On Pi day, we eat pie; On Tau day, we eat Taoists?
I’d like to start by wishing everyone a Happy Pi day (even if for some of you it was yesterday).
Today, going about my usual Pi day celebration (which included pi(e) of the chocolate, cherry, apple, and movie variety), I stumbled across pi-protesters, who spoke of Tau-ism. For those who haven’t heard, Tauist claim that Tau, represented by the Greek letter T, is the real circle constant. There’s one proponent and his arguments here: http://tauday.com/
I read the article, saw the points that were made, and I’ve remained impartial (despite being a mathematics major). I can see Tau’s usefulness; I can see why pi hasn’t changed (and hardly would need to). So I decided to do something else: Present this claim to the LessWrong community, for those who are interested. What do you think?
I think that the true fundamental constant is ‘bar’ which is the reciprocal of tau. Physicists are always talking about hbar, for example.
Even more interesting, though, is the issue of which is more fundamental: e or 1/e? I’m getting to the age where I consider decay more fundamental than growth.
As far as e goes, I would say that the true fundamental there is the function exp(z) = e^z. Then e and 1/e are just special values of that function, exp(1) and exp(-1) -- nothing to be terribly interested in.
I favor 1/e, because I am demented.
Spoiler alert:
“Tau” is 2pi.
That was anticlimactic, I have to say.
Yes, 2pi is arguably even more fundamental than pi. In fact, some of my friends and I once celebrated “2pi day” one summer, in view of that fact. That said, writing that long of a manifesto on how “pi is wrong” (or, if you prefer, “tau/2 is wrong”) is way overdoing it.
However, on behalf of my left-handed friends, I claim that -i is the true square root of −1.
The Feynman point is actually one 9 longer in tau.
I think that settles the matter.
But is my “i” is the same as your “i” or your “-i”? The physical facts about us cannot settle this question either way. Therefore physicalism is wrong!
I agree that the long manifesto on how “pi is wong” is overdoing it. After all, pi works for all intents and purposes (with one disagreement, and it’s not even about the math).
On the other hand, tau, while only being 2pi, does make a number of equations look nicer (or fit how others look, in the example about quadratics), and makes understanding angles in radians more intuitive.
I can’t find a good reason to keep pi around for any more than historical purpose, and I was curious if anyone had some. My main reason for not changing to tau is a mix of habit and to avoid confusion for my math professors :)
Both i and -i are square roots of −1. For any non-zero complex number c there exist n n-th roots, corresponding to a rotationally symmetric partition of a circle centered on the origin into n “wedges” such that one boundary falls along the line joining the origin and c.
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The map x+iy → x-iy is an isomorphism. So i and -i are mathematically indistinguishable.
Yes, that was precisely the joke. :-)
Base 10 is a rather awkward choice for arithmetic, being only divisible by 2 and 5, but we’re kind of stuck with it...
I totally agree with the first part, and slightly disagree with the last part. If I could, I would give everybody an extra two fingers and cause the world to be converted to base twelve. Time notation would be less annoying, there would be more available factors, and everybody would have two more fingers.
I thought it was silly to even argue. When I was a little kid, I thought the diameter of a circle was the natural way to measure it. When I understood enough to realize the radius made more sense, of course you’d use the ratio of the circumference to the radius.
Later on, I understood even more, and realized e was better than both of them anyway. (Well, e^x. e is to e^x as pi is to 2*pi).
Unfortunately, I started memorizing digits when I was a little kid, so now I have 67 digits of an ugly number memorized. Also, I found out memorizing digits is ugly anyway.
If you want to memorize something pretty, try Sum(x^k/k!)
Tau looks like r, which is used for radius length, which is relevant to some equations that use the circle constant. Of all possible letters, why use tau? Are they trying to mess with students and teachers whose handwriting makes it ambiguous whether a symbol is tau or r? Maybe it was just because it’s half the pi symbol.
I’m pretty sure people only care about Pi Day because it sounds like pie. Tau Day will never be as celebrated, unless you call it 2Pi Day, which defeats the point, but is still a good excuse to eat pie.
Correction: it’s a good excuse to eat TWICE as much pie.
This video on the argument is entertaining.
Bah. If you want to alter it for convenience reasons, then π/2 is much nicer as it gets rid of more fractions, and a quarter turn is a pretty natural unit.
But actually I prefer keeping π as it is. The relation between the half-integral values of the Γ function and π (which shows up in many integral) is rather nice. And despite 2π appearing nicer for circles, when you generalize to n-spheres, it’s clear that π is more useful with the surface area of formula 2 π^(n/2) / Γ(n/2) and volume of π^(n/2) / Γ(n/2 + 1).
I don’t know whether to be relieved or disappointed that the Gregorian calendar won’t support an e day.
We may not get a day to celebrate, but 1828 was a hell of a year.
You could just use the decimal part of 2.718… as July 18 (7/18). Or you could interpret the blocks of two (71 and 82) as percentages, and the 71% as a month would be August and 82% as a day of August would be the 25th day (so 8⁄25). Or you could interpret the 7182 as 71.82% and convert that to a moment during the year, which corresponds to 2011-10-27T07:12:00.
EDIT: updated to fix numbers due to mistyping the initial decimals of .718281828 as 712 instead of 718.
Any excuse to take an ecstasy tab, eh?
2.718281828 …
Doh, thanks. Can’t believe I made that mistake, as I know it’s 18281828.