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For lack of a nail... Benoit Mandelbrot on the article that made a difference

October 18, 2010 by Jacob Bettany   Comments (0)

Here at MoneyScience, I was very sad indeed to hear about the passing of Benoit Mandelbrot, who died last Thursday at 85, and was one of the first supporters and contributors to the MoneyScience project, as it was then in 2004. I started working with him long before that, from 2001 when he joined the Advisory Board of the journal of Quantitative Finance. I'd been a fan for years, ever since my uncle gave me a copy of James Gleick's popular title, Chaos: Making A New Science and I started discovering the amazing world of fractal geomety myself with software packages like Fractint and XaoS (bigger list here). We published several articles by Mandelbrot in my years on the journal including this one (pdf) in which he traces the merits and pitfalls of power-law scaling models from antiquity to the present.

Above: MoneyScience meets Mandelbrot. After 4 years of email contact I finally got to meet Benoit at the 2005 Workshop on Economic Heterogeneous Interacting Agents.

Below you will find the article he wrote for MoneyScience in 2004.

For lack of a nail... Benoit Mandelbrot on the article that made a difference

Today, power laws are widely used in finance, their emergence and evolution are very well documented, and their main actors are still active. The story began with a three-page 'Note' I published in the Paris Academy's, Comptes Rendus (Vol 254, 3668-3970, 1962). The title was self-translating: "Sur certains prix speculatifs: faits empiriques et modele base sur les processus stables additifs de Paul Levy".

It was soon followed in 1963 by a full paper in the Journal of Business that has become a widely reproduced Citation Classic. As to the path that led me to that 1962 Note, it had been unusually narrow, winding, and unprobable. It too began, in Comptes Rendus (Vol 232, 1638-1740, 1951) by another 'Note' that was arguably the first sophisticated discussion and explanation of a power law of any kind, 'Adaptation d'un message a la ligne de transmission'.

From the viewpoint of the present column, it is significant that my 1951 Note and what followed from it had been entirely triggered by a short earlier publication that had been thrown into a wastebasket before being handed to me. It was not even a scientific paper but a review of a book. Moreover, it was not published in a scientific journal of record, but in the popular magazine Scientific American in August 1949 . Finally, the review was not objective but highly selective and partisan.

The book under review was 'Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology' by G.K.Zipf. The reviewer, the mathematician J.L.Walsh (1), was a friend of the author and put the book in the best possible light. The slight piece he wrote became the hook on which my life's work was destined to hang. Or perhaps I should rather say that it hooked me on power laws for life. Nobody else paid attention to that review; I wonder why. For lack of a nail, a kingdom can be lost. For a very different improbable reason, I realized soon enough that I had a whole kingdom all for myself to play as whim and resources allowed.

The book under review was 'Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology' by G.K.Zipf. The reviewer, the mathematician J.L.Walsh (1), was a friend of the author and put the book in the best possible light. The slight piece he wrote became the hook on which my life's work was destined to hang. Or perhaps I should rather say that it hooked me on power laws for life. Nobody else paid attention to that review; I wonder why. For lack of a nail, a kingdom can be lost. For a very different improbable reason, I realized soon enough that I had a whole kingdom all for myself to play as whim and resources allowed.

The realization that this kingdom incorporated finance involves another story, triggered later, in 1961, by an equally improbable event. It was not a review retrieved from a wastebasket before it had been emptied, but a picture retrieved from a blackboard before it had been cleaned.

Related tales of small transient causes triggering durable developments are detailed in a book that has just been published by Basic Books in New York and Profile in London by B.Mandelbrot and R.Hudson: ''The (mis)Behavior of Markets. The Fractal View of Risk, Ruin, and Reward.''

© Copyright, Benoit Mandelbrot, October 2004

You can read more about Professor Mandelbrot on his home page at Yale.

(1) Joseph L. Walsh, Sept. 21, 1895 - Dec. 10, 1973

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