Date: Sat, 27 Apr 91 22:24:35 PDT From: ctm@math.berkeley.edu (Curtis T. McMullen) To: doyle@math Subject: How it works Peter, I finally understand the terrific beauty of our quintic algorithm, in a way that maybe you explained to me once. It's that the dodecahedron, like a quintic polynomial, is this beautiful symmetric object with all the vertices intrinsically undistinguishable. The key to finding a root is to break the symmetry. This is done with the device of a *random* initial guess. The initial uncertainty is amplified and titrated by iteration until it selects, like a recalcitrant witness, one vertex to distinguish among the twenty. The Julia set is a sieve, by which we pan the nugget of a root from the stream of uncertainty. Curt