Anurag Jain's Blog on Bangalore Events, Travel, IIM Bangalore, IIM, IIMB, Management

Sunday, March 13, 2005

Posted 5:31 PM by Anurag

Interesting Concept Puzzle!

Reproduced from today's Mindsport (A weekly column by Mukul Sharma of Mindsport), a great concept puzzle.

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! Two questions: (a) Is there anything theoretically wrong with this premise? (b) Could it work in practice?

For your take on this write to MS at this email ID: mindsport AT touchtelindia.net Or, if you were sleeping through the technology boom, write to him by snailmail at: D-268 Sushant Lok-I, Gurgaon, Haryana 122001.

Anywhoo, here's my take on this: Theoretically, I am not sure if anythng is wrong with this idea. About implementation, however, there would be a few issues:
# The decimal fraction would have huge amount of digits. To arrive at that fraction, super computer must be able to read the two lengths a and b, irrespective of measuring units, to a huge number of decimal places.
# To be able to read the precise fraction, the scratch mark should be highly precise. Nanometers of deviation could read the whole Encyclopedia as some alien code.
# We are only talking of raw data here (no formatting). Hence, either we are assuming that the original Encyclopedia itself is plain text, or else we are willing to forego the formatting.
# I am not sure if with the available computing power, we can calculate the two lengths a and b (2 parts of fraction) so as to yield the gigantic fraction.

As long as we are fantasizing, here's a brilliant idea I had once: I thought of burning the Encyclopedia, dissolving the resultant ash in the water (or beverage of your choice, as it won't really affect the molecular structure of Encyclopedia ash :-), and drink it in the belief that I'd get the whole knowledge contained in Encyclopedia in a jiffy! Only ptoblem was that my mom wouldn't lemme burn the Encyclopedia, or any other book that I was willing to sacrifice for the advancement of science! (That's why Calvin and Hobbes say "Mothers are the necessity of invention". )

You can also compare this hare-brained idea to the Matrix-style knowledge transfer from machines to humans through an electronic/data plug in our bodies! But hey, what do I know. I am a mere non-sci-fi mortal!

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