Category: Science

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.

The presidents of the United States have had, collectively, almost half again as many sons as daughters ((148 to 102 if I’ve counted correctly). Far more strikingly—because the sample size is so much larger—the people listed in Who’s Who have, collectively, about 15% more sons than daughters. (For the latter statistic, I rely on the testimony of the biologist Robin Baker, writing in his remarkable book Sperm Wars.)

Why do high-status parents have more sons? Presumably because high-status sons can give you lots of grandchildren (Baker points to an ex-emperor of Morocco with 888 children). A daughter is far more likely to give you about the average number of grandchildren. On the other side, low-status boys die childless more often than low-status girls. (On average, boys and girls have the same number of offspring—they must, because each offspring has one mother and one father. But girls are clustered around the average, while boys veer off to both extremes.)

So if you want a lot of grandchildren (and whether you want them or not, your genes do) you’ll want sons if you’re near the top of the status heap and daughters if you’re near the bottom.

Now: What’s the mechanism to accomplish all this? One suggestion from the biologists—and one that makes very good sense to an economist—is that a pregnant woman’s body, in deciding how much to invest in nourishing the embryo, takes account of the parents’ status and the embryos’ sex. High status mothers give more nourishment to male embryos; low status mothers give more nourishment to female embryos; better nourished embryos are more likely to be born alive.

How can a process as involuntary as nourishing an embryo respond to conscious information like the status of the father? Well, how can a process as involuntary as sweating with fear respond to conscious information like the approach of a tiger? Clearly this kind of thing happens all the time. More fundamentally, decisions like how much to nourish your embryo are among the most important economic problems the body ever faces. Is it really plausible that the body would simply throw away highly relevant information when it’s making a decision like that?

Incidentally, this ties into my earlier post about stress and daughters. There is evidence that stressed parents, like low-status parents, have more daughters, presumably for the same reason: stressful circumstances, like low-status parents, tend to depress reproductive success.

Annual U.S. Deaths Due to the Flu: approx 36,000.
Annual U.S. Deaths Due to Anthrax: ~1.

Spending on R&D to fight Flu: $283 million.
Spending on R&D to fight Anthrax and other biological agents: $5.6 billion.

Will your children see an exponential growth explosion? Here is Robin Hanson’s latest:

A revised postcard summary of life, the universe, and everything, therefore, is that an exponentially growing universe gave life to a sequence of faster and faster exponential growth modes, first among the largest animal brains, then for the wealth of human hunters, then farmers, and then industry. It seems that each new growth mode starts when the previous mode reaches a certain enabling scale. That is, humans may not grow via culture until animal brains are large enough, farming may not be feasible until hunters are dense enough, and industry may not be possible until there are enough farmers.

Notice how many “important events” are left out of this postcard summary. Language, fire, writing, cities, sailing, printing presses, steam engines, electricity, assembly lines, radio, and hundreds of other “key” innovations are not listed separately here. You see, most big changes are just a part of some growth mode, and do not cause an increase in the growth rate. While we do not know what exactly has made growth rates change, we do see that the number of such causes so far can be counted on the fingers of one hand.

While growth rates have varied widely, growth rate changes have been remarkably consistent — each mode grew from one hundred and fifty to three hundred times faster than its predecessor. Also, the recent modes have made a similar number of doublings. While the universe has barely completed one doubling time, and the largest animals grew through sixteen doublings, hunting grew through nine doublings, farming grew through seven and a half doublings, and industry has so far done a bit over nine doublings.

This pattern explains event clustering – transitions between faster growth modes that double a similar number of times must cluster closer and closer in time. But looking at this pattern, I cannot help but wonder: are we in the last mode, or will there be more?

If a new growth transition were to be similar to the last few, in terms of the number of doublings and the increase in the growth rate, then the remarkable consistency in the previous transitions allows a remarkably precise prediction. A new growth mode should arise sometime within about the next seven industry mode doublings (i.e., the next seventy years) and give a new wealth doubling time of between seven and sixteen days. Such a new mode would surely count as “the next really big enormous thing.”

Read the whole thing. Yes you should pay attention to these ideas; even if their chance of being right is small, their expected value in terms of importance is high. That being said, I sometimes tease Robin for offering us a secular version of Pascal’s Wager.

Note that Robin makes Arnold Kling look like a pessimist.

The $10 million X-Prize has been won.

To win the X-Prize, a privately funded team had to fly a craft at least 100 kilometers high carrying a payload equivalent to three humans, successfully land and then repeat the feat within two weeks.

With this accomplishment, the SpaceShipOne team may have cracked more than space, as it appears that, just as planned, the X-Prize competition has cracked open the door to space tourism.

Sir Richard Branson recently announced plans to use the SpaceShipOne design for a space tourism company to be called Virgin Galactic.

Rutan, Allen and Branson attended the X-Prize’s victory flight.

A cotton candy-like cloud of simple sugar drifts in the unspeakably cold center of the Milky Way about 26,000 light years away, offering a remote, yet tantalizing, hint of how the building blocks of life may have reached Earth billions of years ago.

This frigid cloud is composed of molecular glycolaldehyde, a sugar that, when it reacts with other sugars or carbon molecules, can form a more complex sugar called ribose, the starting point for DNA and RNA, which carry the genetic code for all living things.

The simple sugar molecule glycolaldehyde was found in this dust and gas cloud, Sagittarius B2. The colors indicate radio emissions of different strengths.

Astronomers have known about sugar in space for some time, but new research reported last week in the Astrophysical Journal Letters showed that gaseous sugar could exist at extremely low temperatures, as are found in regions on the fringes of the solar system where comets are born.

Here is the full story. Here is the press release.

Here is a contrasting story about deforestation:

Do cows improve the view? That is a question which interests the Swiss government, given that it subsidises farmers heavily to graze their cows in the mountains. One justification for the subsidy is that cows eat young trees, and fewer trees mean better vistas of the sort beloved by tourists. But just how much do cows improve the view and where do they provide most value for money?

To help answer these questions, Kai Nagel and his colleagues at the Swiss Federal Institute of Technology, in Zurich, have developed computer models of the Alps and populated them with virtual tourists (or “autonomous agents” in computer-speak) that can wander the electronic landscape. The agents are programmed to behave, as far as possible, like real tourists, and to record their impressions as they go.

Here is the full story. I do not favor the heavy burden of Swiss agricultural subsidies, but it is rarely appreciated how much the “pristine” landscapes of that country owe to careful human planning. Thanks to James Barnett for the pointer.

British scientists are developing a robot that will generate its own power by eating flies.

The idea is to produce electricity by catching flies and digesting them in special fuel cells that will break down sugar in the insects’ skeletons and release electrons that will drive an electric current.

“Called EcoBot II, the robot is part of a drive to make “release and forget” robots that can be sent into dangerous or inhospitable areas to carry our remote industrial or military monitoring of, say, temperature or toxic gas concentrations,” New Scientist magazine said on Wednesday.

Chris Melhuish and his team, who are developing the robot, have to manually feed the flies to EcoBot II because they are still designing some type of pump to suck the insects into it.

And here is an advantage to flies which perhaps you never thought of before:

“One of the great things about flies is that you can get them to come to you,” he said.

Hence the downside of the fully autonomous robot: it will have to use sewage or excrement to attract the flies and is bound to smell appalling.

Here is the link, and thanks to Yana for the pointer.

There are plenty of new science reports, here is a sample:

1. The Americas may have been settled by Pacific navigators in early times.

2. Global suicide takes more lives than war and murder put together.

3. Medieval man was almost as tall as modern American man, and the eighteenth century was a low period for height in the Western world.

4. Being out of shape is a better predictor of heart disease than is being overweight.

Thanks to Cronaca.com for the pointer on the third item.