Plouffe's Inverter

These graphics of the number of entries in Plouffe's Inverter are very intriguing. What it plainly says is that nature has an affinity for characteristic numbers that have the first four digits starting with 1000. For instance pi is really 3141 using this approach. The first graph says that there are 6000 constants like Pi that starts with 1000 as opposed to only 800 constants that starts by 9496. The graph represents a total of about 73 millions constants. This is just fascinating, nobody can explain this phenomena, some people think it is because of the base 10 we use to represent numbers. But it goes beyond just constants in the mathematical world. In the social sciences, it is called Benford's Law. Back in 1938, Benford compiled a list of different numbers coming from different sources and found that in every distribution the first digit was always following a distribution where 1 would occur 30 percent of the time. One of the most recent use of this "law" is its use in tracking financial fraud. I have tried it myself on several datasets and it works OK.