I know diagonalization proofs, they dont prove what you say they prove. Cite any computer science source stating that the existence of hypercomputers are logically impossible. If you keep saying it follows from some diagonalization argument without showing how or citing sources ill move on from this.
I know diagonalization proofs, they dont prove what you say they prove.
Not proofs, plural, not the category. This specific one. The details involve a method to enumerate all programs which is the hard part. IIRC the lecturer doesn’t actually get into that, though. Read the original papers if you want nobody found issue with them in nearly 100 years.
Cite any computer science source stating that the existence of hypercomputers are logically impossible.
Church-Turing is a fundamental result of CS, arguably its founding one, and I will not suffer any more denial of it. It’s like asking a physicist to provide a citation for the non-existence of telekinesis: You fucking move something with your mind, then we’ll talk. In the meantime, I’m going to judge you to be nuts.
Feel free to have a look at the criticism section of Wikipedia’s hypercomputation article, though. Feel free to read everything about it but don’t pester me with that nonsense. Would you even have known about it if I didn’t mention off-hand that it was bunk, serves me right I guess.
church-turing is a a thesis, not a logical theorem. You pointed me to a proof that the halting problem is unsolvable by a Turing Machine, not that hypercomputers are impossible.
The critic Martin Davis mentioned in wikipedia has an article criticizing a kind of attempt at showing the feasibility of hypercomputers. Thats fine. If there was a well-known logical proof of its unfeasibility, his task would be much simpler though. The purely logical argument hasnt been made as far as i know and as far as you were able to show.
You would need to invent a complexity class larger than R, one that contains more than countably infinite programs. Those, too, can be diagonalised, there would still be incomputable functions. Our whole argument would repeat with that complexity class instead of R. Rinse and repeat. By induction, nothing changes, Q.E.D.
