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Comment by anthk | Hacker News Reader

Pi is not bound to God neither the universe. It's just the ratio between a distance and adding up all the existing points around you at that distance.

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Which means it depends on the geometry of spacetime. If spacetime is quantized such that the Euclidean norm doesn't apply, then the value of pi will be different. See the "Extremal values of pi" paper[1].

[1]https://e.math.cornell.edu/people/Nikhil_Sahoo/files/pi_pape...

You can define Pi without universal geometry. And it's still a constant, nothing arbitrary, unlike

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Pi falls out of infinite sums, exponentials and differential equations all over the place. It's a universal constant, first discovered via geometry, but it's independent of geometry.

For example,

pi = the square root of the sum of 6/x^2 over x = (1, 2, 3...).

pi = the smallest positive value of ln(-1)/i.

pi = half the period of non-zero solutions to the differential equation f = -f''.

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