Carnival of Space #20 is up on Music of the Spheres
More like this
So, after the last topology post, we know what a manifold is - it's a structure where the neighborhoods of points are *locally* homeomorphic to open spheres in some ℜn.
Today, I'm going to try to show you an example of why the axiom makes so many people so uncomfortable. When you get down to the blood and guts of what it means, it implies some *very* strange things.
What's the application? Optical tweezers use focused light beams to trap small particles in the focus of the beam, and drag them around by moving the beam.