...though a great mathematician often has a philosophical bent...
Mathematics is often overly mystified by non-mathematicians. In reality the binary system is more natural than the decimals. Halving 10 makes 5, and halving which makes 2.5. Therefore 10 isn't a good base. 8 or 16 are better. 2 is very neat, with the disadvantage that the strings of digits get very long, which, a computer doesn't care.