There’s an interesting and somewhat contradictory piece on Benoit Mandelbrot from the latest Economist Technology Quarterly [12.6.03 : pp35-36]. After praising Mandelbrot for his widespread public recognition [rare for a mathematician] and highlighting his major career moves and accomplishments, the article makes this single, bold claim:
But the study of chaos is now somewhat discredited, having failed to make any useful progess.
The author then jumps behind Mandelbrot by using the mathematician’s proclaimed avoidance of topics “in which the data are not abundant and proof cannot be provided” to label chaos theory and self-organising complexity as “vogue” and “trendy.”
This curious and abrupt dismissal, as if chaos were taboo pseudo-science, is moreover preceeded by exhaltations of Mandelbrot’s transformational insights.
In 1993, when he won the Wolf Prize for Physics, he was cited for “having changed our view of nature.”
Mandelbrot: I overturned a horn of plenty in which all kinds of things humanity has always known were located.
Thus the “father of fractals” revolutionized our views on science and complexity, exposing the underlying organization of nature. So when exactly was chaos theory discredited? [Or perhaps the author meant abandoned instead? Even then the claim is inaccurate.] According to the article, the Mandelbrot set was first printed as a large colorful fractal in 1980. Supposedly 23 years was enough time for a full investigation, and now we are almost certain that it’s bogus, a practically useless tool. For the sake of consistency, let’s not mention the increasing penetration of chaotic dynamics in the fields of medical biology, neuroscience [see W.J. Freeman], evolutionary computation, nano-scale engineering, fluid and aero-dynamics, population dynamics, social networks, etc etc etc. At least we can rest-assured that next-generation nanobots will be logical entities with predictable, linear behavioral patterns.