Abstract:
The essence of number was regarded by the ancient Greeks as the root cause of the existence
of the universe, but it was only towards the end of the 19th century that mathematicians
initiated an in-depth study of the nature of numbers. The resulting unavoidable actuality of
infinities in the number system led mathematicians to rigorously investigate the foundations
of mathematics. The formalist approach to establish mathematical proof was found to be
inconclusive: Gödel showed that there existed true propositions that could not be proved to be
true within the natural number universe. This result weighed heavily on proposals in the mid-
20th century for digital models of the universe, inspired by the emergence of the programmable
digital computer, giving rise to the branch of philosophy recognised as digital philosophy. In
this article, the models of the universe presented by physicists, mathematicians and theoretical
computer scientists are reviewed and their relation to the natural numbers is investigated. A
quantum theory view that at the deepest level time and space may be discrete suggests a
profound relation between natural numbers and reality of the cosmos. The conclusion is that
our perception of reality may ultimately be traced to the ontology and epistemology of the
natural numbers.
