Boston says you should be smarter Great cities attract ambitious people. You can sense it when you walk around one. In a hundred subtle ways, the city sends you a message: you could do more; you should try harder. The surprising thing is how different these messages can be. New York tells you, above all: you should make more money. There are other messages too, of course. You should be hipper. You should be better looking. But the clearest message is that you should be richer. What I like about Boston (or rather Cambridge) is that the message there is: you should be smarter. You really should get around to reading all those books you've been meaning to. Paul Graham, Cities and Ambition intelligenceboston
Wang tiles Wang tiles (Hao Wang, 1961) are a class of formal systems. They are modelled visually by square tiles with a color on each side. A set of such tiles is selected, and copies of the tiles are arranged side by side with matching colors, without rotating or reflecting them. The basic question about a set of Wang tiles is whether it can tile the plane or not, i.e., whether an entire infinite plane can be filled this way. The next question is whether this can be done in a periodic pattern. In 1966, Wang's student Robert Berger solved the problem in the negative. He proved that no algorithm for the problem can exist, by showing how to translate any Turing machine into a set of Wang tiles that tiles the plane if and only if the Turing machine does not halt. The undecidability of the halting problem then implies the undecidability of Wang's tiling problem. Wikipedia en.wikipedia.org Truchet TilesThe Tiling Patterns of Sebastien Truchet and the Topology of Structural Hierarchy mathalgorithms