as people, and therefore might help provide explanations for our behavior.
Scientists tested six pigeons with an apparatus with three keys. The keys lit up white to show a prize was available. After the birds pecked a key, one of the keys the bird did not choose…
revere | March 5, 2010I was surfing the other night after a long day of working on the grant and ran across this announcement (hat tip infosthetics) of a new kind of city map, one you don't have to fold but can crumple up. It's made of Tyvek, a soft but durable waterproof material you can crease anywhere you want or just jam it into your pocket, any old way. They aren't available just yet but will be soon for London, Paris, New York, Tokyo and Berlin. I'm not sure what the market for city maps will be when everyone is carrying around smartphones with GPS, but it put me in mind of something completely different, a…
mikethemadbiologist | February 11, 2010While I'm not that big a fan of the project trying to find commonalities between economics and biology, largely because I think explanations of specific phenomena often reduce to those stupid fucking natural history facts, I was struck by this argument by economist Samuel Bowles about the assumption of optimality in the supposed tradeoff between income equality and economic output (italics mine):
Theoryland may be the only place the "equality-efficiency trade-off" really works. Just to prove it wrong, Bowles charts the concept on a whiteboard at SFI.
The vertical axis is economic output. The…
neurophilosophy | January 21, 2010OUR ability to use and manipulate numbers is integral to everyday life - we use them to label, rank, count and measure almost everything we encounter. It was long thought that numerical competence is dependent on language and, therefore, that numerosity is restricted to our species. Although the symbolic representation of numbers, using numerals and words, is indeed unique to humans, we now know that animals are also capable of manipulating numerical information.
One study published in 1998, for example, showed that rhesus monkeys can form spontaneous representations of small numbers and…
jrosenhouse | January 18, 2010
After a lengthy trip that involved not just planes and trains, but automobiles as well, I made it back from San Francisco in one piece. Yay! The conference was a big success, both mathematically and socially. Saw lots of old friends, which is, after all, the point of the conference, and also hopefully made some new ones.
As the sign says, this was the 2010 Joint Mathematics Meetings. The “Joint” refers to the joint sponsorship between the American Mathematical Society and the Mathematical Association of America. No Monty Python jokes, please. Roughly speaking, the AMS deals with the…
jrosenhouse | January 12, 2010Winter term classes started on Monday here at JMU, so I figure this is a good time to get out of dodge! I will be participating in the 2010 Joint Mathematics Meetings in San Francisco. Yay! And while I'm there I expect to take a quick train ride over to Oakland to visit the National Center for Science Education. Double yay!
Should be a fun trip. Regular blogging will resume when I return next week.
pontiff | January 12, 2010Another one from Michael, who spotted an article about one of my favorite mathematical words to use in everyday speech (much the chagrin of non-scientists) used in the Supereme Court of the United States:Supreme Court justices deal in words, and they are always on the lookout for new ones.
University of Michigan law professor Richard D. Friedman discovered that Monday when he answered a question from Justice Anthony M. Kennedy, but added that it was "entirely orthogonal" to the argument he was making in Briscoe v. Virginia.
Friedman attempted to move on, but Chief Justice John G. Roberts Jr.…
mikethemadbiologist | December 15, 2009In short: seven long years. A few months, when everyone was getting all het up about the observation that the rate of increase in the unemployment rate (the second derivative) was decreasing--that is, more and more people were losing jobs, but more and more wasn't growing as fast as it once was, that struck me as pretty thin gruel. Well, the implications of the first derivative--the change in unemployment--are pretty grim too. Mark Thoma:
How long will it take the unemployment rate to go back down to 5 percent? A rough estimate can be obtained by looking at the rate of decline in the…
jrosenhouse | December 10, 2009Science Magazine has now published a letter to the editor in response to the review, published in early October, of the big Monty Hall book. The letter writer is Simon Levay, of West Hollywood, California. Here it is in full:
In his Book Review “Two doors and a goat” (9 October, p. 231), the answer D. O. Granberg offers to the Monty Hall problem is incorrect. He assumes that the contestant should try to win the car. In reality, a car pollutes the environment and adds nothing to the car the contestant already owns. In contrast, a goat replaces noisy lawnmowers and provides milk, cheese, and…
revere | December 8, 2009An interesting blog post came my way yesterday about The Legend of the Boiling Frog. The gist of the post was that the legend was just that: urban (or science) legend. The post apparently started out with a query to a noted biologist who studies amphibians (I originally wrote, "a noted amphibian biologist" until I realized I didn't know if were any biologists who were amphibians):
"I am writing a weekly column for Die Zeit, Germany's major weekly paper, on scientific urban legends that my readers ask me about. Now you surely have heard the story of the boiling frog that is often told by…
jdupuis | November 9, 2009As graphic novels go, Logicomix: An Epic Search for Truth is every bit as good as Maus or Watchmen, if not quite as game-changing. The only other things out there that I can think of that are similar are Chester Brown's Louis Riel or Ho Che Anderson's King: A Comics Biography of Martin Luther King, Jr.
That's high praise and it's well deserved.
So what's Logicomix all about? The core is the story of Bertrand Russell's and his work -- the search for the foundations of mathematics, the most basic kind of truth: logic. His search takes us through the history of mathematics and philosophy in…
jrosenhouse | November 6, 2009Seriously! Go have a look.
It seems my book The Monty Hall Problem: The Remarkable Story of Math's Most Contentious Brainteaser made the list! And to think I wasn't planning to do a blog post today.
Browsing through the other entries, it looks like my reading list just got a bit longer. (Of course, they will have to get in line behind Stephen King's forthcoming magnum opus, coming out on Tuesday. But that's a different post...)
sciencewoman | October 29, 2009There's a few days left in our October DonorsChoose challenge, and even after that there are many more great projects out there waiting for our help.
A few weeks ago, wonderful educator-science-historian-cultural-studies-expert-mother-blogger Leslie Madden-Brooks responded to a plea to help fund some projects, and I was deeply moved by what she wrote to the classroom, so I wanted to share it with you...
I gave to this project because I had such a tough time learning math, and I wish I had been able to develop this kind of mathematical and critical thinking through reading interesting authors…
pontiff | October 21, 2009The Dutch book argument of Bruno de Finetti is an argument which is supposed to justify subjective probabilities. What one does in this argument is gives probabilities an operational definition in terms of the amount one is willing to bet on some event. Thus a probability p is mapped to your being willing to make a bet on the event at 1-p to p odds. In the Dutch book argument one shows that if one takes this operational meaning and in addition allows for the person you are betting to take both sides of the bet, then if you do not follow the axiomatic laws of probability, then the person…
jrosenhouse | October 19, 2009The trip to California went well. Suspiciously well, in fact, to the point where, even though I am now back home, I am still waiting for something to go wrong.
I first became suspicious during the two-hour drive over to Dulles Airport. There was no traffic. How odd. My rule of thumb when flying out of Dulles is to leave home five hours before flight time. That almost never happens, however, and usually it is closer to three and a half hours, which is really cutting it close. Heavy traffic only seems to occur when you are already in danger of missing your flight. Some corollary to…
jrosenhouse | October 15, 2009For my San Bernardino readers, I will be flying out to California tomorrow to deliever one of the keynote talks at the big MAA meeting. The talk will be at CSU San Bernardino at 9:00 am on Saturday morning. Nine am on a Saturday? They didn't mention that when they invited me!
The title of my talk is -- surprise! -- the Monty Hall Problem, Reconsidered. Should be a good time. See you when I return!
jrosenhouse | October 9, 2009And mostly favorably, too. You might need a subscription to read the review, alas. The reviewer is Donald Granberg, a sociologist (now retired) at the University of Missouri. He published several papers on the MHP during the nineties.
I liked this part of the review:
The author does a masterful job of tracing the problem back to its origin.
And this part:
One difficulty with word problems is their ambiguity. Rosenhouse does a superb job of reducing, if not eliminating, this source of endless argumentation with his canonical version.
Not to mention this part:
The Monty Hall Problem…
pontiff | October 9, 2009James Simons, he of the Chern-Simons form, and also, of late, from the hedge fund Renaissance Technologies Corporation, is retiring. The infamous Medallion fund was up last year, apparently, only a mere 80 percent.
Quite a feat, turning
into
pontiff | October 6, 2009Israel Gelfand, one of the great mathematicians of our age, apparently passed away yesterday at the age of 96. Check out the list of results that bear his name on the above linked Wikipedia page. Wow. Today I will, in his honor, think a bit more about Gelfand-Tsetlin basis and what they can be used for in quantum computing.