TonyMcC 87 Posted June 28, 2011 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? 0 Share this post Link to post Share on other sites

baric 17 Posted June 28, 2011 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. 0 Share this post Link to post Share on other sites

ajb 1567 Posted June 28, 2011 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. 0 Share this post Link to post Share on other sites

baxtrom 6 Posted June 28, 2011 (edited) 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 1 Share this post Link to post Share on other sites

baric 17 Posted June 28, 2011 Here's a link with a convincing case: http://tauday.com/ 0 Share this post Link to post Share on other sites

insane_alien 840 Posted June 28, 2011 (edited) 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 2 Share this post Link to post Share on other sites

TonyMcC 87 Posted June 28, 2011 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 0 Share this post Link to post Share on other sites

DrRocket 334 Posted June 28, 2011 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. 0 Share this post Link to post Share on other sites

insane_alien 840 Posted June 28, 2011 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 0 Share this post Link to post Share on other sites

TonyMcC 87 Posted June 28, 2011 "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! 0 Share this post Link to post Share on other sites

DrRocket 334 Posted June 28, 2011 (edited) 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 0 Share this post Link to post Share on other sites

baric 17 Posted June 28, 2011 "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. 0 Share this post Link to post Share on other sites

John Cuthber 3325 Posted June 28, 2011 Why don't they just put a line through it in the way quantum mechanics do with Planck's constant? 1 Share this post Link to post Share on other sites

DrRocket 334 Posted June 28, 2011 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. 0 Share this post Link to post Share on other sites

Hal. 32 Posted June 28, 2011 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 ! 0 Share this post Link to post Share on other sites

TonyMcC 87 Posted June 28, 2011 (edited) 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 0 Share this post Link to post Share on other sites

DrRocket 334 Posted June 28, 2011 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. 0 Share this post Link to post Share on other sites

ajb 1567 Posted June 28, 2011 Back to the beer. We all heard that, DrRocket is buying the drinks tonight! 0 Share this post Link to post Share on other sites

DrRocket 334 Posted June 28, 2011 (edited) 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 0 Share this post Link to post Share on other sites

ajb 1567 Posted June 29, 2011 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... 2 Share this post Link to post Share on other sites

DrRocket 334 Posted June 29, 2011 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. 0 Share this post Link to post Share on other sites

ajb 1567 Posted June 29, 2011 (edited) 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 0 Share this post Link to post Share on other sites

baxtrom 6 Posted June 29, 2011 [math]\tau[/math] denotes shear stress and nothing else! 0 Share this post Link to post Share on other sites

ydoaPs 1589 Posted June 29, 2011 (edited) 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 trivialI'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 0 Share this post Link to post Share on other sites

DrRocket 334 Posted June 29, 2011 [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. 1 Share this post Link to post Share on other sites