Talk:Hypercomputation

message: While there are functions that may not have a limit and/or limit that can be found through numerical means, this does not mean that the limit/integral can't be found by a computer.
Computation > numerical analysis.
203.143.164.204 22:26, 4 November 2007 (UTC)
thread_title:  A note on integration/limits 

message: This article makes it seem as if hypercomputation held any scientific credibility. It does not. The physical impossibility of this "proposal" is not stressed enough, as others have pointed out in the discussion. I recommend that it is made clear that this is a mathematical, hypothetical, concept, that has no model in any known, relevant, physics. At least it must be certain that it is impossible in the observed universe (would need new physics) Exa (talk) 13:36, 30 September 2011 (UTC)
replies: text:  Hypercomputation, as a mathematical or computing science concept, needs to have no "scientific credibility" at all. That said, I believe the article does need to be cleaned up to separate the math from the nonsense (which could all be moved to the article supertask) and extended (for instance, I see no mention of infinite time turing machines, ordinal turing machines, or perhaps (I'm no expert) infinitary lamda calculus) Susy 11 (talk) 15:49, 15 March 2022 (UTC)
thread_title:  Unscientific proposal 

message: Kevin baas said in his edit summary, took out b%llsh@t and inserted usefull categorization.
The b%llsh@t in question was:
:"[Hypercomputation with real valued analogue computing] might require quite outlandish laws of physics (for example, a measurable physical constant with the value Ω)."
Kevin, what are you talking about?  Are you suggesting that analogue computers, in general, can solve the Halting problem? If so, citing a proof would be handy!  If not, then the text should remain.
I am not suggesting that physics actually has improbable properties like this- just that they would be necessary, if, as I believe some articles in the literature have suggested, analogue computers could be hypercomputers. --Pde 04:22, 9 Sep 2003 (EDT)
:: Well, obviously if you could "measure" values in real life that, say, contain the solution to the halting problem or some such, this is equivalent to performing a hypercomputation.  That seems rather far-fetched, however.  Besides, AFAIK it is impossible to create a "perfectly" analog computer in real life - there is quantization at some level for all matter, energy, space, time, etc.  So even if there would exist a theoretical hypercomputer it would not obey the laws of physics, which would put a rather large crimp in its usage.  - JustinWick 18:55, 19 November 2005 (UTC)
replies: text:  It is absolutely far-fetched.  If such measurements could answer the halting problem, and they are not practically achievable, we would say that the universe performs "unharnessable hypercomputation".  It hypercomputes, we can't. -- pde 03:48, 2 February 2006 (UTC)
thread_title:  Analogue computer properties 

message: Well, I am a little scandalized after reading all the stuff in this page (including the magnificent I.Q. of Kevin showing how good is he making such tests), how tolerant can PDE be explaining n times the same and how after n explanations Kevin Bass seems to misunderstood again and again (confusing it with the complexity classes of computation) a simple definition of a term "hypercomputation" simply as the field of proposals on computing functions that are  not computable by Turing machines. On the other hand, I suggest to add to the article the name who has used in first place the name and also a strong remark saying that the concept really have the sense of rejecting the Church-Turing thesis. In this way, it is completely false that Turing had as motivation hypercomputation instead of only have the idea of relativisation of his model (and now the computability standard model).
:Hi, I agree that we should cite Copeland for introducing the term.  But I'm not convinced that talking about hypercomputation necessarily rejects the Church-Turing thesis; to me it makes sense to examine whether and how hypercomputation might be possible without concluding that it actually is possible. -- pde 23:24, 8 March 2006 (UTC)
replies: text: Hmm, surely showing that something is possibly possible entails that it is possible (might be possible => possible this is a theorem of S5). Discussions of hypercomputation concern the conceivability of hypercomputers, and how that relates to possibility is another matter. (Although being conceivable, logically consistent and physically serious are excellent indications of possibility).--NoizHed 03:50, 31 March 2006 (UTC)
replies: text: Haha.  I disagree with your translation of my comment into modal logic :).   I was using two "possibility" operators: "might" was "can imagine universes where this would be" (there is a complicated scientific and epistemological question of what small odds we'd give that our universe is one of those); "possible" is "possible in a particular universe".  -- pde 00:01, 2 April 2006 (UTC)
thread_title:  Scandalized 

message: The link to supertask in the first paragraph seems a bit odd, as the linked article does not address supertasks in the context of computer science (in fact it states this prominently).  Maybe this should be removed?  Or maybe someone wants to start an article on supertasks in computer science (I do not even know what they are).  - JustinWick 18:32, 19 November 2005 (UTC)
thread_title:  Supertask Link 

message: And who is the "her" it could be referring to?--155.143.221.40 01:42, 19 December 2005 (UTC)
thread_title:  Footnote 2 missing referent 

message: More work is required, I'd read the Copeland paper, have to cite it here, and summarize  what he means by a hypercomputer,
and also make the introduction a bit more tangible. Also there is a consisstency problem. In the introduction some models are mentioned
which are not detailed later. --Exa 23:19, 15 March 2006 (UTC)
thread_title:  Copeland, introduction, consistency 

message: I am confused by the following addition
"Even more simply, with no need for some strange number like \Omega, an everyday Turing Machine that has access to an oracle for the halting problem can solve the halting problem."
Isn't omega effectively an oracle?1Z 11:47, 18 January 2007 (UTC)
replies: text: Yes, Omega is just a real number, and it is Turing equivalent to the Haltig problem, so given either one of them it is possible to compute the other.  There is nothing special about Omega, and knowing the definition of Omega doesn't illuminate hypercomuptation any more than knowing the definition of the halting problem does.  It is a mistake for this article to treat it Omega as if it is something special CMummert · talk 12:07, 18 January 2007 (UTC)

text: Probably the author had in mind a specific set of natural numbers called the "halting problem", for example the set { e : φe(e) halts }, and when the author said "oracle for the halting problem" they meant specifically an oracle for this set rather than just any oracle with the same Turing degree.   As I said above, I don't think it is worth mentioning Omega at all, because up to Turing degree Omega is the same as the halting problem.  I think you are raising the same objection in different language. CMummert · talk 13:07, 18 January 2007 (UTC)
replies: text: Indeed, this was my point in adding the original comment starting "even more simply".  I don't have the nerve to remove absolutely every reference to Omega on this page, but it should be done.  Omega is irrelevant in a straightforward characterization of hypercomputation.  It is just obscuring matters completely to bring it up repeatedly in this article.  Nor is Omega an oracle.  An oracle is something that provides an external decision procedure for a question directly, by taking in an input and returning the answer to the question for that input.   You could have an oracle for the question "is bit i of Omega a 1" if you wanted, but why bother with such a convoluted thing in order to solve the halting problem? 32F 11:59, 28 January 2007 (UTC)
replies: text: Removing all references to Omega here would be fine with me; I agree it has nothing to do with hypercomputation.  In contemporary terminology in recursion theory, "an oracle" is a synonym for "a set of natural numbers" or "a sequences of 0s and 1s", so that part isn't quite wrong. CMummert · talk 12:07, 28 January 2007 (UTC)

text: I removed the paragraph in question. THe broader problem is that AIT does not illuminate hypercomputation any more than regular recursion theory does. CMummert · talk 12:44, 28 January 2007 (UTC)
replies: text:  Oh, that is much much better.  Even the title of that thankfully deleted section "The challenge of hypercomputation", makes no sense.   What "challenge" is mentioned in there?  And it makes the, I think, false claim that algorithmic information theory "helps us to understand" hypercomputation. It helps us less than "regular recursion theory" since the latter is the framework in which the concept of hypercomputation is even defined.  AIT is just something else entirely.  (Incidentally, it would be nice to have a "blockquote" that more clearly set off quotes like the one above, for example by putting them in a box and colouring them a nice light pastel colour. 32F 12:53, 28 January 2007 (UTC)
replies: text: A while back, I put the following CSS in my monobook.css file for that effect. It is not beautiful, and the margins don't align correctly, but it does set off blockquotes visually from the rest of the text. CMummert · talk 13:02, 28 January 2007 (UTC)
replies: text: Excellent thanks.  I didn't know about the monobook file (haven't looked around too much in what having a user id lets you do...) 32F 13:34, 28 January 2007 (UTC)
thread_title:  Is Omega an oracle 

message: Hi, the introductory passage of the history of hypercomputation cites Turing's refusal to unbox the oracle in the O-machine as Turing not being interested in the implementability of the O-machine. But as Jack Copeland's paper Turing's O-machines, Searle, Penrose and the Brain (p.5) suggests, Turing wasn't concerned about the implementability of any of the machines he had proposed in the 1930s, whether universal or O. So placing such emphasis on the implementability of the O-machine seems misguided.
--69.149.116.161 18:15, 15 August 2007 (UTC)
thread_title: Turing's Stance on Implementability

message: Hi, The "external links" section includes a link to a paper by Paolo Cotogno (I've corrected the author's name in the link). However, if you follow that link, you actually find a PDF version of a paper - Paolo Cotogno (2003) Hypercomputation and the Physical Church-Turing Thesis. Brit. J. Phil. Sci. 54, pp. 181-223. - that appeared in the British Journal for the Philosophy of Science. It is usual for copyright to be assigned to a journal prior to publication, so the link may be providing access to material in violation of copyright. Mike.stannett (talk) 00:50, 29 December 2007 (UTC)
thread_title: Possible copyright clash with BJPS

message: I removed a few citation requests in the "proposals" section, recently attached to sentences that mainly refer to wikilinked articles (e.g. Zeno machine) that contain reasonable sourcing (plus added an internal link for one of them).  The person who added the requests might check the linked articles before reinserting the tags or adding further ones.  —Preceding unsigned comment added by 207.241.238.233 (talk) 02:41, 15 January 2008 (UTC)
replies: text: I added a cite for the thing about real-valued computation.  The cited paper probably doesn't satisfy the request directly (e.g. it doesn't use anything like Chaitin's omega) but shows how to solve "hard" problems quickly using real-valued computers.  This should be reasonably satisfactory as a mathematical answer and I don't see anyone expecting it to be a physical answer.  I noticed that the "proposals" section is now a mixture of purely mathematical concepts (like the transfinite Turing machine) and concepts that claim some kind of connection with physics.  Maybe these two classes of ideas should be separated from each other in the section. 207.241.238.233 (talk) 08:12, 8 February 2008 (UTC)
thread_title:  cite requests 

message: I agree with Unzerlegbarkeit's removal of the definition section  that Peterdjones reverted.  The article's first sentence gives an adequate definition and matches up with the one in SEP . The stuff about super-recursive algorithms is way too long-winded and should be moved further down and shortened.  It also seems to have spread to a bunch of other articles recently and should be cleaned up from them too.  CBM, if you're still watching this page, would you mind taking a look into that situation and telling us what you think?  Thanks. 207.241.238.217 (talk) 04:05, 31 July 2008 (UTC)
replies: text: Yes, the previous definition was correct. It seems the article did just fine with that definition until about [ a month ago], when someone decided that we simply couldn't define hypercomputation without reference to Burgin's super-recursive algorithms. --Unzerlegbarkeit (talk) 14:36, 31 July 2008 (UTC)
thread_title:  definition section 

message: I removed a tendentious sentence about the "Turing myth" which was extremely far from a mainstream view.  Given the generally fringe-ish nature of the article topic, I suppose Siegelmann's claims are noteworthy enough to deserve a mention, but they should be cited and described neutrally. 207.241.238.217 (talk) 07:55, 13 November 2008 (UTC)
replies: text: Siegelmann's claims are basically just a re-iteration of what we already know regarding Metaheuristic or Hyper-heuristic algorithms, though applied to hardware such that there are orders-of-magnitude efficiency increases.  there's nothing really revolutionary or "fringe"-ish about them.  they just represent a limit case of metaheuristic algorithms using massively parallel low-precision analog hardware.   the basic result, that metaheuristic algorithms have super-turing performance if you compare the computational time classes side-by-side with their non-metaheuristic equivalent (e.g. traveling salesmen problems), is well established. Kevin Baastalk 18:46, 27 September 2010 (UTC)
thread_title: Siegelmann and "Turing myth"

message: Why is there nothing in here about analog recurrent neural networks? 216.54.131.130 (talk) 16:02, 23 February 2009 (UTC)
replies: text: There is now. 207.241.239.70 (talk) 10:14, 27 February 2009 (UTC)
replies: text:  This was a bit surprising for me to find. I skimmed the paper and couldn't make much sense out of it. And I couldn't find more information praising or criticizing Siegelmann's work. In the least, I think it should be explained in what way ARNNs are hypercomputers. To do more would be to create a wikipedia article about them, if it is truly the case that they are so important as being proven hypercomputers. Right now this article just says that she "proved that it could perform hypercomputation." It seemed a bit suspicious to me.   —Preceding unsigned comment added by 141.156.179.133 (talk) 00:18, 21 January 2010 (UTC)
replies: text: ARNN's are hypercomputers but like the Zeno machine, they are abstract constructions that are not physically realizable.  It's not all that interesting. 66.127.55.192 (talk) 09:46, 10 February 2010 (UTC)

text: They are perfectly physically realizable.  Our brains are but one example.  Perhaps you mean noise-less ARNN's, which is just absurd.  even in perfect isolation, an ARNN will generate it's own "noise".  a noiseless ARNN is not even a valid construction, real OR abstract. Kevin Baastalk 18:52, 27 September 2010 (UTC)

text: Here is a new article discussing the expressive power of analog recurrent neural networks (http://www.sciencedirect.com/science/article/pii/S0304397512000990)150.135.222.230 (talk) 00:19, 8 March 2014 (UTC)

text: An ARNN with noise can be simulated to arbitrary precision with a Turing machine...so they have the same limitations.  Only a perfect ARNN could do something that a turing machine can't - and in a universe with quantum randomness and plank quantization there's always going to be a source of noise. SteveBaker (talk) 14:28, 7 August 2014 (UTC)
thread_title:  ARNNs? 

message: In the first bullet on Hypercomputer proposals, usual time dilation can't do this, I suppose you need a Malament-Hogarth space time. Furthermore, this computation takes an infinite amount of energy, so it should be considered impossible. 
This bullet shouldn't be put first since it's so fantastic. I'd like to see this bullet be struck completely. 
This article should be cleaned up for writing style and content.  —Preceding unsigned comment added by Pulu (talk • contribs) 20:01, 20 November 2009 (UTC)
thread_title: Time Dilation

message: processing is entropic transfer.  if superliminal (non-entropic) transfer is not possible, neither is superliminal entropic transfer ("processing").  i suppose the question comes down to channel capacity.  i'm pretty sure the math works out. Kevin Baastalk 18:41, 27 September 2010 (UTC)
thread_title:  dubious - superliminal processing 

message: I think that the section on "Hypercomputer proposals" could be greatly improved. Section 2 (pp. 3-7) of a recent paper by Aran Nayebi (which can be found here: http://arxiv.org/abs/1210.3304) provides a rather thorough and accurate survey of these models as well as the criticisms of their physical realizability in the literature. I will try to get to this cleanup soon when I get the time, but in the meantime those who would like to commence feel free to do so.
Also it does appear that the author provides his own new criticisms of hypercomputation in general (see Section 3 of the article) and proposes an alternative direction for hypercomputation (what he calls "plausible hypercomputability") in Section 4. And interestingly enough, in the Acknowledgements section (pg. 26) it appears that Martin Davis, one of the main critics of the current hypercomputation movement, has supported Nayebi's proposal for a "plausible hypercomputability". Perhaps this proposal should be mentioned in this Wikipedia page?  — Preceding unsigned comment added by 198.228.216.21 (talk) 02:15, 22 October 2012 (UTC)
thread_title:  Cleaning up "Hypercomputer proposals" section 

message: It seems that a turing machine can reasonably simulate the physical world - figure out the mass & velocity of every particle and calculate where it'll end up at some time in the future.   Doesn't that mean that any physically realizable device (such as a hypothetical hypercomputer) can be simulated by a piece of software running on a turing machine.   Since no piece of software running on a turing machine can solve the halting problem, neither can a simulation of a hypercomputer...or an actual hypercomputer.   Ergo they can't exist.
The only get-out clause is if (using black holes or something) you can run the hypercomputer at infinite speed...which is the same thing as a turing machine running at infinite speed simulating that device.
So the bottom line here is not whether there is something "better" than a turing machine - it's whether you can (through various relativity trickery) get the turing machine to run at literally infinite speed.
But even that isn't physically realizable because the reliability of any physical machine is guaranteed to be finite (because of quantum fluctuations) and hence in the machine's own frame of reference, it can't run forever.  In our frame of reference, the machine will break down without producing the answer you need the very instant you turned it on.
But (for example) you don't need to build an actual turing machine in order to prove the existence of the halting problem - so maybe you don't need a hypercomputer to make interesting and important discoveries from considering what it would be like if you DID have one just sitting around on your kitchen table.
SteveBaker (talk) 14:22, 7 August 2014 (UTC)
thread_title:  SImulation. 

message: Greetings. This is my very first time on Wikipedia talk page so I hope I'm following the guidelines. Please correct me if that is not the case.
I am entering into university as a computational neuroscience student and while learning about different computational systems for artificial intelligence, I came across this paper about how minds can be seen as hypercomputation systems.
Before getting my hopes up about a method to create AI with human or greater intelligence, I would like to know the opinion of people who have participated on this page to whether super-turing machines can lead to such a thing.
NAStrahl (talk) 18:51, 30 August 2014 (UTC)
replies: text: As I explained in my previous post, it seems that a Turing machine can adequately simulate the behavior of a collection of atoms - and since the human brain is composed of atoms, there is no seeming objection to a Turing machine being able to solve any problem in finite time that a human brain can solve in finite time.  If we define "hypercomputation" as being some form of computation that a Turing machine cannot perform, then it follows that human brains cannot be hypercomputers. SteveBaker (talk) 21:55, 30 August 2014 (UTC)
thread_title:  Super-Turing Computation As Being Equivalent To A Mind 

message: Hello fellow Wikipedians,
I have just modified 2 external links on Hypercomputation. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
*Added archive https://web.archive.org/web/20070709100858/http://edelstein.huji.ac.il/staff/shagrir/papers/Supertasks_Accelerating_Turing_Machines_and_Uncomputability.pdf to http://edelstein.huji.ac.il/staff/shagrir/papers/Supertasks_Accelerating_Turing_Machines_and_Uncomputability.pdf
*Added archive https://web.archive.org/web/20111005150801/http://jdh.hamkins.org/Publications/2000e to http://jdh.hamkins.org/Publications/2000e
When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.
Cheers.—InternetArchiveBot (Report bug) 09:06, 7 April 2017 (UTC)
thread_title:  External links modified