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Call me when you found a way to encode transcendental numbers.
Perhaps you can encode them as computation (i.e. a function of arbitrary precision)
Hard to do as those functions are often limits and need infinite function applications. I'm telling you, math.PI is a finite lie!
Do we even have a good way of encoding them in real life without computers?
Just think about them real hard
\pi
Here you go
ⲡ
May I propose a dedicated circuit (analog because you can only ever approximate their value) that stores and returns transcendental/irrational numbers exclusively? We can just assume they're going to be whatever value we need whenever we need them.
Wouldn't noise in the circuit mean it'd only be reliable to certain level of precision, anyway?
I mean, every irrational number used in computation is reliable to a certain level of precision. Just because the current (heh) methods aren't precise enough doesn't mean they'll never be.
You can always increase the precision of a computation, analog signals are limited by quantum physics.