It’s a really neat result that I want to demonstrate to talk about the implications of this finding.
Are there any non-trivial ones? Having skimmed the webpage it sounds like the result can basically be summarized as “if you enumerate all possible sequences of 0s and 1s, then one of them encodes a solution to the halting problem”. Which is true but IMO doesn’t have much implication for how we should think about the solubility of the halting problem.
I didn’t suggest that it did exactly solve the halting problem in the way people think, but the key here is that computing and simulating things are very different entities, and one can simulate hard problem solvers without being able to solve the problem, so computability and simulatability are distinct concepts, not the same.
In essence, a Universal Turing Machine can simulate computers that solve the halting problem without itself being able to solve the halting problem. And the main result is Universal Turing Machines can enumerate all possible sequences of 0s and 1s to simulate hyperconputation on the real numbers, so long as you do the simulations in parallel.
I might want to edit the post to explain why computability!=simulatability, or why computability and simulatability are distinct concepts.
Are there any non-trivial ones? Having skimmed the webpage it sounds like the result can basically be summarized as “if you enumerate all possible sequences of 0s and 1s, then one of them encodes a solution to the halting problem”. Which is true but IMO doesn’t have much implication for how we should think about the solubility of the halting problem.
I didn’t suggest that it did exactly solve the halting problem in the way people think, but the key here is that computing and simulating things are very different entities, and one can simulate hard problem solvers without being able to solve the problem, so computability and simulatability are distinct concepts, not the same.
In essence, a Universal Turing Machine can simulate computers that solve the halting problem without itself being able to solve the halting problem. And the main result is Universal Turing Machines can enumerate all possible sequences of 0s and 1s to simulate hyperconputation on the real numbers, so long as you do the simulations in parallel.
I might want to edit the post to explain why computability!=simulatability, or why computability and simulatability are distinct concepts.