Tau versus Pi

[TonyMcC]

It has been proposed that Pi should be replaced with the Tau for mathematical purposes. The Tau has twice the value of Pi. The reasoning behind this change seems to be that it would simplify many formulae since"2*Pi" is much more common in formulae than Pi on its own.

This certainly seems to be the case in electronics and it seems some eminent scholars are convinced. What do you think?

[baric]

It has been proposed that Pi should be replaced with the Tau for mathematical purposes. The Tau has twice the value of Pi. The reasoning behind this change seems to be that it would simplify many formulae since"2*Pi" is much more common in formulae than Pi on its own.

This certainly seems to be the case in electronics and it seems some eminent scholars are convinced. What do you think?

 

Interesting. I have thought for some time that 3.14 was not the best arbitrarily-chosen value to represent curvature and came to the conclusion that 6.28 was better.

 

Of course, it only slightly improves the symbolism and is not even remotely worth the effort to overcome the value that has become ingrained in our sciences for millenia.

[ajb]

I have come across arguments that [math]\tau = 2 \pi[/math] is more natural that just [math]\pi[/math]. It is true that [math]2\pi[/math] appears quite often in mathematics.

 

 

It is clear that [math]\pi[/math] is established (both as a number and notationally). It would probably cause more confusion at first if people started to use [math]\tau[/math]. I see it as more of a conventional or notational thing rather than anything very deep.

[baxtrom]

One could likewise argue that a better constant than [math]\pi[/math] would be [math]\sigma=\frac{\pi}{4}[/math], so that the constant is the ratio of areas of a unit circle to a unit square. Or, [math]\sigma=\pi^2[/math] so that [math]\int_{-\infty}^{\infty} e^{-x^2} \mathrm{d} x = \sigma[/math]. Et cetera.

 

I think there are natural reasons to why the ratio of circumference to diameter instead of radius was chosen thousands of years ago. It's simpler to measure the diameter. The diameter is, in my opinion, a more natural way of describing the size of a circle than the radius. If a handful mathematicians think it will be useful to adopt the [math]\tau[/math] constant, so be it. It will however most likely be known as two times [math]\pi[/math]..

Edited June 28, 2011 by baxtrom

[baric]

Here's a link with a convincing case: http://tauday.com/

[insane_alien]

it would make no difference.

 

if we switched to tau then we'd just have the same number of people complaining about tau/2 being in so many functions.

 

if you can't handle multiplication or division by 2 then what the hell are you doing with pi thats so important?

Edited June 28, 2011 by insane_alien

[TonyMcC]

it would make no difference.

 

if we switched to tau then we'd just have the same number of people complaining about tau/2 being in so many functions.

 

if you can't handle multiplication or division by 2 then what the hell are you doing with pi thats so important?

 

I think the point is that tau/2 would rarely be used because tau,itself, would be used in most formulae. That's another way of saying pi (alone) is rarely used because "2*pi" is used in most formulae. Of course we who are used to pi might not like it, but future students who have formulae to remember and manipulate might benefit

[DrRocket]

It has been proposed that Pi should be replaced with the Tau for mathematical purposes. The Tau has twice the value of Pi. The reasoning behind this change seems to be that it would simplify many formulae since"2*Pi" is much more common in formulae than Pi on its own.

This certainly seems to be the case in electronics and it seems some eminent scholars are convinced. What do you think?

 

"Tau Day revelers" either

 

a) understand very little real mathematics

 

b) really like beer

 

or

 

c) both.

[insane_alien]

and still, what difference would it make. a multiplication by 2 is so trivial that it's not worth the bother to remove it.

 

the current standard notation is to use pi. EVERYTHING uses pi. It'd be a fair effort to go back through the sum of human mathematical history and edit it to show tau. all for trivial benefit.

 

an example of the pointlessness (despite any merit it may have) is if somebody decided e would be better when shown mirrored. you'd have to change all forms all sinage etc etc. to satisfy a triviality.

 

if it was going to have some big massive impact that would make maths fundementally easier then i'd say go for it. but really all its doing is changing the way you write down '2*pi' its trivial

lets define a millimeter at 0.01mm longer than it currently is because that makes hammers slightly easier to hold.

 

etc. etc.

 

seems like a lot of make work. i can't stand this type of stuff these days, it all seems like some buerocraticly minded person trying to make a name for himself by making lots of work for everyone else that ultimately gets us back to where we were before.

 

2*pi isn't broken and it's not so crushingly impeding that it needs fixing

[TonyMcC]

"Tau Day revelers" either

 

a) understand very little real mathematics

 

b) really like beer

 

or

 

c) both.

 

You can argue this one out with Bob Palais, Research Professor of Mathematics, University of Utah. In the meantime I'll have another beer lol!

[DrRocket]

You can argue this one out with Bob Palais, Research Professor of Mathematics, University of Utah. In the meantime I'll have another beer lol!

 

I would be happy to. I know that department pretty well. Where has Bob taken a position on this, trivial, issue ?

 

If you mean this tongue-in-cheek piece, then I suggest that you have another beer.

Edited June 28, 2011 by DrRocket

[baric]

"Tau Day revelers" either

 

a) understand very little real mathematics

 

b) really like beer

 

or

 

c) both.

 

I object!

 

It did not take me long to realize that the value for pi was arbitrarily chosen from several possible values -- most likely for convenience. Some mulling on the issue made it seem obvious (to me) that 6.28... would have been a better choice, although I had no idea until yesterday that others had even entertained similar thoughts.

 

Of course, it is silly to argue that the use of tau is superior simply because a) the use of pi is entrenched, and b) multiplication by 2 is trivial.

 

No, the argument for tau relies solely on elegance. That's a notion that any mathematician can appreciate, with or without imbibing any beers.

[John Cuthber]

Why don't they just put a line through it in the way quantum mechanics do with Planck's constant?

[DrRocket]

Why don't they just put a line through it in the way quantum mechanics do with Planck's constant?

 

Using the same meaning for the bar produces a rather inscrutable way to write 1/2.

 

And eliminates a perfectly good reason to go get another beer.

[Hal.]

If people want to define , tau = 2 * pi , they can independently do that anytime they like currently . Tau has many uses and so does pi , ask the greeks !

[TonyMcC]

I would be happy to. I know that department pretty well. Where has Bob taken a position on this, trivial, issue ?

 

If you mean this tongue-in-cheek piece, then I suggest that you have another beer.

 

Cheers and bottoms up! I am in no sense a mathematician, just a retired lecturer in Electrical and Electronic Engineering (and other things). During the mathematical content of the syllabus just about every time I encountered pi it was multiplied by 2. Tau would have made life a little simpler (and the formulae more elegant?) for me and my students. I think you will understand that when I found an entry on today's news on this subject I found it interesting and wondered what "real" mathematicians would make of it. It would seem to be quite a contentious issue. Bob Palais seems a bit less tongue in cheek in this link :- http://www.math.utah.edu/~palais/pi.pdf

Edited June 28, 2011 by TonyMcC

[DrRocket]

Cheers and bottoms up! I am in no sense a mathematician, just a retired lecturer in Electrical and Electronic Engineering (and other things). During the mathematical content of the syllabus just about every time I encountered pi it was multiplied by 2. Tau would have made life a little simpler (and the formulae more elegant?) for me and my students. I think you will understand that when I found an entry on today's news on this subject I found it interesting and wondered what "real" mathematicians would make of it. It would seem to be quite a contentious issue. Bob Palais seems a bit less tongue in cheek in this link :- http://www.math.utah.../~palais/pi.pdf

 

 

Nothing published in the Ontelligencer ought be taken too seriously.

 

"Real" mathematicians, and I am one and so is Bob Palais, don't worry overmuch about whether one needs to multiply by 2 or not.

 

Back to the beer.

[ajb]

Back to the beer.

 

We all heard that, DrRocket is buying the drinks tonight!

[DrRocket]

We all heard that, DrRocket is buying the drinks tonight!

 

Only if you can get over here tonight. We can invite Bob Palais and the math department at "The U" -- to this bar, where they used to congregate in the past. http://utah.citysear...ifes_place.html

 

Let me know if you can arrange supersonic transport. Happy hour should start in a couple of hours.

Edited June 28, 2011 by DrRocket

[ajb]

Let me know if you can arrange supersonic transport. Happy hour should start in a couple of hours.

 

 

I would like to have joined you yesterday, but my TARDIS is in need of repair. I just can't seem to get the calculations right needed to guide my repairs. Hang on, I am being stupid, it is [math]\tau[/math] not [math]\pi[/math] in my equations! Silly me.

 

I'll come for that drink last week...

[DrRocket]

I would like to have joined you yesterday, but my TARDIS is in need of repair. I just can't seem to get the calculations right needed to guide my repairs. Hang on, I am being stupid, it is [math]\tau[/math] not [math]\pi[/math] in my equations! Silly me.

 

I'll come for that drink last week...

 

The [math]\tau[/math] required for proper TARDIS operation is torsion in the geometry of spacetime, not just [math] 2 \pi [/math] (as any geometer ought to realize). So, get with it and we can still meet for that beer yesterday.

 

BTW Bob Palais recognized that torsion competes for the [math]\tau[/math] moniker in that Intelligencer article linked earlier in the thread.

[ajb]

See it is already confusing!

 

Also [math]\tau[/math] is often used for "odd time" in the theory of supermanifolds. But that really is another story.

 

As an aside, I would use [math]T[/math] to denote the geometric torsion, ie. [math]T(X,Y)= \pm\nabla_{X}Y \pm \nabla_{Y}X \pm [X,Y][/math] (I forget the necessary signs on a supermanfold) for all vector fields [math]X,Y[/math] and [math]\nabla[/math] some affine connection on the manifold.

 

Torsion of curves in 3 dimensional space is usually denoted by [math]\tau[/math]. Mechanical torsion is also commonly denoted by [math]\tau[/math].

Edited June 29, 2011 by ajb

[baxtrom]

[math]\tau[/math] denotes shear stress and nothing else!

[ydoaPs]

an example of the pointlessness (despite any merit it may have) is if somebody decided e would be better when shown mirrored. you'd have to change all forms all sinage etc etc. to satisfy a triviality.

I don't think that the analogy holds as I'll explain below.

 

if it was going to have some big massive impact that would make maths fundementally easier then i'd say go for it. but really all its doing is changing the way you write down '2*pi' its trivial

I've seen it argued that it WOULD make a massive impact on the way one learns trig. It is more intuative and elegant. We use the circle constant by the radius rather than the diameter, so why not use the circle constant that is based on the radius rather than the diameter?

 

Tau is conceptually more intuative in that it represents one whole rotation(or *gasp* turn). It makes learning trig easier as it doesn't really make a whole lot of sense to learn angles in terms of half rotations.

 

Oh, and it's awesomely elegant for one reason:

[math]e^{{\tau}i}=1[/math] ties together e, the circle constant, i, and 1 without manipulation. Well, that actually has a little bit of manipulation as it really is [math]e^{{\tau}i}=1+0[/math] which ties together e, the circle constant, i, 1, and 0 far more naturally than if you would use pi.

 

 

So, like I said, your analogy doesn't quite hold since changing the letter e is neither conceptually more simple nor more elegant. Having said all that, however, it is still a simple substitution at the end of the day.

Edited June 29, 2011 by ydoaPs

[DrRocket]

[math]\tau[/math] denotes shear stress and nothing else!

 

Then by choosing prinhciple axes we can make [math]\tau[/math] go away. So [math]\pi[/math] is universal, but [math]\tau[/math] is just an artifact of the local coordinate system.