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PI has this particular value only in a particular geometry.


This is not just academic, the geometry of the space we are living into is not flat, and thus the PI we measure is not the one you'd expect.

The effect of this space time distortion is what keeps you from floating around, and keeps the air you breath stick to the sphere you call home, which btw has that shape for the same reason.

So, even though the PI value discrepancy caused by earth gravitational field is very small, it shapes our lives and our origins in a dramatic way.

Well, you are measuring two different things. Pi is not changing at all.


exactly, same thing for α: if it were different (numerically) that would mean that we are talking about a different universe, i.e. we would measuring a different fine structure constant. People in that universe would still call it "α", because we define "α" to be the fine structure constant. That wouldn't change the (numerical) value of α in this universe.

In the same way, we define PI to be "the ratio of a circle's circumference to its diameter", and that depends on the kind of geometry where you lay that circle on.


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