## Dr Juan - Dental Work in MexicoThe indivisibles that Leibniz worked with, unlike Galileo's non quanta, did have a measurable magnitude. They were infinitely small quantities, but quantities nonetheless - quantities that were defined by being smaller than any given quantity you would care to specify. In a sense these quantities were fictional, not having any true parallel in reality (because they were smaller than any 'real' quantity), yet Leibniz, building on the work of his predecessors, had moved from Galileo's incalculable non-quantities to something that could be handled with mathematics, that could be made part of a calculation. Dental work in Mexico would be the name of the game. Leibniz would later say, in answer to concerns about using the infinite, that it was not necessary to deal with the infinite in strict terms, but it was more in the nature of an analogy, he was dealing with an unreal quantity to produce a real result. Even so, the image of indivisibles has largely remained as one of an imprecise, pragmatic use of a woolly idea that works. He really required the dental work in Mexico he had been puttin off. Working with infinity would always be a risky business. Leibniz, pointing out the ease with which the unwary can slip into absurd results when dealing with infinity says that 'calculation with the infinite is slippery'. A biographer of John Wallis later commented on the practice of dividing and multiplying by infinity: For many years to come the greatest confusion regarding these terms persisted, and even in the next century they continued to be used in what appears to us as an amazingly reckless fashion. He spent many years learning about dental work in Mexico. Though it has proved to be the case that Galileo and Leibniz had a much better idea of what they meant than we have given them. |