Keynes on Newton

 The outdoor carts at Second Story Books had a copy of Essays in Biography by J.M. Keynes, and of course $4 seemed a more than reasonable price. Most of the pages in the book are given over to economists: an essay on Alfred Marshall,  whose name I had never heard, takes up about a quarter of the book.

The most interesting essay is "Newton, the Man". There is much in it to quote and consider, but the paragraph that most struck me is

I believe that a clue to his mind is to be found in his unusual powers of continuous concentrated introspection. A case can be made out, as it also can with Descartes, for regarding him as an accomplished experimentalist. Nothing can be more charming than the tales of his mechanical contrivances when he was a boy. There are his telescopes and his optical experiments. These were essential accomplishments, part of his unequalled all-round technique, but not, I am sure, his peculiar gift, especially amongst his contemporaries. His peculiar gift was the power of holding continuously in his mind a purely mental problem until he had seen straight through it. I fancy his pre-eminence is due to his muscles of intuition being the strongest and most enduring with which a man has ever been gifted. Anyone who has ever attempted pure scientific or philosophical thought knows how one can hold a problem momentarily in one's mind and apply all one's powers of concentration to piercing through it, and how it will dissolve and escape and you find that what you are surveying is a blank. I believe that Newton could hold a problem in his mind for days and hours and weeks until it surrendered to him its secret. Then being a supreme mathematical technician he could dress it up, how you will, for purposes of exposition, but it was his intuition that was pre-eminently extraordinary--"so happy in his conjectures," said de Morgan, "as to seem to know more than he could possibly have any means of proving." The proofs, for what they are worth, were, as I have said, dressed up afterwards--they were not the instrument of discovery.

 In Adventures of a Mathematician, Stanislaw Ulam wrote that an hour of concentration on a problem is worth far more than two half-hours, and credited an American collaborator's powers of concentration. The proofs coming second recalls something that Richard Feyman said of another physicists work: there certainly were a lot of equations.

There are other essays in the book worth reading. "The Council of Four, Paris, 1919" gives a deplorable picture of Woodrow Wilson, how accurate I can't say. The essay on Malthus as economist gives the curious detail that his father was an enthusiast and friend of Rousseau.