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The fundamental constants (e.g. the mass of the electron, the universal gravitation constant, Planck's constant) are given that name for good reason: all computations used to understand or model the physical universe rely on their values.
In addition to the fundamental constants, there are other constants that define our universe. These numbers are really the statistics of the world, e.g. the heights of mountains, lengths of rivers, masses of the planets, etc.
There is a very odd, hard-to-believe-at-first- sight mathematical law that describes the distribution of these constants. In 1938, Frank Benford analyzed over 20,000 numbers taken from the fundamental constants of physics and far-removed areas such as sports stats and street addresses. Benford wanted to measure the frequency distribution of the starting digits for these numbers because of another odd fact - in antique tables of logarithms, the first few pages are often more worn, indicating that the log user was thumbing through the first pages much more frequently than latter pages, i.e. the logs with a "1" as a leading digit.
Now here's the amazing part. Instead of determining that starting digits from 1-9 appeared with approximately the same frequency, Benford found that the numbers he was studying began with a "1" a disproportionate 30% of the time. Benford went further, measuring the entire frequency distribution of starting digits, and developed a formula that predicts this distribution - a formula known as Benford's Law. The Law predicts that the frequency of occurrence of a digit drops off logarithmically with increasing digit size, and therefore numbers starting with 9 appear less frequently than all other numbers .
The explanation for the law comes from the fact that the numbers
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