As Einstein said, "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[1]

As Einstein said, "As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality."[1] Forgive me for not addressing directly what you said, as you seem to be using "countable" to mean something other than "in bijection with the natural numbers". I don't really understand exactly what you mean. But it appears to me that you're trying to perfectly reconcile mathematics with experimental reality. This is impossible. Also, a lot of mathematical physics is very distant from experimental reality. -- [1] http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_geometry.html http://www-groups.dcs.st-and.ac.uk/history/Extras/Einstein_g...