pi-winning

March 14, 2011 5:20 AM

Happy half-τ day! What's a half-τ? You know it as π, but π is wrong. (via)
posted by DU (100 comments total)

Hmmm. I don't know if I should I feel transcendental or irrational about this.

I'm going with my usual choice: irrational.
posted by three blind mice at 5:24 AM on March 14, 2011 [5 favorites]

DU: That's exactly how I feel.
posted by cthuljew at 5:27 AM on March 14, 2011

The cake pi is a lie.
posted by Cat Pie Hurts at 5:32 AM on March 14, 2011

We already know about τ.
posted by Plutor at 5:35 AM on March 14, 2011

So it's gone around again, has it? Ah well. τ-τ little post!
posted by DU at 5:44 AM on March 14, 2011

If pi is wrong, I don't wanna be right.
posted by drlith at 5:53 AM on March 14, 2011

IF THIS POST IS DELETED IT IS EVIDENCE THAT THE CABAL IS CENSORING THE TAU!!!1!! PREPARE TEH METATALK FOR RESISTANCE!!!

Seriously though, this is amazing - throughout my physics degree, pi has always seemed just a little awkward, but I never considered this as a possible solution. It's quite brilliant. If we have an apocalypse, I hope the next incarnation of human civilization decides to use tau. Short of that, though, it's not gonna happen.
posted by Salvor Hardin at 6:01 AM on March 14, 2011

A constant's a constant.
posted by grobstein at 6:06 AM on March 14, 2011

Tau is no good. You cannot make pie jokes with tau. I guess that would be a tautology, but I will not even dignify that by... sigh.
posted by GenjiandProust at 6:09 AM on March 14, 2011 [6 favorites]

The pie is a lie, dude.
posted by dzkalman at 6:09 AM on March 14, 2011

I think he's right, tbh.

Two Pi's are all over the place in advanced physics.
posted by empath at 6:10 AM on March 14, 2011

Man, I can't wait for June 28th, when I will get to eat many tasty taus.

In related news, pancakes are wrong. Who eats just one pancake? No one. I propose that we instead refer to three pancakes as a panpile.
posted by phooky at 6:12 AM on March 14, 2011 [1 favorite]

panpile panoply
posted by robocop is bleeding at 6:13 AM on March 14, 2011 [2 favorites]

♪Pi♫
posted by zarq at 6:20 AM on March 14, 2011 [1 favorite]

Short of that, though, it's not gonna happen.

How can we switch from π to τ?
The next time you write something that uses the circle constant, simply say “For convenience, we set τ=2π”, and then proceed as usual. (Of course, this might just prompt the question, “Why would you want to do that?”, and I admit it would be nice to have a place to point them to. If only someone would write, say, a manifesto on the subject…) The way to get people to start using τ is to start using it yourself.

posted by DU at 6:22 AM on March 14, 2011

Tau is already excessively overloaded, it should not be assigned additional uses.
I do like his three-legged two-pi symbol, however.
posted by overyield at 6:28 AM on March 14, 2011 [2 favorites]

I brought apple and cherry π into the office today, to much appreciation.
posted by Faint of Butt at 6:29 AM on March 14, 2011

This is the dumbest idea ever, because it ruins Euler's identity.
posted by TypographicalError at 6:29 AM on March 14, 2011 [7 favorites]

Two Pi's are all over the place in advanced physics.

I think every Physics student at some point has an "A Ha!" moment, scribbles tau (or some other variable) = 2*pi in the margins, and substantially reduces the amount of handwriting necessary to complete a proof.

Hell, I did this all the time with (much) longer chains of constants that would tend to make long derivations icky and tiresome (and I do not claim any credit for being particularly clever with Physics).
posted by schmod at 6:32 AM on March 14, 2011 [1 favorite]

Tau is already excessively overloaded, it should not be assigned additional uses.
...

This is the dumbest idea ever, because it ruins Euler's identity.

Read the link.
posted by DU at 6:34 AM on March 14, 2011

This doesn't make any sense. If anything τ should be 1/2π, or possibly a little more. Just look at it.

Here's a Unicode-friendly alternative to the three-legged 2π: ╔╗.
posted by jedicus at 6:37 AM on March 14, 2011

This reads like a billboard on the side of the road to Timecube.
posted by stevis23 at 6:40 AM on March 14, 2011 [2 favorites]

This reads like a billboard on the side of the road to Timecube.

No, it really doesn't. It's perfectly reasonable.
posted by empath at 6:48 AM on March 14, 2011 [5 favorites]

No, it really doesn't. It's perfectly reasonable.

As reasonable as people who seriously advocate for pronoun reform.
posted by TypographicalError at 6:49 AM on March 14, 2011 [3 favorites]

Tau is the DVORAK of trigonometry.
posted by Blazecock Pileon at 6:52 AM on March 14, 2011 [11 favorites]

As reasonable as people who seriously advocate for pronoun reform.

Stuff like this happens all the time in math -- see the reduced planck's constant, which was introduced just to take 2*pi out of a bunch of equations.
posted by empath at 6:54 AM on March 14, 2011 [2 favorites]

Now we only need to invent a delectable desert (that can also be eaten for breakfast), name it Tow, and reopen then pungates!
posted by itstheclamsname at 6:55 AM on March 14, 2011 [2 favorites]

then=the

obviously

but still
posted by itstheclamsname at 6:56 AM on March 14, 2011

Another seemingly 'ridiculous' thing that physicists did was to change the values of all the physical constants to 1 -- hbar, c, the gravitational constant, etc... Just so they could stop writing c's and hbars are all over the place.

Changing pi to 2 pi is small potatoes compared to that.
posted by empath at 6:57 AM on March 14, 2011 [1 favorite]

TypographicalError: "This is the dumbest idea ever, because it ruins Euler's identity."

It makes Euler's identity better. Clumsy:

e^iπ + 1 = 0

Elegant:

e^iτ = 1

posted by Plutor at 6:57 AM on March 14, 2011 [6 favorites]

Oh, sure, Tau are great from a distance, but hoo boy do things go badly once they gets within 5 feet of something.

wait what
posted by MidAtlantic at 7:01 AM on March 14, 2011

I was going to protest that the real constant of interest here is 2 pi i, but I see I already did that in the other thread.

In the circular spirit of the day, though, I guess it's OK for me to say it again.

The real constant of interest here is 2 pi 1.
posted by escabeche at 7:03 AM on March 14, 2011

The first expression is more beautiful, in some ways, as it ties in another mathematically interesting number: zero.

Sometimes, simplicity hides away too much.
posted by Blazecock Pileon at 7:04 AM on March 14, 2011 [1 favorite]

Also, pi day would be more interesting if we pronounced the name of the Greek letter correctly.
posted by escabeche at 7:04 AM on March 14, 2011 [1 favorite]

Math class is tough!
posted by Rarebit Fiend at 7:05 AM on March 14, 2011

No, hbar was not introduced just to take 2*pi out of equations, it represents the Planck constant in angular frequency. It has the same effect, but there are sensible reasons for using it.

And as a card-carrying physicist, even I assert that setting all the constants to unity is pure claptrap.
posted by stevis23 at 7:05 AM on March 14, 2011

The first expression is more beautiful, in some ways, as it ties in another mathematically interesting number: zero.

Read the link.
posted by DU at 7:06 AM on March 14, 2011 [3 favorites]

It makes Euler's identity better.

Those equations you wrote are completely different, of course. Only the original can properly be called Euler's identity. Besides which, the original has some historical cachet, whereas the latter does not.

Even if I agreed with the idea that tau is the correct constant to be using as opposed to pi, it wouldn't matter, because this will absolutely never catch on. Just like New Math didn't catch on, just like English pronoun reform won't ever catch on. Hell, just like the metric system won't ever catch on. Any energy spent creating that webpage was utterly wasted.
posted by TypographicalError at 7:10 AM on March 14, 2011

If Zeno'd ever got around to thinking about it I bet he could have proven that circles don't exist and saved us all this confusion in the first place.
posted by Wolfdog at 7:10 AM on March 14, 2011

And as a card-carrying physicist, even I assert that setting all the constants to unity is pure claptrap.

You never work in planck units?
posted by empath at 7:11 AM on March 14, 2011

I am constantly amazed by people's inability to follow and willingness to ignore simple reasoning simply because it disagrees with what they already believe. Sigh. RTFA.
posted by cthuljew at 7:12 AM on March 14, 2011 [2 favorites]

Hell, just like the metric system won't ever catch on.

Huh?
posted by empath at 7:12 AM on March 14, 2011 [2 favorites]

The first expression is more beautiful, in some ways, as it ties in another mathematically interesting number: zero.

e^(i*tau) -1 = 0

Happy?
posted by empath at 7:14 AM on March 14, 2011 [4 favorites]

Now we only need to invent a delectable desert (that can also be eaten for breakfast), name it Tow, and reopen then pungates!

Why don't we call the new constant cheesecake and denote it Ч, perhaps. Brilliant. I used to be against it, but now I'm for it.
posted by Wolfdog at 7:15 AM on March 14, 2011 [1 favorite]

The problem with the people who get hung up on the difference between 2πr and πd are the ones who are missing the calculus relations between r and circumference, area and volume with respect the radius (not diameter).

Area is what you get when you integrate the formula for circumference. Volume is what you get when you integrate the formula for area. There is no diameter in all that.

These two sets of formulae are equivalent:

C = 2πr
A = πr²
V = 4/3πr³

C = τr
A = 1/2τr²
V = 2/3τr³

I'm used to the first set. The second have a certain uniform appeal to them, but nothing that makes me want to get all, "GRAR! π IS BAD!"
posted by plinth at 7:16 AM on March 14, 2011 [1 favorite]

Even if I agreed with the idea that tau is the correct constant to be using as opposed to pi, it wouldn't matter, because this will absolutely never catch on. Just like New Math didn't catch on, just like English pronoun reform won't ever catch on. Hell, just like the metric system won't ever catch on. Any energy spent creating that webpage was utterly wasted.

You are sure expending a lot of energy and scorn defending against something that's such a non-threat.

PS: If you listen to Lehrer's song, the "regular way" he describes is completely incomprehensible. The way you and I learned is much more similar to "new math" than it is to what Lehrer apparently learned.

PPS: The metric system is doing very well all over the world as well as in most areas of science and many in engineering in the US.
posted by DU at 7:16 AM on March 14, 2011

And more to the point, if you think you can't reshape how an entire culture does basic math operations, you don't have any kids in school. Check out the "lattice method" of multiplication, for instance, that my kids have learned. In some ways, it's a lot better than the partial products method. (Also, they learn something called "partial products" but it is slightly different than what I learned. And better.)
posted by DU at 7:21 AM on March 14, 2011

No, hbar was not introduced just to take 2*pi out of equations, it represents the Planck constant in angular frequency.

They could have just as well have used h/(2*pi), but instead they introduced a new constant that equalled h/(2*pi) so they didn't have to write 2*pi all over the place. My point stands. Physicists introduce new constants all the time to make equations simpler to work with.
posted by empath at 7:21 AM on March 14, 2011 [1 favorite]

Also, anyone who denies the ongoing changes in English pronoun usage is kidding themselves.
posted by escabeche at 7:21 AM on March 14, 2011 [3 favorites]

The real constant of interest here is 2 pi 1.

Oops, when I cycled back after four years and tried to repeat it, it changed to something else.

Monodromy!
posted by escabeche at 7:23 AM on March 14, 2011 [1 favorite]

That lattice method of multiplication is crazy awesome, except I realize that with my chronically bad handwriting nobody would ever have been able to follow my work in grade school.

Also, I have no problem with half-tau or Tau as a new constant for pedagogical reasons, but I mean come on...PIE!
posted by lizarrd at 7:25 AM on March 14, 2011

but I mean come on...PIE!

True fact: The formula for determining the volume of a pizza with radius 'z' and depth 'a' is:

pi*z*z*a
posted by empath at 7:29 AM on March 14, 2011 [7 favorites]

I came here just to say pie aren't square. Pie are round.

Complaining about writing 2*pi to the point where you want everyone else to write 2*hbar/2 instead is just silly.
posted by Nanukthedog at 7:29 AM on March 14, 2011

Yeah, it doesn't "make Euler's identity better", it completely changes it. At least the other equations, he's just swapping a 3-legged symbol for every instance of 2pi. In Euler's identity, he actually changes it.
posted by King Bee at 7:33 AM on March 14, 2011

You crazy Tau-ists and your protracted wars.
posted by molecicco at 7:34 AM on March 14, 2011

Complaining about writing 2*pi to the point where you want everyone else to write 2*hbar/2 instead is just silly.

Obv, you'd have to change the value of hbar.
posted by empath at 7:34 AM on March 14, 2011

Yeah, it doesn't "make Euler's identity better", it completely changes it.

This doesn't make sense to me. Euler's identity is euler's identity no matter what units you use. It's a geometric relationship.
posted by empath at 7:34 AM on March 14, 2011 [1 favorite]

Yes, Euler's identity is Euler's identity no matter what units you use. In that case, he needs to write "e^(.5*tau*i) + 1 = 0".

The point being that the number in the exponent is 3.14somethingsomething times i, not 6.28somethingsomething times i.
posted by King Bee at 7:57 AM on March 14, 2011

Like the concept, hate the name. τ looks far to much like T. π is at least fairly obviously not an English letter. Come back when you have a better symbol.
posted by fings at 7:59 AM on March 14, 2011 [1 favorite]

And if it's "just a geometric relationship", then I propose that we get rid of the whole pesky pi thing altogether and substitute x=1 in Euler's formula to achieve e^i = cos(1) + i sin (1). There, much better. No Greek symbols at all!
posted by King Bee at 7:59 AM on March 14, 2011

This seems like the math equivalent of the American/USian argument.
posted by rocket88 at 8:36 AM on March 14, 2011

Vi Hart (previously) weighs in
posted by DowBits at 8:50 AM on March 14, 2011 [2 favorites]

There are several reasons why pi is simply the wrong constant, and I happen to agree! It's a brilliantly argued website there. But their choice of "tau" is problematic. Sure, "τ" resembles "π" outwardly, but if anybody seriously believes that people will stop using and saying "two pi" they have another thing coming. These derivative characters stand about as much chance of catching on as all of those invented neuter pronouns.

But there IS another solution! A ligature of 2 and π together. This ligature would have an obvious intuitive meaning, as well as a pronunciation: /tupi/ or "two-pi." There's really no reason to change to another constant, or to an unpronounceable symbol. The spirit of the thing is what is most important: that 2π is really the basic constant.

This sort of shift would be very gradual and easy-to-swallow. I've already started writing all my "two pi"s as a two with legs. It's quicker, easier, conceptually cleaner, and is conveniently pronounced exactly the same. Eventually, the name for the constant will become "twopi," and nobody will feel any stranger about this being one word than they feel about "nobody" being one word.
posted by phenylphenol at 9:17 AM on March 14, 2011 [4 favorites]

DowBits: Indeed, cute little video. Her treatise still depends also on students remembering what the sine and cosine functions are, instead of memorizing cryptic nonsense given to them by idiot teachers who do not understand their subject (like "SohCahToa" and so forth).

As a mathematician, I really do not care either way. If we want to stop using pi and use tau as twice pi everywhere, fine. I can easily make the change, as could nearly any mathematician. Hell, if you want to start using 1/e as "the new e" (as is also sort of suggested in the OP), I'm fine with that also. Just tell me what symbols you want me to use and what quantities they represent. It doesn't change any of the mathematics.
posted by King Bee at 9:25 AM on March 14, 2011

You realize of course, King Bee, that classic equations get reformulated all the time. The way Maxwell wrote his equations in the 19th century barely resembles their most common form now, because as a community we decided on new and better standards for how equations should be written.

If you want to be a math purist that only uses equations in their original form, you've got bigger fish to fry than defending Euler from the scourge of tau.
posted by auto-correct at 9:27 AM on March 14, 2011 [1 favorite]

If you listen to Lehrer's song, the "regular way" he describes is completely incomprehensible. The way you and I learned is much more similar to "new math" than it is to what Lehrer apparently learned. (DU)

Lehrer's "New Math" lyrics are:

Consider the following subtraction problem, which I will put up here: 342 - 173.

Now remember how we used to do that:
three from two is nine;
carry the one, and
if you're under 35 or went to a private school you say seven from three is six,
but if you're over 35 and went to a public school you say eight from four is six;
carry the one so we have 169

In other words, digit by digit from the least-significant end, borrowing a one when necessary. I'm in college right now, and this is how I subtract. What's incomprehensible about it, and what did you learn?
posted by d. z. wang at 9:30 AM on March 14, 2011

I'm glad I don't know what you all are talking about else I'd not have thought that >this< was half-T.

I'll go back to sleep, now.
posted by Man with Lantern at 9:33 AM on March 14, 2011

auto-correct: I'm not "defending Euler from the scourge of tau", I was just pointing out that with tau, the equation says something different than it does with pi in its place. It is not the same thing he is doing in the other equations (substituting tau in the place of twice pi).

And like I said above, I really don't care. For all the people who complain about 2pi radians being "once around the circle" and they don't like that, why don't we just change the system to newradians, then? So that what is current a radian is 1/2 newradian? That solves the problem too.
posted by King Bee at 9:33 AM on March 14, 2011

King Bee- we want to keep radians as they are, because 1 radian around a unit circle has arc length 1.
posted by Jpfed at 9:42 AM on March 14, 2011

I propose

π

as a compromise between tau and new symbol/ligature. Seems a lot easier to tell people that pi with a line through it or 'pi-bar' is 2*pi than the other alternatives.
posted by Throw away your common sense and get an afro! at 9:46 AM on March 14, 2011 [1 favorite]

Pie r round, cornbread r2. Until we resolve this bistromath paradox science is at a stand still.
posted by humanfont at 9:47 AM on March 14, 2011

So much for "Those who know the τ do not speak."
posted by GenjiandProust at 9:47 AM on March 14, 2011 [2 favorites]

tangentially related:* WTF, Google, for not having a great graphic for pi day this year.

Slackers.

*see what I did there?
posted by misha at 9:49 AM on March 14, 2011

Now remember how we used to do that:
three from two is nine;
carry the one, and
if you're under 35 or went to a private school you say seven from three is six,
but if you're over 35 and went to a public school you say eight from four is six;
carry the one so we have 169

In other words, digit by digit from the least-significant end, borrowing a one when necessary. I'm in college right now, and this is how I subtract. What's incomprehensible about it, and what did you learn?

You say "3 from 2 is 9, carry the one"? And from trying to work this out on paper the way he describe it, it sounds like the "carry" is to the bottom number, which I know I never learned. The second step works similarly.

Obviously it's mathematically equivalent, but I'd sure hate to explain to a 5 year how you take 3 apples from 2 apples, get 9 and have 10 left over to "carry".
posted by DU at 10:12 AM on March 14, 2011

We were just discussing how everything is made greater by pi the other day. Sorry, but "half tau" just doesn't have the same ring...
posted by TheCoug at 10:15 AM on March 14, 2011

You never work in planck units?

No, when I was still in academia, I worked in the lab.
posted by stevis23 at 10:20 AM on March 14, 2011 [2 favorites]

Yeah, working in the planck unit was really cramped. Nothin' but asses and elbows.
posted by BitterOldPunk at 10:23 AM on March 14, 2011 [1 favorite]

Oh and the way I do 342 - 173 is: "You can't take 3 from 2, 2 is less than 3 so you look at the 4 in the tens place, now that's really 4 tens so you make it 3 tens...." I.e. "new math", but in the base 10 verse not the base 8 verse.
posted by DU at 10:24 AM on March 14, 2011

No, when I was still in academia, I worked in the lab.

So you didn't do the kind of work that is made easier by setting constants equal to one, but that doesn't mean it's not useful for theoreticians.
posted by empath at 10:24 AM on March 14, 2011

Well at least Darren Aranofsky's got a name for his sequel now.
posted by condour75 at 10:31 AM on March 14, 2011 [2 favorites]

You cannot make pie jokes with tau.

Mmmm...tau

Nope, it doesn't go.
posted by dry white toast at 10:39 AM on March 14, 2011

Making pie with filling from a can is wrong.
posted by kenko at 10:57 AM on March 14, 2011

The glyph we use for pi is the lowercase version of the Greek letter. Since this tau thing is twice that much, why not use the capital version? π becomes Π.
posted by LogicalDash at 11:27 AM on March 14, 2011

Here's a quite good YouTube video on this.
posted by Neiltupper at 11:46 AM on March 14, 2011

I still like Pi Day.
posted by inigo2 at 1:09 PM on March 14, 2011

It makes Euler's identity better. Clumsy:
e^iπ + 1 = 0
Elegant:
e^iτ = 1

Some people like writing it:

e^iπ = -1

I guess the tau method does save two strokes.
posted by weston at 1:49 PM on March 14, 2011

PIE-DAY PIEE-DAY PIEE-DAY
posted by Pruitt-Igoe at 1:55 PM on March 14, 2011

Clumsy:
e^iπ + 1 = 0
Elegant:
e^iτ = 1

On the contrary! The "clumsy" method is actually much more elegant than the "elegant" method, since the former but not the latter includes e, i, π, the multiplicative identity, and the additive identity.
posted by kenko at 2:06 PM on March 14, 2011

Did no one read the link?
posted by DU at 3:19 PM on March 14, 2011

The whole concept of pi being "wrong" seems silly to me. Of course its not wrong it's correct by definition, its just not the most convenient for certain purposes.
posted by ozomatli at 3:21 PM on March 14, 2011

Jesus H. Christ, we read the link.
posted by Blazecock Pileon at 3:21 PM on March 14, 2011 [1 favorite]

DU: I thought by specifically referencing things in the link, it would show that I looked at it. I guess not.
posted by King Bee at 3:23 PM on March 14, 2011

Why do I get the suspicion that the guy who wrote this Tau Manifesto is also a big proponent of Esperanto?
posted by rocket88 at 4:59 PM on March 14, 2011 [3 favorites]

I actually know someone else who is pushing for π to be replaced by τ/2. But her birthday is June 28 and so she's a bit biased.
posted by madcaptenor at 5:26 PM on March 14, 2011

Don't worry, ozomatli - pi is only wrong by a constant.

Alternatively, pi is wrong by pi.
posted by Earl the Polliwog at 5:43 PM on March 14, 2011

Lattice multiplication just looks like a parlor trick to me. It works fine on paper, but I can't imagine doing mental math without partial products.
posted by HumuloneRanger at 8:02 PM on March 14, 2011

An alien civilization is broadcasting the first 10000 digits of the number τ to us over and over, but to scientists on Earth, it is nothing but gibberish.
posted by eye of newt at 9:54 PM on March 14, 2011

eye of newt: they'd probably broadcast it in binary, so we're okay.
posted by madcaptenor at 10:09 PM on March 14, 2011 [1 favorite]

I can't imagine doing mental math without partial products.

Agreed. OTOH, the lattice method is nicely compartmentalized. That is, it's easy to see where you went wrong, if you did, because each digit pairing is laid out and the carries are all saved until the end. So it's good as a teaching method. Which seems to be how it's used in our school system. Kids are required to learn both systems but can use either. Then in middle school they have to use the partial products.
posted by DU at 4:39 AM on March 15, 2011

An alien civilization is broadcasting the first 10000 digits of the number τ to us over and over, but to scientists on Earth, it is nothing but gibberish.

The deleted twist ending to His Master's Voice.
posted by Wolfdog at 7:20 AM on March 15, 2011