Saturday,  June 9, 2001
M I N D  G A M E S


The man who saw reason

IT is easy for the blind man to sense that there are at least two other men, besides him, in the room where he has been lodged for the night — these two have been fighting over trivial issues for the past one hour. From their arguments, the blind man learns that both are education ministers — one of a Hindu state and the other of a Muslim nation.

The Hindu minister says, "Our system of mathematics is better than any other in the world. We have produced great minds like Sridhara, who in the tenth century AD, had written mathematical works like ‘Trisatika’, ‘Patiganita’, ‘Bijaganita’, ‘Navasati’, ‘Brhatpati’ and ‘Ganitapancavimsi’. ‘Patiganita’ is written in verse and contains algorithms for carrying out elementary arithmetic operations and extraction of square roots and cube roots. Sridhara was one of the first mathematicians to give a rule to solve a quadratic equation."

"You are a liar," says the Muslim, "Concepts of algebra and algorithms were introduced by Abu Abdullah Muhammad Ibn Musa al-Khwarizmi, who was born at Khwarizm (Kheva), a town south of river Oxus in Uzbekistan. The name ‘algebra’ is derived from his famous book ‘Al-Jabr wa-al-Muqabilah’. He developed trigonometric tables containing the sine functions that were, later, extrapolated to tangent functions."

 


"Excuse me, gentlemen," says the blind man, "but Sridhar and Al-Khwarizmi were great mathematicians not because they were Hindu or Muslim, but because they were men of reason." "Do you think that you are a man of reason?" say the opponents. "One tries to be," says the blind man. "Can you resolve our dispute on who discovered algebra?" the ministers say. "That’s easily settled," says the blind man, "I have a problem and the first one to solve it can claim that algebra is in his blood. In a right triangle with sides 3, 4, and 5 feet, respectively, a mouse starts at the vertex of the right angle and crawls straight (perpendicular) towards the opposite side. After this, it turns and crawls straight towards the closer opposite side. If it keeps turning and crawling to the closer side indefinitely, what distance will it cover?" Hours pass, but even countless prayers to Allah and Ishwara are not enough to make the solution enter the closed minds of the ministers.

When it is time for him to leave, the blind man says, "Gentlemen, the first part of the mouse’s trip divides the triangle into two similar triangles — one 4/5 the original size, the other 3/5 the original size. The first part is thus 4/5(3)=3/5(4)=12/5 feet long. Each succeeding part will divide the triangle as before (using 3/5 since that side is nearer). Therefore, the total distance is an infinite sum: S=12/5+12/5(3/5)+12/5(3/5)(3/5)+...; However, (3/5)S=S-12/5, so, solving the equation gives S=6 feet. The distance is covered in finite time if the mouse maintains its speed."

"How did you solve it?" say the hardliners. "I am blind, but not to reason," says the man. "Who are you?" they ask him. He says, "I can be anyone — Nicolas Saunderson, fourth Lucasian Professor of Mathematics at Cambridge who was recommended to the chair by Isaac Netwon, or Leonhard Euler or even Arnold Fast, who was hired by Konrad Zuse in 1941 to program the world’s first fully programmable digital computer, the Z-3."

— Aditya Rishi