David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Ezio Di Nucci
Jack Alan Reynolds
Learn more about PhilPapers
Minds and Machines 13 (1):115-153 (2003)
Does Nature permit the implementation of behaviours that cannot be simulated computationally? We consider the meaning of physical computation in some detail, and present arguments in favour of physical hypercomputation: for example, modern scientific method does not allow the specification of any experiment capable of refuting hypercomputation. We consider the implications of relativistic algorithms capable of solving the (Turing) Halting Problem. We also reject as a fallacy the argument that hypercomputation has no relevance because non-computable values are indistinguishable from sufficiently close computable approximations. In addition to considering the nature of computability relative to any given physical theory, we can consider the relationship between versions of computability corresponding to different models of physics. Deutsch and Penrose have argued on mathematical grounds that quantum computation and Turing computation have equivalent formal power. We suggest this equivalence is invalid when considered from the physical point of view, by highlighting a quantum computational behaviour that cannot meaningfully be considered feasible in the classical universe.
|Keywords||Church–Turing thesis computability hypercomputation recursion scientific method super-Turing machine|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
Lukáš Sekanina (2007). Evolved Computing Devices and the Implementation Problem. Minds and Machines 17 (3):311-329.
Similar books and articles
David J. Chalmers (1994). On Implementing a Computation. Minds and Machines 4 (4):391-402.
Amit Hagar & Alex Korolev (2007). Quantum Hypercomputation—Hype or Computation? Philosophy of Science 74 (3):347-363.
Paolo Cotogno (2009). A Brief Critique of Pure Hypercomputation. Minds and Machines 19 (3):391-405.
Nir Fresco (2011). Concrete Digital Computation: What Does It Take for a Physical System to Compute? [REVIEW] Journal of Logic, Language and Information 20 (4):513-537.
Philip D. Welch (2004). On the Possibility, or Otherwise, of Hypercomputation. British Journal for the Philosophy of Science 55 (4):739-746.
Tim Button (2009). SAD Computers and Two Versions of the Church–Turing Thesis. British Journal for the Philosophy of Science 60 (4):765-792.
Toby Ord & Tien D. Kieu (2005). The Diagonal Method and Hypercomputation. British Journal for the Philosophy of Science 56 (1):147-156.
Tien D. Kieu (2002). Quantum Hypercomputation. Minds and Machines 12 (4):541-561.
Paolo Cotogno (2003). Hypercomputation and the Physical Church-Turing Thesis. British Journal for the Philosophy of Science 54 (2):181-223.
Added to index2009-01-28
Total downloads38 ( #107,979 of 1,907,655 )
Recent downloads (6 months)5 ( #158,844 of 1,907,655 )
How can I increase my downloads?