Mathematics
edyong | April 24, 2008You all know the score. A train leaves one city travelling at 35 miles per hour and another races toward it at 25 miles an hour from a city 60 miles away. How long do they take to meet in the middle? Leaving aside the actual answer of 4 hours (factoring in signalling problems, leaves on the line and a pile-up outside Clapham Junction), these sorts of real-world scenarios are often used as teaching tools to make dreary maths "come alive" in the classroom.
Except they don't really work. A new study shows that far from easily grasping mathematical concepts, students who are fed a diet of real-…
jrosenhouse | April 20, 2008Well, I finished the first draft of the big Monty Hall book this past week. Still need to make some diagrams, and there's probably a fair amount of rewriting in my future, but the “words from nothing” phase is now over. Yay!
If anyone would care to give me some feedback, here is the first chapter. And also the bibliography for the book, to make the citations work out properly. I'm already aware of a number of typos, but don't hesitate to point them out anyway. I'm more interested in what people think of the tone and the style. Or anything else it occurs to you to comment on.
pontiff | April 15, 2008For those interested in accessing the arXiv on your iPhone, here is a web based iPhone page:http://arxiv.mobi. Sweet! This has been on my list of things to do, and now I can cross it off without having to do it myself!
pontiff | April 8, 2008Whatever 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…
pontiff | April 8, 2008Did the Monte Hall problem, trip up a huge number of psychologists? So claims this New York Times article. For a good detailed explanation see here. For even more detail see the actual paper.
pontiff | March 14, 2008Happy Talk like a physicist day, Happy Pi day, and Happy birthday dear uncle Albert.
So how does one talk like a physicist? I mean its hard for me to say, because I'm a physicist (or was, or am, or was molded into who I am by physicists.) But one can certainly sing like a physicist! Here is a song from grad school:Schrödinger's cat, is getting rather fat
He wants to play, must way for radon decay
Why is he trapped in that box (clap, clap, clap)
He would rather be alive than dead
Schrödinger's kitten, stuck their sittin'
Stuck in a superposition, a quantum mechanical prison
Why is she…
mikethemadbiologist | February 14, 2008A while back I came across a survey that reported more people would not vote for a 72 year-old than for a Mormon (which, given the bigotry against Mormons, is pretty remarkable). So, I wanted to figure out how likely it was that each of the remaining candidates would keel over in office. Who knows? Maybe the public does know something after all.
Using these mortality tables developed by the CDC, I figured out what the probably would be that a given candidate would die in office. Here are their ages upon assuming office for reference:
Obama: 47
Clinton: 60
Huckabee: 53
McCain: 72
And here'…
mikethemadbiologist | February 11, 2008Actually, the Mad Biologist's Rule of Base Ten Numbers is a pithier way of describing how certain numerical estimates or quantities are chosen based on little or no evidence. For example, when asked what an appropriate sample size is, someone will often respond, "ten." Of course, it might very well be that either nine or eleven are, in fact, the appropriate sample sizes, but we have a tendency when making shit up to focus on numbers divisible by five or ten, or, if we're dealing with really large quantities, increasing the quantities ten-fold (i.e., moving from 100 to 1000).
To give a…
mikethemadbiologist | February 4, 2008Rolex has rolled out a new watch that costs over $20,000. But there's a small flaw with the design:
What? You didn't see it? Let me help:
IIII!No.
IV.
Would you spend thousands of dollars to show the world that you're illiterate? This is what you would expect to see on a cheap knockoff bought on the street corner, not the original.
We need an FMT: a Fucking Moron Tax. It would be 100% of the value of the offending item, plus an additional 50% for making everyone else's brain hurt.
mikethemadbiologist | February 2, 2008One should be more informed, not less after watching a presidential debate. Jamison Foser, in an otherwise excellent post about the recent Democratic debate, makes one small error when he accuses CNN's Wolf Blitzer of being imprecise, when, in fact, Blitzer is just wrong:
Blitzer said, "I just want to be precise" -- but he was the opposite of precise. Clinton and Obama had given precise answers; Blitzer then restated their positions in less precise terms.
Here, let's look at all three statements again, in the order in which they were made:
OBAMA: "Part of it is paid for by rolling back the…
jrosenhouse | February 2, 2008Here's a little brainteaser to think about if the Super Bowl ends up being a bit dull. Imagine that you are standing at the baggage carousel at an airport waiting for your bag. A percentage x of the bags from your flight have already appeared on the carousel and yours is not among them. How large does x have to be before there is a probability greater than one half that your bag has been lost by the airline?
Of course, we need to make a few assumptions before we can attempt a proper mathematical analysis of the situation.
First, you can assume that the airline loses two percent of all the…
jrosenhouse | February 1, 2008Via Mark Chu-Carroll I just read this article, from the USA Today, about a mathematician at the University of Pennsylvania who believes that fractions have no place in the elementary and middle school mathematics curriculum:
A few years ago, Dennis DeTurck, an award-winning professor of mathematics at the University of Pennsylvania, stood at an outdoor podium on campus and proclaimed, "Down with fractions!"
“Fractions have had their day, being useful for by-hand calculation,” DeTurck said as part of a 60-second lecture series. “But in this digital age, they're as obsolete as Roman numerals…
mikethemadbiologist | January 29, 2008I know I've been attacking John Aravosis for his disdain of helping the poor. But he is right that the twenty percent of unelected Democratic convention delegates known as superdelegates is an undemocratic idea. Unfortunately, his arithmetic is a little off:
As you know, the Democratic nomination is going to be decided by how many delegates each candidate has. And as you also know, candidates win delegates by winning state primaries and caucuses (or at least placing in those states that don't award all the delegates to the top candidate). Well, what you may not have known is that your vote…
jrosenhouse | January 15, 2008We are all familiar with optical illusions. These are situations where your eyes misperceive the nature of some image or physical object.
For some time now psychologists and cognitive scientists have been discussing the reality of cognitive illusions. These are situations where people just don't reason properly about some readily described situation. The Monty Hall problem is sometimes described as an example of such an illusion, which, indeed, is why I have been thinking about this recently.
Below the fold is an interesting example drawn from elemenatry logic. I found it in the book…
jrosenhouse | January 12, 2008I just got back from six days in San Diego, participating in the annual Joint Mathematics Meetings. Why “Joint”? Because they are jointly sponsored by the two major American mathematical organizations. I refer, of course, to the Mathematical Association of America (MAA) and the Amercian Mathematical Society (AMS). (No Monty Python jokes, please.)
The Joint Meetings are one of the highlights of the mathematical calendar. It's an enormous affair, with several thousand mathematicians attending. That day in December when the book-length program arrives is an exciting one in my little corner…
pontiff | January 2, 2008Last 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?
I find this problem interesting because while I can do the calculation and…
pontiff | December 29, 2007Miguel 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:
jrosenhouse | December 18, 2007Meanwhile, the big Monty Hall book is slowly coming together. It seems like every day I discover new technical articles on the subject. Recently I thought to search through the PubMed database, looking for any articles that might have eluded the various other searches I have done. Most of the articles that came up were ones I already had in my file, but there were a few others that were new to me. I quickly rounded them up.
Then I noticed an article entitled, “Eye Movement Responses of Heroin Addicts and Controls During Word and Object Recognition,” published in the journal…
jrosenhouse | December 12, 2007Here is an interesting variation on the Monty Hall problem. For now I will simply present it cold, without indicating the context of where I saw it. Feel free to leave your proposed solutions in the comments. Everything from vague intuitions to hard-core Bayesian analysis is welcome.
Adam and Barney are contestants on a game show hosted by Monty Hall. Each player knows that the other one exists. They are confronted with three identical doors. One of the doors conceals a car, while the other two conceal goats. Both players select one of the doors, but neither player knows which door…
pontiff | December 2, 2007Books off the queue and lodge securely somewhere behind my eyes: "A Mathematician's Apology" by G.H. Hardy and "A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation" by Richard Bookstaber
A Mathematician's Apology by G.H. Hardy (with a foreword by C.P. Snow)I was really looking forward to reading this classic, since mathematicians certainly have a lot to apologize for. Sadly Hardy instead writes a fairly depressing defense of mathematics from a fairly dogmatic view of the subject. Of course, he has every right to this view (unlike me, who barely deserves…