The Pi Manifesto

http://www.thepimanifesto.com/

by zerovox • 15 years ago

116 82 15 years ago

wccrawford• 15 years ago

I disagree with change for change's sake. This whole tau thing is born of some idealist that thinks things only make sense his/her own way.

The only thing I didn't see in the article is that the symbol visually looks like a T, so when you see it in a formula, you have to really look at it to know what's going on.

edw2• 15 years ago

I would add that this stupid tau thing speaks to the conspiratorialist instinct common to many HN readers. You see, the self-evident truth of tau's superiority has been masterfully obscured by powerful dark forces in an attempt to protect their crude economic self interest, and if you don't agree, you're obviously either part of the conspiracy or one of the sheeple that's been snowed by it.

sesqu6• 15 years ago

I have had that thought, but find it incredibly hard to entertain. Do you genuinely believe it, or is it just something that explains why others' opinions might differ?

willvarfar• 15 years ago

I've considered refactoring my pathfinding code - 2.0 is this magic constant that is floating around all over my code.

Inertia has prevented me.

aidenn0• 15 years ago

Off topic, but if you're using floating-point for pathfinding code, you're going to have different results depending on your distance from the origin.

fexl5• 15 years ago

When you ask hard-core Tauists what the area of a unit circle is, do they actually answer "tau over two"? Or do they just say "pi"?

By the way, this whole discussion reminds me of what W.V.O. Quine called "mathematosis".

yobbobandana• 15 years ago

personally, i'd answer "half tau".

half tau r^2 is a fine equation for an area.

fexl5• 15 years ago

:) Still, two syllables instead of one.

I suppose if I found myself writing "2 * pi" or "4 * pi^2" a lot, I might throw in a dash of tau here and there for brevity. Otherwise it's all the same to me.

orangecat• 15 years ago

As the tau manifesto discusses, "half tau" is the more meaningful answer: the area of a circle is equal to the area of a triangle whose base is the circumference and whose height is the radius.

lotharbot• 15 years ago

It's the integral of tau * r * dr from 0 to 1, which is tau/2.

bascule2• 15 years ago

It's τ/2. The area of a circle is τr²/2. You may be familiar with the idea of x²/2 from calculus: it's an integral, which can be used to compute areas.

fexl5• 15 years ago

Yes, that certainly is the integral of x * dx. So voila, there's your 1/2. And tau relates the triangle to the circle. Nice trick.

Mind you, I don't have a dog in this hunt so I'm not all up to speed on it. All I know for sure is that tau = 2 * pi, so I won't be terribly upset if I see either usage. I generally favor the use of notations which better reveal an underlying concept, but I don't like it when people get all high and mighty about things.

scythe12• 15 years ago

Damnit, this is just as bad as the tau manifesto. The point is that it doesn't matter what the bloody constant is, we don't need any -more- goddamn manifestos. Call it an arc constant or an angle constant or whatever you want.

However, there is one massive abuse of terminology that is driving me insane, which is the use of the phrase "Quadratic forms". E = 1/2 k x^2 is not a quadratic form. A quadratic form is a homogeneous polynomial of degree two, and it's a topic discussed in number theory:

http://en.wikipedia.org/wiki/Quadratic_form

The vast majority of people will never encounter a legitimate quadratic form. Call it a quadratic equation or whatever -- it's not a quadratic form. Both the tau manifesto and the pi manifesto got this bit manifestly wrong.

cpa3• 15 years ago

I don't see why E = 1/2 k x^2 isn't a quadratic form. It's a quadratic form in a vector space of dimension 1 (here, the real numbers), which matrix is just (1/2 k). In fact here, we're dealing with a (degenerated) conic.

What's your point? Should the author have written E(x) = ...?

Besides, tau is pointless because a tau pie isn't nearly as fun as a pi pie.

scythe12• 15 years ago

At best, it's a cubic form, since the spring constant is also a variable. Similarly 1/2 a t^2 is a cubic form. pi r^2 however is a quadratic form.

stayjin• 15 years ago

For me this debate is the monumental evidence that when people get obsessed over something their intellectual openness shrinks to a very small dividend of pi, sorry I meant tau :)

jannes• 15 years ago

TLDR:

- The area of a unit circle is Pi.

- The Tau Manifesto is full of selective bias. They pinpoint formulas that contain 2π while ignoring other formulas that do not.

SonicSoul• 15 years ago

eagerly awaiting π vs τ rap wars..

adavies42• 15 years ago

i wonder if we can get monzy and mc++ to take opposite sides....

natural219• 15 years ago

I just want to ask all of the Pi/apathetic people-- how long did it take you to understand radians? For me, it was a week before I was comfortable naming any angle in radians in a reasonable amount of time (this is after a week of drilling).

This is just my point of view, but calculating radians was a significant roadblock into making quick trigonometric calculations. In fact, I'd have to say it was the biggest roadblock. This has nothing to do with how "clean" it looks or how I "feel" about how it's presented.

That said, I don't think it's worth it to make the switch because of all the hassle. I'm just curious about all of the hostility towards Tauists.

tldr; it has nothing to do with any mathematical formula looking "cleaner," but everything to do with teaching math effectively.

loup-vaillant• 15 years ago

The teaching argument (which by the way this article did not address) is for me the most powerful one. All the other arguments look secondary to me.

> That said, I don't think it's worth it to make the switch because of all the hassle.

It would be no hassle for pupils. I bet that it would be easier and faster to teach Tau first, then mention that Pi is half Tau. In my opinion, teaching should have the priority. I don't really care if the rest of the world use Pi, but I'll teach Tau first.

flomincucci• 15 years ago

I agree with teaching Tau first. Personally, it took me at least a week to begin to understand radians, and almost a month to understand it pretty well. Tau is more intuitive than Pi in this case.

amalcon4• 15 years ago

It only took me about a day, but I suspect that's because I was already used to cycles at the time (1 cycle=2pi radians). Getting used to cycles took me about a week.

To my mind, the problem is not with pi; the problem is with degrees. Everyone learns about degrees first, and then must "un-learn" these artificial numbers and begin thinking in fractions of a circle (with an extra constant thrown in there one way or the other, in the case of radians). If we began labeling globes, protractors, and the like in radians (or fractional cycles), this problem would go away.

sesqu6• 15 years ago

I don't think in radians, I think in cycles (radians/tau). I used to think in degrees, and could never get the hang of radians. Unfortunately, I cannot imagine the mathematical world moving to cycles, ever. The most I can hope for is that teachers introduce others to a single intermediary constant (tau) rather than two (2,pi).

roundsquare3• 15 years ago

"the problem is with degrees"

I partly disagree. For kids, defining something using irrational numbers would probably be very confusing. Using integers is much easier.

So, why 360? Because we talk about right angles a lot and we want to have a third, a half, etc... and (I'm guessing) they wanted it to be a multiple of 10.

I think the point is to be able to teach geometry to kids without worrying about them getting confused by fractions and/or irrational numbers.

ianterrell14• 15 years ago

1. This is a good discussion to have. Those who are dismissive show, in my opinion, a lack of intellectual curiosity. Elegance for the sake of elegance is a worthwhile goal.

2. From a pragmatist point of view, you're right, it doesn't matter. You continue reading and writing PHP and using π. They both get the job done. You don't have to participate any further.

3. There will be 2s floating around some equations forever, whether using π or τ. That's not the point. The point is not "cleanliness" or even teaching efficacy. The point is elegance and that comes from meaning. What does the equation say? Equation cleanliness and ease of understanding are both worthwhile side effects, but it's meaning that's important.

4. Going from π to τ would be nontrivial, and would involve confusion of its own. That makes it not worth it to some people, and that's a valid opinion.

5. This article suffers from more selection bias than the Tau Manifesto. The radius is the undisputed king of the circle; it defines it. The area of a circle is not, after all, π * (D/2)^2. But it's not about prettiness, it's about meaning! Area is a property defined by the integral, which has a natural meaning and result with τ. The result may be a little equation that's pretty or not depending on your point of view, but it's just a shortcut.

6. The other examples in the article similarly fall apart when meaning is considered.

stianan• 15 years ago

I really don't appreciate the argument that "it doesn't matter what the constant is". Of course it doesn't matter if you are only interested in the result of a calculation, but like you say, it does matter when you're trying to understand what the formulas express.

I find it surprising that this article, and many mathematicians asked to comment in the media, pull out the area formula as their prime counter-example, seemingly forgetting that using pi is only obscuring the mechanics behind it.

Rusky• 15 years ago

Area is defined by integrals- good point.

bascule2• 15 years ago

The section of the Tau Manifesto on the area of the circle (which the author describes as pi's coup de grace) was the one that convinced me tau makes more sense.

MostAwesomeDude4• 15 years ago

The area of the traditional unit circle is π, which has strong ties to the definition of every trigonometric function, and the reason that radians of common fractions of the unit circle are expressed in terms of π is related to the integrals used to derive arc length.

Just as an exercise, try setting the area of the unit circle to 2π, and then see how meaningful your radian measurements are. How many radians are in a quarter arc of the circle with area 2π? :3

ianterrell14• 15 years ago

> The area of the traditional unit circle is π

The area of the unit circle is 3.14(etc) units squared. The result is a number; it's how you get there that's important. You get there by integrating. The "right" equation for area is not πr^2 or τr^2/2; it's the integral that leads to either of those equations. The 1/2 in the τ version is meaningful because it is an artifact of the integration. The lack of the 1/2 in the π version shows why it's "wrong"—it's not as meaningful.

> try setting the area of the unit circle to 2π

This is a nonsensical statement. As is "traditional unit circle," but I let that one slide already.

> the reason that radians of common fractions of the unit circle are expressed in terms of π

The reason they're expressed in terms of π is because a circle constant is needed, and π was chosen. And it was chosen hastily.

Your arguments are unsound!

sesqu6• 15 years ago

Why do you refer to the area? Why not the diameter or the circumference? If you care about the area, why not use the unit circle with area 1?

A quarter arc of a circle is π/2 radians, regardless of area.

colanderman• 15 years ago

The circumference of the traditional unit circle is τ, which has strong ties to the definition of every trigonometric function, and the reason that radians of common fractions of the unit circle are expressed in terms of τ is related to the periods of sine and cosine.

…it's a poor argument that supports your opponent after switching key nouns.

mikeash2• 15 years ago

I consider myself to have intellectual curiosity but don't see this discussion to be particularly compelling. I don't think there is anything about intellectual curiosity which requires one to consider every question that's raised no matter what. There simply isn't enough time to consider everything, so prioritization is always necessary.

ianterrell14• 15 years ago

I agree with the sentiment expressed in your last sentence, but it's hard for me to imagine that one wouldn't give priority to something so fundamental as the circle constant (which touches so much in math, science, engineering, software, etc). That's doubly true considering the time investment for reading about the arguments is rather small, 15 minutes or so. And it's triply true considering that very many other people have vetted the argument for you, enough that mainstream media are writing articles on the topic.

So no, you don't have to consider every question that's raised "no matter what" to be considered intellectually curious, but this is hardly such a trivial, general case as that implies.

omaranto• 15 years ago

  1. This is a good discussion to have. Those who are dismissive show, in my opinion, a lack of intellectual curiosity. Elegance for the sake of elegance is a worthwhile goal.

Life is too short to argue over notation. I for one will show my "lack of intellectual curiosity" and go back to learning mathematics (with short breaks to argue with people on HN :P).

brudgers• 15 years ago

Is the authors replacement of "Tauists" with "Taoists" and "Tau" with "Tao" an indication that he is repressing his subconscious belief that Tau is the way?

afhof• 15 years ago

And I open my eggs on the little end...

sophacles• 15 years ago

Here is what is wrong with the "anti-tauist" rants:

They take a bunch of people who already learned the subject and presume that those people are experts a teaching said subject. These people always assume that the way they learned is best, because "dammit, it was good enough for me". They just can't see any other way.

Sadly, this ignores all of the other people, who may be capable of understanding and properly using the subject if presented in a different way.

For pedagogical purposes, Tau is worth a shot, if it helps some people get to the point that they realize "for the math the constant doesn't matter".

Just like anything else: try to teach broadly, and let the experts do the adjusting, not make the novice bend to the expert's will or be damned.

kwantam• 15 years ago

The practical problem with tau is, as was pointed out in the article, tau is already used for other things. Shear stress, torque, time constants, you name it.

pi is a notational freak in that it represents something so fundamental that few dare tread upon the usage---pi truly is a globally reserved name. To a lesser extent, the same is true of e, but even a number as important as i doesn't enjoy this property: electrical engineers use j for sqrt(-1) because i is current.

So let's say we all start using tau. Then I decide I'm going to do some basic rotational mechanics, and now I have two taus, one for torque and one for 2pi. OK, that's a no-go. How about we just redefine pi=2pi? Well... how do we know whether someone means pi=~6.28, or pi=~3.14?

It's just no good. Tau is not a viable candidate name for the constant equal to 2pi. Find another character in another language. How about Pei (Hebrew)?

sesqu6• 15 years ago

Pi is not globally reserved. It is commonly used in, for example, statistics to refer to multinomial probabilities, and wikipedia tells me it's also the name of the prime-counting function and parallax.

I should note that this was annoying to me when dealing with IRT, in which some models have 2pi in the normalizing constants. Not to say tau isn't used in statistics already as well.

There just aren't enough greek letters. I have wondered about what the symbol for tau should be, and I keep thinking of a circle including a radius line that extends slightly outside the circle, but tau is much easier to write, especially when using ascii.

jblow• 15 years ago

I stopped reading early, when he's claiming pi is better for the area of a circle, because that revealed that the author hasn't really thought about this very much.

If you look at the equations for the volumes of spheres in n dimensions (with 2D being just one of them), tau shows a clean pattern. pi leaves you with a mess.

ThaddeusQuay• 15 years ago

Given the nature of the debate, I think it's funny that the HN URL here ends in "404".

simcop2387• 15 years ago

All this will ever lead to is Indiana passing a new law that Tau is exactly 6.

https://secure.wikimedia.org/wikipedia/en/wiki/Indiana_Pi_Bi...

The Pi Manifesto

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