125
" Typical of the form is an item from the Wall Street Journal’s Washington Wire blog of June 24, 2013: The Social Security Administration’s inspector general on Monday said the agency improperly paid $31 million in benefits to 1,546 Americans believed to be deceased. And potentially making matters worse for the agency, the inspector general said the Social Security Administration had death certificate information on each person filed in the government database, suggesting it should have known the Americans had died and halted payments. Why do we allow this kind of thing to persist? The answer is simple—eliminating waste has a cost, just as getting to the airport early has a cost. Enforcement and vigilance are worthy goals, but eliminating all the waste, just like eliminating even the slightest chance of missing a plane, carries a cost that outweighs the benefit. As blogger (and former mathlete) Nicholas Beaudrot observed, that $31 million represents .004% of the benefits disbursed annually by the SSA. In other words, the agency is already extremely good at knowing who’s alive and who’s no more. Getting even better at that distinction, in order to eliminate those last few mistakes, might be expensive. If we’re going to count utils, we shouldn’t be asking, “Why are we wasting the taxpayer’s money?,” but “What’s the right amount of the taxpayer’s money to be wasting?” To paraphrase Stigler: if your government isn’t wasteful, you’re spending too much time fighting government waste. "
― Jordan Ellenberg , How Not to Be Wrong: The Power of Mathematical Thinking
131
" This reminds me of an old story from the Harvard math department, concerning one of the grand old Russian professors, whom we shall call O. Professor O is midway through an intricate algebraic derivation when a student in the back row raises his hand. “Professor O, I didn’t follow that last step. Why do those two operators commute?” The professor raises his eyebrows and says, “Eet ees obvious.” But the student persists: “I’m sorry, Professor O, I really don’t see it.” So Professor O goes back to the board and adds a few lines of explanation. “What we must do? Well, the two operators are both diagonalized by . . . well, it is not exactly diagonalized but . . . just a moment . . .” Professor O pauses for a little while, peering at what’s on the board and scratching his chin. Then he retreats to his office. About ten minutes go by. The students are about to start leaving when Professor O returns, and again assumes his station in front of the chalkboard. “Yes,” he says, satisfied. “Eet ees obvious "
― Jordan Ellenberg , How Not to Be Wrong: The Power of Mathematical Thinking
137
" What I like about stochastic gradient descent is how nuts it sounds. Imagine, for instance, that the president of the United States made decisions without any kind of global strategy; rather, the nations chief executive is surrounded by a crowd of shouting subordinates, each hollering for policy to be tweaked in a way that suits their own particular interest. And the president, every day, chooses one of those people at random to listen to, and changes course accordingly. That would be a ridiculous way for a person to run major world government, but it works pretty well in machine learning! "
― Jordan Ellenberg , Shape: The Hidden Geometry of Information, Biology, Strategy, Democracy, and Everything Else
140
" John Leech, in the 1960s, used one of Golay's codes to build an incredibly dense packing of twenty-four dimensional spheres, in a configuration now known as the Leech lattice. It's a crowded place, the Leech lattice, where each of the twenty-four-dimensional spheres touches 196,560 of its neighbors. We still don't know whether it's the tightest possible twenty-four-dimensional packing, but in 2003, Henry Cohn and Abhinav Kumar proved that if a denser lattice exists, it beats Leech by a factor of at most
1.00000000000000000000000000000165.
In other words: close enough "
― Jordan Ellenberg , How Not to Be Wrong: The Power of Mathematical Thinking
