Random encoding idea

This is one of those ideas that someone else has probably thought up, designed, and implemented. Oh well.

It occurred to me today that because the real number line is infinitely divisible, every possible string of digits can be represented by pointing at a single spot on some segment of this number line. The only limitation on the number of digits we can represent is the precision of our “pointing” device. If I have a sharp pencil, I can make a more precise mark at 0.325, but with a dull pencil it might be hard to determine whether my mark was supposed to mean 0.330 or 0.325.

And if we can represent digits, then with predetermined codes and protocols we can represent any type of digital information. In binary, 0.325 is 0.011. That could be interpreted as an opcode, an ASCII character, anything you want. With a really sharp pencil, you could point at 0.2957198301284949204, translate it to binary…

0.0100101110110100010010110111011100101110001110010100000110
011000101001100111010100110011011111101000100000010001101101
110110110001111111101010010100111111001110111001000001111100
111011101001001010011010010001110110101111111001000000100001
101100010011000010111100100001100100000001110100101111111001
011100000010101010011000110101000000000100001001111101110111
101011111000000101101001111110111001000110110100101001001001
100011011100100010111101000110010101011011000110111000001000
001110110100101101011010111110000111010011111001101110011000
111110001011110101011001000010110110000011111010010001111110
011100011110011001111000101111110100010111011100111011011110
010000101000101100011110101110101010111101000000111100010110
000001110100111011101000000000100110001011101000011101101101
100010010101101000111001000000110110111000011100010110111111
010110100011010000010010000111110001110101100000011111010110
100101011000001011111110100011001110000011000011100110111111
011110000100001100010101001101110000010001110110010101100001
0001

…and voila, you have a BIN file or maybe a small computer program. More likely, you could encode a file that you already wrote onto a single, precise mark.

By hand, I wonder how much information you could write on a single piece of paper using a well-designed code.

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