anála: (from anás, a monad, and alath, knowledge); a concept.
Specifically, anála refers to an entity of the conceptual plane; for example, a philosophical form, a geometric shape, or mathematical concept, such as the computed value of π. This specifically excludes any knowledge-monads which are contingent upon the material plane, such as physical concepts or laws – including things such as the speed of light, or the measured value of π – which are determined empirically and which may vary between localities or universes.
A few questions.
Why is π included when we haven’t used empirical methods to calculate it in centuries? We’ve had infinite series that asymptotically converge to π for centuries. Even in warped elliptic/hyperbolic/otherwise non-euclidean spaces where the ratio of circumference/diameter ≠ π as you shrink your circle further and further the apparent spatial curvature lessens and circumference/diameter converges upon π, just as a circle 1000 km across drawn on the curved surface of the Earth wouldn’t have a C/D of π, a circle 1 meter across, while technically still very slightly curved, has a C/D incredibly close to π. Even the inhabitants of deeply warped universes should be able to infer the existence of the number we call π and realize that it is an important mathematical constant, though perhaps not as important to them as it is to us.
Taking this concept to its logical extreme, could it be argued that the universe be an anála if the it from bit proponents are right and universe is in fact a mathematical/informational entity or is mathematically isomorphic to one? Or for a less extreme example would someone’s mindstate qualify as an anála since as a string of 1s and 0s it can easily be mapped onto a natural number simply by reading the string as a number that’s been encoded in base-2. This would be an extremely large number with no obviously special properties about it unless you knew how to decode it but it would be a number, as real as 7 or Graham’s number or 9^9 or 616. So does that count?
On 1, because they’re talking about π, not π.
Which is to say, π the physical coefficient of space-time inflection, not π the mathematical constant. The thing you measure with a pi-meter, rather than compute.
Best not to get your π mixed up with your π.