The problem is systemic. People believe that the pursuit of monetary and financial profits by corporations will lead to the creation of benevolent artificial intelligence. I personally think this is essentially a religion because it is obvious that the pursuit of profits can not actually create anything benevolent, let alone intelligence.
It's a made up concept and it includes all possible ways people can think anything. If you want something concrete then you can consider sheaves of finitely presented algebras on the nervous system considered as a topological space with the obvious covering relations, continuous transformations, and algebra morphisms.
How can you tell the difference between (r,r) and (r+ε,r+ε)? The argument in the article assumes that there is an ε such that it is impossible to tell the difference between r and r+ε. So this means that the entire square can be covered by squares of side length ε and since the unit square is compact this means that there are only finitely many ε squares required to cover the entire unit square. Variation within the ε squares is imperceptible so this means there are only finitely many symbols that can be perceived to be different.
Interesting argument. This assumes that cognition must also be happening on a compact manifold which seems like a reasonable assumption but the conclusion is somewhat counterintuitive because it means there are only finitely many personality types and ways of thinking.
In the case of computers it turns to waste heat and whatever is radiated away is not usable energy and is essentially waste heat. Computers are basically devices for converting useful energy into waste radiation.
Fundamentally, yes. All motion does end up adding entropy to the environment. This is especially egregious for fossil fuels which are literally combusted/oxidized to move chunks of metal on wheels carrying different kinds of cargo. Electric vehicles change the dynamics somewhat but the motion of magnets still ends up contributing entropy to the environment at a somewhat reduced rate than fossil fuel vehicles.
You'd still have to write a proof for verifying semantic equivalence before implementing the optimization so I don't see what the neural network gains you here unless it is actually supplying the proof of correctness along with the optimization.
JIT optimizers operate at runtime, there are no test suites to verify before/after. It's happening live as the code is running so if you use AI then you won't know if the optimization is actually valid or not. This is why the article is using Z3 instead of neural networks. Z3 can validate semantic equivalence, neural networks can't.
I meant how do you make sure the optimization suggested by the AI is actually valid. If you're using AI to modify bytecode for faster execution then you have to make sure the optimized and unoptimized code are semantically equivalent. Neural networks can't do logic so how would you know the suggestions were not bogus?