  By combining a renormalization group argument relating the charge e and mass
m of the proton by e^2 ln m ~ 0.1 pi (in Planck units) with the
Carter-Carr-Rees anthropic argument that gives an independent approximate
relation m ~ e^20 between these two constants, both can be crudely estimated.
These equations have the factor of 0.1 pi and the exponent of 20 which depend
upon known discrete parameters (e.g., the number of generations of quarks and
leptons, and the number of spatial dimensions), but they contain NO continuous
observed parameters. Their solution gives the charge of the proton correct to
within about 8%, though the mass estimate is off by a factor of about 1000 (16%
error on a logarithmic scale). When one adds a fudge factor of 10 previously
given by Carr and Rees, the agreement for the charge is within about 2%, and
the mass is off by a factor of about 3 (2.4% error on a logarithmic scale). If
this 10 were replaced by 15, the charge agrees within 1.1% and the mass itself
agrees within 0.7%.
