Tantalus, Zeno and Me

Thu, 24 Aug 2000

"The lyf so short, the craft so long to lerne, Th' assay so hard, so sharp the conquerynge."

-- Geoffrey Chaucer (c. 1343 - 1400) "Parliament of Fowls" [1380 - 1386]

"Plato's was a manner of speaking; perfection's an idea that body and soul make a run at. Falling short, they fill the world instead with the lopsided jumble that is . . ."

-- John Updike (1932 - ) "A Pear Like a Potato" [1986]

Tantalus, king of Lydia, son of Jupiter, husband of Dione, father of Niobe, dwells for his impiety in hell up to his neck in water. Cursed with thirst, tormented with hunger, the water withdraws as he leans to drink, the luscious fruits above his head are whipped away by a gust of wind when he reaches out for them. Always yearning, never sated.

Zeno of Elea, son of Teleutagoras, is thought to have been born toward the beginning of the fifth century, B. C. The pupil and friend of Parmenides, he left a series of paradoxes to discredit the belief in plurality and motion. The most clearly stated is the paradox of the arrow: So long as anything is in one and the same place, it is at rest. Hence, an arrow is at rest at every moment of its flight, and therefore also during the whole of its flight.

This paradox refers to his somewhat more complex argument: Before a body in motion can reach a given point, it must first traverse half of the distance; before it can traverse half the distance, it must first traverse the quarter; and so on ad infinitum. Hence in order that a body may pass from one point to another, it must traverse an infinite number of divisions. But, an infinite number of divisions cannot be traversed in a finite amount of time.

Leaving aside the profound mathematical implications, meat and drink to longer heads than mine, these two ancient Greeks together sum up the condition of learning: You never can reach perfection in art or skill. At the beginning, when you are an apprentice, it is easy to acquire a half-knowlege, then, the same amount of time and energy is required to attain the next quarter, then the same for the succeeding eighth, and so on, ad infinitum. It is a logarithmic progression, in which an infinite number of divisions cannot be traversed in a finite amount of time. As your hand reaches for the knowledge, as your lips dip to drink from the well of skill, even at that moment they withdraw, and you are left gasping with desire, always yearning, never satisfied.

No one ever attains that pinnacle of perfection in art and skill. Even as the journeyman learns, he creates new things to learn. The wealth of knowledge is indeed infinite, and we mortals cannot encompass it. The arrow never reaches its target. Achilles never catches the tortoise. Death intervenes and puts all to rest before we're even halfway.

August 17, 2000

Tantalus, Zeno and Me