James Tauber's Blog 2005/10/02
The Circle is Not Simply Connected
In the comments to Number of Connected One-Dimensional Manifolds, I questioned why the circle (or more precisely the one-dimensional sphere S^1) was not simply connected. I wasn't trying to argue—I just didn't have the intuition myself, for some reason.
It's funny because now it's bleeding obvious to me that it isn't simply connected. A loop that goes from one point to another then back again clearly isn't homotopic to a loop that simply goes around the circle.
I think I was letting my intuition that S^n is simply connected override this fact. I was over generalising in my mind. S^n is simply connected only for n > 1. Thanks to Michael Hamm and Allan Engelhardt for setting me straight.
UPDATE: next post
by James Tauber : Created on Oct. 2, 2005 : Last modified Aug. 9, 2007 : Categories poincare_project : 1 comment (permalink)
The Power of Editing
This has already gone around the blogosphere but I shouldn't assume that people that read this blog read the same blogs as I.
I think the first time I truly realised the power of editing in film was listening to the writer/director commentary on Jerry Maquire. Cameron Crowe said that the Tom Cruise - Renee Zellweger story was secondary in his script and during shooting. It was editor Joe Hutshing's rough cut that dramatically altered the story's emphasis and Crowe decided that he preferred it.
It's almost impossible to tell from the final cut of a film just how much the editor did to change the story. An editor may save a film but you'd never be able to tell this without seeing the raw footage. I once asked an editor "how do you judge good editing for, say, the Academy Awards, given that without seeing the raw footage, you really don't know just how much the editor contributed." His response: "you can't and that's the dirty secret of editing awards".
by James Tauber : Created on Oct. 2, 2005 : Last modified Oct. 2, 2005 : Categories filmmaking : (permalink)