On this site I discuss a theory that the information of reality is expressed in base e.
One feature of this theory is that the information of reality is encoded in a transcendental base. This is good; I think it can be shown through “Reductio Ad Absurdum” that the true information of reality must exist in a transcendental base.
If reality is composed of a non-transcendental base, it would be “algebraic” and therefore any discrete information it contains it could be manipulated by calculation. If it were calculable, there would exist an axiomatic system that would be capable of perfectly characterizing it. But Godel’s Incompleteness theorems have proved that no such axiomatic system exists, because if it did, it would include undecidable statements, and by including undecidable statements, it fails to perfectly characterize reality.
So putting aside the information efficiency argument, it seems to me that we should be able to conclude that the true information of reality must exist in a transcendental base.
If the information of reality must exist within a transcendental base, and we only have to choose a transcendental number to occupy that space, e makes the strongest case I know, due to its role in information efficiency.