Achilles and the Tortoise
The author of this paradox is Zeno (born circa 490 B.C.E.) The
few surviving fragments of his work take the form of references to it by
other writers, e.g. Aristotle a century later, and Simplicius, a thousand
years later.
"[The] second [paradox] is the one called Achilles. This
says that the slow will never get caught in running by the fastest. For
the pursuer must first get to where the pursued started from, so that it
is necessary that the slower should always be some distance ahead." (Aristotle,
Physics, 239b, 14-18)
Can anything perform infinitely many tasks ?
See Jonathan Barnes, The Presocratic Philosophers,
London: Routledge, 1982, pp. 231-295, and especially pp. 273-5.
FCTM
19 September 1997