21 May 2011

Calculus, Certainty, and Monarchism

The Intermediate Value Theorem, an important part of differential calculus, (I would even say an "integral" part, were that not a groaner of a pun) was first clearly stated in a textbook written by an iconoclastic royalist Frenchman, Augustin-Louis Cauchy in 1821.

That intrigues me for a couple of reasons. One, those of us who are pikers in calculus tend to infer from what little we're heard of its history that Newton and Leibniz simultaneously created it fully blown. That what they created was tentative and only gradually developed into the body of work we have today -- that higher mathematics has an intruguing history with a lot of players -- is itself a bit counter-intuitive for some of us.

A more specific reason to think about Cauchy is ... Cauchy. He must have been a fascinating guy.

In Cauchy's own mind, it appears, his contributions to higher math melded with his own monarchical politics. In the introduction to his Cours d'Analyse. he wrote, "It would be a grave error to think that one only finds certainty in geometrical demonstrations, or in the testimony of the senses; and although no person until now has tried to prove by analysis the existence of Augustus or of Louis XIV, every sensible man will agree that this existence is as certain for him as the square of the hypotheneuse or Maclaurin's theorem."

Note that the example of an unquestionable human-world truth here is the existence of great monarchs, and that the renowned pillar of both Bourbon rule and Bourbon memories, Louis XIV, is one of only two of the monarchs named.

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Knowledge is warranted belief -- it is the body of belief that we build up because, while living in this world, we've developed good reasons for believing it. What we know, then, is what works -- and it is, necessarily, what has worked for us, each of us individually, as a first approximation. For my other blog, on the struggles for control in the corporate suites, see www.proxypartisans.blogspot.com.