September 13, 2016 at 02:43AM

Today I Learned: 1) Ever heard of a Nash Equilibrium? Informally, it says that in any game (economist-speak for an interaction between two or more parties where different outcomes have different values) satisfying certain conditions, there is a stable set of strategies that the players could arrive to for which no player would gain by switching strategies. There is no guarantee that the equilibrium is *good* for all, or even any, of the players, nor that the players will actually arrive at that equilibrium (even if they play perfectly rationally), but an equilibrium definitely exists. Today I learned a semi-formal set of conditions under which the Nash Equilibrium Theorem holds. It holds with a game of any finite number of perfectly rational players, where each player has a finite set of "pure strategies" that can be mixed probabilistically (i.e., a voter on a committee might vote for proposition A, proposition B, or proposition A with 10% probability and proposition B with 90% probability, or any other combination of probabilities). And... that's about it. The choice of strategies can, as far as I understand, be arbitrarily complex, as long as the decision ends up being some probabilistic combination of pure strategies. That's a shockingly powerful theorem, if you ask me. Thanks to George Artavanis for presenting about, among other things, Nash Equilibria. 2) John Wilkins, the 18th century natural philosopher, tried to write a universal language capable of communicating any thought in a clear fashion. I'd read a little bit about this scheme in Neil Stephenson's "Quicksilver", but today I learned a few more details about it. The universal language was motivated as a replacement lingua franca for latin -- something traders and diplomats could speak in any language. It was to be developed roughly in two parts -- a "real character" set and a "philosophical language". The real characters were to be a system for generating written characters that could representing any idea, in an abstract, non-verbal way (kind of like the way chinese writing acts as a non-verbal medium for speakers of different dialects). The philosophical language was, in some sense, a mapping from the real characters to spoken word. In general, the philosophic language was structured so that each additional character in a word would narrow down the meaning of the word, in some systematic way -- for example, "be" might be the word for machines, "ben" might be the word for electronic machines, "beni" might be the word for computers, "benit" might be the word for desktop computers, and so forth. The universal language was met with great excitement when it was first announced, but as you can probably guess, it never really went anywhere. 3) It turns out that there *is* a rule describing how adjectives are arranged in English! Ever noticed how you can have a big red ball, but a red big ball sounds strange? I've been wondering what rules define what order adjectives come in for a while now, and while it seemed that there were some generalizations about things like color coming after size, I never found a complete set of rules. It turns out there is one! It's not even that complicated! According to one Mark Forsyth (not the W&M one), The rule is that adjectives must come in the order "opinion-size-age-shape-color-origin-material-purpose noun". A complete example he gives is a lovely old rectangular green French silver whittling knife. Now, the question is, how the heck do we all learn this rule without ever actually learning *about* it? Thanks to Mengsha Gong for finally bringing me some peace on this subject!