Re:How to fit any dataset with a single parameter
by rnhmjoj on Wednesday September 29, 2021 @07:19PM
(#28701269)
Note that π, like practically any constant or number normally found in mathemathics is constructive and contains a finite amount of information. What the author consider unphysical are the non-constructive reals: unfathomable numbers that can't be defined or written in any finite amount of words or paper. It's hard to argue they play some role in our physical world: it would basically amount to metaphysics.
However, even if rarely used outside of proofs, they are the vast majority of the reals, in fact there are only countably infinite constructive/computable numbers.
Basically, the universe can just as well be approximated in two different ways. One, it's all straight lines, and anything that looks like a circle/curve is actually a piece of a veeery many sided polygon if you look closely enough at it. Two, it's all curves of some curvature, and anything that looks like a straight line is actually a segment of a veeery large circle. The first perspective corresponds to taking the rational numbers as physical. The second one corresponds to taking pi as physical (and then it's unclear whether e is also physical, or which other transcendental numbers are, but 1 is definitely un-physical then).
Probably the constructive framework is the best way to express this concept, just starting from whatever constant we chose to define as the unit.