# It's twice as good as Pi!

June 28, 2010 12:36 PM Subscribe

This seems misguided to me. The natural quantity which deserves to be denoted by a single Greek letter is evidently 2 pi i, which is the integral of dz/z around the unit circle. Or, if you like, it's the logarithm of 1.

posted by escabeche at 12:55 PM on June 28, 2010

posted by escabeche at 12:55 PM on June 28, 2010

Escabeche; how do you know you're using the right square root of negative one? For all you know you're really denoting -2πi by a single symbol.

posted by madcaptenor at 1:00 PM on June 28, 2010

posted by madcaptenor at 1:00 PM on June 28, 2010

There you go again, thinking of the ring of motivic periods as something with a canonical embedding into the complex numbers!

posted by escabeche at 1:02 PM on June 28, 2010 [2 favorites]

posted by escabeche at 1:02 PM on June 28, 2010 [2 favorites]

*There you go again, thinking of the ring of motivic periods as something with a canonical embedding into the complex numbers!*

I mean,

*duh*.

posted by axiom at 1:05 PM on June 28, 2010 [2 favorites]

Why do Michael Hartl and Bob Palais hate 2? Isn't that what their insidious anti-π agenda is really all about?

I'm just asking questions.

posted by weston at 1:34 PM on June 28, 2010

I'm just asking questions.

posted by weston at 1:34 PM on June 28, 2010

Too late. I'm sorry, but there's no way I'm memorizing Tau to 50 digits.

posted by straight at 1:34 PM on June 28, 2010 [1 favorite]

posted by straight at 1:34 PM on June 28, 2010 [1 favorite]

Also, while we're fixing ancient conventions, could we please have electrons be positive charges and protons negative charges?

posted by straight at 1:36 PM on June 28, 2010 [2 favorites]

posted by straight at 1:36 PM on June 28, 2010 [2 favorites]

YES! Although, I'm kinda shocked there is no facebook group for this....yet.

posted by redbeard at 1:45 PM on June 28, 2010

posted by redbeard at 1:45 PM on June 28, 2010

Yeah, good luck with that. Here in the US of A we haven't even hipped to the metric system even if it is demonstrably better. Also, he'd better watch out for Hasidic conspiracies.

Regardless, I'm convinced of the superiority of Tau. The preponderance of 2*pi in common equations has always irked me. We've even come up with ways of avoiding actually writing it out, simplifying Plank's constant h-bar (h/(2*pi)) with a nifty dash through the letter h.

posted by StrangerInAStrainedLand at 1:50 PM on June 28, 2010 [2 favorites]

Regardless, I'm convinced of the superiority of Tau. The preponderance of 2*pi in common equations has always irked me. We've even come up with ways of avoiding actually writing it out, simplifying Plank's constant h-bar (h/(2*pi)) with a nifty dash through the letter h.

posted by StrangerInAStrainedLand at 1:50 PM on June 28, 2010 [2 favorites]

I just want to know how she is going to get the liquid out of that Klein bottle.

posted by Kikujiro's Summer at 1:56 PM on June 28, 2010 [1 favorite]

posted by Kikujiro's Summer at 1:56 PM on June 28, 2010 [1 favorite]

She can drink from the Klein bottle by turning it over. Technically, I suppose she can't get it 'out' because there's no 'in'. Just one surface.

posted by echo target at 2:02 PM on June 28, 2010 [1 favorite]

posted by echo target at 2:02 PM on June 28, 2010 [1 favorite]

It doesn't matter what the constant is because you can use maths to make it the constant you want.

Hungry? 2pi. Lazy? pi/2.

posted by doublehappy at 2:11 PM on June 28, 2010

Hungry? 2pi. Lazy? pi/2.

posted by doublehappy at 2:11 PM on June 28, 2010

I'm down with Tau. That was an excellent explanation. So far as I can think of right now, the best reason to stick with pi is that on pi day you have an excuse to eat lots and lots of delicious pie. As soon as someone comes up with a baked good called tau (or even 'tao') that is as tasty as pie, I'll start evangelizing.

In fact, pi gives us TWO days on which we can eat delicious pie, thanks to its oft-ill-bespoken-of brother, Pi Approximation Day. It's coming up, even... Order your pies now and beat the rush...

posted by kaibutsu at 2:14 PM on June 28, 2010

In fact, pi gives us TWO days on which we can eat delicious pie, thanks to its oft-ill-bespoken-of brother, Pi Approximation Day. It's coming up, even... Order your pies now and beat the rush...

posted by kaibutsu at 2:14 PM on June 28, 2010

I also wonder, on Tau day, does that mean we need to make (and eat) 2 pies?

Or super-sized single pies?

I'm all for more pie!

posted by redbeard at 2:38 PM on June 28, 2010

Or super-sized single pies?

I'm all for more pie!

posted by redbeard at 2:38 PM on June 28, 2010

You might expect me to be down with this, it being my birthday, but once again Americans forget the large number of people in the world who write the date day/month. It's 28/6 today, damn it, not 6/28!

It's a quixotic kind of thing to challenge anyway, because it's largely a contingent definition that now has so much history behind it, it's impossible to change. It would be like trying to change the number of seconds in a minute.

Also, there are many formulae that do not have 2pi in them. Coulomb: factor of 1/

And the h-bar thing: physicists'd continue to write h-bar even if it replaced h/tau instead of h/2pi. (Particle physicists would continue to seek a way of defining their units so that pi=1)

Also: tau has many other uses in the physics namespace: more so than pi - because pi is reserved for the circle constant one tends to avoid using it as a variable. So tau often gets used for characteristic times, like the inverse of the decay constant.

posted by Electric Dragon at 2:51 PM on June 28, 2010

It's a quixotic kind of thing to challenge anyway, because it's largely a contingent definition that now has so much history behind it, it's impossible to change. It would be like trying to change the number of seconds in a minute.

Also, there are many formulae that do not have 2pi in them. Coulomb: factor of 1/

**4**pi, GR: factor of**8**pi.And the h-bar thing: physicists'd continue to write h-bar even if it replaced h/tau instead of h/2pi. (Particle physicists would continue to seek a way of defining their units so that pi=1)

Also: tau has many other uses in the physics namespace: more so than pi - because pi is reserved for the circle constant one tends to avoid using it as a variable. So tau often gets used for characteristic times, like the inverse of the decay constant.

posted by Electric Dragon at 2:51 PM on June 28, 2010

*There you go again, thinking of the ring of motivic periods as something with a canonical embedding into the complex numbers*

This was funny when I said it in my Reagan voice.

posted by gimonca at 3:31 PM on June 28, 2010

*So tau often gets used for characteristic times, like the inverse of the decay constant.*

You mean... Lamda?

/annoyed at nobody getting his previous reference.

posted by Artw at 3:33 PM on June 28, 2010

*Also, while we're fixing ancient conventions, could we please have electrons be positive charges and protons negative charges?*

Only if we can call protons controns. Or negatrons (which wikipedia says is what electrons used to be called). Although that would cause confusion with positrons, which are the antimatter counterpart to electrons.

This is why I didn't study physics.

Actually, there are a lot of reasons I didn't major in physics. I did like free-body diagrams, though. *Goes and plays with his computer.*

posted by spaceman_spiff at 3:45 PM on June 28, 2010

*Also, there are many formulae that do not have 2pi in them. Coulomb: factor of 1/4pi, GR: factor of 8pi.*

Erm, 4pi and 8pi are both multiples of 2pi...

posted by axiom at 4:11 PM on June 28, 2010

*Erm, 4pi and 8pi are both multiples of 2pi...*

Exactly. You're trading one multiple for another.

posted by Electric Dragon at 4:18 PM on June 28, 2010

Pi is an important part of the equation that links the elite with the meaning of life, the universe and everything.

posted by Obscure Reference at 4:37 PM on June 28, 2010 [1 favorite]

posted by Obscure Reference at 4:37 PM on June 28, 2010 [1 favorite]

*Erm, 4pi and 8pi are both multiples of 2pi...*

Exactly. You're trading one multiple for another.

Exactly. You're trading one multiple for another.

In some cases you're right, but in most cases a symbol for 2*pi would be a simplification. Either way, it's never, ever, going to happen, and won't make a difference whatsoever in terms of mathematical achievements possible with one symbol versus the other. It's more about the purity of the idea. Who can argue, against the beauty of the Tau-based quadratic for the area of a circle that mirrors the other simple quadratics found in nature through one integration?

posted by StrangerInAStrainedLand at 4:37 PM on June 28, 2010

This notation is probably most convenient when you find yourself doing a lot of Fourier transforms. For instance, here's a textbook derivation where the factors of 2π are carried around together for a while rather than "simplified" by combining them in an intermediate step with the factors of two that creep in from a different place. It's much harder to do this sort of bookkeeping when you're wasting a second trying to remember whether 2

I like Palais's original manifesto quite a bit. I'm surprised at how emboldened I feel by Hartl's suggestion to use τ rather than Palais's three-legged dog to pick up this habit outside my own notes. Notations are powerful.

posted by fantabulous timewaster at 5:39 PM on June 28, 2010

^{6}is 32 or 64.I like Palais's original manifesto quite a bit. I'm surprised at how emboldened I feel by Hartl's suggestion to use τ rather than Palais's three-legged dog to pick up this habit outside my own notes. Notations are powerful.

posted by fantabulous timewaster at 5:39 PM on June 28, 2010

Does anyone know what is meant by proving Matt Groening wrong by memorizing 50 digits of pi? It's proving a little awkward to google.

posted by rubah at 7:55 PM on June 28, 2010

posted by rubah at 7:55 PM on June 28, 2010

rubah, Figure 3 in the link is a video, it happens there.

posted by fantabulous timewaster at 8:06 PM on June 28, 2010

posted by fantabulous timewaster at 8:06 PM on June 28, 2010

We haven't adopted the metric system because, looking at the unit circles of the Tauday website, we should, obviously, adopt base 12 first.

posted by wobh at 8:22 PM on June 28, 2010 [2 favorites]

posted by wobh at 8:22 PM on June 28, 2010 [2 favorites]

That is the first time I have ever really truly understood radians. I am a freaking geometry tutor and I have never *gotten* it. I just memorized and went with it. But now? I seriously get them! That is so rad! (If I had any sort of cool cred, I fear I would need to turn it in immediately.)

posted by stoneweaver at 9:47 PM on June 28, 2010 [2 favorites]

posted by stoneweaver at 9:47 PM on June 28, 2010 [2 favorites]

Reminds me of an engineering professor I once had who taught that e=m, and that the c² was just needed to do conversion of units.

(Note I said engineering, not physics).

posted by eye of newt at 10:19 PM on June 28, 2010

(Note I said engineering, not physics).

posted by eye of newt at 10:19 PM on June 28, 2010

Stoneweaver: seriously? Go read up on the unit circle, the idea that a radian is a measure of arclength is pretty fucking basic.

posted by spaceman_spiff at 10:57 PM on June 28, 2010

posted by spaceman_spiff at 10:57 PM on June 28, 2010

Damn!

I have some chops here, a math degree - and this actually is quite a viable idea. I remember very early (11 or 12?) being annoyed by that extraneous 2 he mentions.

Yes, Euler's identity would have an extra /2 in it. This is a little less neat, but it actually makes it clearer - the idea is "half of a full circle rotation is the same as multiplying by -1".

escabeche: surely you mean log(-1)? log(1) is 0.

Also, I totally don't buy your argument. pi occurs in tons and tons of places that have nothing to do with imaginary numbers, where imaginaries are in fact forbidden. Why glue those two concepts together? Instead, keep i and pi/tau separate and use Euler's identity to connect 'em.

posted by lupus_yonderboy at 11:22 PM on June 28, 2010

I have some chops here, a math degree - and this actually is quite a viable idea. I remember very early (11 or 12?) being annoyed by that extraneous 2 he mentions.

Yes, Euler's identity would have an extra /2 in it. This is a little less neat, but it actually makes it clearer - the idea is "half of a full circle rotation is the same as multiplying by -1".

escabeche: surely you mean log(-1)? log(1) is 0.

Also, I totally don't buy your argument. pi occurs in tons and tons of places that have nothing to do with imaginary numbers, where imaginaries are in fact forbidden. Why glue those two concepts together? Instead, keep i and pi/tau separate and use Euler's identity to connect 'em.

how do you know you're using the right square root of negative one?This isn't a real problem. You can't distinguish between the two square roots of minus one - you introduce a new symbol, i, that has the property that it is -1 when squared, and then -i has that same property. If I were to switch i and -i in all that work, nothing would change...

posted by lupus_yonderboy at 11:22 PM on June 28, 2010

"escabeche: surely you mean log(-1)? log(1) is 0. "

Not really. Depending on how you want to deal with it, the complex logarithm is multivalued. log(1) is 0 plus any number of multiples of~~2pi~~ tau.

posted by edd at 4:17 AM on June 29, 2010

Not really. Depending on how you want to deal with it, the complex logarithm is multivalued. log(1) is 0 plus any number of multiples of

posted by edd at 4:17 AM on June 29, 2010

*So far as I can think of right now, the best reason to stick with pi is that on pi day you have an excuse to eat lots and lots of delicious pie.*

MATHS JOKE:

What is the volume of a pizza of radius

*z*and height

*a*?

posted by EndsOfInvention at 6:10 AM on June 29, 2010 [1 favorite]

This will not see widespread adoption until there is an xkcd about it.

posted by Eideteker at 7:06 AM on June 29, 2010

posted by Eideteker at 7:06 AM on June 29, 2010

And another thing: why pollute our simple, clean integer number line with all these irrational and transcendental numbers? I think we should use the inverses of all these and keep them contained between 0 and 1.

posted by wobh at 7:44 AM on June 29, 2010

posted by wobh at 7:44 AM on June 29, 2010

*"escabeche: surely you mean log(-1)? log(1) is 0. "*

Not really. Depending on how you want to deal with it, the complex logarithm is multivalued. log(1) is 0 plus any number of multiples of 2pi.

Not really. Depending on how you want to deal with it, the complex logarithm is multivalued. log(1) is 0 plus any number of multiples of 2pi.

Not 2 pi, but 2 pi i. If you like, you can say that log(1) -- i.e. the preimage of the identity under the exponential -- is naturally identified with 2 pi i Z. So it seems reasonable to take a generator for this group as the fundamental constant. Of course, as madcaptenor points out, there are two choices of generator, corresponding to the two square roots of -1; but as lupus_yonderboy says, it doesn't matter which one you choose.

posted by escabeche at 8:00 AM on June 29, 2010

it doesn't matter which one you choose.This is only true once.

posted by fantabulous timewaster at 8:37 AM on June 29, 2010

Seriously?

Yeah, seriously. All that reading about the unit circle just never made it click. 15 years later, one little tiny shift in thinking was enough to make all of that fall into place. There's a big difference between

posted by stoneweaver at 12:47 PM on June 29, 2010

Yeah, seriously. All that reading about the unit circle just never made it click. 15 years later, one little tiny shift in thinking was enough to make all of that fall into place. There's a big difference between

*knowing*something and really getting it. The shift between the two is a wonderful thing. If it hasn't happened to you, I highly recommend it. If it has, I recommend not being an ass to other people about it.posted by stoneweaver at 12:47 PM on June 29, 2010

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