Tuesday, March 13, 2012

Happy Half Tau Day

Even though I concur with Bob Palais that Pi is Wrong, I hope you have a good day tomorrow.

I am swamped at home and at work, and the tutorial on how to knit a circle in any stitch pattern will have to wait. Perhaps Tau day would be a good target deadline. After all, the method relies on the crucial fact that
circumference = τ*radius
which looks so much more elegant than
circumference = 2*π*radius

I never did like how it takes 2π radians to go one full rotation. The beauty of τ is that one τ is one rotation. How intuitively easy to remember! τ and π were both in historical usage but π had better PR and edged out the more elegant τ.

May I suggest you view Vi Hart's lighthearted take, Pi is (still Wrong)?



Math and physics aficionados should read Pi is Wrong and the Tau Manifesto. The first time I read Pi is Wrong, I smacked myself on the forehead. Doh, why didn't I think of it before? I am not to blame for those pesky factors of two; it's the stupid notation! Read section 3.1 Quadratic Forms of the Tau Manifesto and admire the elegance and consistency.

Aside:
I took Numerical Analysis with Bob Palais while he was teaching at UC Berkeley. It was a really fun class and I never forgot the lessons he taught me. I remember the day he explained higher order Runge-Kutta schemes and their numerical stability looked to be the best thing since sliced bread. Then he broke out in a rendition of The Rolling Stones' You can't always get what you want.

Unfortunately, there is always a catch. Numerical stability and accuracy is gained at the cost of computational speed and memory usage.

When I needed to implement Runge-Kutta integration of Hamiltonian systems for my PhD research, I found myself humming the Rolling Stones. I found the right trade-off balance so that my molecular dynamics simulations converged quickly and accurately enough to allow me to graduate. Thanks, Bob. ;-)

7 comments:

  1. I had never heard this before. It makes sense, but I still like Pi Day. Tau just isn't nearly as fun. ;)

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  2. But tau lets you have twice as much pie and more pie is better.

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  3. Only you could say numerical analysis was "a really fun class".
    xo :)

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  4. I love this! As a team cake member, I say, down with pi.

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  5. I still love pi! May be this is a physicists point of view, but too many things are labeled tau - time, torque... and pi is unique! And second - one of the amazing things I learned is that pi^2=g (acceleration due to gravity)! How cool is that?!

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  6. @IrkaDblrka I agree that tau is unfortunate nomenclature. I prefer Palais formulation with the 3 legged \newpi instead.

    For TeX users, that looks like:
    \def \newpi{{\pi\mskip -7.8 mu \pi}}

    http://www.math.utah.edu/~palais/pi.html

    To quote Palais:
    "I was still cautious about not violating the design principle of non-conflict with existing uses, e.g. torque, time constants, and shear stress for τ, but began to seriously consider the proposal. Then, shortly before June 28 (6/28), I was also contacted by Michael Hartl to alert me to the impending release of the `Tau Manifesto'. My initial reaction to both emails was that no one needs my approval to make such a proposal, though at the same time it was very kind of them both to contact me for my involvement and support. The combined effect and independent arrival at the same conclusion by these two scientists forced me to rethink my opposition, and I eventually realized that though τ may conflict with previous use, it should not be difficult to avoid conflict in any future publication by choosing among the many reasonable alternatives whenever a torque or time constant is being discussed simultaneously. Therefore, I am pleased to lend my support to their case for τ and am honored to pass the torch that I truly inherited from predecessors like Hoyle to these and future advocates of more natural clarity in our notation for rotational measure!

    Since then, I have noticed another potential conflict that is still (3/14/2011) not mentioned on the Wikipedia page on Tau, the torsion of a space curve that occurs in the Frenet-Serret equations. Amusingly, as that latter page is now written, it uses tau both for torsion and as a dummy variable of integration! This either shows the risks of ambiguous symbols, or perhaps it shows that they are not a big deal, and can be understood in context, even in close proximity!"

    OTOH, &pi also has a conflict as it is also used for product notation.

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  7. Very interesting! We don't have "Pi" day here since to put the month before the date is counterpoint to how the dates here are written anyway... :)
    I will recommend your previous post to a few bloggers I know, that is excellent advice! Thank you!
    and also thanks for your comment on my red dress win...

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