# Tau day is tenJune 28, 2020 3:07 PM   Subscribe

It's been ten years since the original publication of the Tau Manifesto, advocating the simplification of a broad range of mathematical formulae by replacing pi with a bigger, better circle constant. Check out the celebratory State of the Tau report for the latest, including new translations of the manifesto and an endorsement from Drake*.

[* - Caveat: Drake appears only in meme form, and (so far) supports tau only insofar as the meme creator had not been sued.]
posted by kaibutsu (57 comments total) 18 users marked this as a favorite

We got diameter 'cos you can measure it. Radius? Not so well.
posted by scruss at 3:49 PM on June 28 [1 favorite]

I'm surprised the Wall Street Jornal didn't go with the "Tau Jones Industrial Average" or even "The Tau of Pooh"
posted by chavenet at 4:06 PM on June 28 [2 favorites]

The biggest problem with Tau day is that there is no food that people love associated with it. Anybody have suggestions?
posted by TedW at 4:07 PM on June 28 [3 favorites]

A wheel of cheese!
posted by Maxwell's demon at 4:12 PM on June 28 [3 favorites]

Tau fu?
posted by chavenet at 4:12 PM on June 28 [5 favorites]

(My kids and I have been celebrating Tau day by mooing at each other)
posted by Maxwell's demon at 4:17 PM on June 28

Forget it Jake, toe will never replace pie.
posted by tspae at 4:21 PM on June 28

"The Tau of Pooh"

"Assume a spherical turd..."
posted by eviemath at 4:26 PM on June 28

Dear, the internet, please stop trying to make tau happen. It's never going to happen.

Sincerely,
A professional mathematician who kinda hates "Pi day" but forgives it because pie is delicious. Tau day has nothing to redeem it.
posted by 3j0hn at 4:59 PM on June 28 [22 favorites]

Two times an infinitely long number is still an infinitely long number. How does that solve anything, in a practical sense? Can someone nutshell that for me?

In theory, it’s still infinitely long, anyway. Mathematically, it might not be.
posted by drivingmenuts at 5:02 PM on June 28

Tau day has nothing to redeem it.

What we really need is a Greek letter denoting the square root of tau. Now that would be useful!
posted by eviemath at 5:10 PM on June 28 [3 favorites]

IS TODAY THE DAY WE CAN TALK IN ALL CAPS
posted by gc at 5:16 PM on June 28 [17 favorites]

Tau day is gonna be the day
That they're gonna throw it back to you
By now you should've somehow
Realized what you gotta do
I don't believe that anybody
Feels the way I do about you now
posted by bleep at 5:54 PM on June 28 [15 favorites]

> The biggest problem with Tau day is that there is no food that people love associated with it. Anybody have suggestions?

> Forget it Jake, toe will never replace pie.

> Sincerely, A professional mathematician who kinda hates "Pi day" but forgives it because pie is delicious. Tau day has nothing to redeem it.

Seriously, is double Pi not good enough for anyone?
posted by Enturbulated at 6:08 PM on June 28 [4 favorites]

Please tell the mathematicians that are promoting this thing that Tao is pronounced Dao and that their attempts at ecumenical humor by equating tau with Tao and using the yin-yang symbol as a circle just looks dumb.
posted by njohnson23 at 7:29 PM on June 28 [8 favorites]

$raku -e 'say τ' 6.283185307179586$ raku -e 'say tau'
6.283185307179586
$raku -e 'say π' 3.141592653589793$ raku -e 'say pi'
3.141592653589793

Checks out!
posted by zengargoyle at 8:53 PM on June 28

>Two times an infinitely long number is still an infinitely long number. How does that solve anything, in a practical sense? Can someone nutshell that for me?
There's lots of places where "2 * pi" is a constant which leaves many powers of 2 cluttering up otherwise elegant equations (says the Tau-praganda*).

*: I kid about propaganda but the point remains that, if it's really more elegant, then a comment at the start of your paper or book to say 'we use \tau in place of 2*\pi where it simplifies formulae' will catch on for self-evident benefits.
posted by k3ninho at 8:55 PM on June 28 [2 favorites]

Dear, the internet, please stop trying to make tau happen. It's never going to happen.

One could say, 'Hey, Roman numerals suuuuuuuuck,' and another could respond, 'Yeah, but I'm a group theorist, so it doesn't matter,' and thus completely miss the point. Pi vs Tau strikes me as a bit of laziness with regard to cleaning up the entry levels of mathematics: It's maaaybe slightly more comfortable for the existing generation, but could make life slightly better for the next generation. And hopefully there's a lot more, and larger, future generations than there are current generations.

Once you start considering it, there's a whole lot of utility in ruthlessly making things easier, wherever possible. It's not just a matter of helping young potential-mathematicians, but also a matter of 'readabilty' and portability of results to other fields. And the effort has a kind of compound-interest. Suppose you've got three 'hard' pieces that need to combine into an interesting result. To do this, you've got to get not just the three hard pieces, but the 'interface' between them, which will be at least as difficult as the component parts. Once the parts are simple enough to fit in short-term memory with no strain, juggling and recombining them becomes much easier. (A similar parable from software: Debugging is harder than writing code. So if it takes the full brain power of the smartest person on my team to write this piece of code, then no one - including the author - will be able to debug it.)

Ok, well, I posted this because I thought it was funny that ten years had passed, but I guess I have Feels, too. (though I agree the tau/tao thing is worse than dumb.)
posted by kaibutsu at 8:56 PM on June 28 [4 favorites]

I kinda love that tau has been recently added to the Python and forthcoming .Net math libraries. The revolution continues!
posted by Popular Ethics at 9:05 PM on June 28 [1 favorite]

Feels the way I do about you now

Surely it should be "... about you, tau"?
posted by eviemath at 9:11 PM on June 28 [2 favorites]

Back on topic, related to kaibutsu's comment: Research Debt
posted by eviemath at 9:13 PM on June 28 [1 favorite]

We'd need to write the old MIT chant "Tangent, secant, cosine, sine. Three point one four one five nine!"

How about "Square root, cube root, integrate. Six point two eight three one eight"
posted by It's Never Lurgi at 9:55 PM on June 28 [11 favorites]

At first, I was skeptical, like reading about the guy who pushed base-12 math as more natural, because he once used to deliver eggs for a living, which he transported to their destination in batches of 144.

Then I read the manifesto and was won over (tau, not base-12). I just don't know how to switch people over, though, short of teaching both constants in high school and hoping the new constant wins over time and usage.

What I'm saying is that QWERTY will never die.
posted by They sucked his brains out! at 10:50 PM on June 28 [2 favorites]

But. But. Euler's identity. Surely argument enough for π just by itself?
posted by offmessage at 12:34 AM on June 29 [5 favorites]

Euler's identity remains neat: eiτ=1
posted by reynaert at 1:16 AM on June 29 [10 favorites]

2 is just annoying. Wherever it shows up. There’s a conservation of annoyance. Same with factors of 2pi, or tau.

I am also not sure what the Tau Manifesto author has against gamma functions. They have some complaint about the integral representation thereof (when they are trying to show tau is also nice for the volume and surface area of hyperspheres, which fine but the twos will come back and haunt you somewhere else then) but that’s just one representation. Personally I like thinking about gamma functions as the simplest function that has a single pole at every negative integer, but many people prefer to think of them as the natural analytic continuation of the factorial to complex numbers (and therefore to noninteger reals). From that perspective it’s pretty cool that they show up in the n-sphere volume.

Anyhow my personal adoration of gamma functions and the beauty of complex analysis notwithstanding, what do tau proponents have to say about the handy approximation that pi^2 is close to ten?
posted by nat at 2:12 AM on June 29

he once used to deliver eggs for a living, which he transported to their destination in batches of 144.

Urgh, that's gross.
posted by ambrosen at 2:47 AM on June 29 [4 favorites]

The case for pi.

Euler's identity remains neat: eiτ=1

Any multiple of pi will keep it neat. But as the pi manifesto explains : "What is the smallest positive solution x so that e^ix is an integer?"

The answer is pi. So it is more fundamental than τ.
posted by vacapinta at 3:06 AM on June 29

The biggest advantage of tau is when working with radians.

Instead of degrees, you can say the angle when the arc length equals the radius, that's 1 radian. So to go round a whole circle is 2 pi radians, (or 360 deg).

So half a circle is pi radians (180 deg), and a quarter circle is pi/2 radians (90 deg). A 16th of a circle is pi/8 radians. Uh, ok.

With Tau, 360 degrees is tau radians, a half circle is tau/2 radians, a quarter circle is tau/4 radians, a 16th of a circle is tau/16. This is simply more intuitive, and makes working with sine waves etc much simpler; the highest point of a sine wave is at 1/4 tau radians, the midpoint is 1/2 tau, the lowest at 3/4 tau, and back to the start point at 1 tau.

This makes more sense to me than 90, 180, 270, 360 or 1/2 pi, pi, 3/2 pi, 2 pi.

When I did electrical engineering many years ago, I think my life would have been MUCH more intuitive using Tau instead of Pi for phase, fourier transforms and other such work with oscillating waves which are fundamental to a lot of real world electrical signals

I'm not a Tau diehard by any means, and pi makes sense for some things, but where tau is simpler and makes more intuitive sense, we should use it instead of shoehorning in 2 times pi.
posted by Absolutely No You-Know-What at 3:54 AM on June 29 [9 favorites]

Why the hell do we keep overthinking this? Just make pi = 3 as God intended and be done with it. Simple.
posted by Naberius at 5:35 AM on June 29

It's bad enough that the formula for area is pi*D^2/4. Now you want to make me divide by 8?

If we're going to have tau, it should be pi/2. It even looks like half of pi.

(Measuring diameter >> measuring radius. If you ever specify the radius of a complete circle to be measured in real life, you've made a very strange choice.)
posted by Huffy Puffy at 5:38 AM on June 29 [3 favorites]

Metafilter: many people prefer to think of them as the natural analytic continuation of the factorial to complex numbers
posted by sammyo at 6:32 AM on June 29 [1 favorite]

If you ever specify the radius of a complete circle to be measured in real life, you've made a very strange choice.

Sure, but on the other hand, if you ever specify the diameter of a circle you want someone to draw in real life, they're gonna divide it by two and use a compass.
posted by solotoro at 6:36 AM on June 29 [6 favorites]

If you ever specify the radius of a complete circle to be measured in real life, you've made a very strange choice.

For a lot of applications the circle is created by the radius of some thing. A length of rope for example, the reach of a sprinkler.

Orbits also come to mind. The radius is the distance of the orbiting object from the object it is orbiting. Thats natural and leads to polar coordinates too. Nobody cares what twice the Earth's distance to the Sun is.
posted by vacapinta at 7:35 AM on June 29 [2 favorites]

As a programmer, I'm up for a good refactoring every now and then. I like turns more than half-turns, and I like radii more than I like diameters, so tau seems like an improvement. But I think mathematicians kinda don't care, so all the discussion happens between math-adjacent folks.
posted by Jpfed at 7:58 AM on June 29 [1 favorite]

I want to cosign this comment. Whether you use tau or pi, sometimes a power of 2 will show up in your formulas. However, converting times around a circle into multiples of pi and back is pointless cognitive load.

This whole discussion kind of reminds me of how some people got upset when astronomers said that Pluto shouldn't be classified as a planet.

It's bad enough that the formula for area is pi*D^2/4. Now you want to make me divide by 8?

I'm not sure if this is a joke, but a lot of us learned that formula as pi * r^2. If you learned and like to use pi * D^2 / 4, then I don't see the problem with tau * r^2 / 2. Unless you're saying that you frequently have to measure diameters of circles and compute their areas, in which case, yes, I want to make you divide by 8.
posted by jomato at 8:14 AM on June 29 [1 favorite]

But I think mathematicians kinda don't care, so all the discussion happens between math-adjacent folks.

Not an actual mathematician but I did want to grow up to be one once, and to me this is like just substituting one variable for another. What's the big deal? But if you're in one of those professions/interests that actually applies math to something (which, why would you do that? math is perfect by itself tyvm!) I could see how it would be useful if you don't like algebra or something? But everyone has their favorite notation so of course this is going to turn into some epic war that will last for centuries and will only be decided in a battle to the death in a circle constructed using (2*(tau/2)*d^2)/(2^2) until the world's supply of 2's is exhausted and we can't have halves anymore and no more couples or pairs or doubles (gloves and glasses and shoes are gonna be a problem) - it will be disastrous.

So we've all decided that pi is right and good and best, yes?
posted by LizBoBiz at 8:23 AM on June 29 [1 favorite]

Sure, but on the other hand, if you ever specify the diameter of a circle you want someone to draw in real life, they're gonna divide it by two and use a compass.

I think solotoro has it. Sometimes the measurement that gets picked is because of the task being done. This is the same reason why the Imperial measurement system just works better than the metric system in some cases. If you have a gallon of milk and have no measuring tools at all, but still have a few containers, you can still measure out a half-cup. Good luck trying to get a deciliter out of a liter of milk.
posted by nushustu at 8:57 AM on June 29

I'm a mathematician and I agree that tau is a more natural constant, that tau/4 is better notation for a right angle than pi/2, and so on. It wouldn't make much difference to me to switch, and I can imagine it might be easier for people learning trig for the first time. But it'd be inconvenient not to be able to use tau as a name for a variable anymore - when you've already used t and T, it's so useful to have another letter that's kind of like t, but not quite, and pronounced differently. If only capital tau were written differently than capital T, it would be the perfect variable name.
posted by ectabo at 9:01 AM on June 29 [2 favorites]

Oh my god no don't do this! If you replace pi with tau, the whole universe might collapse. Like don't even attempt it! What's wrong with you?
posted by sexyrobot at 9:09 AM on June 29 [1 favorite]

There's a lot of notational inertia to overcome, like how you would represent shear stress and other quantities that are traditionally denoted by τ. Also, in πd2/4, π/4 (~0.7854) is the ratio of the area of the circle to the square that contains it.
posted by Monday, stony Monday at 9:42 AM on June 29

Sure, but on the other hand, if you ever specify the diameter of a circle you want someone to draw in real life, they're gonna divide it by two and use a compass.

Maybe. It depends on if you want a hole in your paper or not.

Also depends on what that circle is for.
posted by Huffy Puffy at 9:53 AM on June 29

But it'd be inconvenient not to be able to use tau as a name for a variable anymore - when you've already used t and T, it's so useful to have another letter that's kind of like t, but not quite, and pronounced differently.

Wait’ll you hear what the electrical engineers have done with “i”.

(To be fair, they had to, since “current” begins with a “c”.)
posted by Huffy Puffy at 9:55 AM on June 29 [2 favorites]

what do tau proponents have to say about the handy approximation that pi^2 is close to ten?

... I have never used this approximation. I can't even think, quickly off the top of my head, of an application where pi2 shows up. Just square root of 2pi = square root of tau.
posted by eviemath at 10:07 AM on June 29

Well, there's the Basel problem, but that's pi^2/6. (Or 2 tau^2 / 3.)
posted by kaibutsu at 10:36 AM on June 29 [1 favorite]

Wait’ll you hear what the electrical engineers have done with “i”.

I think I remember this from undergrad physics -- I is current, so j is the square root of -1. And I is current because c was already taken for the speed of light? But wasn't current discovered before electromagnetic radiation?
posted by ectabo at 10:48 AM on June 29

Pi squared is in the volume of a 4-sphere.

But I was actually thinking of various physics-y estimation problems; that’s the context in which pi^2 being tennish is useful. Also occasionally useful is pi^2 being close to g in meters per second^2. And, there are around pi*10^7 seconds in a year. Good for getting order of magnitude problems quickly, basically.
posted by nat at 10:55 AM on June 29

Tau day has nothing to redeem it.

Ouch. Tau day is my birthday.
posted by hwyengr at 11:08 AM on June 29 [3 favorites]

Belated happy birthday wishes, hwyengr!
posted by Jpfed at 12:02 PM on June 29 [3 favorites]

Well, there's the Basel problem

Wrap it in a constant to get an answer in units of tau. Problem solved!
posted by They sucked his brains out! at 12:24 PM on June 29 [1 favorite]

Two times an infinitely long number is still an infinitely long number. How does that solve anything, in a practical sense?

Well, at least we know the last digit of τ will be even …

(I'll get me coat)
posted by scruss at 1:01 PM on June 29 [4 favorites]

Oh my god no don't do this! If you replace pi with tau, the whole universe might collapse. Like don't even attempt it! What's wrong with you?

Nothing's wrong with us. No one is replacing pi with tau.

We're replacing it with tau/2, as nature intended.
posted by fings at 1:27 PM on June 29 [4 favorites]

(derp. pi = tau/2, so the tau solution to the basel problem is tau^2 / 24, which is nicer. i will go drink more coffee now. but yeah, switching will probably eventually lead to the loss of a mars rover or something.)
posted by kaibutsu at 2:56 PM on June 29 [2 favorites]

Tau and Tau/2 are two totally different things! If you can't tell them apart... you know what, just don't touch anything until I get there.
posted by sexyrobot at 3:16 PM on June 29

When I used to do generative art, const TAU = Math.PI * 2; was a thing for a reason. #TauLife
posted by ryoshu at 4:39 PM on June 29

You can't use diameter to guarantee (define) a circle. A Reuleaux triangle has the same diameter all around but isn't a circle.
posted by zengargoyle at 5:05 PM on June 29 [1 favorite]

Reuleaux forms aren't easy to make without a moving centre or articulated tooling. I suspect the ancient Greek physical examples of round things weren't up to today's standards, but they would have a better fixed centre than Reuleaux.

Pi and Tau are far too big: everything useful stops at 45°
posted by scruss at 7:53 AM on June 30

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