Posts Tagged ‘ Russia ’

Brutally Hard Math Is Its Own Reward

Jordan Ellenberg in Slate:

The New York Times recently reported that reclusive Russian geometer Grigory Perelman has apparently proved the century-old Poincaré conjecture. The Times calls Poincaré “a landmark not just of mathematics, but of human thought.” But just whyit’s so significant is left a bit hazy. Big mathematical advances often generate the same kind of lofty but content-free rhetoric found in political speeches about “the family.” Like the family, math is a subject everyone agrees is very important without being able to specify exactly why.

I’m here to help. (With the Poincaré conjecture. As for the family, you’re on your own.)

Poincaré conjectured that three-dimensional shapes that share certain easy-to-check properties with spheres actually arespheres. What are these properties? My fellow geometer Christina Sormani describes the setup as follows:

The Poincaré Conjecture says, Hey, you’ve got this alien blob that can ooze its way out of the hold of any lasso you tie around it? Then that blob is just an out-of-shape ball. [Grigory] Perelman and [Columbia University’s Richard] Hamilton proved this fact by heating the blob up, making it sing, stretching it like hot mozzarella, and chopping it into a million pieces. In short, the alien ain’t no bagel you can swing around with a string through his hole.

That’s zingier than anything theTimes will run, but may still leave you without a clear picture of Perelman’s theorem. Indeed, it’s pretty hard to give an elementary account of the statement that Poincaré conjectured and that Perelman seems to have confirmed. (If that’s what you’re after, Sormani’s home page links to a variety of expositions, including one in the form of a short story.) Instead, I’ll try to explain why Perelman’s theorem matters without explaining what it is.

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War in the fifth domain

From The Economist:

Are the mouse and keyboard the new weapons of conflict?

AT THE height of the cold war, in June 1982, an American early-warning satellite detected a large blast in Siberia. A missile being fired? A nuclear test? It was, it seems, an explosion on a Soviet gas pipeline. The cause was a malfunction in the computer-control system that Soviet spies had stolen from a firm in Canada. They did not know that the CIA had tampered with the software so that it would “go haywire, after a decent interval, to reset pump speeds and valve settings to produce pressures far beyond those acceptable to pipeline joints and welds,” according to the memoirs of Thomas Reed, a former air force secretary. The result, he said, “was the most monumental non-nuclear explosion and fire ever seen from space.”

This was one of the earliest demonstrations of the power of a “logic bomb”. Three decades later, with more and more vital computer systems linked up to the internet, could enemies use logic bombs to, say, turn off the electricity from the other side of the world? Could terrorists or hackers cause financial chaos by tampering with Wall Street’s computerised trading systems? And given that computer chips and software are produced globally, could a foreign power infect high-tech military equipment with computer bugs? “It scares me to death,” says one senior military source. “The destructive potential is so great.”

After land, sea, air and space, warfare has entered the fifth domain: cyberspace. President Barack Obama has declared America’s digital infrastructure to be a “strategic national asset” and appointed Howard Schmidt, the former head of security at Microsoft, as his cyber-security tsar. In May the Pentagon set up its new Cyber Command (Cybercom) headed by General Keith Alexander, director of the National Security Agency (NSA). His mandate is to conduct “full-spectrum” operations—to defend American military networks and attack other countries’ systems. Precisely how, and by what rules, is secret.

Britain, too, has set up a cyber-security policy outfit, and an “operations centre” based in GCHQ, the British equivalent of the NSA. China talks of “winning informationised wars by the mid-21st century”. Many other countries are organising for cyberwar, among them Russia, Israel and North Korea. Iran boasts of having the world’s second-largest cyber-army.

What will cyberwar look like? In a new book Richard Clarke, a former White House staffer in charge of counter-terrorism and cyber-security, envisages a catastrophic breakdown within 15 minutes. Computer bugs bring down military e-mail systems; oil refineries and pipelines explode; air-traffic-control systems collapse; freight and metro trains derail; financial data are scrambled; the electrical grid goes down in the eastern United States; orbiting satellites spin out of control. Society soon breaks down as food becomes scarce and money runs out. Worst of all, the identity of the attacker may remain a mystery.

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