Wald press

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Award-winning fiction and nonfiction. Abraham Wald was born in in what was then the city of Klausenburg in what was then the Austro-Hungarian Empire.

By the time Wald was a Wald press, one world war was in the books and his hometown had become Cluj, Romania. He was the grandson of a rabbi and the son of a kosher baker, but the younger Wald was a mathematician almost from the start.

His talent for the subject was quickly recognized, and he was admitted to study mathematics at the University of Vienna, where he was drawn to subjects abstract and recondite even by the standards of pure mathematics: Wald was rescued by a job offer from Oskar Morgenstern.

Morgenstern would later immigrate to the United States and help invent game theory, but in he was the director of the Austrian Institute for Economic Research, and he hired Wald at a small salary to do mathematical odd jobs.

That turned out to be a good move for Wald: Despite the ever-worsening political situation, Wald was reluctant to take a step that would lead him away from pure mathematics for good.

After just a few months in Colorado, he was offered a professorship of statistics at Columbia; he packed up once again and Wald press to New York.

Kenneth Wald | NYU Langone Health

And that was where he fought the war. The Statistical Research Group SRGwhere Wald spent much of World War II, was a classified program that yoked the assembled might of American statisticians to the war effort — something like the Manhattan Project, except the weapons being developed were equations, not explosives.

In another apartment, a team of researchers from Princeton was developing protocols for strategic bombing. But the SRG was the most high-powered, and ultimately the most influential, of any of these groups.

The atmosphere combined the intellectual openness and intensity of an academic department with the shared sense of purpose that comes only with high stakes. So was Leonard Jimmie Savage, the pioneer of decision theory and great advocate of the field that came to be called Bayesian statistics.

Savage was almost totally blind, able to see only out of one corner of one eye, and at one point spent six months living only on pemmican in order to prove a point about Arctic exploration. Just thought that was worth mentioning. Norbert Wiener, the MIT mathematician and the creator of cybernetics, dropped by from time to time.

This was a group where Milton Friedman, the future Nobelist in economics, was often the fourth-smartest person in the room. The smartest person in the room was usually Abraham Wald. Wald was, in some ways, an unlikely participant. His inclination, as it always had been, was toward abstraction, and away from direct applications.

But his motivation to use his talents against the Axis was obvious. And when you needed to turn a vague idea into solid mathematics, Wald was the person you wanted at your side. But armor makes the plane heavier, and heavier planes are less maneuverable and use more fuel. Armoring the planes too much is a problem; armoring the planes too little is a problem.

The reason you have a team of mathematicians socked away in an apartment in New York City is to figure out where that optimum is.

The military came to the SRG with some data they thought might be useful. When American planes came back from engagements over Europe, they were covered in bullet holes.

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There were more bullet holes in the fuselage, not so many in the engines. The officers saw an opportunity for efficiency; you can get the same protection with less armor if you concentrate the armor on the places with the greatest need, where the planes are getting hit the most.

But exactly how much more armor belonged on those parts of the plane? That was the answer they came to Wald for. The ones that would have been all over the engine casing, if the damage had been spread equally all over the plane? Wald was pretty sure he knew. The missing bullet holes were on the missing planes.

Whereas the large number of planes returning to base with a thoroughly Swiss-cheesed fuselage is pretty strong evidence that hits to the fuselage can and therefore should be tolerated.

In this case, the variable to tweak is the probability that a plane that takes a hit to the engine manages to stay in the air. Setting that probability to zero means a single shot to the engine is guaranteed to bring the plane down.

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