"There is nothing I can say about myself as a whole simply and completely, without intermingling and admixture. The most universal article of my own Logic is Distinguo. I always mean to speak well of what is good..."
-Michel de Montaigne, "Of the inconstancy of our actions", tr. M.A. Screech
James Gleick's new book Isaac Newton is a crisp summary, with no equations, of that fascinating though not very likeable individual's life and work. Simply because Newton is not likeable does not mean he is not loveable, and Gleick clearly loves him, though he is scrupulous about not recounting events for which he has no access to many eyewitnesses, like those recorded in Chaos and Genius. In place of dramatic incidents like the confrontations in Chaos ("Sir, do you intend to offer numerics or a proof?"), he offers a striking perspective on the beginning of the modern world:
Information flowed faintly and perishably then, through the still small human species.
which is the sort of shift of perspective that Stephen Baxter gave me in Manifold: Time by blithely referring to the present day as "the afterglow of the Big Bang" - the Universe young still. Newton the scientist is well portrayed, but a judicious selection of his alchemical and theological writings makes it clear that Newton himself never felt he lived in a clockwork universe - as Keynes (quoted in the epilogue) puts it, he was the last of the magicians, not the first of the scientists. In his alchemical writings, he asserts:
Nothing can be changed from what is without putrefaction. All things are corruptible. All things are generable.
Proton decay would not have astonished him at all.
Frances Yates in The Art of Memory, and Paolo Rossi in Clavis universalis, trace the history of the idea of the universal language - Leibniz's universal characteristic - from Ramon Lull, through Giordano Bruno, to the natural philosophers of the 17th century - Descartes, Leibniz, Newton. For centuries it was pure mysticism, pure nonsense - the idea that all the intractable complexity of reality could be rendered into symbols, whose grammar would reflect the structure of the things they represent, and that new, unknown truths could be obtained by manipulating these symbols simply according to a body of formal rules - a calculus. As a computer scientist and logician, I find this thread of intellectual history close to the most compelling, and I do wish Gleick had traced it more. Newton and Leibniz produced the integral/differential calculus, which we learn in high school simply as "calculus": though since Boole's time, and especially since the time of Church, Turing and Tarski, calculi have blossomed riotously, a garden of forking derivations. Even the calculus of Newton and Leibniz was imperfectly formal, leaning on intuition and geometry - it would take the still-unsung efforts of Weierstrass, Cauchy to put a foundation under that castle.
Stephen Toulmin, in Cosmopolis: The Hidden Agenda of Modernity, looked at the drive for the universal language, which yielded up calculus and, centuries later with Boole, Frege, Russell, Godel, and their successors, the foundations of computer science, against the backdrop of the European Wars of Religion, and specifically the Thirty Years' War, which turned central Europe into a fair simulacrum of present-day Afghanistan, and for similar reasons. In the face of ideological warfare like that, he argued, there was hope that reason, honed to a sharp enough edge, could decide the truth of the matter without bloodshed. Sadly, a vain hope, by all appearances; if I thought that formal logic would ever stop a knife-fight, let alone a war, I'd be much less apologetic about explaining that I spend my days studying and using it.
I'm fond of the conceit, which appears in Mary Gentle's "What God Abandoned" and other works of fantasy, that the age of Descartes marked not a change in worldview, but a change in the world: that the last magicians and alchemists chose consciously to replace the chaos of a magical world with the predictability of a mechanistic one. There's a temptation to look at this conceit as a stand-in for real changes in our societies, but this is doubtless an oversimplification.
These cover the years and the miles And talk one style's dialects from London to Omsk ... Events move now in a smoother control Than the swords of lords and the orisons of nuns The poor have choice of purchase, the rich of rents ... Sir, if you made verse you would doubt symbols When the means are autonomous, they are deadly When words slip from verse, they hurry to rape souls When sensation slips from intellect, expect the tyrant. -Charles Williams, "Bors to Elayne: On the King's Coins", from Taliessin through Logres