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.