Borzacchini, Luigi. Incommensurability, music and continuum: a cognitive approach. (English). Arch. Hist. Exact Sci. 61, No. 3, 273-302 (2007).
Borzacchini argues that music ratios provides the “secret of the sect” for the irrational continuum. Plato’s Timeaus is based on Pythagorean philosophy but using irrational numbers as music tuning. This is tied to Archytas and Eudoxus.
Karl Popper stated that Kepler’s Pythagorean philosophy was the precursor of Schrodinger and Poppler then stated that harmonic resonance governs science and reality.
I wonder if this is tied to Egypt using 9/8 for solving the area of a circle with 9/8 also as the major 2nd music interval from Egypt’s sacred unit fraction of 2/3. The 2/3 has to be the subharmonic or inversion of 3/2, the Perfect Fifth music interval, which was squared to 9/4 and then halved to 9/8. So then 9/8 cubed was the solution for the square root of two as the tritone music interval. This is also discussed by musicologist Ernest McClain’s book the Pythagorean Plato.