41
42

Computing the Uncomputable: "[Joel David] Hamkins showed there's a Turing machine that [...] can compute the uncomputable... but only in some weird "alternative universe" where the natural numbers aren't what we think they are." (johncarlosbaez.wordpress.com)

DevFRus が 投稿

並べ替え:
ベスト
トップ新着論争中古い順Q&A
あなたは単独のコメントのスレッドを見ています。

残りのコメントをみる →

[–]barsoap -7ポイント-6ポイント  (24子コメント)

Usually, Ultracomputers work on the principle, "given an oracle that can compute some uncomputable function, here's a machine that can compute any uncomputable function".

The problem, being, of course, that there's no such oracles.

And this is no different, it's just obfuscated better. Ultracomputing doesn't only defy the laws of physics, nay, it defies the laws of logic. Imagining a universe with another set of physical laws is one thing, imagining a universe in which fundamental logic doesn't hold is... psychotic? Nay, not even, psychotic people at least are internally consistent, even if it doesn't show.

EDIT:

  • Hello, /r/badmathematics! A formalist is formally defined as a mathematican that can't possibly know whether they're being inconsistent.

  • The lack of basic education in psychology in /r/compsci is palpable. You messed up your chance of me explaining things by being knee-jerk hostile.

[–]FunctionPlastic 4ポイント5ポイント  (15子コメント)

psychotic people at least are internally consistent

This is unrelated but are they?

[–]raging_goldfish 1ポイント2ポイント  (1子コメント)

Psychotic reporting in, can confirm.

[–]DoctorJanus 1ポイント2ポイント  (0子コメント)

different psychotic reporting in, can oppose

fite me irl

[–]thbb 3ポイント4ポイント  (1子コメント)

A Turing Machine with an infinite tape is just as a-physical as other models of computation that involve real numbers or inductive Turing Machines.

The point is about what does the a-physical concept allows to model that's useful? Classical Turing Machines are useful to model computations meant to compute a function, irrespective of memory constraints. Inductive Turing Machines (Burgin), as well as Interactive Turing Machines (Wegner), have their uses to model computations that are not about a function, but a continuously running system (such as an OS, a living organism...) for similar purposes.

Saying some sound mathematical concepts are psychotic and defy the laws of logic, just because they were not part of your standard CS curriculum is just obtuse.

[–]barsoap -3ポイント-2ポイント  (0子コメント)

We dealt with oracles plenty. Mostly, to write proofs by contradiction because "given a flying pig grass is purple" is not a useful result.

The thing is: Once you get into language such as "computes the uncomputable" you've left CS theory behind and entered the realms of esoterica.

[–]TotesMessenger 1ポイント2ポイント  (0子コメント)

I'm a bot, bleep, bloop. Someone has linked to this thread from another place on reddit:

If you follow any of the above links, please respect the rules of reddit and don't vote in the other threads. (Info / Contact)

[–]PM_ME_UR_OBSIDIAN 1ポイント2ポイント  (0子コメント)

https://en.m.wikipedia.org/wiki/Not_even_wrong

[–]Workaphobia 1ポイント2ポイント  (0子コメント)

I don't know what you're saying and I probably disagree with it, but I like your formalist definition. Have an upvote.

[–]naasking 0ポイント1ポイント  (0子コメント)

The real numbers hardly defy the laws of logic, and you can implement hypercomputation using real arithmetic.

[–]jackmott 0ポイント1ポイント  (0子コメント)

Don't know why you are being downvoted. I guess because you maybe unwisely used the word psychotic in the post. Your general point about this being no different than the oracle, just obfuscated, seems correct.

[–]fatoms -1ポイント0ポイント  (0子コメント)

Do I miss something or is this basically saying that if we can not compute a function we can imagine a set of rules under which we would be able to compute it, but not actually compute it, and then claim it is computable?