I'm currently interested in the possibility of hyperturing computation, i.e. modes of computation that are strictly more powerful / can do more than a Turing machine. So far I only found three possible candidates which are however not as satisfying as I desire them to be.

>Malament-Hogarth spacetime

Purely theoretical, possibly unphysical

>quantum computation

No evidence so far that it is actually hyperturing. Might actually be possible to emulate on a Turing machine. Please let me know if it has been proven already.

>free will

Impossible to formalize mathematically.

Does LULZ know more possible candidates for hyperturing computation?

The experts on >>>/x/ would be able to deal with your post better

How is theory of computation suddenly paranormal?

A Turing machine is just one of many models and might have its flaws.

Free will is the paranormal thing here

It's been proven that anything computable is computable with a Turing Machine. That doesn't mean Turing is fastest in all cases, or that there are no equivalents (there are, lambda calc is one) but it does mean that if it's computable, you can compute it with a Turing Machine. You might come up with an algorithm that'll take longer to run on some particular machine, than the universe has left before it dies of heat death, but that algorithm is still computable.

"Hyperturing" is sort of a nonsense term here, in terms of what you're reaching for. You aren't looking for a system of computation, you're looking for something else and trying to conflate it with computation, so the prestige of the word "Turing" rubs off on it.

If you want some /x/ fuel, there are some AI scientists who seriously debate about if consciousness is a computation or not. The answer to that question has some interesting implications. I personally think that brains are made of parts which are finite and countable and that the interactions between different parts of the brain are also finite and countable, so I think consciousness is computable, but like everyone else engaging in the conversation, I don't really know.

>It's been proven that anything computable is computable with a Turing Machine

Nope, undergrad kiddo. The Church-Turing hypothesis is a philosophical statement. Some like to use it as a definition for computability, thereby willfully restricting themselves to a certain view on the topic. It is however not a mathematically provable statement. Only a pseud undergrad midwit would adopt it as dogmatic truth.

>philosophy

I don't care about anything philosophy studies. It's the only field of "knowledge" that has managed to exist for essentially all of human history without producing a single thing of value. Philosophy is co sisterly dragged kicking and screaming into modernity by people who actually know what they're talking about (aka scientists). Philosophy is just mental maturation. It feels good, but it has no substance and only a small niche of dysfunctional people will be interested in watching you do it.

Do you have a real argument or are you just trying to convince people in magical extra levels of computation with snark?

I fully agree that most of philosophy is useless bullshit. Hence I reject the unproven dogmatic assertion that the model of the Turing machine fully captures the notion of computability (which yet has to be defined independently without circularly referring to Turing machines - or else we cannot even evaluate whether the Church-Turing hypothesis holds).

>doesn't like philosophy

>immediately uses philosophy to prove his point of the lack of value in philosophy

Classic post-modernist joke.

>le everything is philosophy!!

I philosophied your mother yesterday night

>logically defending your position is philosophy

While you could have done a better job, defined your terms a little clearer, refined your sentences to better reflect your idea, it was philosophy.

There are a handful of post-modern writers that you'd love. They touch on the same ideas you were talking about.

>The Philosophy of Undercutting Irony

Just a truthful joke.

"On Computable Numbers" by Turing which founded computer science is a work of philosophy and the Church-Turing thesis is a philosophical statement

>Turing which founded computer science

I wish this myth would die. It's almost as bad as the one about Ada Lovelace being the first programmer.

>Magically believes without proof that there is a “hyperturing” computation

>Shits on philosophy as “magical.”

Stay stupid and pompous /sci

Nta and he does seem stupid, but if that's what you got out of his argument you have the reading comprehension of a fourth grader.

>is just one of many models and might have its flaws

You have no idea what you're talking about. Try learning about the concept first before you start speculating.

Please provide a formal mathematical proof (or a reference to such a proof) that it is impossible to define a notion of computability which cannot be simulated by a Turing machine. In order to avoid circularity you must provide a most general definition of computability without referencing the concept of Turing machines. Furthermore, you must provide proof that your definition of computability cannot be extended in such a way that it becomes hyperturing.

I will accept any book, paper, lecture notes or other publication that contains such a proof. Do it, undergrad kid.

A Turing machine can compute anything which is computable. "Hyperturing" is a nonsense idea.

>"Hyperturing" is a nonsense idea.

LOL look at this pseud who hasn't taken an advanced course on computability

could knock her out with one punch

>could knock her out with one punch

>Being this insecure about muscular women

Lol cope chud.

>not "knock her up"

one job

God damn, I didn't even think of that. I'll delete my message, so you can post something way funnier.

Hello OP, I too am currently interest in hyperturing computation. I'm finding the work in memristor based neural nets and optical phase-conjugate based error correction architectures, along side principles of QUBO to be quite stimulating.

It's called hypercomputation, not hyper-Turing computation. For example, a machine that can take a countably infinite number of (classical) steps in a single step would be capable of hypercomputation. True randomness also leads to hypercomputation (although it's not as exciting). It's pretty unlikely that any physical system (with our understanding of physics) would be capable of hypercomputation.

The only exception I could think of would be a perfect analog computer, which can work with all real numbers and not just computable real numbers. Assuming that uncomputable reals actually exist in nature. It wouldn't be possible to measure them with complete precision, of course, but theoretically it might be possible to eliminate error from calculations and only have to worry about measurement error.

>No evidence so far that it is actually hyperturing.

"Evidence?" It is proven that quantum computers have the same computability capabilities as Turing machines

Source?

Why would you think otherwise? A quantum computer can be simulated by a turing machine it just may take way longer to do anything.

How about quantum randomness? A pseudorandomness generator is not as good as a source of perfect randomness. Or is there proof that it makes no difference?

That would only be true if you can prove 'quantum randomness' has infinite Kolmogorov complexity. Then we're back to the philosophical arguments I guess.

https://en.wikipedia.org/wiki/Lavarand

Nice gimmick, but it doesn't answer the question.

not evidence of universality. op is talking about evidence that quantum computers in the real world can solve QP problems in polynomial time.

Thing is, in Bitcoin game theory, there is little incentive to publically declare you have a specialized computing architecture specially designed to inter dimensionally rip threads or drastically reduce the search space of the discrete log problem.

You keep it hidden, beating the next best has by one difficulty point, you run sandwhich attacks by agitating uncle forks