Astronomical Images : Zeno's stadium paradox

Aristotle

Astronomical Images

<p style='text-align: justify;'>This work comprises Aristotle's <i>Physics</i> and Thomas Aquinas's commentary edited by the Augustinian, Timoteo Maffei of Verona (d. 1470). Aristotle discussed the nature of motion in the latter books of <i>Physics</i>, often referring to figures to elucidate his points. These figures were not always illustrated, and there was no traditional stock of figures like the wind diagrams or concentric circles associated with the Aristotelian analysis of motion. This edition makes an effort to supply such figures. Aristotle's <i>Physics</i>, book 6, chapter 9 is devoted to refuting four arguments advanced by Zeno against the reality of motion. The fourth argument, often called the stadium paradox, supposes three objects equal in number and bulk. The first set AAA is stationary in the middle of the stadium. BBB forms a train stretching from the middle of the As in one direction. CCC is a train set at the end of the stadium moving in the opposite direction. The front of B is opposite the end of A (and the rear of C) at the same time as the front C is opposite the (other) end of A (and the rear of B) when they move past one another. It then appears that the front of C has passed all the Bs while the front B has passed half that number of bodies (i.e. the As) so that B's time is half the Cs time, though either takes the same time in passing each body. Aristotle points out that Zeno's fallacy lies in assuming that a moving object takes an equal time in passing another object equal in dimensions to itself, whether that object is stationary or in motion. (Aristotle, <i>Physics</i> VI.9.239b33-240b7, trans. Wicksteed and Cornford.) The woodcut figure supplied here ' showing the trains B and C as circles, the stadium as a square behind it, and the amount of time for the motion ' does not quite work for this argument since it requires the front of B and the front of C to be touching in the middle of A.</p>