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Happy Tau Day

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Re: Happy Tau Day

#101

Post by JadeNB »

skrebbel wrote: post #30

If mathematics has a bikeshed, this is it. I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.

> If mathematics has a bikeshed, this is it.

In my experience, few professional mathematicians care about this. The question that Bromskloss (https://news.ycombinator.com/item?id=11993750) mentions, of whether or not 0 is a natural number, is likely to incur a far more passionate response. (At the risk of downvotes: it is.)

Re: Happy Tau Day

#102

Post by lamontcg »

jessriedel wrote: post #77
skrebbel wrote: post #30

If mathematics has a bikeshed, this is it. I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.

You're right about the bikeshedness, but that doesn't mean there isn't a clearly better bike shed design. I also find that these sorts of inefficiencies/inelegances compound. One or two are trivial, but when you have 30 of them, suddenly the mental tax becomes noticeable. Furthermore, the cost falls mostly on the students, while the experts have already paid it and don't see the need to worry about it anymore.

Yeah, but this bikeshed got decided hundreds of years ago.

Its only appealing to internet hipsters who want to brag about their organically grown free range tau.

Making the next generation of math students use "2 pi" in their formulas is going to be vastly easier than literally rewriting all the books.

Re: Happy Tau Day

#103

Post by squeaky-clean »

gravypod wrote: post #65
jeffwass wrote: post #61

Earlier quoted context omitted.

You wrote "This is to uniform a hole slew of previously unrelated equations that can now be represented similarly." You seem to be saying that introducing a new constant tau=2pi and redefining a slew of previously unrelated equations in terms of tau instead of pi is suddenly going to make them "uniformly represented". I don't understand why they're not considered uniformly represented when defined just as consistentl…

Have you watched the linked video? If not I will not be able to explain what's going on as well as the presenter. He is able to show that many common physical calculations for volume or area all relate to the same generic form. He also is able to present many other cases where pie wins out. It is very much worth a watch.

Getting a "This video does not exist." error from your link.

Re: Happy Tau Day

#105

Post by andrewla »

thanatropism wrote: post #88

What's a nice infinite series summing to tau that isn't merely 2S(n) where S(n) sums to pi?

The simplest formula that I can think of is

  pi/4 = tau/8 = atan(1) = 1 - 1/3 + 1/5 - 1/7 + ...
4 vs 8 doesn't seem like a change in the arbitrariness of the constant. The other major simple ones are:

  pi^2 / 6 = tau^2 / 24 = 1 + 1/(2^2) + 1/(3^2) + 1/(4^2) + ...
  pi^2 / 12 = tau^2 / 48 = 1 - 1(/2^2) + 1/(3^2) - 1/(4^2) + ...
Once again, 6 vs 24 (and 12 vs 48) is an arbitrary difference in arbitrariness. I'm not really aware of any commonly used series expansions that don't involve a constant multiply just to get to pi. On the other hand, I'm not aware of anything super-elegant that yield tau here either, so I think it's a tie at best.

Re: Happy Tau Day

#106

Post by Asooka »

lamontcg wrote: post #102
jessriedel wrote: post #77

Earlier quoted context omitted.

You're right about the bikeshedness, but that doesn't mean there isn't a clearly better bike shed design. I also find that these sorts of inefficiencies/inelegances compound. One or two are trivial, but when you have 30 of them, suddenly the mental tax becomes noticeable. Furthermore, the cost falls mostly on the students, while the experts have already paid it and don't see the need to worry about it anymore.

Yeah, but this bikeshed got decided hundreds of years ago. Its only appealing to internet hipsters who want to brag about their organically grown free range tau. Making the next generation of math students use "2 pi" in their formulas is going to be vastly easier than literally rewriting all the books.

https://news.ycombinator.com/newswelcome.html

Essentially there are two rules here: don't post or upvote crap links, and don't be rude or dumb in comment threads.

The most important principle on HN, though, is to make thoughtful comments. Thoughtful in both senses: civil and substantial.

So the principle here is: don't say anything you wouldn't say face to face.

Re: Happy Tau Day

#107

Post by tempodox »

skrebbel wrote: post #30

If mathematics has a bikeshed, this is it. I enjoy the ridiculousness of it all, but people who consider this anything other than a well-executed joke really should get a hold of themselves.

I find your interpretation rather benign. Saying, “pi is wrong, tau is right” is the equivalent of mathematical bigotry to me.

Re: Happy Tau Day

#108

Post by kej »

kazinator wrote: post #97
kej wrote: post #90

Earlier quoted context omitted.

Writing it equal to 0 isn't a hack, it's a common method of understanding a function. You factor polynomials by setting them equal to 0, for example. In the case of Euler's identity, what we're really asking is "what values of x make e^(i x ) + 1 = 0 true?" and the answer is "every multiple of π". Using τ instead hides half of the answers.

You mean "every multiple of 2π, shifted by π". The value -1 only comes around once per revolution of the unit circle! The solutions to e^(ix) + 1 = 0 are { π, 3π, 5π, ... } Whereas the solutions to e^(ix) - 1 = 0 are: { 0, 2π, 4π, 3π, ... } i.e. { 0, τ, 2τ, 3τ, ... } Also, note that when we set a polynomial to zero, the roots appear subtracted on the opposite side from the independent variable: (x - r0)(x - r1)...(x…

Poor phrasing and math-before-coffee on my part. The point I was going for is that e^(ix) has real values for each multiple of π. That is mathematically interesting, and is obscured if you use τ instead.

Re: Happy Tau Day

#109

Post by agumonkey »

Steuard wrote: post #78
agumonkey wrote: post #52

Earlier quoted context omitted.

Reminds me of Taylor series. The factorial terms eluded me for so long until I realized it was a cancelling factor for accumulated derivation of polynomials. Now there's this link in my mind between powers / derivation / factorials.

What polynomials are being derived, and from what premises? Are you thinking of how to derive series solutions to differential equations or something? I'm unclear on what you're getting at here. (Or, oh: did you mean "differentiation" when you said "derivation"? That would fit what you've said. Sorry for the pedantic post; I'll just leave this here in case anyone else is confused.)

Sorry for the fuzzy vocabulary. TBH I wasn't even convinced I understood taylor series correctly. A quick search on wikipedia hint at that derivation is used sometimes; derivative; differentiation etc etc.

About the point:

    d(n)(x^n.dx)
    = n d(n-1)(x^(n-1).dx)
    = (n * (n-1 * (...)))
    = n! * x
    hence the 1/n! term.

Re: Happy Tau Day

#110

Post by kazinator »

kej wrote: post #108
kazinator wrote: post #97

Earlier quoted context omitted.

You mean "every multiple of 2π, shifted by π". The value -1 only comes around once per revolution of the unit circle! The solutions to e^(ix) + 1 = 0 are { π, 3π, 5π, ... } Whereas the solutions to e^(ix) - 1 = 0 are: { 0, 2π, 4π, 3π, ... } i.e. { 0, τ, 2τ, 3τ, ... } Also, note that when we set a polynomial to zero, the roots appear subtracted on the opposite side from the independent variable: (x - r0)(x - r1)...(x…

Poor phrasing and math-before-coffee on my part. The point I was going for is that e^(i x ) has real values for each multiple of π. That is mathematically interesting, and is obscured if you use τ instead.

Yes; similarly, that a sinusoidal crosses zero twice in each period is obscured by a focus on the period itself.
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