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The Poincare conjecture

Has the Poincare Conjecture been solved? Possibly. Read this recent news report about a new proof by an obscure Russian loner, Grisha Perelman. The Conjecture is one of the famous Millennium Problems in mathematics.

“This is arguably the most famous unsolved problem in math and has been for some time,” said Bruce Kleiner, a University of Michigan math professor reviewing Perelman’s work.

Here is the clearest statement I can find of what the whole thing means:

To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes — the sphere — there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe.

Or try this:

[the] work has huge implications for our understanding of partial differential equations. PDEs (as they are known in the trade) are the mainstay of physics and engineering. Mazur notes that physicists and engineers use PDEs to model everything from the flow of water to the buildup of heat in aircraft engines. “I would expect this work to have enormous applications in many fields of science,” he says.

There may also be applications for scientists studying DNA…Some kinds of DNA wrap themselves into knot formations that can be insanely difficult to decipher. But Mazur says Thurston’s classification [referring to related work] may provide a way to calculate the exact nature of any knot – so in theory it could be used to work out the structure of knotty DNA molecules.

The upper reaches of mathematics can often seem absurdly detached from life down here on planet earth, but Mazur points out that you can never know where things might lead. He cites the case of James Clerk Maxwell. In the late 19th century Maxwell worked out the equations of electromagnetism. “At the time it would have been easy to write off Maxwell’s ideas about invisible forces as a mystical abstraction,” Mazur says. But Maxwell’s work laid the foundations for the development of radio, and hence the communications revolution. Every time we turn on the TV or pick up a cellphone or log onto a WiFi system we are reaping the rewards of Maxwell’s equations.

Another bottom line: Perelman will receive a million dollars if his result stands up. Alex says this is another win for bounty hunters!

Oxford Encyclopedia of Economic History

Oxford University Press has just published a five-volume Encyclopedia of Economic History, edited by Joel Mokyr of Northwestern University.

Virginia Postrel offers a good review and some interesting details:

Did you know that the oldest records of chemical pest control date back 4,500 years, to Sumerian farmers who used sulfur compounds to kill insects and mites?

Or that a century ago, railroad companies accounted for half the securities listed on the New York Stock Exchange? (Before the railroads, with their huge demand for capital, securities markets traded almost entirely in government debt.)

Or that in 1850, shoemaking employed more workers in the United States than any other manufacturing business?

The past doesn’t look quite like we tend to picture it: many of the people who got rich from the Industrial Revolution were not industrialists, but landowners who held urban real estate or property with access to water power or mines. From 1880 to 1914, unions went on strike at least 50 times to stop American employers from hiring black workers. Above all, Professor Mokyr says, “in the Middle Ages and in classical antiquity, the destitute were the vast majority of the population.”

And what is the bottom line to economic history?

Professor Mokyr says: “There are certain unifying themes that you see everywhere. People have to make a living. People would rather have more than to have less. On the whole, they don’t behave stupidly. They do as well as they can under the circumstances. The variation is in the circumstances, in the richness and diversity of human economic institutions that have emerged over time.”

That is not all:

“Economic history,” Professor Mokyr writes in the preface, “covers nothing less than the entire material existence of the human past.” The encyclopedia gives theoretical economists a way to check their ideas against the realities of the past. “You guys can’t write these big, fancy models without looking at the details,” Professor Mokyr says.

I have not yet seen the volumes but most likely the set will not be surpassed anytime soon.

Vernon Smith on Iraq

Our colleague, Vernon Smith writes in today’s Wall Street Journal about privatizing the Iraqi economy, based in part on an idea pioneered in Alaska. See also my earlier post on why oil has been a curse to the discovering countries. Here are some key quotes:

For long-term success, the enormous task of nation rebuilding in Iraq requires attention to more than the creation of a political democracy. No matter how well-intentioned and democratic it might be, the next government will be tempted to corruption, violation of rights and expanded political power if it owns and controls the great economic wealth potential of Iraq. This is the time, and Iraq is the place, to create an economic system embracing the revolutionary principle that public assets belong directly to the public …

In Iraq, the rights in question are to the former government’s producing properties, transportation, terminal facilities, waterways, land and subsurface rights. These assets should first be declared transferred to the account of the citizens, recognizing the birthright of each citizen to a personal, empowering property right in the land and assets of the country of their birth. All citizens should have an equal share in this fund and be issued the same number of share claims to the fund.

Over a period of several decades, all Iraqi assets should be auctioned to the highest bidders in an individual, national and international business competition so that each asset or bundle of complimentary assets is transferred to the bidders who value them most for production, development or exploration. The auction could begin by selling existing producing oil properties, refineries, pipelines, and gathering, separating and terminal facilities over the next several years, then move to mineral, oil and gas exploration leases, and to land surface rights.

The proceeds would be deposited in a giant mutual fund for investment in index securities of the world’s stock markets and monitored — but not managed — by the U.N. Investing in stock indexes would minimize the need for discretionary financial management, and the prospect of the next government exercising or re-establishing any central control over Iraqi assets. The Iraqi Fund should be a closed-end fund whose shares are tradable and listed on world stock exchanges. The proceeds of each new property auction would be deposited to the account for investment in index funds. Redemptions at market value would go to any Iraqi citizen who elects at any time to cash out any portion of his shares.

There is a very important precedent, in part, for this action — the Alaska Permanent Fund. The state of Alaska elected to put a portion of its vast Prudhoe Bay annual royalty revenue into a citizens’ Permanent Fund for investment in securities. Each year a dividend from this fund is paid to every Alaskan citizen. This Fund was the first to recognize the full rights of citizens to share directly in the income from public assets.

This Fund, however, had three important shortcomings that should not be repeated in the proposed Iraqi Fund.

†¢ First, Alaska did not put all of Prudhoe Bay state revenue into the people’s account. A portion of it went to the state government. When oil prices went up, the state succumbed to the temptation to repeal its income tax and spend its oil income like there was no tomorrow. Consequently, today the Alaskan state government has a budget crisis and a deficit gap, but the 600,000 Alaskan citizens still share equally in the dividends from their Fund, now worth $27 billion….

†¢ Second, the Alaska Fund is not a ready source of private investment and venture capital for its individual owners. This is because there are no tradable certificate shares in their mutual fund. This lack of liquidity denies citizens’ access to capital markets: An individual citizen cannot sell some portion of his shares for investment in a private start-up business, or borrow against the shares for such investment. …

The Iraqi People’s Fund would consist of tradable shares; all public property would be held, then sold, for the account of the fund; and the new government would be required to obtain its revenue from taxes levied on the citizens who are willing to elect them and finance their spending programs. The government could not raid the fund to finance its operations. All this could be made explicit in the Iraqi constitution.

There should be room in the proposal for a temporary transition mechanism. For example, sales of citizen shares in the fund might be limited at first, but gradually lifted as citizen registrations and claims were settled, and the auction/sales mechanisms became established. Also, an initial budget set-aside for financing the new government might be in order, but this budget should decline on a fixed planning schedule at 15%-20% per year as the new government gets its tax and spending program together.

This action would launch the new Iraqi state as one based on individual human rights, and the rule of law, and anoint it with rock-hard credibility by giving every citizen a stake in that new regime of political and economic freedom. The objective is to undermine any citizen sense of disenfranchisement in the country’s wealth, economic and political future, and to galvanize citizen support for a democratic regime. Now is the time to act, before post-war business-as-usual creates de facto foreign and domestic spoils-of-war property right claims, leaving out a citizenry brutalized enough by a totalitarian regime, and in sore need of empowerment in their own future.

Earthlike planets may be common in the universe

Read Futurepundit on this topic. This news increases the expected well-being out there in the universe, but probably lowers the expected welfare of mankind. Visiting aliens could be a boon or a disaster but I am risk-averse in this capacity. Neither my juvenile love for science fiction nor my general optimism make me wish to live to see alien visitation. While earth institutions are far from efficient, they could be much worse. Right now the dominant technological power, the United States, is relatively benevolent by the standards of world history. Technologically superior aliens would upset this balance and could leave too much power in the wrong hands.

This whole news about planets only raises the question anew: Where are they? One possibility is that civilizations simply do not last very long on a cosmic time scale. If intelligent life has evolved elsewhere in the universe, most of the time it has expired before having a chance to contact us. If the window of opportunity is sufficienly small, it would help explain why we do not receive signals from other civilizations.

The research also shows that the nature of Jupiter’s orbit may be responsible for intelligent life on earth:

The simulations show that the amount of water on terrestrial, or Earthlike, planets could be greatly influenced by outer gas giant planets like Jupiter.

“The more eccentric giant planet orbits result in drier terrestrial planets,” Raymond said. “Conversely, more circular giant planet orbits mean wetter terrestrial planets.”

In the case of our solar system, Jupiter’s orbit is slightly elliptical, which could explain why Earth is 80 percent covered by oceans rather than being bone dry or completely covered in water miles deep.

This points to another reason why the aliens have not come. The existence of intelligent life requires a very large number of favorable coincident factors, perhaps larger than we have realized to date. But read Brad DeLong on the Fermi paradox, which suggests a large number of intelligent civilizations out there in the universe, even once we account for all the improbabilities.

Dangerous Rice

Rice arrived in Spain in about the eighth century, from the Moors, and the Spanish word “arroz” comes from the Arabic. In medieval times, growing rice was extremely controversial, largely because the rice fields were a breeding ground for malaria. For this reason, the Spanish city of Valencia, to this day renowned for its rice and its paella, was called “land of rice, land of tears.” Various regulations restricted the growth of rice in order to limit malaria. Debates continued to rage throughout the eighteenth century, a distinction was commonly drawn between fields with stagnant water and irrigated fields, which were supposedly safer.

The clincher: Malaria has long been eradicated in Spain, but to this day “the allocation of land or enclosures for rice growing requires special authorization from the office of the Spanish Ministry of Agriculture in Valencia.”

The race to space

Everyone has his or her obsession, one of mine is collecting Mexican amate painting, for some people it is investing in space travel.

The tangible pieces of John Carmack’s dream are scattered around an 8,000-square-foot warehouse: industrial water-purification tank, aluminum cones, compressed air cylinders, used Russian spacesuit.

All are components of the software developer’s project to launch a manned rocket 62 miles up by January 2005.

What binds the pieces together are Carmack’s quiet intellect and considerable bankroll.

“We mostly look at it as a two-horse race,” the 33-year-old millionaire said of the international competition for the $10 million X Prize, offered by a St. Louis-based foundation.

The entrepreneur has a background in computer games and works with a team out of a warehouse, sometimes using the parking lot for small-scale launch attempts. Rather than pursuing secrecy, progress is publicized on the project website, there you can even see videos of failed launch attempts.

NASA had the following response:

NASA has no official comment on the civilian attempts.

“It’s certainly a complicated business. Sometimes [sic] we make it look easy,” said Melissa Mathews, a space agency spokeswoman.

Is Carmack crazy? Beats me, read this interview if you want more data. The whole point is that there is only one way to find out, which is to let him try. Maybe he is right that “Aerospace is plumbing with the volume turned up.”

Thanks to Marko Siladin for the pointer.

What would it cost to send a man to the moon?

Recently the Bush administration has been making noises about sending a man to the moon again. Gregg Easterbrook offers some cogent critical points:

A rudimentary, stripped-down Moon base and supplies might weigh 200 tons. (The winged “orbiter” part of the space shuttle weighs 90 tons unfueled, and it’s cramped with food, oxygen, water, and power sufficient only for about two weeks.) Placing 200 tons on the Moon might require 400 tons of fuel and vehicle in low-Earth orbit, so that’s 600 tons that need to be launched just for the cargo part of the Moon base. Currently, using the space shuttle it costs about $25 million to place a ton into low-Earth orbit. Thus means the bulk weight alone for a Moon base might cost $15 billion to launch: building the base, staffing it, and getting the staff there and back would be extra. Fifteen billion dollars is roughly equivalent to NASA’s entire annual budget. Using existing expendable rockets might bring down the cargo-launch price, but add the base itself, the astronauts, their transit vehicles, and thousands of support staff on Earth and a ten-year Moon base program would easily exceed $100 billion. Wait, that’s the cost of the space station, which is considerably closer. Okay, maybe $200 billion.

What can a man do on the moon that automated vehicles cannot? Virtually nothing, and of course he requires far more maintenance and protection.

Given all that, where should we go from here?

NASA doesn’t need a grand ambition, it needs a cheap, reliable means of getting back and forth to low-Earth orbit. Here’s a twenty-first century vision for NASA: Cancel the shuttle, mothball the does-nothing space station, and use all the budget money the two would have consumed to develop an affordable means of space flight. Then we can talk about the Moon and Mars.

Mostly I agree, though I expect private enterprise can beat NASA in this latter project, at least provided we allow the privatization of space.

Meta-rational animals

Monkeys and dolphins are capable of recognizing when they do not know the answer to a question. Here is a brief summary of the experiments:

In the first one, trained monkeys sat at a computer joystick and watched the density of colored dots in a square on the screen. When there were many dots, the monkey moved the joystick to the square itself, choosing “dense.” When there were few dots, the monkey put the cursor on an “S,” superimposed on the screen, indicating “sparse.”

Gradually, examiners added more dots to the “sparse” test until the monkey reached a threshold where it could not easily discern whether the panel was “dense” or not. At that point, the monkey chose to put the cursor on a star, indicating uncertainty.

Smith said the two monkeys displayed uncertainty at almost the same threshold as seven humans who also took the test. This result, Smith and his co-authors said, “presents one of the strongest existing matches between human and animal performance in the comparative literature.”

In the second test, a bottlenose dolphin was trained to press a lever when it heard a “low” tone, and another lever when it heard a “high” tone. At first, the dolphin was so enthusiastic that it kicked up swirls of water as it raced to the levers.

But when researchers raised the low tone until it approached the high tone, “he would creep in because he didn’t know what to do,” Smith said. “It was the dolphin equivalent of scratching its head.” The dolphin would then resort to a third lever, indicating uncertainty.

In other words, very intelligent animals are aware of their own cognitive limitations, here is the full story. So far it has not been possible to induce comparable behavior in rats, nor in many political commentators.

The bottom line: Of all kinds of rationality, meta-rationality is perhaps the hardest to come by. It is most rare when more than one person, or questions of status, are involved. For whatever reasons, a kind of false certainty must have yielded evolutionary advantages in earlier times, and perhaps still does today. Those animals would really impress me if they dropped their admissions of uncertainty when a member of the opposite sex was watching.

Sleazeball lawyer in a low-cut dress

I am speaking of Erin Brockovich. Sure, I liked the movie but the true story on which it was based was a lie. There was no cancer cluster in Hinkley, no scientific theory of harm, no coverup at the water office (see here for links). Having had one success in Hollywood, Brockovich is now after another this time by fanning hysteria that the kids at Beverly Hills High School (yes, 90210) are getting cancer from a nearby oil well. I smell a movie in the works.

Radar improves the quality of wine

Yup, that”s right. And yes, new ideas do come first to California, at least in this case.

Scientists at the University of California at Berkeley are using ground penetrating radar (GPR), a tool better known for its military uses, to help winemakers create tastier, more uniform wines.

“GPR is an electromagnetic signal that travels in the ground. What we do is try to understand how fast that signal travels and that tells us a lot about the moisture content of the soil,” said Susan Hubbard, a hydrogeophysicist at University of California, Berkeley, and staff scientist at Lawrence Berkeley National Laboratory.

Understanding soil moisture is a critical part of the art and science of winemaking. Cabernet Sauvignon and other red wine grapes prefer drier soil. Chardonnay and other white wine grapes do better in moist soil. But growers say the timing, and the amount of water given to the vines can make the difference between an average and an outstanding crop.

Read here for the full story.

Let’s not forget, the initial French advantage in winemaking was based on technology, albeit of a more informal sort. If the French don’t keep on innovating, they will be left behind.

More on remittances

1. Almost one Mexican in five receives remittances from relatives working in the United States.

2. These payments help feed, house, and educate at least a quarter of the 100 million people in Mexico.

3. The total sent amounts to about $14.5 billion for this year.

4. Some 450,000 Mexicans entered the United States illegally last year.

The New York Times notes:

Most of the money is spent on food, clothing and housing. But Mr. Suro said a growing portion was invested in small business or helped to pay for high school and college educations.

Across much of central Mexico, where men and women have migrated to the United States for so many decades that crossing the border has become more a rite of passage than an escape from poverty, remittances exceed state public works budgets and pay to build roads, schools, water systems and baseball stadiums.

In recent years the United States and Mexico carried out reforms aimed at making it easier and more affordable for migrants to transfer money home. Companies like Western Union cut the fees they charged for wire transfers, halving the cost of transferring money, and American banks have begun allowing illegal immigrants to open accounts so relatives at home can withdraw funds from automatic teller machines.

Bravo, I say. I have spent a good deal of time in rural Mexico and I can attest that these funds make an enormous difference in the lives of millions. By the way, Daniel Drezner offers insightful commentary on my earlier post on remittances.

On Whether To Rebuild Iraq and Whether to Pay for It

I am frankly puzzled about what justification there might be for “rebuilding” Iraq and why outsiders, the United States in particular, should pay for it. Is there some powerful theoretical argument or empirical evidence I am not aware of that suggests that Iraq is likely to become a significantly more friendly and civilized place if its electrical grid, highways, and water and sewage systems are substantially upgraded? And if so, is there some special virtue to outsiders paying for it? If there are strong arguments for either proposition I have not heard them. It would seem to me that helping the Iraqis establish the rule of law, a stable currency, secure property rights, will be far more valuable, considerably cheaper, and sad to say difficult enough. My sense is that a large infusion of cash from the outside will have a pernicious effect. It will encourage the (re)development of a rent-extraction industry.

Our stalled energy bill

Remember all that hubbub about the new energy bill, following the Great Blackout? What ever happened? Lynne Kiesling offers a useful update on where things are at.

Here is part of her overview:

There’s a lot of stuff in those measures that is economically unsound and may even increase net energy use, such as increased ethanol use. But my political science friends tell me that as long as Denny Hastert is speaker of the House and the Iowa caucuses have the power they do in the Presidential election, corn farmers will be able to sock it to us, good and hard…ethanol’s nose gets in the tent through a renewable fuels mandate, not through the federal fuel oxygenate requirement. Ethanol a renewable fuel? Stop for a second to think about how ethanol is made: till soil, fertilize, plant corn, harvest, process it using lots of fossil fuel energy and creating air, water and soil emissions in the process, transport it in trucks, trains and barges to its consumption location. So there are a few parts in the production process that require fossil fuel use, and consequently result in emissions.

In other words, special interests and political rent-seeking are preventing us from adopting a sounder energy policy. Will things ever change? Stay tuned to Lynne’s blog for periodic updates.

Cream Skimming

Glen Whitman at Agoraphilia has some comments on my debate with Tyler on vouchers. He notes that the public school system separates students according to ability with honors classes, AP classes, magnet schools and so forth. Yet, few people call this “cream skimming.” I think Glen’s point blows the peer-effects argument against school choice out of the water.

More generally, the argument in the peer-effects literature is that we shouldn’t let smart kids escape the public school system because their presence gives dumb kids a positive externality. I detest this argument. Children are not pawns to be moved about to satisfy the desires of some grand master. A decent school system treats children as ends in themselves. (In preparation, one might add, for life in a society that treats every individual as an end in themself.)