Your assertion that sodium channel logic and silicon trace logic are 100% identical is the primary problem. It's like claiming that a hydraulic cylinder and a bicep are 100% equivalent because they both lift things - they are not the same in any way.
People chronically get stuck in this pit. Math is substrate independent. If the process is physical (i.e. doesn't draw on magic) then it can be expressed with mathematics. If it can be expressed with mathematics, anything that does math can compute it.
The math is putting the crate up on the rack. The crate doesn't act any different based on how it got up there.
