Jamesian Philosophy Refreshed

  To my mind, one of the most intriguing of the ancient Greek philosophers is the second of the great Eleatics, Zeno of Elea.  But ... does he still matter?  C ome, let us reason together.  If the fastest of warriors, Achilles, can not catch up with a tortoise, then something is of course very wrong with the way we understand our life in the world.  That is of course Zeno's point.  He was defending an Eleatic monism, a sort of Hellenic gaslighting that told the world nothing is as it seems, so he was committed to saying that since the apparent world is illusory, something crazy must be true.  Maybe this is irrelevant now, because we live in the thought world that Leibniz and Newton gave us with the development of calculus. The central idea is that of a converging series.   Consider continuously compounding interest.  You probably have bank accounts that earn it.  You do not regard this as a mystery.  But how can that be compute...

 How does continuous compound interest work?  Well, suppose the magical "Bank of Bernoulli" offers you 100 percent interest per annum. Or, in decimal terms, a return of 1.0.  Great. You put a dollar in the bank and the bank gives you two dollars at the end of the year, one dollar representing the principal, the other the yield. Only one simple computation has to be made, so we can say of this situation that n = 1. It gets better.  Bank of Bernoulli [so named after the great 17th century mathematician Jacob Bernoulli] decides to compound semi-annually.  You put in one dollar, and on June 30 you are credited with 100 percent interest for half a year, or $0.50. In the second half of the year, you earn the same 1/2 of the underlying annual rate, for the redefined principal amount, this time on $1.50.  So you earn $0.75 between June 30 and December 31. This means you have $2.25 waiting for you at the end of the year. You can keep this up, presuming a calculation...