Netflix (or should I say N3tfl1×) got the first season of Numb3rs this week, and I watched the first four episodes with mixed reactions. On one hand, any popular presentation of mathematics in the real world is a treat. But would it be so hard to cut some of the tritest Television Drama Moments in favor of a fuller explanation of the math and some acknowledgement of its limits?

The pilot episode is the best of these. Charlie the mathematician sees a map of attacks by a serial rapist and says, I cannot predict where the next attack will be but I can tell you where he lives. He takes a crash course in criminal psychology from his brother Don the detective, generates a model of the rapist’s behavior, and announces with 96% confidence that the rapist lives in the yellow zone on his map. (Later he insists that 96% is equivalent to certainty.) The map is the output of a single “equation”. In his place I would try several different models and see where their conclusions overlap, but there’s no sign that Charlie even tries varying the weights in his model.

Episode 4 “Structural Corruption” is nonsense. Charlie takes some measurements of a skyscraper’s movement in wind, and announces that the structure is flawed (without saying why he thinks so) but he doesn’t know how. He whips up a software model of the building — it would have to be a very simple model — and extrapolates what would happen in a major earthquake; and from this extrapolation, if I understand right, he infers that the flaw is in the foundation. Huh?

When economists draw supply-demand charts, they put the independent variable (price) on the vertical axis and the dependent variable (quantity) on the horizontal, contrary to the usual practice in physics and pure mathematics. It’s surprisingly hard for me to adjust my thinking to that: causality ought to go the other way, dammit.

In the popular press, I think, the independent variable is horizontal if it is time, otherwise (e.g. in bar charts comparing several populations) usually vertical.

What other conventions are Out There?

weird orbits (cited by John Baez)

rotating infrared Titan

I’ve been hearing on the radio a statement that hospital emergency rooms in California admit 25 thousand people every hour.

That’s equivalent to the entire population every eight weeks. –??–

Solutions to this [public goods] problem in the context of basic research are discussed at some length by Terence Kealey. (The Economic Laws of Scientific Research, New York: St. Martin’s Press, 1996) Knowledge of current cutting edge research – Kealey’s field is biology – is of considerable value, and it is not the sort of knowledge easily summed up on a one page memo. In practice, the knowledge is largely restricted to the people doing the research, both because they are the ones who can understand each other’s work and because they are the ones that the other researchers want to talk to. That makes such researchers valuable employees and consultants for firms and universities. While the researchers are unlikely to internalize the entire value of the information they produce, they may internalize enough so that the resulting income, along with nonpecuniary rewards of their work, make their research worth doing for them, and subsidizing for firms and universities. Kealey’s conclusion, looking at several different fields where government subsidies went from near zero to very substantial, was that there was no observable effect on the rate of progress in the field. One might interpret that as evidence that the cost of misallocation of resources through the political mechanism – diverting smart people into whatever field looked good in the popular imagination at the moment – at least balanced the benefit of the additional money.

David Friedman: Do We Need a Government? Emphasis added. (It’s easier to read in the December 2005 issue of Liberty, because David’s file uses nonstandard encoding for characters such as dash and apostrophe.)

I’ve redone the Wikipedia page on convex uniform tilings of Euclidean 3-space.

It occurs to me that one could enumerate the convex uniform tilings of flat, spherical and hyperbolic 3-spaces by an approach similar to what I’ve used to find fullerenes. First make a list of the vertex figures of convex uniform polyhedra: these are polygons which share the property that their corners lie on a circle. Then use a spiral search to build irregular polyhedra from these polygons. Whenever such a polyhedron’s vertices all lie on a sphere, you have the vertex figure of a candidate solution (some of which will fail for other reasons). The size of the sphere tells you whether and which way the relevant space is curved.

Has this been done?

Gunnerkrigg Court, a newish cartoon-strip set in a decidedly weird boarding school.

This is too good to leave buried in the comments: Loituma perform “Ievan polkka”

Sheldon Richman: Capitalism vs Capitalism

Something Positive: It’s entirely possible that you’ll appreciate this joke more than I can.

You don’t need me to tell you that MC Escher laid down some killer grooves. It’s high time someone made a movie of his last work: Snakes on a plane!