THE dimensionless gravitational coupling constant with mp the mass of some elementary particle, for definiteness taken as the proton, is such a small number that its significance has long been questioned. Thus Eddington1 considered that all the dimensionless physical constants, including this one, could be evaluated as simple mathematical expressions. Dirac2 considered that such an odd number must be related to other numbers of similar size, characterizing the structure of the universe. However, most physicists seem to believe that a dimensionless constant, such as (1), is provided by Nature, cannot be calculated, and is not in any way related to other numbers.
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DICKE, R. Dirac's Cosmology and Mach's Principle. Nature 192, 440–441 (1961). https://doi.org/10.1038/192440a0