6 ms·

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 wor

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 15y 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 15y ago
Area is defined by integrals- good point.
bascule 15y 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.
MostAwesomeDude 15y 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
- ianterrell 15y 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!
  - MostAwesomeDude 15y ago
    > hastily Was two millennia not long enough? We could take another couple centuries, I guess. I don't think we're ever going to get a new answer for the ratio of the circumference of a circle to the diameter of that circle, though. > The lack of the 1/2 in the π version shows why it's "wrong"—it's not as meaningful. Frankly, I don't know what this means. I've read it several dozen times, and each time, it seems increasingly more inane. I can't help but wonder what you would say about the derivative (and antiderivative) of e^x; would you complain that it's not meaningful? Does it need more coefficients? More exponents?
    - ianterrell 15y ago
mikeash 15y 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.
- ianterrell 15y 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.
  - mikeash 15y ago
    I guess the pertinent question is whether this stimulates your intellectual curiosity because you find it to be an interesting question, or at least because it raises interesting questions, or whether it stimulates your curiosity because you think it's exceedingly important and making this change will have big consequences. I think the dismissive types see people obsessing over it as the latter, and this is, at least in my opinion, way more than is called for. There's nothing wrong with considering the consequences of such a change just for some mathematical fun. (After all, who here hasn't drawn out a complete system of units based on furlongs, fortnights, etc. as the fundamental units, rather than mks or cgs? What's that? None of you? Oh....) But the original manifesto seems to be overstating its case severely in terms of the consequences of such a change, and I think that's what others are reacting to. Ignoring the boring costs of switching the installed base of mathematicians, software, etc. from one constant to the other, the benefit of a switch seems to be that certain things become easier and other certain things become harder. At best, there's a small net gain. Hardly seems worth the discussion when considered in that light. If you're considering it as an interesting exercise to extract meaning from equations, well, go for it! But that seems to fit more under the banner of "What would happen if we switched this?" rather than "It would provide enormous benefit if everybody switched this!" as the original manifesto seemed to be saying.
omaranto 15y 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).

stianan 15y 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 15y ago

Area is defined by integrals- good point.

bascule 15y 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.

MostAwesomeDude 15y 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

ianterrell 15y 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!
- MostAwesomeDude 15y ago
  > hastily Was two millennia not long enough? We could take another couple centuries, I guess. I don't think we're ever going to get a new answer for the ratio of the circumference of a circle to the diameter of that circle, though. > The lack of the 1/2 in the π version shows why it's "wrong"—it's not as meaningful. Frankly, I don't know what this means. I've read it several dozen times, and each time, it seems increasingly more inane. I can't help but wonder what you would say about the derivative (and antiderivative) of e^x; would you complain that it's not meaningful? Does it need more coefficients? More exponents?
  - ianterrell 15y ago

mikeash 15y 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.

ianterrell 15y 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.
- mikeash 15y ago
  I guess the pertinent question is whether this stimulates your intellectual curiosity because you find it to be an interesting question, or at least because it raises interesting questions, or whether it stimulates your curiosity because you think it's exceedingly important and making this change will have big consequences. I think the dismissive types see people obsessing over it as the latter, and this is, at least in my opinion, way more than is called for. There's nothing wrong with considering the consequences of such a change just for some mathematical fun. (After all, who here hasn't drawn out a complete system of units based on furlongs, fortnights, etc. as the fundamental units, rather than mks or cgs? What's that? None of you? Oh....) But the original manifesto seems to be overstating its case severely in terms of the consequences of such a change, and I think that's what others are reacting to. Ignoring the boring costs of switching the installed base of mathematicians, software, etc. from one constant to the other, the benefit of a switch seems to be that certain things become easier and other certain things become harder. At best, there's a small net gain. Hardly seems worth the discussion when considered in that light. If you're considering it as an interesting exercise to extract meaning from equations, well, go for it! But that seems to fit more under the banner of "What would happen if we switched this?" rather than "It would provide enormous benefit if everybody switched this!" as the original manifesto seemed to be saying.

omaranto 15y 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).