<== 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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As I see it, the economics profession went astray because economists, as a group, mistook beauty, clad in impressive-looking mathematics, for truth. Until the Great Depression, most economists clung to a vision of capitalism as a perfect or nearly perfect system. That vision wasn't sustainable in the face of mass unemployment, but as memories of the Depression faded, economists fell back in love with the old, idealized vision of an economy in which rational individuals interact in perfect markets, this time gussied up with fancy equations. ... [The central cause of the profession's failure was the desire for an all-encompassing, intellectually elegant approach that also gave economists a chance to show off their mathematical prowess. -- Paul Krugman, "How Did the Economists Get It So Wrong?", New York Times, 2 Sep 2009, from Article

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