Max Tegmark, exploring implications of the External Reality Hypothesis that there exists an external physical reality completely independent of us humans, claims that physics is so successfully described by mathematics because the physical world is completely mathematical, isomorphic to a mathematical structure, and that we are simply uncovering this bit by bit. In this essay we have tried to discover that mathematical structure. We start from the correspondence rule as it has a potential to look at the vast existing empirical domain from a different angle. We do not need new data nor new mathematical structures. We need only this different angle - a paradigm shift. If Geometrical Universe Hypothesis is correct, then the empirical domain and the correspondence rule are redundant in the sense that they can be inferred from Thurston geometries. In his well-known essay, Wigner claimed that “the enormous usefulness of mathematics in the natural sciences is something bordering on the mysterious”, and that “there is no rational explanation for it”. The GUH provides this explanation and more: makes the testable prediction that is uncovered in the conclusion.
Jacek Safuta