The Brain Making Sense of an Orchestra

But our unconscious feats of unweaving and weaving are greater even than this. Think what is happening when you listen to a whole orchestra. Imagine that, superimposed on a hundred instruments, your neighbour in the concert is whispering learned music criticism in your ear, others are coughing and, lamentably, somebody behind you is rustling a chocolate wrapper. All these sounds, simultaneously, are vibrating your eardrum and they are summed into a single, very complicated wriggling wave of p...

 1/9998 Produces Binary Output

The pattern will break down once you get past 8192, which is 2^13. That means that the pattern continues for an impressive 52 significant figures (well, it actually breaks down on the 52nd digit, which will be a 3 instead of a 2). The reason it works is that 9998 = 10^4 - 2. You can expand as   1 / (10^n - 2) = 1/10^n * 1/(1 - 2/10^n) = 1/10^n * (1 2/10^n 2^2 /10^2n 2^3 /10^3n ...) which gives the observed pattern. It breaks down when 2^k has more than n digi...