Scenes of thoroughgoing sameness In places stamped with the monotony and repetition of sameness you move, but in moving you seem to have gotten nowhere. North is the same as south, or east as west. Sometimes north, south, east and west are all alike, as they are when you stand within the grounds of a large project. It takes differences—many differences—cropping up in different directions to keep us oriented. Scenes of thoroughgoing sameness lack these natural announcements of direction and movement, or are scantly furnished with them, and so they are deeply confusing. This is a kind of chaos. Jane Jacobs, The Death and Life of Great American Cities The Image of the CityThe Great Blight of Dullness confusionchaos
Mystery exists in the mind Mystery exists in the mind, not in reality. If I am ignorant about a phenomenon, that is a fact about my state of mind, not a fact about the phenomenon itself. All the more so if it seems like no possible answer can exist: Confusion exists in the map, not in the territory. Unanswerable questions do not mark places where magic enters the universe. They mark places where your mind runs skew to reality. Eliezer Yudkowsky, Rationality: From AI to Zombies The Tao of rationality mysteryconfusion
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