Jamesian Philosophy Refreshed

A recent book by David von Leib (a pseudonym for Barclay von Leib), discusses Von Leib's long career as a derivatives trader. Along the way, the author has much to say about Martin Armstrong, a market guru prominent in the 1990s, when he chaired "Princeton Economics International" and wrote a widely-followed newsletter. For no good reason (though he appears to believe the practice gives him some legal immunity) von Leib gives to many of the figures in his memoir slightly fictionalized names. Accordingly, he refers to Martin Armstrong as Marty Amwell. At any rate, here is a numerological process that, in von Leib's telling, led Armstrong/Amwell to some of his business-cycle hypotheses. Marty thought that there were too many coincidences here not to view the pyramid of Giza as a mathematical treasure chest from history of some sort -- a gift from the heavens perhaps -- something left over from some ancient -- potentially alien -- civilization. Marty also co...

From yesterday's ancients we skip forward quickly (due to my ignorance and subjectivity, as well as the demands of my broader points) to the early modern era in Europe, specifically to a publication by a fellow named Rafael Bombelli, (pictured above) of the city-state of Bologna, in AD 1572. Negative numbers were still new in Europe then, but the more advanced thinkers, including Bombelli, had a handle on that. By way of review: multiplying two negative numbers yields a positive. Multiplying a negative and a positive yields a negative, multiplying two positives yields a positive. One consequence of these rules is that there are no square roots of negative numbers. No rational square roots and no irrational square roots either. No square roots of any level of rationality for negative numbers. Why? Because if you had a square root for a negative number then, by definition, you would have a situation in which the multiplication of that number by itself would yield that negati...

Greg Woolf's new book, Rome: An Empire's Story, says this about Numidia, which presented a threat to the growth of Rome in the 2d century BC, and about its King: Jugurtha. "The lack of political consensus in Rome meant that it was always possible for him [Jugurtha] to find some supporters among the Senate, and as he murdered  and intrigued his way into a more and more powerful position at home, he protected himself from the complaints to the Senate by bribing prominent figures. Sallust puts into Jugurtha's mouth the famous description of Rome as 'A city for sale and ready for destruction just as soon as it finds a buyer.' "By 118 Jugurtha had murdered one heir to the throne and was at war with another, in 112 he ignored a senatorially mediated partition of the kingdom and two Roman embassies, killed his brother (massacring a group of Italian merchants in the final siege of Cirta), and survived both a Roman invasion and a summons to Rome. Eventually ...