This chapter defines paradoxes. It reviews several definitions, demonstrating the difference between contradictions and paradoxes. The essence of paradoxes is that they deliver a certain truth and a higher-level meaning. Contradictions are conflicting elements within the same system, whereas paradoxes are conflicting elements that reveal a previously unknown truth. A definition derived from the field of psychotherapy is also mentioned: Paradoxes are best characterized as unacceptable conclusions derived by apparently acceptable reasoning from apparently acceptable premises. Paradoxes are also seen as unacceptable conclusions derived from apparently acceptable reasoning based on seemingly acceptable premises. The definition proposed for this book is “a statement that is seemingly contradictory or opposed to common sense and yet is perhaps true,” including the broader notion of an “air of absurdity,” provided that this absurdity carries a higher-level meaning. Some historical examples are presented, such as Achilles never catching up with a much slower tortoise, the arrow paradox, the paradox of place, the liar paradox, identity paradox, and the paradox of the stone.

The paradoxes of the Greek philosopher Zeno of Elea seem to be perverse arguments about the nonexistence of bodily motion in time and through space. One of the best-known is that of an arrow that remains stationary during its flight. Aristotle refuted Zeno; most modern experts have done the same. Occasionally a modern – cinematic – view of the arrow’s flight has been advanced; this is the chapter’s topic. To Zeno, the arrow only appears to be moving but is at any one moment occupying one specific place. The images on our screens appear to move only because the unmoving images exposed on a filmstrip are projected so rapidly that they are perceived as moving. Extreme high-speed photography and computer-generated “bullet time,” as in the Matrix films and elsewhere, provide a new understanding of Zeno’s brain teaser. The chapter ends on a lighter note with the appearance of a modern Professor Zeno in a comedy film.