Just another notch

An intriguing thought experiment explains how one might encode the whole of literature in a single fraction, a/b, and how that ratio might be made physical as a notch in a metal rod, whereby the length on the left of the notch is a and that on the right is b.

How might that be done? Well, if we assume we’re using just the English alphabet, we could assign each letter a code, 001 for the letter a, 002 for the letter b, 003 for c, and so on. 000 could represent a space. Numbers beyond 026 would be the punctuation marks.
So, all of literature could be written out as a continuous sequence of those three-digit codes. There’d be a lot, obviously, there are billions and billions of letters across the whole history of the written word. But, it would be possible.
Now comes the clever bit. That number is a finite whole number, it doesn’t go on forever. So, if we put a zero followed by a decimal point at the beginning, we would have a decimal fraction. Any decimal fraction of limited length can be represented as a ratio of two whole numbers. They are rational unlike numbers such as pi or e, which are irrational and can never be calculated fully as they go on forever. Thus, we have that fraction, that ratio. All we need to do now is take out metal rod and put a notch in it at the point where that fraction is represented by the distance from one end to the notch over the distance from the other end to the notch.
It’s clever isn’t it? I imagine this idea has ...

Source: David Bradley Sciencebase - Songs, Snaps, Science - December 23, 2022 Category: Science Authors: David Bradley Tags: Science Source Type: blogs