Tuesday, August 25, 2009
The Hairy Ball Theorem
Someone had left this message in the real, 3D Myrtle Street Review notebook: "Suck ma hairy balls."
We would like to like to point out here that if the gentleman in question wishes to recruit someone for this undoubtedly enchanting task, he needs to leave his name and phone number in the note book. Also his mother's phone number, if he is underage. Which we would bet pretty decent money he is.
Now, we learn in Wikipedia that the hairy ball theorem of algebraic topology states that there is no nonvanishing continuous tangent vector field on the sphere. If f is a continuous function that assigns a vector in R3 to every point p on a sphere such that f(p) is always tangent to the sphere at p, then there is at least one p such that f(p) = 0. The theorem was first stated by Henri Poincaré in the late 19th century.
The hairy ball theorem has applications in computer graphics. Also, it dictates that given at least some wind on Earth, there must at all times be a cyclone somewhere.
Hairy balls are pretty important things.
As you can see, the Myrtle Street Review is following President Obama's example in turning immature outbursts into teachable moments.
The illustration, from Wikipedia, depicts "a failed attempt to comb a hairy ball flat, leaving an uncombable tuft at each pole."