Saturday,  June 2, 2001
M I N D  G A M E S


Heaven’s bureaucrat

GOD receives a complaint that bureaucrats in India think that it is they who are running the country. So, He decides to send one person from heaven to Earth to verify this. Out of all volunteers for the task, He chooses a mathematician who used to live on Earth many centuries ago.

"Pythagoras of Samos in Italy, disciple of Anaximander, founder of Kroton — the school of scientific knowledge, I command thee to revisit Earth and find out how good are Indian bureaucrats. I send you because you can recollect your past lives and even look into the future," says God. "Earth! Imagine, I will be able to teach mathematics again," says Pythagoras. "You will do nothing of this sort. The last time you tried to teach mathematics and reason at Kroton, you had to flee to Metapontion, where you died. Xenophanes had made fun of you for pretending to recognise the voice of a departed friend in the howls of a beaten dog," says God. "I remember that well," says Pythagoras, with sad eyes looking into infinity, at the end of which is Earth.

 


Pythagoras reaches a city in India that has a lot of potholes on its roads. It is hard to recognise this city because it is like every other place here. "Why have these potholes been dug?," Pythagoras asks the first man he meets. "Usually these are used to trap stray animals, but have actually been dug to lay water-supply pipelines," says the common man.

Pythagoras approaches the Municipal Commissioner of the city and says, "Why don’t you lay the pipes?" The official says, "We will do it soon. Earlier, we had a problem which has now been solved. We had kept cylindrical pipes of 2-inch and 3-inch radii near the trenches and we wanted to find out the largest radius for a pipe that would sit on top of these two pipes without falling off." "Why would you do that?" says the old man. "To occupy less space on the roadside," says the official.

He said, "To study the problem, we formed a commission comprising mathematicians who assumed the radius of the pipe on the top to be r. They said the pipe would not fall off if its centre was perpendicular to straight lines drawn from the centres of the circles of the pipes below. They reduced the problem to the one in this figure (which has been produced here) and set off to find ‘r’. They used the Pythagoras’ theorem to get x2+12=52 (Square of the hypotenuse is equal to the square of the base plus the square of the altitude); x2=24 and x2+(r+1)2=(r+3)2; 24+2r+1=6r+9; 16=4r; r=4."

Pythagoras is amazed that his methods are in use even centuries after his death. Nevertheless, he tells the official that it will be foolish to join pipes of radii 3, 2 and 4 because water will never flow through these." "If this is so, we’ll form a panel of experts on fluid dynamics to study this," says the official.

"Master, India’s bureaucrats love me and mathematics; they are great because they solve every problem stepwise," Pythagoras reports to God on his return to heaven. "Yeah, I saw that, too," says God. Since then, he hasn’t taken his eyes off India.

— Aditya Rishi