Thursday, October 19, 2006

Freeman Dyson reviews matho-Francophile history

In last week's New York Review of Books the great physicist and thinker Freeman Dyson reviews a book called The Best of All Possible Worlds: Mathematics and Destiny by Ivar Ekeland. (link) The book doesn't seem particularly worth reading; Dyson says it "gives a slanted and partial view of history." But the review is worth reading. Here's the first couple of paragraphs.
Ivar Ekeland has a Norwegian name and teaches at the University of British Columbia in Canada, but the style and spirit of his book are unmistakably French. The book is a rapid run through the history of the last four hundred years, seen through the eyes of a French mathematician. Mathematics appears as a unifying principle for history. Ekeland moves easily from mathematics to physics, biology, ethics, and philosophy.
After describing the contributions to science of Pierre de Maupertuis (1698-1759), who notably described mathematical axioms that can be used to derive Newton's laws of motion given just the assumption that things move as little as possible, Dyson describes how Ekeland then frames the history of modern thought in terms of both earlier and later thinkers who also thought about optimization and conservatism (in a technical sense, not a political sense). Those thinkers include Galileo, Descartes, Lagrange, Poincare, Darwin, Rousseau, and others. Noting that the majority of those names are French, Dyson comes to the heart of the essay. What does this French perspective say about how the world works, and how science works?
The characters in [Ekeland's] story are mostly French, and the dominant role of mathematics in their thinking is a hallmark of French culture. Nowhere else except in France do mathematicians command such respect.
Ekeland's book puts mathematical optimization at the focus of history. Optimization means choosing the best out of a set of alternatives. Mathematical optimization means using mathematics to make a choice. Maupertuis is the central character of the history because he claimed that the universe is mathematically optimized.
And what would happen if you thought about history in another framework, say, that of English scientists instead of French scientists? Dyson considers another book that could be written, a similar framing of the history of Western modernity, but by Akeland instead of Ekeland.
In Akeland's version of history, the scientist who personified eighteenth-century enlightenment is Benjamin Frnaklin rather than the Marquis de Maupertuis. Instead of the mathematicians Lagrange and Poincare, the scientists who bring us into the modern world are the nineteenth-century British physicists Michael Faraday and James Clerk Maxwell, who set out the basic laws of electricity and magnetism. Bacon, Franklin, Faraday, and Maxwell, the chief characters in Akeland's narrative, are nowhere mentioned by Ekeland.
For Akeland, things are more important than theorems. Experiments are more important than mathematics. The great scientific achievement of the Age of Enlightenment was the experimental study of electricity.
Instead of mathematical optimization, Akeland postulates maximum diversity as the governing principle of the universe. His title is The Most Interesting of All Possible Worlds: Electricity and Destiny.
Dyson concludes with the fairly obvious point, obvious given his insightful discussion summarized above, that science and modern thought requires both mathematics and the experimental work that lead to an understanding of electricity. His review is well worth reading for its consideration of how national culture, in this case the culture of the scientific and philosophical community, can strongly affect how people view history and their own place in the world. Presumably, American scientific culture (which Dyson does not address, aside from Franklin, who lived much of his life in Europe), and its competitive and practical aspects, also view how we think about the world and human nature, and vice-versa too I imagine.

(Edited 10/23/06 to reflect that the full text of the review is now available.)



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