By Ian Stewart
A suite of Ian Stewart's leisure columns from Pour los angeles technological know-how, which exhibit his skill to convey sleek maths to lifestyles.
Read or Download Game, Set and Math: Enigmas and Conundrums PDF
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Extra info for Game, Set and Math: Enigmas and Conundrums
The 0' s and 1' s are binary digits: 1 is a pulse of electricity, 0 the absence of a pulse. Such codes have applications to telephone transmission and radar-mapping. The surface of Venus has been mapped from Earth by radar! Paradoxically, the returning signal is so weak that on average less than one quantum of energy returns. But the quantum is the smallest possible unit of energy! The answer to this paradox is that the coding method is very highly redundant: most digits can be missing and the signal still makes sense.
I thought about that. "You get an electron in location 1. The other locations all lose one electron but gain another . . " "No I don't," he said. "Infinity never comes into it. Each location corresponds to a finite value of n. No, I get an electron in location 1 while everything else ends up the same as it started. Creation from nothing! That's just one of the paradoxes of infinity. And that's not all. Imagine a BILRAM filled up completely with an infinite amount of information . " "Huh? " "How about a complete list of all prime numbers?
And when I do, I'll also be able to realize my design for an infinitely accurate digital watch which shows the time correct to an infinite number of decimal places by using a golden rectangle li quid crystal display which is almost . . " To calm him down, I tried to distract him. "I know a puzzle about infinite machines," I said . "Imagine a light switch . You switch it on . After one second you switch it off. After a further half second you switch it on again . After another quarter second you switch it off, and so on .