LITMIR.BIZ

      The most important mathematical results of the twentieth century concerned the limits of mathematical knowledge. Gödel’s incompleteness theorem showed that not all true theorems could be proved; the Church-Turing thesis led to the understanding that not all problems could be solved algorithmically. The rest of the world shrugged—of course there were some things you couldn’t do with math. One look at the spacey, stuttering basket cases who were good at it suggested that interpersonal communication, fashion, and hygiene were among them. But for mathematicians and scientists of all stripes, the blow to their faith in the descriptive power of their language was shocking. The relation of scientists and nonscientists to the inexplicable is very different. What Keats called negative capability, “when a man is capable of being in uncertainties, mysteries, doubts, without any irritable reaching after fact and reason,” is a daily necessity for social beings. We won’t ever understand why people make the crazy choices they make, love the awful music they love, believe in astrology or baseball or God, but having good manners entails accepting these mysteries. Art entails producing them. Scientists are often bad at both. After leaving the University of Colorado for an abortive two-and-a-half-year effort at a normal high school experience, I started at Stanford as a shy seventeen-year-old with a suitcase full of Nine Inch Nails T-shirts and combat boots and a schedule full of graduate seminars, utterly baffled by actual human beings, utterly confident in my ability to model them algorithmically.

      I wasn’t the first to overestimate myself in this way. After the wild enthusiasm of the field’s early years in the 1950s—the efforts at representation of the world’s entire store of knowledge in logical form, the gradual comprehension that logical propositions were too rigid and inflexible to have much predictive use, the blind alley of “fuzzy logic,” the probabilistic models of belief that grew to dominate the field—artificial intelligence researchers came to understand that the big problems of memory, reasoning, language, and consciousness were much more complex than they had imagined. By the time I went knocking on those researchers’ doors, breaking naive undergraduates of their hazy dreams of programming themselves a computer friend had become a distasteful but necessary part of the job. The fundable problems were the kinds you could get traction on: recognition of handwritten zip codes on envelopes, the parsing of Internet search queries, automated flight control of helicopters. The first major project I was invited to participate in sought to compute Nash equilibria in structured strategic scenarios. Funding came from the Department of Defense.

      It was an exciting time to be in Silicon Valley. Google’s first server, scaffolded on rainbow-colored Legos, rested in a display case in the Gates Building basement. Movies and magazines were awash in romanticized hacker imagery. We few undergrads who had bulled our way into research were a club every bit as proud, in our way, as the Rangers. When we put together presentation slides for the yearly funding meeting with a stodgy, uncomprehending naval officer and a few of his staff, we all laughed together at how shamelessly we were using clip-art icons of tanks and soldiers instead of the usual abstract blue circles as nodes in our directed acyclic graphs. The joke was on the military: we were a bunch of apolitical nerds funneling away their bomb money to do awesome mathematics, all of which was far too theoretical—practically aesthetic in its aims—to have any chance of military application.

      Eight months into the war in Afghanistan, when the legendary Defense Advanced Research Projects Agency (DARPA) announced a $1 million prize for the winning robotic vehicle in an unmanned race across the California desert, I watched hundreds of casually pacifist nerds like me in computer science departments around the country leap into an excited spasm of whiteboard sketching, number crunching, and microcontroller programming. I wasn’t surprised. I wasn’t even bothered, aside from feeling a jealous pang or two at how much cooler their projects were than my own. If you have ever done technical research, you know just how right