Many mathematicians are Platonists in the sense of believing that their major concepts and theorems are discovered rather than invented. It is claimed here that the initial foundational source of those apparently spaceless and timeless mathematical ideas is the invariant Vacuum of physical space-time. This constitutes a non-classical yet “real” Form Heaven for fundamental physics and is a storehouse for all the knowledge of the physical constants, laws, and particles of physics. The intricate structure of the Vacuum is common to all intelligences in our universe and helps to constrain the reality of their emergent knowledge. A reductionist view begins with the basic set of quantum fields living in the Vacuum leading to more complex forms emerging from these fundamentals (protons, nuclei, atoms, molecules). These entities are quantum, and their nature along with the fundamental fields might be said to live in an unusual “square-root of reality.” Mathematics applies logic, intelligence and abstraction to world patterns and then gener- alizes at will forming abstractions of abstractions. But the field of mathematical-physics continually cross-fertilizes math and physics modestly limiting their divergence.
David Lyle Peterson