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Sometimes in an upper-level class I’ll assign a problem I don’t expect students to solve. It either involves some subtle trick, or requires theoretical techniques they haven’t yet learned. I assign them because I want students to struggle a bit with problems for which the solutions aren’t clear. “Wander into the…
How would we know if there was an autonomous conscious superorganism? We would need a Turing Test for a global AI. But the Turing Test is flawed for this search because it is meant to detect human-like intelligence, and if a consciousness emerged at the scale of a global megacomputer, its intelligence would unlikely…
Georges Lemaitre was a pudgy, pinkish Belgian Jesuit abbe—a Catholic priest—who also happened to be a skilled astronomer. Lemaitre had noticed that Einstein's general theory of relativity would have implied that the universe was expanding but for a troublesome little mathematical term called the cosmological constant…
That the universe is expanding was news to Einstein. But the possibility that the galaxies are moving away from each other had been proposed a few years before Hubble's papers on theoretical grounds arising from Einstein's own equations. In 1922, Russian physicist and mathematician Alexander Friedmann investigated…