Probabilistic Applications of Integration
“Lest men suspect your tale untrue, Keep probability in view.”*
John Gay, English poet and dramatist (1685–1732)
At the beginning of the nineteenth century, the prevailing scientific view was a clockwork universe in which everything was determinable, if not actually determined. An asteroid hitting Earth was not a chance event; rather, it could have been anticipated if the position and velocity of all asteroids in the solar system were known. This was the view of Pierre-Simon Laplace (1749–1827) whose methods on how to compute future positions of planets and comets from observations of their past positions were published in a five-volume treatise titled Méchanique céleste. A century later, the clockwork view of classical mechanics was shattered by twentieth century quantum mechanics, built on Werner Heisenberg's (1901–1976) uncertainty principle. This principle implies that the precision with which both the position and velocity of any object can be known at a given point in time is limited. Einstein's difficulty in ...