Courtesy : Sunday Times, 13th March 2005
Let’s say you get a terrific idea one day – one which sends your head reeling into trans-Uranian orbit immediately. Assume you’ve discovered how to encode the entire Encyclopaedia Britannica onto a tiny scratch on a six-inch bar of metal. And as if that wasn’t enough to rock Neptune around the Sun, that scratch of yours wouldn’t even contain any information on it like those old vinyl short, medium and long-playing records used to. While the whole world falls at your feet in delirious astonishment, you produce your starburst.
There are, you explain to them gently like one talking to a bunch of silent lambs, fewer than 100 different letters and symbols in the print encyclopaedia. What you plan to do is assign a two-digit number to each of these symbols. For instance the letter A might be 01, the letter B something like 02, a semicolon could be 34, a space between words, 99, and so on till you have them all covered. Now, just like with this cipher system the word “bat” could be encoded as, say, 020120, you can also, and obviously, encode the entire encyclopaedia into one huge number.
As many Earthlings faint with awe, you then unleash your master stroke by putting a decimal point in front of this monster number and converting it into a decimal fraction. Then you place a scratch on the bar dividing it precisely into lengths a and b so that the fraction a/b equals the decimal fraction of the code. All you have to do now is, have a supercomputer measure the rod, compute the fraction a/b, and print out a copy of the entire encyclopaedia!
(a) Is there anything theoretically wrong with this premise?
(b) Could it work in practice?