<== 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: Expansion Reflection (wait 30-60 seconds to see the display).

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The work then proceeds in a manner unique to science. Because practitioners publish their work electronically, through the e-print archives at the Los Alamos National Laboratory in New Mexico, the entire community can read a paper hours after its authors finish typing the last footnote. As a result, no one theorist or even a collaboration does definitive work. Instead, the field progresses like a jazz performance: A few theorists develop a theme, which others quickly take up and elaborate. By the time it's fully developed, a few dozen physicists, working anywhere from Princeton to Bombay to the beaches of Santa Barbara, may have played important parts. -- Gary Taubes, from "String Theorists Find a Rosetta Stone", Science, 23 Jul 1999, pg. 513.

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