The topic is entanglement, and the headline reads Quantum Quirk May Give Objects Mass.

In my post about Alexandre Grothendieck, I pointed readers to the streaming video of a brilliant lecture by Colin McLarty. I ought also have pointed to McLarty’s even more brilliant paper as well.

Alexandre Grothendieck, born in 1928, was the greatest mathematician of the twentieth century and arguably the greatest of all time. Between 1958 and 1972 he reformulated the fundamental concepts of geometry —concepts like point, space and covering (as in, “the northern and southern hemispheres cover the entire earth”) so completely that it is no longer possible to imagine what geometry would be about if Grothendieck had never lived.

In this endeavor, he collaborated with several of the world’s finest mathematicians who put their own research agendas on hold for the privilege of attending Grothendieck’s daily seminars, fleshing out his ideas, and committing them to paper. The resulting documents, totalling over 10,000 pages, revolutionized geometry, arithmetic and algebra by viewing all of mathematics from a height of abstraction at which subjects blend together, every unnecessary detail is stripped away, and essential truths are almost automatically revealed.

Today he lives alone in a cabin in the Pyrenees, tending a garden and refusing visitors.

It’s been over 30 years since Grothendieck’s abrupt retreat from civilization, and for most of that time I’ve been waiting for someone to write his biography. This is, after all, a compelling story. Its hero is a brilliant eccentric described by everyone who’s known him as a man of indescribable charisma. (It was this legendary charisma, no less than the brilliance and clarity of the Grothendieck vision, that lured so many first-rate mathematicians away from their own research for the sake of the grand collaboration.) Besides his mathematical work, he’s given us several thousand pages of introspective autobiography, philosophy and theology, including a several-hundred page proof of the existence of God. (The thrust of the argument, as I understand it: We all have dreams, don’t we? And what could dreams be, if not messages from God? And how could God send us messages if he didn’t exist? Q.E.D.)

It’s a story touched by many of the defining events of the twentieth century: a father who died in Auschwitz, a leadership role in the antiwar and counterculture movements of the late sixties, and a career abandoned at its height partly to protest NATO’s role in the funding of mathematical research—and then, to add to the drama, decades of isolation punctuated by cryptic pronouncements and long rambling screeds that, in the opinion of many former friends and colleagues, indicate he’s gone stark raving mad.

The telling of this tale is long overdue but it looks like the waiting is over. Allyn Jackson’s superb two-part article has appeared here and here, and a full length book (by Winfried Scharlau) is apparently in the works. There is also a brilliant lecture by Colin McLarty on Grothendieck’s philosophy of mathematics. Both McLarty’s and Jackson’s pieces require some mathematical sensibility. It remains to be seen whether someone will distill the Grothendieck story down to the comfort level of, say, the average New Yorker subscriber while remaining true to the spirit and breathtaking beauty of the Grothendieck revolution.

Women living with their male partners are more likely to give birth to boys than are single women. The “marriage effect” (strictly speaking cohabiting effect) is small (51.5% boys in the cohabiting group versus 49.9% in the single group) but statistically significant. The marriage effect combined with an increase in the number of single mothers may be large enough to explain the decline in male births observed in many developed countries.

The cads versus dads theory had predicted the opposite result. Cads should have more sons than dads because big cads, by their very nature, have good male genes that are ideally passed on to little cads.

Earlier Steve noted that high status parents are more likely to have sons which makes evolutionary sense because succesful males are more likely to have children than unsuccesful ones while females are likely to have children regardless, so you want to specialize in boys when times are good and in girls when times are bad. The “marriage effect” could be an expectational consequence of the same logic. If women “know” that their male partners are unlikely to be around they know that they are more likely to have low-status in the future and thus should have girls.

I have not read the original research but it is easy to go wrong. Since girls cause divorce (and presumably also separation) it is critical to measure cohabitation before conception in order to distinguish “cohabiting causes boys” from “girls cause separation.” The research claims to measure cohabitation before “birth/conception” but retrospective bias could easily cause mothers to say that the father left before the birth (or before the child’s sex was known).

Here is an article from The Economist, here is a New Scientist piece that emphasizes different factors and here is the original research ($)

Here is a new way to get at the truth:

Drazen Prelec, a psychologist at the Massachusetts Institute of Technology in Cambridge, US, has devised a scoring system, or “Bayesian truth serum” to encourage people to divulge their honest opinions…

Prelec says if people truly hold a particular opinion, they tend to give higher estimates that other people share it. So if someone did have more than 20 recent sexual partners – but lied about it – that person would probably assume a higher rate of such behaviour in general than someone who had not had so many partners…

For example, he describes a situation where two paintings are viewed by a group of 10 people who are then asked, privately, to pick their favourite. Seven people say they prefer painting A, while three vote for painting B. If, on the second question, all 10 people said they thought everyone else would prefer painting A, then those three people expressing a personal preference for painting B might be thought of as a safer bet for having told the truth. That is because, argues Prelec, despite what they thought was more popular, those individuals still chose the other painting.

In other words, thinking that others are disagreeing with you predicts truthtelling. Prelec claims that the formula works best on groups of ten or greater.

I can, of course, think of caveats. The group must be your peers rather than hated rivals; conformity often brings social benefits but not always. But nonetheless I expect there is a grain of truth here.

Do you recall the old saying? “The surest way to get good information from a person is to ask for advice.”

Here is the full story.