For The Encyclopedia of Nonbelief to be published by Prometheus Books. The Anthropic Coincidences

In 1919, mathematician and physicist Hermann Weyl puzzled why the ratio of the electromagnetic force to the gravitational force between two electrons is such a huge number, N1 = 1039.1 Weyl wondered why this should be the case, expressing his intuition (and nothing more than that) that "pure " numbers, like p, that is, numbers that do not depend any system of units, when occurring in the description of physical properties, should most naturally occur within a few orders of magnitude of unity. Why 1039? Why not 1057 or 10-123? Some principle, Weyl thought, must select out 1039. In 1923, astronomer Arthur Eddington agreed: "It is difficult to account for the occurrence of a pure number (of order greatly different from unity) in the scheme of things; but this difficulty would be removed if we could connect it to the number of particles in the world—a number presumably decided by accident.2 He estimated that number, now called the "Eddington number, " to be N =1079. Well, N is not too far from the square of N1. In 1937, physicist Paul Dirac noticed that N1 is the same order of magnitude as another pure number N2 that gives the ratio of a typical stellar lifetime to the time for light to traverse the radius of a proton.3 That is, he found two seemingly unconnected large numbers to be of th