Saturday, May 18, 2002
M I N D  G A M E S

Men with telescope and foresight

In questions of science the authority of a thousand is not worth the humble reasoning of an individual.

— Galileo

GALILEO did not invent the telescope; a Dutch spectacles maker named Zacharias Janssen came up with one in 1604, but he had acquired it from someone in Italy way back in the 1590s. In 1608, another Dutch spectacles maker, Hans Lippershey, claimed to have independently discovered the principle that distant objects appeared greatly magnified if viewed through two lenses separated by a suitable distance. He made the device and sold it to the Prince of Holland for military purposes. Another Dutchman, James Metius, applied for a patent on the telescope, but his claim was rejected.

In 1610, Galileo, a teacher at the University of Padua (a place known for Aristotelian beliefs, where professors refuted the possibility of the existence of any new planets or stars), was at his desk, writing this note: "About 10 months ago a report reached my ears that a certain Fleming had constructed a spyglass by means of which visible objects, though very distant from the eye of the observer, were distinctly seen as if nearby…"

Soon, he had made such an instrument for himself and taken on the university and the Church. The news of his discovery of the four major moons of Jupiter, about which he wrote in his work, 'The Sideral Messenger', reached Kepler in Germany.


It was with Kepler that he used to exchange cipher messages - do you recall his friend in a similar cloak as he, who helped him defeat the Bishop - does it "ring a bell"? He looked a lot like a German. Kepler was a good riddle solver; still he used to take hours to decipher Galileo's string of characters. The discovery of Saturn's peculiar shape was one of the occasions when Galileo sent Kepler coded messages.

Galileo set out at noon to walk from East Tower to West Tower, and his friend (Kepler, for sure) started at 2 pm on the same day to walk from West Tower to East Tower. They met on the road at five minutes past four, and each man reached his destination at the same time. You had to tell what time was it?

Let the rates of the two walkers be rx and ry, the distance be d, and the meeting time be t in minutes after 2 pm. The equations for the meeting (1) and the trip (2,3) are: (1) d = 245*rx + 125*ry; (2) d = (120+t)*rx; (3) d = t*ry. Substituting (3) into (1): (4) 245*rx = (t-125)*ry; (4b) rx/ry = (t-125)/245; Substituting (3) into (2): (5) 125*ry = (t-125)*rx; (5b) rx/ry = 125/(t-125). Equating (4b) and (5b): (6) rx/ry = (t-125)/245 = 125/(t-125); (6b) (t-125)^2 = 125*245; (6c) t^2 - 250t - 120*125 = 0. Solving the quadtratic equation for t: (7) t = 125 +/- sqrt(125^2 + 120*125); (7b) t = 125 +/- 175. Choosing positive, t = 300; so, both arrived at their destinations at 7 pm. This is the best solution that I have received.

Readers who got it right were Suresh Mankotia, Anuj Sharma of Ludhiana, Shubhangi of Kurukshetra, Sapan Gupta, Gaurav and Vrinda Prasad Tiwary of Panipat, out of which, only two have explained how they deduced the time. Read about Galileo Galilei - it's an education in encryption. Write at The Tribune or

— Aditya Rishi