CompuServe Messages

Dietmar: Trying to make me contradict myself, eh? <g> If I knew exactly what I wanted someone to learn from a topology primer, I wouldn't need it myself! Yes, visualizing spaces of dimensions higher than 3 is a challenge, but there often are lower-dimension analogues that can help someone "see" what's happening (Roger Penrose uses this technique well in "The Emperor's New Mind"). It's been a while since I've thought much about this subject, but I recall after reading Gleick's book and another by Ian Stewart that I went looking for a topology book which would provide something beyond the "intelligent layperson's" approach, but not up to the university level. I'm not afraid of equations or calculus, but I can't follow page upon page of differential equations. Often a *picture* of an equation helps fix it in my mind. Here's one example: As I understand it, many attractors (e.g., the Henon attractor) are (2D) Poincare sections of 3D orbits. A primer might show the equations of motion for the orbits (with some likely account of why a particular equation generates a particular type of orbit), animate the orbit, and then let the user place a plane somewhere to generate the Poincare section. Another example (although I don't know whether this is part of topology): There are lots of *descriptions* of how the Mandelbrot set is generated, but why not let the user pick different values for c, and then *show* the iterations in action? – Mark M.