Power makes knowledge sufficient Whether it is civil rights' violations in many countries, whether it is the increasing numbers of unemployed people in our own country, whether it is the homeless we see on our way to work, it isn't as though we don't know. But there is that horrible realization that, while the knowledge of facts may be a necessary condition for action, and we talk about democracy in civic action, it is unfortunately not a sufficient one. While knowledge may be a necessary condition, it may in fact be a less necessary condition that the one that makes that a sufficient condition, and that is access to power. Ursula M. Franklin, Every Tool Shapes the Task power
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