Why does Benford's Law (or Zipf's Law) hold? Both Benford's Law (if you take a list of values, the distribution of the most significant digit is rougly proportional to the logarithm of the digit) and Zipf's Law (given a corpus of natural language utterances, the frequency of any word is roughly inversely proportional to its rank in the frequency table) are not theorems in a mathematical sense, but they work quite good in the real life. 
Does anyone have an idea why this happens?
(see also this question)

My explanation comes from a storage perspective: Uniformly distributed high-precision numbers that range over many powers are very expensive to store. For example, storing 9.9999989 and 99999989  is much more expensive than storing 10^1 and 10^8 assuming "they" are okay with the anomaly. The "they" refers to our simulators ;-) Yes, I'm referring to the possibility that we are in a simulation. Instead of truly random numbers, using small randomness just around whole powers might result in huge cost savings. This type of pseudo-precision probably works really well in producing "realistic" simulations while keeping storage costs to a minimum.
