These essays lead the reader through the land of the wonderful shrinking genie to the warehouse where the 'infinity machines' are kept. By careful examination of a lamp that is switched on and off infinitely many times, or the workings of a machine that prints out an infinite decimal expansion of pi, we begin to understand how it is possible for Achilles to overtake the tortoise. The concepts that form the basis of modern science -- space, time, motion, change, infinity -- are examined and explored in this edition. Includes an updated bibliography. A reprint of the Bobbs-Merrill edition of 1970.