<== This is a picture from the interactive geometry
package Cinderella showing the behavior of 10,000 starting
values in the rectangle [0,1]x[h-1,h+1], where h is the height of the
horizontal line, after six iterations of the algorithm which reflects
a point x in the sphere then reflects the outcome in the line and then
averages the result y with x. It is an accessible prototype for a
remarkable image reconstruction algorithm known variously as
Douglas-Ratchford, Lion-Mercier, Fienup's method, and
"divide-and-concur." Some related graphics can be generated and
displayed at these URLs:
(wait 30-60 seconds to see the display).
Quote of the day (refresh browser to select another):
Rather, [scientists] cling to the dogma imposed by the long post-Enlightenment hegemony over the Western intellectual outlook, which can be summarized briefly as follows: that there exists an external world, whose properties are inde-pendent of any individual human being and indeed of humanity as a whole; that these properties are encoded in "eternal" physical laws; and that human beings can obtain reliable, albeit imperfect and tentative, knowledge of these laws by hewing to the "objective" procedures and epistemological strictures prescribed by the (so-called) scientific method. -- Alan Sokal, tongue-in-cheek "critique" of modern science, from his famous postmodern science parody-hoax, "Transgressing the Boundaries: Toward a Transformative Hermeneutics of Quantum Gravity," Social Text, Spring-Summer 1996, pg. 217-252, also available at Sokal hoax.
The complete list of quotes is available