Simple explanation for Benford's Law: When numbers expand out into an additional digit through doublings, a "1" is always present, "2" is usually present, and s

Simple explanation for Benford's Law: When numbers expand out into an additional digit through doublings, a "1" is always present, "2" is usually present, and so on down the line. The law is present in proportion to the degree that the sample set possesses logarithmic distribution. The distribution doesn't have to be limited to doublings. The law also applies to triplings, quadruplings, halvings, etc. The key is logarithmic/exponential/geometric distribution. Try it for yourself on the calculator and see how rarely 9s come up as the first digit for every x^n. A good real world example would be the distribution of frequencies of musical pitch in equal temperament. In this case, the exponential multiplier (x) for x^n is 21/12, or about 1.059. Here's (http://en.wikipedia.org/wiki/Piano_key_frequencies http://en.wikipedia.org/wiki/Piano_key_frequencies) a list of the frequencies; notice how the first digits have tons of ones and almost no nines.