Taking pride in ignorance First and foremost, concentrate on your strengths. Put yourself where your strengths can produce results. Second, work on improving your strengths. Third, discover where your intellectual arrogance is causing disabling ignorance and overcome it...First-rate engineers, for instance, tend to take pride in not knowing anything about people. Human resources professionals, by contrast, often pride themselves on their ignorance of elementary accounting or of quantitative methods altogether. But taking pride in such ignorance is self-defeating. Go to work on acquiring the skills and knowledge you need to fully realize your strengths. Peter F. Drucker, Managing Oneself ignorancearrogance
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