Bad word problems

An example of a bad word problem, from Frank Quinn's article The Nature of Contemporary Core Mathematics, who is at Virginia Tech:

Bubba has a still that produces 700 gallons of alcohol per
week. If the tax on alcohol is $1.50 per gallon, how much tax will Bubba pay in amonth? [Set up and analyze a model, then discuss applicability of the model.]

I have given an example with obvious cultural bias because I am not sure I could successfully avoid it. At any rate students in my area in rural Virginia would think this problem is hilarious. We have a long tradition of illegal distilleries and they would know that Bubba has no intention of ever paying any tax.

New MathOverflow-type sites?

As some of you may have noticed, I spend lots of time at MathOverflow these days. This explains my lack of posting.

Actually, my lack of posting is also in part because of taking a break after finishing my PhD. But I am now trying to prepare for the Next Step. The Next Step is an academic job, in fact, so if you've been holding your breath and wondering if I got one, you can breathe again. Details will follow, but the job is technically not official yet, so I don't want to say where it is here. My productive efforts are going towards preparing for courses I'll be teaching, factoring my dissertation (warning: large PDF) into papers, and moving my worldly possessions.

I'm posting in order to mention two potential sites hosted on the StackExchange platform that might be of interest to my readers (and also to MO users); these are one for statistical analysis and one for mathematics. The mathematics site will differ from MathOverflow in being somewhat lower-level, which I think is valuable; one of the things that's plagued MathOverflow from the beginning is that there are frequently questions which are clearly below the level of the site but we have nowhere good to send these questions! Similarly, MathOverflow gets a lot of statistics questions that the MO readership isn't equipped to handle. (People try on the questions that are really about probability, but some are about the more "practical" side of statistics and we don't have too many experts in that.)

If you click on those links, you can "commit" to participating in one or both of these sites. The idea is that once enough commitments are made, the site will be launched. This is StackExchange's new model; their old model was that people paid to have a site hosted with the software. This is the model on which MathOverflow works -- using money from Ravi Vakil's research funds -- but they don't do this any more, because there were ghost sites. See a fuller explanation.

Euler's identity geometrized

How to explain Euler's identity using triangles and spirals, by Brian Slesinsky. (Euler's identity refers, here, to e^iπ = -1.) Uses the geometric interpretation of complex multiplication to explain this fact.

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.