Funny to use the word transcendental there, since the Pythagoreans held ratios to be divine but couldn't figure out irrational numbers, like pi. They had trouble squaring that circle.
That's why I think Pythagoras refused to write down his doctrines. He knew there was more to be empirically discovered -- and he was wary of how text could become dogma. The divine he uncovered was based on a mathematical, harmonious cosmos; but he recognized it was beyond understanding in a lifetime. That's why Pythagorean mysticism is compatible with modern science -- he didn't write anything down!
2000 years later, Kepler had faith in a harmonious cosmos, and charged his model of harmony so it could fit the evidence. He elipsed the circles, instead of squaring them.
Fun fact #1: it is impossible to square a circle [1]
Fun fact #2: the Pythagoreans conducted the first attested scientific experiment in Western history (according to a recent PhD thesis at UMich [2])
2000 years later, Kepler had faith in a harmonious cosmos, and charged his model of harmony so it could fit the evidence. He elipsed the circles, instead of squaring them.
Fun fact #1: it is impossible to square a circle [1]
Fun fact #2: the Pythagoreans conducted the first attested scientific experiment in Western history (according to a recent PhD thesis at UMich [2])
[1] https://en.m.wikipedia.org/wiki/Squaring_the_circle
[2] https://deepblue.lib.umich.edu/handle/2027.42/150050