The whole ‘tau’ vs ‘pi’ thing is basically crap. pi is just as legitimate, and for every case where a tau would make things better, there is another where it makes it worse. the zeta function isn’t a bad example, where it converges to a real value is an expression in terms of even powers of pi, such expressions with tau end up having a random power of 2 in the denominator, which makes the constants uglier.
The reality is, most math uses pi, and that’s because the supposed benefits of using some other constant aren’t enough to justify converting swaths of mathematics. pi is a perfectly acceptable constant and tau doesn’t admit a good cost/benefit analysis when taking the whole of mathematics into account.
Pardon, it occurs to me I was unclear – I mean it’s a different random power of two, it’s not really better or worse, just different. My argument is that tau presents no substantive, non-aesthetic difference, and I’m dubious that it makes the mathematics any easier to understand or perform. It reminds me a bit of Node.js, but for the math world. Something which is unreasonably popular for mostly superficial reasons, but which ultimately presents little benefit and may ultimately be more confusing in the long run.
I think tau presents a clear advantage in one case, when discussing circular functions on the unit circle – precisely the situation that would interest the most the kind of person who wants to reform mathematical notation.
It be interesting to see if a single man, Michael Hartl, can convince the whole of mathematics to change its way.
Ultimately, the only truly compelling point to be made on this issue is convention, which is utterly and completely in favor of pi.
My favorite argument is that tau is wrong because it’s 2pi but has half as many legs. =)
We begin repairing the damage wrought by [Math Processing Error] by first understanding the notorious number itself.
Internet Explorer not supported?
I think it’s using something like mathjax.js to render the math – do you have JS turned off?
No, JS is on
Tau is clearly wrong since adopting it would mar the most beautiful equation of all: Euler’s Identity
I guess I should have put the smiley at the end of this post. I didn’t realise people took this tau thing so seriously. 4 people bothered to mark a humorous observation as incorrect :)
This is addressed on the site. eiτ = 1 is not any less beautiful than eiπ = -1.
eiπ = -1 implies eiτ = 1, but not the other way around.
Now don’t get me wrong, I like Euler’s Identity as much as the next guy, but I think there are prettier results around.
Ignoring for a moment that making substantive choices based purely on elegance (or lack thereof) is foolish at best, here are some aesthetic arguments about why Euler’s Identity is pretty meh in context.
Firstly, it’s a very mechanical / arithmetical sort of identity, isn’t it? I don’t know about your experience in mathematics, but for my part, these sorts of identities don’t really make my socks roll up and down – I much prefer something with a bit more meat on it. Something like a Pappus' Theorem in projective geometry, or the theory of Space Filling Curves. See, to me, Euler’s identity is beautiful only in the same way a single color – not yet put to canvas – is beautiful. It’s a component of a bigger thing. Burnt Sienna or Deep Red are beautiful colors, but the “Happy little tree” that they make – that’s the art.
So while tau might alter the color of this (admittedly very nice) pigment, I’m less concerned about that, and more concerned about how it effects the whole painting. Tau doesn’t substantively improve the beauty of mathematics as a whole, and indeed may mar it were we try to transition from one ‘color’ to the other. That’s why – if at all – it’s “clearly wrong.”
I look at Euler’s Identity and marvel how you can make -1 simply by combining 3 numbers that can’t be written down using natural numbers.