Geometrization Conjecture Coming to a Runway Near You

The same post at Quomodocumque has this completely odd video of an interview with William Thurston and fashion designer Dai Fujiwara. Apparently, Thurston provided the inspiration for Issey Miyake’s fall fashions, “8 Geometry Link Models as Metaphor of the Universe”.

You can see the finale of their Paris fashion show here, including Thurston joining Fujiwara on stage. (The whole thing didn’t seem real to me until I saw Thurston walk on-stage in that clip. I have no idea what the designs have to do with the Geometrization Conjecture, but the title of the show certainly suggests that’s what they had in mind.)

The proof of the Geometrization Conjecture was sketched by Perelman (it implies the Poincare Conjecture). I wonder if the brief burst of publicity in the wake of Perelman led to the show.

Legal System Versus Probability

This article in the Washington Monthly tells a startling story of a conflict between the legal system and probability. DNA tests use a certain number of genetic markers to match DNA samples. The samples are well-short of a complete sequencing, which means any randomly selected person has a 1 in a million chance of matching. When DNA testing is used on a few suspects, then the chances of matching an innocent person are pretty low. But now, governments are compiling large databases of DNA and data mining them for matches, which radically increases the odds of matching an innocent person. This would not necessarily lead to false convictions as long as juries are made aware of the consequences, but at least one judge ruled evidence that a DNA match happened by mining a database inadmissible: the jury never heard it.

(In the particular case of the article, the victim was raped and murdered, and the defendant was found in a database of sex offenders. The article claims the correct probability of a match in this case is 1 in 3. It’s not clear from the article if this is the unconditional probability of being found in a database of that size, or the conditional probability given that it was a database of sex offenders.)

Via Quomodocumque.

Lukac’s Characteristic Functions

I was curious to see the proof for this theorem, so I’ve started reading Lukac’s Characteristic Functions. It’s a good book, but as written expresses absolutely no interest in the subject of probability. While about a subject that is interesting because of its connection with probability — a characteristic function is the Fourier transform of a probability distribution function — the discussion is entirely in terms of characteristic functions. For example, studying the characteristic functions for infinitely divisible distributions is motivated by the question of which characteristic functions have the property that every n-th root is also a characteristic function.