The staccato roller coaster: A simple physical model of the staccato run

摘要

I present a simple model of Grünbaum's staccato run in classical mechanics, the staccato roller coaster. It consists of a bead sliding on a frictionless wire shaped like a roller coaster track with infinitely many hills of diminishing size, each of which is a one-dimensional variant of the so-called Norton dome. The staccato roller coaster proves beyond doubt the dynamical (and hence logical) possibility of supertasks in classical mechanics if the Norton dome is a proper system of classical mechanics with metaphysical import. If not, challenges raised against the metaphysical significance of the Norton dome are shown to be challenges against various arguments for the dynamical possibility of supertasks, and the staccato roller coaster clearly shows the importance of meeting these challenges. And the staccato roller coaster can provide, as well as interesting lessons, illuminating analyses of Burke's (Mod Schoolman 78:1-8, 2000) attempt to refute the dynamical possibility of the staccato run and Pérez Laraudogoitia's (Synthese 148:433-441, 2006) rebuttal of it.