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The Pi Manifesto

thepimanifesto.com

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Re: The Pi Manifesto

#21

Post by loup-vaillant »

natural219 wrote: post #18

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 roadb…

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.

Re: The Pi Manifesto

#22

Post by ianterrell »

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.

Re: The Pi Manifesto

#23

Post by stianan »

ianterrell wrote: post #22

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 forev…

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.

Re: The Pi Manifesto

#24

Post by brudgers »

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?

Re: The Pi Manifesto

#25

Post by amalcon »

natural219 wrote: post #18

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 roadb…

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.

Re: The Pi Manifesto

#27

Post by orangecat »

fexl wrote: post #4

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".

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.

Re: The Pi Manifesto

#28

Post by flomincucci »

loup-vaillant wrote: post #21
natural219 wrote: post #18

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 roadb…

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…

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.

Re: The Pi Manifesto

#29

Post by sophacles »

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.

Re: The Pi Manifesto

#30

Post by fexl »

fexl wrote: post #17
yobbobandana wrote: post #8

Earlier quoted context omitted.

personally, i'd answer "half tau". half tau r^2 is a fine equation for an area.

:) 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.

Though in fairness to tau, one can always choose a pithy question whose answer is shorter either way, to wit:

What is the area of a unit circle? Pi.

How many radians are in a circle? Tau.

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