Anonymous at Sun, 2 Jun 2024 00:16:06 UTC No. 16205459

Interaction ???

Anonymous at Sun, 2 Jun 2024 01:46:51 UTC No. 16205556

That's why we just define it with Turing's machine and equivalent models in practice. A lot of math is based on intuitive concepts that don't have a formal definition anyway, and so far it has worked and if we ever encountered something that breaks it we would just redefine it. Surprising but a lot of math stands this way.

Anonymous at Sun, 2 Jun 2024 01:56:08 UTC No. 16205571

>>16205455
Also Turing PLAGIARIZED Church's work and then tried to pretend he'd never heard of it.

Anonymous at Sun, 2 Jun 2024 02:13:48 UTC No. 16205589

>>16205571
Gödel literally allowed this to btfo the Amerilard and fuck twink boipussy.

Anonymous at Sun, 2 Jun 2024 02:39:10 UTC No. 16205611

>>16205455
Aren't computers basically just turing machines with finite memory? If you can prove it takes finite memory you prove it's computable

Anonymous at Sun, 2 Jun 2024 02:46:00 UTC No. 16205619

>>16205611
The problem is that you're defining what computability is with a tool that tries to be computable based on an intuitive notion of what is effectively calculable.

Anonymous at Sun, 2 Jun 2024 03:15:24 UTC No. 16205665

>>16205611
actually, any language that can be recognized using only finite memory is necessarily a regular language. because all physically realizable computers have finite memory, we cannot actually accept even all the computable languages (indeed, not even all the context-free ones). TMs are still a useful model of computation since the amount of memory we can put in computers is big enough that most interesting languages can be accepted up to most interesting string lengths using the TM model. the Church-Turing thesis is that any effectively computable language is computable by TMs. it's a thesis, not a theorem, because it's basically just defining what "effective computation" is. but if somebody can build a machine that solves the halting problem deterministically (or more realistically, invents a new formalism that seems physically realizable enough that does the same) then the thesis just goes away.

Anonymous at Sun, 2 Jun 2024 03:31:53 UTC No. 16205693

>>16205665
>but if somebody can build a machine that solves the halting problem
Hypercomputation is not physically possible so this is not the real issue. The actual problem is that while we know that anything that a Turing Machine accepts is computable, we cannot prove that all effectively calculable things are accepted by a Turing Machine. The common consensus and experience tells us that this is likely true, but it cannot be proven because the concept of effective calculable is not a formal one and now it just gets linked back to computability since it's the common belief, which is defined by TMs. Absolutely circular.