Two interesting things about taking a bath… The first was, while singing in the bathtub, I hit a resonant frequency, and I wondered: what can be deduced about the shape of my bathtub (well, bathroom) from this frequency? The second was that I heard something fall into Tasha’s water dish; thinking nothing of it, I was rather […]

Here are some very ill-thought-out ideas on Kolmogorov complexity. We define a metric on the space of bit-strings . For a universal Turing machine , let be the “length” of the shortest program that outputs on input , or outputs on input . This should measure how difficult it is to […]