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Profile: Mark Hogarth (Cambridge University)
Profile: Mark Hogarth (Cambridge University)
  1. Mark Hogarth (forthcoming). A New Problem for Rule Following. Journal of Applied Mathematics and Computation.
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  2. Mark Hogarth (forthcoming). Non-Turing Computers Are the New Non-Euclidean Geometries. International Journal of Unconventional Computing:1--15.
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  3. Mark Hogarth (2004). Deciding Arithmetic Using SAD Computers. British Journal for the Philosophy of Science 55 (4):681-691.
    Presented here is a new result concerning the computational power of so-called SADn computers, a class of Turing-machine-based computers that can perform some non-Turing computable feats by utilising the geometry of a particular kind of general relativistic spacetime. It is shown that SADn can decide n-quantifier arithmetic but not (n+1)-quantifier arithmetic, a result that reveals how neatly the SADn family maps into the Kleene arithmetical hierarchy. Introduction Axiomatising computers The power of SAD computers Remarks regarding the concept of computability.
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  4. Mark Hogarth (1997). A Remark Concerning Prediction and Spacetime Singularities. Studies in History and Philosophy of Science Part B 28 (1):63-71.
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  5. Jeremy Butterfield, Mark Hogarth & Gordon Belot (eds.) (1996). Spacetime. Dartmouth Pub. Co..
  6. Mark Hogarth (1996). Predictability, Computability and Spacetime. Dissertation, Cambridge University
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  7. Rob Clifton & Mark Hogarth (1995). The Definability of Objective Becoming in Minkowski Spacetime. Synthese 103 (3):355 - 387.
    In his recent article On Relativity Theory and Openness of the Future (1991), Howard Stein proves not only that one can define an objective becoming relation in Minkowski spacetime, but that there is only one possible definition available if one accepts certain natural assumptions about what it is for becoming to occur and for it to be objective. Stein uses the definition supplied by his proof to refute an argument due to Rietdijk (1966, 1976), Putnam (1967) and Maxwell (1985, 1988) (...)
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  8. Mark Hogarth (1994). Non-Turing Computers and Non-Turing Computability. Psa 1994:126--138.
    A true Turing machine (TM) requires an infinitely long paper tape. Thus a TM can be housed in the infinite world of Newtonian spacetime (the spacetime of common sense), but not necessarily in our world, because our world-at least according to our best spacetime theory, general relativity-may be finite. All the same, one can argue for the "existence" of a TM on the basis that there is no such housing problem in some other relativistic worlds that are similar ("close") to (...)
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  9. Robert Clifton & Mark Hogarth (1993). Time, Space and Philosophy. Philosophical Books 34 (2):123-125.
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  10. Mark Hogarth (1993). Predicting the Future in Relativistic Spacetimes. Studies in History and Philosophy of Science Part A 24 (5):721-739.
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  11. Mark Hogarth (1992). Does General Relativity Allow an Observer to View an Eternity in a Finite Time? Foundations of Physics Letters 5:173--181.
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