How did Obama do among Prius owners?

Here's a question: Did Obama do better among African-Americans or Prius owners?

The consensus is that he did better among African-Americans. (96% of African-Americans who voted voted for him, which is a pretty high bar.)

But how would one go about estimating how he did among Prius owners?

Innumeracy and the NBA draft lottery

I don't really know much about basketball. But this New York Times article suggests that the first pick in the NBA lottery might not be worth much this year, and then goes on to say:

But history suggests that he [Rod Thorn, president of the New Jersey Nets] will not have that decision to make. Since 1994, the team with the worst record has won the lottery only once — Orlando in 2004.

Here's how the NBA draft lottery works. In short: there are thirty teams in the NBA. Sixteen makes the playoff. The other fourteen are entered in the draft lottery. Fourteen ping-pong balls (it's a coincidence that the numbers are the same) are placed in a tumbler. There are 1001 ways to pick four balls from fourteen. Of these, 1000 are assigned to the various teams; the worse teams are assigned more combinations. 250 are assigned to the worst team, 199 to the second-worst team, "and so on". (It's not clear to me where the numbers come from.)

Then four balls are picked. The team that this set corresponds to gets the first pick in the draft. Those balls are replaced; another set is picked, and this team (assuming it's not the team already picked) gets the second pick. This process is repeated to determine the team with the third pick. At this point there's an arbitrary cutoff; the 4th through 14th picks are assigned to the eleven unassigned teams, from worst to best. The reason for this method seems to be so that all the lottery teams have some chance of getting one of the first three picks, but no team does much worse than would be expected from its record; if the worst team got the 14th pick they wouldn't be happy.

So the probability that the team with the worst record wins the lottery is one in four, by construction; this "history suggests" is meaningless. (And the article even mentions the 25 percent probability!) This isn't like situations within the game itself where the probabilities can't be derived from first principles and have to be worked out from observation.

Also, let's say we continued iterating this process to pick the order of all the lottery teams. How would one expect the order of draft picks to compare to the order of finish in the league? I don't know off the top of my head.

On swashbuckling experimentalists

Chad Orzel, physicist, writes why I'd never make it as a mathematician. He calls himself a "swashbuckling experimentalist" and says that he doesn't like thinking too hard about questions of convergence and the like. This is in reference to Matt Springer's most recent Sunday function, which gives the paradox:

1 - 1/2 + 1/3 - 1/4 + ... = log 2

1 - 1/2 - 1/4 + 1/3 - 1/6 - 1/8 + ... = (log 2)/2

I find that I tend to act "like a physicist" in my more experimental work. Often I'm dealing with the coefficients of some complicated power series (usually a generating function) which I can compute (with computer assistance) and don't understand too well. Most of the time the things that "look true" are. This work is, in some ways, experimental, which is why it's tempting to act like a physicist.

Oh, yeah, I graduated today.

Are you smarter than a Fields medalist?

Take the Economist's numeracy quiz.

If you get all five questions right, you did better than Terence Tao.

The quiz is linked to this article, which states that people who are better at doing simple financial calculations seem to be less likely to fall behind on their mortgages.

Rather annoyingly, The Economist doesn't even tell you the names of the people who did the study. But it's Financial Literacy and Subprime Mortgage Delinquency: Evidence from a Survey Matched to Administrative Data, by Kristopher Gerardi, Lorenz Goette, and Stephan Meier. I will admit I have not read it, because it's 54 pages. (But yes, they controlled for income. My first thought was that maybe people who are better with numbers also tend to make more money.) Gerardi also writes for the Atlanta Fed's blog on real estate research.

The NIST Handbook of Mathematical Functions

The National Institute of Standards and Technology has released what you might call a "trailer" for the revised edition of Abramowitz and Stegun's Handbook of Mathematical Functions. The original version is available online (it's public domain).

The print version is called the NIST Handbook of Mathematical Functions, and is available in hardcover and paperback.

There is also, not surprisingly, an online version, the Digital Library of Mathematical Functions, which takes advantage of new technology: three-dimensional graphics, color, etc. Think MathWorld, but less idiosyncratic. It jsut went public today.

And it includes Stanley's Twelvefold Way, which makes me smile.

However, some small part of the original Handbook's primacy as a reference comes from the fact that in a list of papers which are alphabetical by last name of the first author, it usually comes first. The first editor of the new book is Frank Olver, so it won't have that advantage.

Fibonacci cutting board

The Fibonacci cutting board is being sold by 1337motif at etsy. (Note: that's pronounced "leetmotif"; it took me a while to figure it out.) It's basically this tiling, where a rectangle of size F_n by F_n+1 is repeatedly decomposed into a square of size F_n by F_n and a rectangle of size F_n-1 by F_n, but made of wood instead of pixels.

There's also the double Fibonacci cutting board made in a similar pattern.

1337motif is Cameron Oehler's work. Nost of his other work is inspired by video games; you can see it here. I wonder how often the cutting boards get used as cutting boards; at $125, if I had one I'd hang it on the wall and not get food on it. Personally, I'd like a Sierpinski triangle cutting board.

Proof Math is Beautiful

Proof Math is Beautiful is a blog of pictures which come from mathematics.