Saturday, October 26, 2002
M I N D  G A M E S


Athenian candidate
Aditya Rishi

It isnít that they canít see the solution. It is that they canít see the problem. ó G.K. Chesterton (1874 - 1936)

330 BC Greece: Moving in Athens has become painful for Plato, as every corner of the town reminds him of his tutor, Socrates, who was made to drink poison in a public execution. Socrates wanted him to teach logic and ethics to the youth, so, now, he runs a school of thought, which has added to his burden of grief, as he is unable to find a suitable pupil who could carry on the unfinished work of Socrates. It is in this state of mind that he receives a letter of recommendation for a youth.

Plato, by now, has lost faith in the world and his judgement of it, so, he tries to imagine how Socrates would have approached the request. Socrates valued honesty in young men, but young men of today consider it a passion of the fools. Honesty, now, can only be found in works of mathematics, the reason why Plato is fond of geometry and would like to have a successor who shared his passion. Once, a highly recommended youth had disappointed him. In a rejection letter addressed to the person who had recommended his name, he had said: "He is unworthy of the name of man who is ignorant of the fact that the diagonal of a square is incommensurable with its side." The latest letter of recommendation has come from the same person.

 


Prejudice loses to patience and Plato agrees to meet the candidate. Aristotle walks in for the interview and finds Plato holding a prism and staring into empty space. When silence tires Aristotle, he breaks it by saying: "The line has magnitude in one way, the plane in two ways, and the solid in three ways; and beyond these there is no other magnitude because the three are all."

Plato: "The knowledge of which mathematics aims is indeed the knowledge of the eternal, but I have hardly ever known a mathematician who was capable of reasoning. He who can properly define and divide is to be considered a god, not a mathematician." Aristotle: "Now that practical skills have developed enough to provide adequately for material needs, one of these sciences which are not devoted to utilitarian ends [mathematics] has been able to arise in Egypt; the priestly caste there having the leisure necessary for disinterested research. I come here seeking such leisure." Plato: "Ah, yes; there still remain three studies suitable for free man. Arithmetic is one of these. Mathematics is like checkers in being suitable for the young, not too difficult, amusing, and without peril to the state. You seem to be a widely travelled man, tell me, when Plato says that something is impossible, can it be made possible?"

Aristotle senses that he is at the brink of rejection, that the old man is not interested in him, but he is determined to get admission. He says: "If you give me your undivided attention, I can turn impossible into possible." He, then, creates a little n by n table, the little squares of which are filled with numbers, all of which are different. The smallest numbers in each row are marked, and it turned out that all the marked numbers were in different columns. "Now, if the smallest numbers in each coluumn are also marked, it will turn out that these marked numbers are in different rows. Both times, the same numbers will be picked up," says Aristotle. "Impossible," says Plato. "Possible," says Aristotle and writes the proof on sand. The baton of Socrates passes on to him; but what was his proof? Write at The Tribune or [email protected].