Jamesian Philosophy Refreshed

Economist William Baumol, a professor emeritus at Princeton University, passed away on May 4. I imagine he couldn't bear the thought of witnessing one more silly pseudo holiday where Yankees pretend we care about Mexican history in order to drink tequila. In that case, his timing was perfect.  Baumol is one of the two gentlemen immortalized in the name of the  Baumol-Tobin model of the transactions demand for money. (The other, of course, is James Tobin who passed away 15 years ago.) Baumol's paper outlining this theory preceded Tobin's by four years, but the model seems to have languished in obscurity until Tobin's revival.  Baumol did much else, too, but I'd like to write about transactions demand today. Indeed, I'm going to criticize its role in subsequent developments. This may seem a violation of the old rule "speak no ill of the dead." So I should preface it by saying the following: I'm certain Baumol made many other contributions more ...

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...