The fabric of our physical reality contains dozens of pure numbers, from which all measured constants can in principle be calculated. • Some key physical entities such as empty space, elementary particles and the wavefunction appear to be purely mathematical in the sense that their only intrinsic properties are mathematical properties. • The External Reality Hypothesis (ERH)—that there exists an external physical reality completely independent of us humans—is accepted by most but not all physicists. • With a sufficiently broad definition of mathematics, the ERH implies the Mathematical
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