Talk:Super-Turing computation

Is there any reason this needs to be distinct from hypercomputation? Populus 22:06, 19 Dec 2003 (UTC)

Yes. Because they are two different things. For example, an analog recursive neural network is super-turing, but it is not a hypercomputer.

They are also two different approaches. Super-turing computation views a computer as a dynamical system. Hypercomputation views the computer as an artificial structure, and deals with it as an abstract mathematical construct rather than a dynamical system. -User:Kevin_baas 2003.12.20

Dynamical systems cannot be modeled as abstract mathematical constructs? Populus 14:17, 20 Dec 2003 (UTC)

No, they cannot. A very small subset of them (infinitesimal) can be represented by a set of differential equations, and a very small subset of these equations are analytic. However, for the most part, they are non-analytic. See also chaos theory.

Furthermore, you miss point entirely: the point is the idea of a dynamical system as opposed to a fixed construct. The computer exists as a flow, not as an entity. It is a subtle philosophical distinction but it is also a very important distinction. In Kantian terms, the computer is not "a prioiri analytic", but rather "a posteri synthetic". It is the product of a stable configuration of nonlinear materials (such as transistors), which dissipate a flow of energy. It can only exist as such. - As an information channel; it can never exist as an "abstract mathematical construct", even as we think of it. As we think of it, it is a flow of electricty and nueral semiotics.

The point is dealing with it as such - as a dynamical system manifested in the feedback loops of nonlinear materials, and to consider this process from an information theoretic perspective. This is in contrast to a "pure mathematics" approach. And this is why super-turing computation and hypercomputation differ. -Kevin Baas 2003.12.22

I'm not quite sure where you are getting all the ding-an-sichness from. I'm aware of a small but significant literature on super-Turing capabilities of various theoretical analog computers (I'm thinking of Bournez and Cosnard or Hava Siegelmann's work), but this is all (a) theoretical work that involves mathematical modeling of dynamical systems, (b) extensions of the perfectly respectible real-computation work of Blum, Shub, and Smale; and (c) not known to be physically realizable at present. If you've got cites for experimental work that shows e.g. exponential speedups for analog or pulse computers solving arbitrarily large instances of well-defined problems, then you've got something to say. But at the moment your claim seems to be that (a) certain kinds of analog computers are inherently more powerful in the real world than digital computers (a position that doesn't appear to be supported by current experimental evidence) and (b) this position does not need to be evaluated by the standard techniques of mathematics and/or science because it is involves nonlinear dynamics, a claim that will be of interest to the many physicists and mathematicians that study nonlinear dynamical systems. It's also a position that is not taken by the people you ought to be citing.

Now, if you'd like to write up an article about super-Turing capabilities of some analog computing models, that would be a useful contribution. But my suggestion would be that you cite sources and be careful about what claims the article makes (ideally, sourcing the claims rather than delivering contentious philosophical arguments ex cathedra), so that you don't trigger everybody's intellectual antibodies. I'd also suggest starting by extending one of the existing articles on analog computers, neural networks, or hypercomputation; we can always split the new stuff out if the parent article grows unwieldy. Populus 13:48, 23 Dec 2003 (UTC)

Real computation: I looked up real computation on wikipedia, but I got redirected to a different article, so I'm sorry, I'm thereby unfamiliar with the work that you are refering to.

Here's a little proof for you: Analog computers are at least as powerfull as digital computers because a digital computer is a special type of analog computer. (is made out of analog parts) To understand this more clearly, one would study nonlinear dynamics.

Here's a disproof of the universe being a giant turing machine: [[strange attractor]s.

You want me to cite my sources?: The Pope. The Pope said it. I saw it on T.V. It must be true, then. He talks to God, so he must be a pretty authoritave source. (The capacities for human reason aside - my church tells me not to use them.)

What has philosophy done for us? When do we use it? Nothing! Never! For today we have our modern tools: the tools of Logic (citation:Aristotle) and Phenomenology (citation: Russerl). We have no use anymore for critical thinking, or evaluating belief! Besides, why should we stand anything on such shaky ground? Let us not look at where we place our feet, for our hands much reach upwards ever higher!

Tell me this, what topic should the synthesis of dynamical systems and information theory be under, if not computation? (Don't answer please, that was rhetorical.) Tell me this as well: how else does one expect to compute? --Kevin Baas 2003.12.24

Kevin, I think you're not making sense. You shouldn't push an edit war on this until (a) you make sense and leave the rhetoric, (b) drop the phony mathematical and philosophical distinctions, and most importantly (c) show this article, as you'd like to see it, is more than a personal point of view. It is simply not the case that WP hosts distinctive personal arguments.

Charles Matthews 17:32, 15 Jan 2004 (UTC)

I'm sorry if my mix of satire, sarcasm, interdisciplinary arguments, logical proofs, analysis, sythesis, philosophy, and common sense is too thick for you. Perhaps I'm not making sense to you. At the same time, upon review, I find nothing illogical, contradictory, invalid, or unsound in what I have said. Perhaps it is then that I am using a language that is strange to you.

Whatever the case, I did not start an edit war. I simply created a page under a established topic, under its established title, and put content on that page that was clear, relevant, and neutral. Populus then deleted the content and redirected the page to a topic that, although it is in the same general field, is altogether different. Metaphorically, he redirected a page on "oranges" to a page on "apples". Yes, they are both fruit, but I do think it proper to distinguish between them.

(a) I'm sorry if you don't think rhetoric is appropriate for a talk page. That must be quite a handicap. Fortunately, however, your actions are not in agreement with your beliefs.

(b) I'm sorry if you don't understand me. I assure you that I am equally burdened by this.

(c) The talk pages and user pages are for distincive personal arguments. The article pages are for sociological dialectics, debates, dialogue. Knowledge is not a metaphysical absolute. See Socrates for more phony philosophical distinctions. -- Kevin Baas 22:06, 16 Jan 2004 (UTC)

What's now on the page is science fiction. OK, that takes some science fiction off the hypercomputation page; it has effectively no merits in encyclopedic terms. What you have written above is bluster (leave the Pope out of it, will you - there's a good boy). The article pages are not for those things, sctually.

Charles Matthews 10:33, 17 Jan 2004 (UTC)

Hypercomputation is science fiction. Nonlinear dynamics and information theory is legitimate. -- Kevin Baas 17:23, 17 Jan 2004 (UTC)

The following example of super-Turing computation is given: "Solving problems that can be solved on a Turing machine, in a lower time complexity class than they can be solved in on a Turing machine." But even my desktop PC can solve many problems in a lower time complexity class than a TM, simply because a PC has random access to its memory, as opposed to a TM's sequential access. Surely my PC isn't "super-Turing"? --Chris Pressey 20:49, 3 October 2005 (UTC)

Exactly. Initially, I have decided they suppose "reduced volume of computation" as compared to Turing V=T*S; that is, accomplishing with less energy. However, the disambiguation between super-Turing and Hypercomputation obfuscates completely: Super-Turing computation is any form of information processing that a Turing machine cannot do. Brrrr. As to my knowledge, the Turing thesis (his machine) postulates the theoretical limits of computation - the machine can do everything that is possible that is possible in math. Alan does not state how long will the machine be working for the tasks, Turing just tells whether it stops in finite time (the task is decidable) or will run forever (undecidable). The theory of complexity elaborates on that, telling more definitely the order of time it will take to solve a given decidable task on a device with memory-computing power S. The "disambiguating" definition clearly states that the proposed super-Turing comp is not just faster (less computation intensive) than the complexity theory predicts, rather it enables undecidable tasks to complete. While the article on quantum computation states that power (set of decidable tasks) matches with that of Turing, qubits are just fast sometimes. Otherwise, if Turing machine turns out to be unstoppable on some tasks which turn out decidable, his thesis would be wrong (incomplete) or that it is math which badly describes physics. Finally, it is not even understandable where the following sentence is referring to: "There are no restrictions on the class of super-Turing machines beyond this" - beyond what, do they mean that super-Turing is restricted from below by the Turing class? So, the article is too much controversial. Do I miss something?--Javalenok 15:57, 2 January 2006 (UTC)

Regarding the power of random computer (Finite State Machine) vs. Turing machine, it is hard for us, illiterate mortals, to understand why the miserable TM can be computationally more powerful. On the other hand, the von Neuman computer can simulate any Turing automata... Turns out, thay are equal. --Javalenok 17:11, 2 January 2006 (UTC)

I should clarify my criticism, since my previous comment was more of an exclamation of surprise, intended to be somewhat illustrative, rather than anything of substance. The definition of "super-Turing" used in the article seems to imply (or at least be obfuscated by a hidden assumption to the effect) that Turing machines are physical objects, when in fact they are just models of computation. There are other models of computation, too, for example the lambda calculus, Random-Access Machines (RAMs), and the "Machine over a Ring" defined by Blum, Cucker, Shub, and Smale in Complexity and Real Computation. Just like a Turing machine, we can precisely describe any of these models, but we can't physically build one (although we can approximate a RAM by building, say, a desktop PC.) But the RAM model and other models are, by the definition used in this article, "super-Turing", because they "do things that a Turing machine cannot" (work with irrationals, solve problems in lower time complexity classes, etc.) As a term used to describe these models, I think "super-Turing" is too vague to be useful, while also being misleading (in implying that there are any "physically realizable" Turing-complete models of computation.) Honestly, I suspect the phrase "super-Turing" was invented by some group of researchers, possibly in AI or philosophy of mind, who only had a passing knowledge of what a Turing machine is, and no substantial familiarity with any of the work done in the theory of computation. At least, that's the impression the article currently gives; if there's something more rigorous hiding behind it, the article definately needs to be tuned. --Chris Pressey 23:48, 26 January 2006 (UTC)

Let me address the criticism with two points: 1. This article, like the hypercomputation article, is about a theoretical possibility (that ironically, is not neccessarily theoretically possible), not an existing machine. 2. On a theoretical point regarding Godel's incompleteness theorem and turing's essay on computable numbers: your point is that all problems that are decidable can be decided by a turing machine - so perhaps a super-turing computer would not decide undecidable problems? I'm serious here. Perhaps noise in an analog computer is not a obstacle to true analog computing, but a manifestation of true analog computing. When you switch from accuracy to precision, your result may always be "close", but by definition it can never be exact - you just can't get exact readings from analog instruments. This not being exact is the not deciding completely. Also the noise part - the not always coming up with the same solution to the same problem - is not deciding. However, this does not neccessarily mean that such a mechanism would not be useful in ways that turing machines aren't, and it doesn't mean they don't "compute", if by compute one means process information. Kevin Baas^talk 18:00, 27 January 2006 (UTC)

On the redirect to hypercomputation

OK. I think this should be a redirect to hypercomputation, clearly the superior page. I see the two topics as being different names for the same thing. But someone has reverted my redirect, so I assume that person disagrees with me. Perhaps they could explain why, or provide references that the two concepts are different? Ben Standeven 08:19, 26 January 2007 (UTC)

"I see the two topics as being different names for the same thing." Funny you said that because you recently removed the section of this article that explains the difference between the two.

IMHO, hypercomputation is a bunch of mumbo-jumbo that is logically impossible, whereas super-turing computation is a different approach to information processing that may have useful applications.

Sorry, but what means "logically impossible"? If something is stringently defined, which both hypercomputation and superTuring are, then it is "possible" given the constraints the definition is built upon. Or... do you consider the whole concept of mathematics and infinitesimal calculus "logically impossible" as well... hypercomputation may theoretically require infinite precision, but... you can get a quite good approximation with analogue models as well, and even if we would put the Planck length as a lower limit for precision we would have a well working feasible model. Do you believe in strange attractors for instance, even they would be "logically impossible" with your reasoning then... And, regarding SuperTuring that is simply the effect that parallel system can solve problems more efficient than sequential systems as you can achieve exponential to super exponential convergence towards solutions. Roland.orre (talk) 21:24, 10 December 2014 (UTC)

One approach to super-turing computation is through the paradigm of attractors, such as spike-time attractors in cortical networks. Kevin Baas^talk 17:40, 27 January 2007 (UTC)

Mmmm. Only relevant passage I found was "The computational capabilities of analog discrete time recurrent NNs were reviewed by Siegelmann (1993) and Orponen (2000). Finite analog RNNs with rational weights employing a saturated linear activation function can simulate arbitrary Turing machines step by step. If the weights are real, these networks may have, in theory, super-Turing computational capabilities (Siegelmann & Sontag, 1995).", which is indeed about hypercomputation. I believe there is a page dedicated to discussing alternative approaches to recursion theory, but I don't recall its name at the moment. In any event, I still think this page should be redirected. Ben Standeven 01:51, 29 January 2007 (UTC)