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Benoit Mandelbrot: 20 November 1924-14 October 2010
Article Type: Obituary notices From: Kybernetes, Volume 40, Issue 1/2
The mathematician Benoît Mandelbrot has died aged 85. He is best known as the inventor of fractal geometry and the Mandelbrot set. These topics are sufficiently fundamental in the study of systems of interest to cyberneticians, that a picture of a Mandelbrot set was adopted in 2001 as part of the logo of the Cybernetics Society, designed by D.J. Stewart, and has appeared on the front cover of Kybernetes since the start of 2010, as well as on the Society’s web site with an explanatory note at: www.cybsoc.org/about-soc/about-fractal.htm. References cited in the note as sources of both relevant theory and attractive multi-coloured images include Gleick (1987), Peitgen et al. (1992) and Dewdney (1985). In the Guardian obituary notice, Mandelbrot is quoted from one of his books (Mandelbrot, 1975) as observing that:
Why is geometry often described as cold and dry? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline or a tree. […] The world we live in is not naturally smooth-edged and regularly shaped like the familiar cones, circles, spheres and straight lines of Euclid’s geometry: it is rough-edged, wrinkled, crinkled and irregular.
The new topic of fractal geometry offered a systematic way of approaching phenomena that look more elaborate, the more they are magnified, and was applied not only to natural objects like clouds and coastlines and living systems but also to economic data. A suggestion that intelligence might be seen as fractal has been advanced by Andrew (2009) though not greatly developed. The principles are also fundamental to chaos theory, bearing on systems of the “small causes large effects” type of which the weather is a clear example.
Numerous obituary notices are readily available on the internet, as are also collections of attractive coloured images of Mandelbrot sets. Two notices, both with admirable accounts of the significance of Mandelbrot’s work, are at: www.guardian.co.uk/science/2010/oct/17/benoit-mandelbrot-obituary, and at: www.telegraph.co.uk/news/obituaries/science-obituaries/8069558/Benoit-Mandelbrot.html. There is also an official biography site at: www.math.yale.edu/mandelbrot/
Benoît Mandelbrot was born in Warsaw, Poland, into a family of Lithuanian Jewish extraction. As a boy, he was introduced to mathematics by two uncles. In 1936, the family emigrated to France where one uncle, Szolem Mandelbrot, was a Professor of Mathematics. David Stewart of the Cybernetics Society has pointed out that there is a further link here to the history of cybernetics, since the uncle was a member of the Bourbaki group whose work on set theory was the basis of much of Ashby’s theoretical work.
After completing his education in France, Benoît Mandelbrot moved to America and eventually, sponsored by John von Neumann, enrolled at the Institute for Advanced Study in Princeton. He returned to France in 1955 and then again to America where in 1958 he was appointed an IBM fellow at the company’s laboratories. After retirement from there, he became a Professor of Mathematics at Yale and held various other appointments including one at Harvard. It was no doubt while fulfilling his commitment there that he called at nearby MIT and chatted with Jerry Lettvin, as recalled by Brad Howland, another former member of the McCulloch group (personal communication). Although their researches had been very differently directed, it is easy to imagine these two maverick thinkers finding they had a good deal in common.
Mandelbrot was a victim of pancreatic cancer and died in a hospice in Cambridge, Massachusetts. He is survived by his wife Aliette and his two sons, Laurent and Didier.
Ernst von Glasersfeld 8 March 1917-12 November 2010
The philosopher Ernst von Glasersfeld died of pancreatic cancer in the morning of November 12 at his home in Leverett, Massachusetts. He was Emeritus Professor of Psychology at the University of Georgia, Research Associate at the Scientific Reasoning Research Institute, and Adjunct Professor in the Department of Psychology at the University of Massachusetts, Amherst.
He was the after-dinner speaker at the Conference of the American Society for Cybernetics in the Summer of 2010, and originator of the subject of radical constructivism (von Glasersfeld, 1995). Obituaries with accounts of his eventful life can be found at: http://en.wikipedia.org/wiki/Ernst_von_Glasersfeld and www.boston.com/news/world/europe/articles/2010/11/12/intellectual_ernst_von_glasersf
Alex M. Andrew
Andrew, A.M. (2009), A Missing Link in Cybernetics: Logic and Continuity, Springer, New York, NY
Dewdney, A.K. (1985), “Computer recreations: a computer microscope zooms in for a look at the most complex object in mathematics”, Scientific American, August, pp. 16–25
Gleick, J. (1987), Chaos: Making a New Science, Viking Penguin, New York, NY
Mandelbrot, B.B. (1975), The Fractal Geometry of Nature, Freeman, New York, NY
Peitgen, H.-O., Jürgens, H. and Saupe, D. (1992), Chaos and Fractals: New Frontiers of Science, Springer, New York, NY
von Glasersfeld, E. (1995), Radical Constructivism: A Way of Knowing and Learning, Falmer Press, London (reviewed in Kybernetes, Vol. 24 No. 9, 1995, pp. 68-71)