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