Why we can’t change pi to tau/2

It’s pi day, and there’s been yammerings that “pi is wrong”, e.g. tau day and Qiaochu Yuan’s statement.

Like most greek letters, it’s overused. tau. Pi is also used to mean the prime number counting function. There have been papers that use pi in both contexts in short order. On zeros of cubic L-functions, for instance.

$\pi$ might be conceptually the wrong number, but we’re stuck with it, and $\tau$ is not what we want to replace it by. Why?

The nome $q = e^{2\pi i \tau}$ is not going away, and if we really are committed to finding some new symbol for $2\pi$, then we need to commit ourselves to changing a whole swath of mathematical literature at once, which we may not be able to do easily.

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4 responses to “Why we can’t change pi to tau/2”

1. These issues are all addressed in the manifesto. You don’t have to change any existing literature to start adding in new mathematical literature, “we adopt the convention that $\tau = 2 \pi$.” I don’t see why something being hard is a reason not to do it. In fact, it’s probably one of the worst reasons not to do something.

• I’m not arguing with the point of the manifesto. The manifesto stands. The choice of symbol, however is not the best in the universe. We should avoid overloading symbols that already have established meanings. Theta functions (the nome in particular) already have $n$, $\pi$, $\tau$, and $i$ in the nome, and these are already a typographically miserable arrangement of characters. We call it one turn, or whatever, but we should not give it a symbol that looks like $\pi$.

By the token of “hard things”, mathematicians are kind of strait-jacketed by TeX right now. Things are improving. We should be willing to use non-greek and non-latin symbols to reduce potential confusion.

• Then shouldn’t you have titled your post “why we can’t change $\pi$ to $\frac{\tau}{2}$?”