- The Fractalist: Memoir of a Scientific Maverick by Benoit Mandelbrot
Pantheon, 324 pp, £22.50, October 2012, ISBN 978 0 307 37735 7
Benoit Mandelbrot, who died in 2010, was a Polish-born, French-educated mathematician who flourished and became famous in America. His special genius was his ability to disregard disciplinary boundaries and find a common pattern underlying disparate phenomena. From adolescence on he was possessed by an urgent desire to invent a mathematical object that would transform the way we look at the world. By most accounts, certainly his own, he was successful: ‘What shape,’ he asks,
is a mountain, a coastline, a river, or a dividing line between two river watersheds? What shape is a cloud, a flame, or a welding? How dense is the distribution of galaxies in the universe? How can one describe – to be able to act upon – the volatility of prices quoted in financial markets? How to compare and measure the vocabularies of different writers? … These questions, as well as a host of others, are scattered across a multitude of sciences and have been faced only recently … by me.
Vol. 35 No. 23 · 5 December 2013
Brian Rotman’s review of Benoit Mandelbrot’s The Fractalist models what the Zipf-Mandelbrot law predicts (LRB, 7 November). In his review, roughly a 3000-word sample of written English, the (ranked number one in frequency in written English) appears very close to twice as often as of (number two) and nearly three times as often as and (number three). All looks good. Historically, however, of has not always been number two in frequency. In early Old English, occurrences of of were quite rare – inflectional endings did much of the grammatical work now handled by of. Then, from the eighth through to the 15th century, of steadily began to signal more and newer concrete and abstract relationships, to the extent that the entry for of in the Oxford English Dictionary now takes up six pages (triple columns, fine print). As of worked its way up to number two in frequency, it caught up with and eventually passed and, a word that had been very common even in Old English. So, as of passed and, there would have been a period of perhaps fifty or a hundred years, when of and and were essentially ‘tied’ for second place. Does the Zipf-Mandelbrot law allow for such linguistic change? More important, let’s suppose that of continues to increase in frequency and eventually overtakes the to become the new number one. Would of suddenly appear twice as often as the, as the law predicts? It seems unlikely. Why is it, though, that the law seems to be valid?
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