Jamesian Philosophy Refreshed

I can't really write about the Borgia family -- as I did yesterday and as I am about to do again -- without deploying my favorite quotation from The Third Man.   Restraint in this matter would do grave violence to my nature. Harry Lime, the worst racketeer in occupied Vienna, tells an old friend who has gone to a good deal of trouble to track him down, "Don't be so gloomy. After all it's not that awful. Like the fella says, in Italy for 30 years under the Borgias they had warfare, terror, murder, and bloodshed, but they produced Michelangelo, Leonardo da Vinci, and the Renaissance. In Switzerland they had brotherly love, they had 500 years of democracy and peace, and what did that produce? The cuckoo clock." What were the 30 years of Borgian dominance Harry had in mind?   I suppose you might start the clock running in 1481, when Ludovico Sforza took power in the duchy of Milan. The fates of the Borgia and Sforza families were closely intertwined (anot...

Leonhard Euler (1707-1783) was surely one of the most prolific of great mathematicians. Among his contributions, we need to mention two, each of which comes down to us as a single letter: the letter e and the letter i .  E uler was born in Basel, Switzerland, so his life and work might fittingly be considered a riposte to the old anti-Swiss jibe (originally from The Third Man ) that Switzerland has produced nothing for all its years of peace and democracy more than the humble cuckoo clock.   Since Euler’s day and because of his work, i stands for the simplest of the numbers that Descartes had called “imaginary.” This i refers to the square root of -1. We don’t need to bother ourselves further with the question “ what is the square root of -1?” It is simply  i , by stipulation. We don't end there, of course, but we can start from there and build something new and important.   Also since Euler’s day and because of his work, e stands for perhaps the m...