I never could figure out some of the details of the tau proposal. For example, the range of inverse trigonometric functions is π, but why? Isn’t π supposed to be unnatural? I can imagine a civilization finding arc-of-sine to be the most interesting operation, and choosing π/2 or π/4 as their preferred constant.
The Basel problem is mentioned obliquely, by its connection to the Riemann Zeta function. I find this interesting. The appearance of π² might normally be completely surprising, and not convertible, but we can rewrite it as τ² over 24, a famously meaningful number who refuses to stop showing up in fundamental ponderings of the universe.
Circular area is not the only place where we use π; it also shows up more generally for the area/volume of any n-ball/n-sphere, and its appearances are not readily convertible. Powers of π/2 are not any better when converted, and neither are denominators of √π. It has been pondered for a while why this recurrence is so oddly shaped. The author claims, in Section 5, to put this to rest, and I agree that their Equations 20-28 are pretty, but we’re left with no more answers than before; the floor function has no more business being here than √π. As the appeal continues, we start talking of π/2? They do arrive at an interesting insight about symmetries, but I’m not sure why it is the octahedral symmetry and not one of the other possible spherical symmetries.
Secton 5.2, meanwhile, openly contradicts itself; it can’t decide whether π is a member of σ, but does show that yes, it is. A lot of focus in this document on where everything “naturally” is supposed to go, as if there is some unseen guiding force inspiring us to make the right choices of notation. This section claims that the appearance of π is a pun, but the pun is actually better than that. The shape and area of a circle varies as we change the norm which we are working in. When we choose the Euclidean norm, a very “natural” norm which appears in any number of dimensions, we get π. This is also the only norm which gives the circle an infinitely-large symmetry group, S¹. So π is a pun that relates not just surface area and volume, but also distance and infinity and symmetry, borne along the Euclidean norm.
I’m glad that they’re responding to arguments made by critics, and that the dialogue is still relatively polite after all this time of acrimony.
I don’t think this is appropriate. Let the Pi people have their day, and post this on Tau Day instead. :-)
To quote Marilyn Manson, I wasn’t born with enough middle fingers for this.
It’s a case of Poe’s Law to me. But, because Tau is merely pointless rather than completely bananas, it’s twice as hard to distinguish sincerity from satire. You might even say it’s… 2(Poe’s Law).
Maybe a fear of the following pattern: one pretend to be joking while announcing a loud statement, and when there are enough people showing their actual belief in the “joke”, one change its public opinion from “joking” to “we actually mean it”.
This is extremely irrelevant to any student of math or working mathematician. If you have interesting pop-math to write about, just write about it directly, without the ridiculous pretense.
I propose a new metric unit of length, the perimetre, defined to be the circumference of a circle with a diameter of one metre. Now pi is one, which is eminently more sensible than 3-and-a-bit or six-and-a-bit, and all I need is a collection of blog posts.
That is not how it works. In your proposal pi is one perimetre, while in reality pi is a dimensionless unit.
Then we shall redefine one to be 1/π. That way we’ve just scaled everything up a bit. If my calculations are correct, everything should work out the same.
1=1/π=(1/π)/π=1/π²=… ad infinitum
Pi is one perimetre per metre, which is length/length ergo dimensionless.
Then pi isn’t one, or it doesn’t make sense. How do you add 1 perimetre + 1 metre?