No Pi for Mr. Palais Please

Its understandable that with the development of Mathematics over the years by countless numbers of highly intelligent people that it has become difficult to contribute meaningfully to the field. It must be pretty tough for up and coming mathematicians to make a name for them selves with the level of complexity that goes into new research and progress. Just about the only field that requires new mathematics is theoretical physics, mainly string theory, and lets just say that 11 dimensional topology is very complex. That being said, I offer no excuses and no sympathy for the attention seeking author of Pi is Wrong.

Let me start by saying that I think it would be inappropriate to change any fundamental constant of nature or mathematics. A massive body of knowledge has been built on the basic principles of math and physics, not to mention civilization as we know it. These principles are apart of who we are, not unlike how history defines culture. To change these constants would in a way be like trying to re-write history. But there is also the issue of it being impractical. Ask any kid what the area of a circle is and he will tell you "pi R squared," ask him what pi is and he'll say "3.14 something." Everybody knows what pi is and what it means. Its written in millions of textbooks, programmed into millions of calculators and taught in thousands of classrooms. Simply put, redefining pi would cause confusion and add complexity. You can imagine some theoretical physicists are working on a groundbreaking problem in string theory, on the verge of a breakthrough, when all of a sudden someone asks "which pi are we talking about?" The train of thought breaks and the geniuses are now caught up in an argument about pi, needlessly.

Ok, so aside from the obvious reasons why no fundamental constant should be changed, how does Mr. Palais's argument stack up? His angle of attack is basically aimed at the semi-common factor of two that appears in front of pi, if it is so common 2pi must be the "real" fundamental constant he says. Now this wouldn't be the first time a constant had an annoying factor. In physics it is rare to see plank's constant without it being divided by two pi. The physicists of the early 1900s became so tired of having to write h/2pi that they created a new constant h-bar which was equal to h/2pi. In many cases this new constant h-bar eliminated not only the factor of two but also the pi, so for those equations the argument is mute. You may recognize plank's constant from the equation of a photon's energy:
As I've already mentioned, the equation for the area of a circle has no factor of two and the volume of a sphere has a factor of four thirds, so no help there. The circumference of a circle is equal to two pi R, but if you write it in terms of the diameter of a circle the factor of two goes away. Besides, why is Mr. Palais so interested in two dimensional geometry, after all we live in a three dimensional world. The surface area of a sphere is four pi R squared, so maybe he should argue that pi should become four pi. I will give him credit for ponying up to the fact that all the angles in a triangle add up to pi radians, strong evidence against his argument. Then we have Euler's identity, which Richard Feynman called the "most remarkable formula in mathematics," no factor of two there. In fact, if you go through all the major formulas that define pi very few actually have the factor of two. In wikipedia's entry on pi I counted only five equations out of 55 listed from mathematics and science where re-defining pi would eliminate a factor. In fact, from a cursory glance, a factor of one half seems much more common. Here are a couple that I ran into:
His argument about the factor of two being everywhere is bogus, laughable really. Mr. Palais really shines when he tries to say that the equation for the area of a circle should look like the equation for kinetic energy. Yes, isn't it obvious, since one half mass times velocity squared is kinetic energy, one half pi (his new version) R squared should be the area of a circle! Genius! I jest, but this is no laughing matter. Pi beautifully appears in many, many equations. Sometimes it appears with other factors, but those factors are not two much more often than they are. Mr. Palais's claim is not only disrespectful the the beauty of pi but outright wrong.


Theres nothing like a blatantly absurd statement like "I believe pi is wrong" to get attention for yourself, and it worked. I found this article doing my daily scan through digg.com as it was one of the most "digged" articles on the web that week. I can only hope that those who "dugg" the article did so because they were amused by the author's idiocy, in fact I was.