Processors include many optimization tricks, but I wonder if plain simplicity would be the fastest design of all. The traditional computer design presupposes a procedural, numerical paradigm. We are given registers which hold numbers, which index memory cells, etc. This arithmetic bias seems a roundabout way to achieve Turing completeness, sort of like working with logical statements using only their Gödel numbers.

I wonder if the classical Von Neumann architecture arose from the schoolboy viewpoint of “math is numbers.” Early education stresses brute manipulation rather than deductive mathematical structure and might have predisposed us to design computers the way we do.

Since modern programmers are far removed from the abstraction of machine code, why do we bother to make it “helpful?” We include a host of arithmetic operations at the cost of complicating the basic hardware. Why not let arithmetic be defined in a higher level language? Can brute hardware be reduced to some single simple principle, like propositional logic operators can be reduced to the Sheffer stroke? I am aware that circuits are reduced to NAND gates in this way, but you understand my analogy.

If we find that full computation can be based off one simple operation, then we can search for a sort of isomorphism of this operation in physics. Find a simple movement of molecules or energy which embodies our operation and which happens so quickly that its speed makes up for the amount of these small operations it takes to do significant calculations.

What might we choose for our operation? Consider combinatory logic which can code lambda calculus without the inconvenience of variable binding.