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# Topic: Hypercomputation

 Home Page - Hypercomputation Research Network (http://hypercomputation.net) Hypercomputation concerns the study of computation beyond that defined by the Turing machine, and is also known as super-Turing, non-standard or non-recursive computation. If you publish or come across any books, articles or papers that you feel may be relevant to researchers in hypercomputation, please send us the details for inclusion in our comprehensive bibliography. If you are active in the field and wish to be involved in discussions relating to it, you may benefit from joining the Hypercomputation Mailing List. hypercomputation.net   (386 words)

 Hypercomputation - Wikipedia, the free encyclopedia Hypercomputation refers to various proposed methods for the computation of non-Turing-computable functions. The hallmark of a hypercomputer is that it can solve the general halting problem, a feat impossible for ordinary computers. A real computer (a sort of idealized analog computer) might be able to perform hypercomputation if physics admits general real variables (not just computable reals), and these are in some way "harnessable" for computation. en.wikipedia.org /wiki/Hypercomputation   (926 words)

 Hypercomputation Hypercomputation is the theory of methods for the computation of non-recursive[?] functions. Hypercomputation was first introduced by Alan Turing in his 1939 paper Systems of logic based on ordinals, which investigated mathematical systems in which an oracle was available to compute a single arbitrary (non-recursive) function from naturals to naturals. An analog computer might be able to perform hypercomputation if physics admits real variables (not just computable reals), and these are in some way "harnessable" for computation. www.ebroadcast.com.au /lookup/encyclopedia/hy/Hypercomputation.html   (229 words)

 Wikipedia: Hypercomputation Hypercomputation was first introduced by Alan Turing in his 1939 paper Systems of logic based on ordinals, which investigated mathematical systems in which an oracle was available to compute a single arbitrary (non-recursive) function from naturalss to naturals. This might require quite outlandish laws of physics (for example, a measurable physical constant with an oracular value, such as Chaitin's constant), and would at minimum require the ability to measure a real-valued physical value to arbitrary precision despite thermal noise and quantum effects. Until this is well established and explained, the possibility of quantum hypercomputation is deserving of investigation. www.factbook.org /wikipedia/en/h/hy/hypercomputation.html   (384 words)

 Finitism and Hypercomputation Plausibly finitistic ways to define properties of high complexity or to prove strong consistency statements were simply not known before this paper. Hypercomputation refers to idealized computers computing non-recursive functions. Thus, a language is decidable in the model iff it is hyperarithmetic. web.mit.edu /dmytro/www/FinitismPaper.htm   (3168 words)

 Toby Ord -- hypercomputation   (Site not responding. Last check: 2007-10-08) Hypercomputation is the relatively unexplored field in which models of computation with more power than the Turing machine are studied. I've tried my hardest to present hypercomputation in a manner that is both useful for active researchers in the field and accessible to the casual (but interested) reader. In late 2004 I was asked to write an introduction to hypercomputation for a special issue of the Journal of Applied Mathematics and Computation. www.amirrorclear.net /academic/research-topics/hypercomputation.html   (675 words)

 Hypercomputation: Facts and details from Encyclopedia Topic   (Site not responding. Last check: 2007-10-08) Hypercomputation refers to methods for the computation of non-computable function computable function quick summary: Hypercomputation was first introduced by Alan Turing[Click link for more facts about this topic] in his 1939 paper Systems of logic based on ordinals, EHandler: no quick summary. An analog computer (american english) or analogue computer (british english) is a form of computer using electronic or mechanical phenomena to model... www.absoluteastronomy.com /encyclopedia/h/hy/hypercomputation.htm   (1710 words)

 Abstract: Stannett (2001) Hypercomputation is Experimentally Irrefutable (http://www.dcs.shef.ac.uk/~mps)   (Site not responding. Last check: 2007-10-08) We demonstrate that one of these interpretations supports the construction of a hypercomputational device, while the other is a physical tautology (it is always true in the Standard Model). Therefore, the falsity of hypercomputation is logically inconsistent with the Standard Model. Hypercomputation is either logically entailed by, or else logically independent of, the Standard Model. www.dcs.shef.ac.uk /~mps/research/abstracts/2001HypercomputationIrrefutable.html   (178 words)

 Hypercomputation: Computing More Than the Turing Machine   (Site not responding. Last check: 2007-10-08) The new field of hypercomputation studies models of computation that can compute more than the Turing machine and addresses their implications. In this report, I survey much of the work that has been done on hypercomputation, explaining how such non-classical models fit into the classical theory of computation and comparing their relative powers. I also examine the physical requirements for such machines to be constructible and the kinds of hypercomputation that may be possible within the universe. www.comdig.org /print_article.php?id_article=9257   (141 words)

 DCS Publications Archive - The Case for Hypercomputation   (Site not responding. Last check: 2007-10-08) We examine some 20 physical and mathematical models of computation that are either known or suspected to have super-Turing or hypercomputational capabilities, and argue that there is nothing in principle to prevent the physical implementation of hypercomputational systems. Hypercomputation may indeed be intrinsic to physics; recursion emerges from hypercomputation in the same way that classical physics emerges from quantum theory as scale increases. Furthermore, even if hypercomputation were one day shown to be physically infeasible, there would still remain a role for hypercomputation as an organising principle for advanced research. publications.dcs.shef.ac.uk /7455   (145 words)

 Learn more about Hypercomputation in the online encyclopedia.   (Site not responding. Last check: 2007-10-08) Learn more about Hypercomputation in the online encyclopedia. Hint: Play with putting spaces before and after your words to see the different results you get. Toby Ord, Hypercomputation: computing more than the Turing machine, Honours Thesis, University of Melbourne, 2002. www.onlineencyclopedia.org /h/hy/hypercomputation.html   (434 words)

 Hypercomputation and the Singularity   (Site not responding. Last check: 2007-10-08) X-Message-Number: 25584 References: < > From: Peter Merel < > Subject: Hypercomputation and the Singularity Date: Wed, 19 Jan 2005 13:35:31 +1100 In researching the next round of replies on the "fantasy" thread I stumbled over Tien Kieu's 2002 paper that argues quantum computers can solve Turing-incomputable problems including the Halting Problem. Given a hypercomputer capable of Tien Kieu's Hamiltonian, we need only formally specify the parameters of MNT design and their constraints, and a globally optimal design will pop out without any delay. The fundamentals of mathematics must be reframed to account for hypercomputation. www.cryonet.org /cgi-bin/dsp.cgi?msg=25584   (160 words)

 Hypercomputation / Field Computation Bibliography Hypercomputing may be defined as computing outside of the bounds of Turing-computability. The narrower interpretation is that hypercomputation permits the computation of functions that are not Turing-computable. The broader interpretation calls into question the entire set of assumptions on which Turing-computability is based (discrete symbols, finite data structures, discrete finite rules, discrete-time operations, etc.), and thereby provides a new model of computation orthogonal to the Turing model. www.cs.utk.edu /~mclennan/hypercomp-fc-biblio.html   (1051 words)

 Super Computer   (Site not responding. Last check: 2007-10-08) Hypercomputation is a sub-class of super-Turing computation, which is able to compute non-computable functions, i.e. In other words, not all super-Turing machines are Hypercomputers, but all Hypercomputers are super-Turing machines. Hypercomputation views the computer as an ''artificial structure'', and deals with it as an abstract mathematical construct rather than a dynamical system. www.wwwtln.com /finance/174/super-computer.html   (628 words)

 Logic & Semantics   (Site not responding. Last check: 2007-10-08) Hypercomputation is "the study of computation beyond that defined by the Turing machine, and is also known as super-Turing, non-standard or non-recursive computation." This is a relatively new multidisciplinary area and remains something of a speculative backwater. However, many research ideas here fit rather naturally into my general areas of philosophical research: in particular, relations between the foundations of mathematics/logic and physics, and my work on theories of truth, and more recently philosophy of mind and psychology. (1) To discuss what the implications of hypercomputation might be: implications for the foundations/philosophy of mathematics, and connections with some philosophical ideas about the Church-Turing Thesis, "supertasks", and other oddities. www.cl.cam.ac.uk /Research/LS/Talks/2000_01/01_03_02.Abstract.html   (131 words)

 Online resources and download centre - Hypercomputation Research Network (http://hypercomputation.net) All files listed here remain the intellectual property of their respective owners, and are made available here for personal research and classroom use only. Papers marked Trends'06 are those submitted in "pre-proceedings" form to the 2006 workshop on Future Trends in Hypercomputation. Subsequent versions of these papers may also exist as peer-reviewed articles in the International Journal of Unconventional Computing or elsewhere, and you are advised to consult these later versions where possible. www.hypercomputation.net /resources.html   (339 words)

 Learning Computation: Spooky science This is part of a special issue devoted to "super-recursive algorithms and hypercomputation". As far as hypercomputation is concerned, I believe that all of the thus-far proposed models are not known to be physically implementable. I'm no hypercomputation expert either - but articles which appear in our journals are vetted by the editors and referees and Elsevier has little input on what subject matters the journals cover. www.learningcomputation.com /blog/2005/10/spooky-science.html   (1454 words)

 Hypercomputation Mailing List (hypercomp-request@dcs.shef.ac.uk) - Hypercomputation Research Network ... The Hypercomputation Mailing List is an international discussion list for researchers interested in hypercomputation (also called super-Turing, non-Turing, or non-recursive computation) who want an opportunity to exchange ideas with others. The hypercomputation websites (.com/.net/.org) are registered to Mike Stannett under his trading name 'NoiseFactory'. Please remember that publication on a mailing list almost certainly does constitute public disclosure for patenting and libel purposes, and that when you send a message to this list, both copyright in, and responsibility for, your mailing remain with yourself or the existing owner. www.hypercomputation.net /discussion.html   (334 words)

 CSE 4/510 & PHI 498, Spring 2004, Phil. of Comp. Sci.: What Is Hypercomputation?   (Site not responding. Last check: 2007-10-08) A 1994 email exchange on interactive computing, message passing, and AI actors, with numerous references. This paper has almost convinced me that there just might be something to all of this "hype" about "hypercomputation". Cotogno, P. "Hypercomputation and the Physical Church-Turing Thesis", British Journal for the Philosophy of Science 54(2): 181-224. www.cs.buffalo.edu /~rapaport/510/whatishypercomputation.html   (366 words)

 Peak Oil News and Message Boards Forums >> Post 152321 >>   (Site not responding. Last check: 2007-10-08) The logic circuits that would produce meaningfull (to humans) results of quantum computation are very complex and great intellectual feat, as what they need to do (as far as I understand) is to restrict the quantum computation power from (nearly) infinite to meaningfull to human (mathematical/logical) languages. I guess what this means is that - according to interpretation of QM on chooses to follow, on the level of superpositions and entanglements there can happen hypercomputation, but not with logic gates based on qubits that aim to avoid/restrict hypercomputation in order to create a Turing machine. BTW interestingly, perhaps in support of the quantum consciousness hypethesis, there are case studies of "savant idiots" that can factor primes/find large primes in their minds much faster (in seconds and minutes) than any digital computers. www.peakoil.com /post152321.html   (4313 words)

 Workshop Home Page - Future Trends in Hypercomputation, Sheffield, 11-13 September 2006 ... The Post-Proceedings of the Future Trends in Hypercomputation 2006 Workshop will be published, after a formal refereeing process, as a volume of the We encourage you to submit research papers on the subject of hypercomputation, its aims, its philosophy and its physical feasibility (or lack thereof). Work relating to hypercomputation that was not presented at the workshop may also be submitted for the proceedings. www.hypercomputation.net /hypertrends06   (216 words)

 Bibliography, sorted by date - Hypercomputation Research Network (http://hypercomputation.net) Welch P.D. On the Possibility, or Otherwise, of Hypercomputation. Cotogno P. Hypercomputation and the Physical Church-Turing Thesis. Hypercomputation Workshop, University College London, 24 May 2000. www.hypercomputation.net /bib_by_date.html   (2173 words)

 Hypercomputation and the Physical Church-Turing Thesis - Cotogno (ResearchIndex)   (Site not responding. Last check: 2007-10-08) Hypercomputation and the Physical Church-Turing Thesis - Cotogno (ResearchIndex) We review the main approaches to computation beyond Turing definability (`hypercomputation'): supertask, non-well-founded, analog, quantum, and retrocausal computation. Cotogno, P. Hypercomputation and the Physical Church-Turing Thesis. citeseer.ist.psu.edu /641241.html   (203 words)

 Citebase - The Diagonal Method and Hypercomputation We then demonstrate why such a situation does not occur for the methods of hypercomputation under attack and why it is unlikely to occur in any other serious methods. A hypercomputation model named Infinite Square Well Hypercomputation Model (ISWHM) is built from quantum computation. This model is inspired by the model proposed by Tien D. Kieu quant-ph/0203034 and solves an Turing-incomputable problem. www.citebase.org /cgi-bin/citations?id=oai:arXiv.org:math/0307020   (951 words)

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