Do the ‘special’ values of the constants of physics and cosmology need an explanation?

In his book Galaxies, Nuclei and Quasars [1], Fred Hoyle wrote that ‘one must at least have a modicum of curiosity about the strange dimensionless numbers that appear in physics’. Hoyle was among the first to conjecture that the so-called ‘constants of nature’ might not be truly universal. He outlined two possible attitudes to them. One is that ‘the dimensionless numbers are all entirely necessary to the logical consistency of physics’; the second possibility is that the numbers are not in the broadest sense universal, but that ‘in other places their values would be different’. Hoyle favoured this latter option because then

Whatever one thinks of its motivation, Hoyle's conjecture is now even more attractive. The ‘portions of the universe’ between which the variation occurs must now, we realise, be interpreted as themselves vastly larger than the spacetime domain our telescopes can actually observe — perhaps even entire ‘universes’ within a multiverse.

If we ever established contact with intelligent aliens, how could we bridge the ‘culture gap’? One common culture (in addition to mathematics) would be physics and astronomy. We and the aliens would all be made of atoms, and we would all trace our origins back to the big bang 13.7 billion years ago. We would all share the potentialities of a (perhaps infinite) future. But our existence (and that of the aliens, if there are any) depends on our universe being rather special.