Computer science is not physics

I've read Existential Type for a while and gotten to the post Languages and Machines, which discusses models of computation. It all makes a lot of sense: there are different ways of modelling computation and they are good for different things, the only catch is that all but one models a machine. A machine with computational units, storage, and what not.

A programming language is not used for manipulating registers and mutating memory cells, it's used for expressing thoughts and ideas. Thoughts and ideas does not live in the physical world (a least that's what I've heard) so why should we rely on a language (read: C/C++/Java/etc) that inherently is bound to a (more or less) physical machine?

No one questions that the field of maths is unrelated to the physical world we live in, right? Maths would exists with or without humans discovering mathematical truths and proofs. That's because maths uses some axiomatic system (that just happens to be very useful in the real world). However, I'd hope that no one in their right mind would argue that maths is about the physical realisations of the axioms, e.g., that 1 apple + 2 apples is 3 apples. Maths is not about apples -- apples just happen to fit in the axiomatic system.

Dijkstra famously said:

Computer science is no more about computers than astronomy is about telescopes.

I guess an equivalent statement about maths would be maths is no more about numbers than astronomy is about telescopes... Let me now rephrase the previous paragraph to emphasis my point.

No one questions that the field of computer science is unrelated to the physical world we live in, right? Computer science would exists with or without humans discovering computational truths and proofs. That's because computer science uses some computational model (that just happens to be very useful in the real world). However, I'd hope that no one in their right mind would argue that computer science is about the physical realisations of the models, e.g., the NAND gate. Computer science is not about NAND gates -- NAND gates just happen to fit in the computational model.

So why not call it computation science, or automated maths? No one would question the above paragraph if  I'd written automated maths instead of computer science.