The point is that a random Turing Machine’s output is technically uncomputable, which is nice, but it’s entirely useless because it uses an entirely flat prior, because it entirely picks randomly from all possible universes, and a No Free Lunch argument can be deployed to show why this isn’t useful, because it picks at random from all possible universes/functions.
This, incidentally resolves gedymin’s question on the difference between a random hypercomputer and a useful hypercomputer: A useful hypercomputer trades off performance for certain functions/universes in order to do better in other functions/universes, while a random hypercomputer doesn’t do that and thus is useless.
The point is that a random Turing Machine’s output is technically uncomputable
What do you mean? The output of any Turing machine is computable by definition. Do you mean solving the halting problem for a random Turing machine? Or a random oracle?
Non-sequitur, the no-free-lunch theorems don’t have anything to do with the physical realizability of hypercomputers.
The point is that a random Turing Machine’s output is technically uncomputable, which is nice, but it’s entirely useless because it uses an entirely flat prior, because it entirely picks randomly from all possible universes, and a No Free Lunch argument can be deployed to show why this isn’t useful, because it picks at random from all possible universes/functions.
This, incidentally resolves gedymin’s question on the difference between a random hypercomputer and a useful hypercomputer: A useful hypercomputer trades off performance for certain functions/universes in order to do better in other functions/universes, while a random hypercomputer doesn’t do that and thus is useless.
What do you mean? The output of any Turing machine is computable by definition. Do you mean solving the halting problem for a random Turing machine? Or a random oracle?