For your analogy with Turing machines, do you have a better mathematical model of a computer? Nobody works directly with the TM model when they're doing theoret

For your analogy with Turing machines, do you have a better mathematical model of a computer? Nobody works directly with the TM model when they're doing theoretical CS anyway, they just describe the algorithm and everyone understands that if you really really wanted to you could work it down to a TM. The same is true of mathematics. It might be hard to get everything precise, but that's not the point of mathematics. Nor is the point to be close to reality.