31–40 of 85 posts
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…
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…
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)?
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 th…
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: electr…
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.
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…
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
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.
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.
Earlier quoted context omitted.
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 th…
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).
I've never understood the particular argument of "single intermediary constant (tau) rather than two (2,pi)". 2pi is one constant that contains multiple glyphs, just as 1/2 is one constant, just as tau/2 would be one constant. That it is derived logically from other constants does not make it two separate constants. Even multi-digit numbers are derived logically from their component glyphs (12 = 10+2).
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.
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…
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…
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!