Update: I wonder whether you will agree that this (the first is audio) description of the differences between men and women is fair and insightful:
The original text follows: Sean Carroll from The Preposterous Universe at University of Chicago has kind of complained about a certain event - I would rather call it a non-event - at Harvard University.
As a Czech person, I find the reaction of some people particularly bizarre because in the Czech Republic, the people who would find Prof. Summers' reasoning controversial virtually don't exist - neither on the left wing, nor on the right wing. In Central Europe, you won't find too many people who think that the girls in average like math, physics, computers, and engineering as much as the boys. When democracy was being re-introduced into the former Eastern bloc, many of us were saying that the difference between the U.S. and Czechoslovakia is that in Czechoslovakia, we had the freedom of speech, while in the U.S., you also had the freedom after speech. ;-) Given the reaction of some people, maybe the difference was not too dramatic...
Incidentally, Summers' speech was not problematic for most Americans either - just look at the polls in various web newspapers. Also, some participants of that economic conference, such as Prof. Claudia Goldin and others, remained very rational and appreciated inspiring ideas.
I also know enough to guarantee that our president would never discriminate against the women or against the men - or against any minority or majority, for that matter. The reason why I am so sure about it is that I've heard his opinions in a relatively private environment of a party (see below) where the people are much more open than during their speeches at conferences. The President's web page with his statement is here:
When the daughter called the trucks "baby truck" and "daddy truck", different people may draw different conclusions. My conclusions based on this observation - but also many other, more detailed observations - are probably much closer to those of Prof. Summers' rather than those of Sean Carroll's, but no one has ever had any problems at Harvard for making different conclusions - since the origin of various behavioral differences and correlations remains largely an open question.
Actually, I still have not evaluated a simple integral. During a party for the new faculty who met with Prof. Summers a month+ ago, I've made many silly comments - for example I mentioned some statistics (who knows where I got them from) indicating that the average distance of the birthplaces of the husband and his wife in the U.S. is 400 miles or how much exactly it was. Prof. Summers asked what is the average distance if the distribution for both the husband and the wife is uniform over a disk of radius R. Well, the average distance is obviously R times a numerical constant as Prof. Summers remarked immediately - but I will have to calculate this constant. Summers' estimate was 1. ;-)
If you can integrate it quickly, the required integral (for R=1), derived in the polar coordinates, is:
- [ int (0,1,r) r int (0,1,s) s int (0,2.pi,f) sqrt(r^2+s^2-2.r.s.cos(f)) ] / [ int (0,1,r) r int (0,1,s) s int (0,2.pi,f) ]