Happy Tau Day!

(This post assumes a certain amount of knowledge about math.)

I think it's really cheesy to do something on June 28 just because the decimal expansion of τ begins “6.28...”, but well, I might as well do it today as any day.

If you've studied mathematics in the modern world, you've probably run into a number called pi, or π, which represents the ratio of a circle's circumference to its diameter. That's weird and confusing, because pretty much every other mathematical concept about circles is based on the radius of the circle, not its diameter. The diameter is exactly twice the radius, so lots of formulas involving π end up referring to the quantity 2π.

This is pretty silly, becuase the “2” in “2π” doesn't really mean anything. It's just a correction factor to make up for the fact that the number we're calling “π” is exactly half of what the natural value for the circle constant is. That leads to confusing things like the fact that rotating by π radians is a half-rotation, not a full rotation... and if you want to rotate by three-quarters of a circle, you have to rotate by 3π/2, which is completely confusing.

So, a lot of mathematicians, including myself, are now using a new name for the quantity “2π” – namely, tau, or τ. Its value is approximately 6.283185307..., hence the cheesy date of June (the sixth month) 28.

More information at http://tauday.com/.

– Eli

Game theory, contracts, altruism

In my story Capitalism Sat, “Mathematics” says a few things about game theory that I've worked on myself. I'll discuss them here. Knowing some game theory helps, but you might be able to understand without any prior background.

The classic paradox from game theory is the Prisoner's Dilemma, or the more general tragedy of the commons – a situation where players can either cooperate or betray each other, and benefit from betraying, but are better off if everyone cooperates instead of everyone betraying. There are a lot of attempts to “solve” the Prisoner's Dilemma – that is, to find a reason why purely self-interested players should cooperate. Superrationality is one of them, but it only works for a limited set of situations. A more effective solution would be [...]

My rules of Go, on arbitrary directed graphs

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Our ruleset uses stone scoring because it's super simple and clear what that means. It uses divide-and-choose for komi because the first move is more valuable on some graphs than others. It uses a novel divide-and-choose method to address (super)ko. An ordinary superko rule would be well-defined here too.

The rules

INTRO: Go is a class of infinite combinatorial games¹ between two players, one for each finite² directed graph and [...]