Thursday, June 21, 2007

Spread This Number?

AACS encryption key controversy

This bad boy?

13,256,278,887,989,457,651,018,865,901,401,704,640

So where was I when all the noise about this was going on in April? Ah, illegal numbers. What will they think of next? Anything that can be represented digitally can be represented as a single (usually very large) number. Software, movies, music, etc..

That reminds me of a story I read once about a civilization that encoded all its existing knowledge as a single mark on a stick. The position of the mark on the stick divided by the length of the stick yielded a decimal number less than one. The digits of the fractional part of that number represented the totality of the civilization's knowledge in an encoded form.

Could this work?

Let's think about this. A proton has a diameter of about 1.5E−15 m. That means we'd get only about 16 decimal digits before we're measuring sub-subatomic dimensions. And Shannon tells us it would take lots of digits to represent that knowledge in any reasonable form. Actually, it would take about 2.3 million decimal digits per megabyte of data. And we're talking at least trillions of megabytes of data.

So no, there is no way - now or ever - that this could work.

2 comments:

Colin C. said...

Unless you didn't know very much.

Senzee said...

Ha, true enough!

Still, the knowledge of division (and information technology) it takes to make the mark in the right spot would consume more than 16 digits..