This paper investigates the view that digital hypercomputing is a good reason for rejection or re-interpretation of the Church-Turing thesis. After suggestion that such re-interpretation is historically problematic and often involves attack on a straw man (the ‘maximality thesis’), it discusses proposals for digital hypercomputing with Zeno-machines , i.e. computing machines that compute an infinite number of computing steps in finite time, thus performing supertasks. It argues that effective computing with Zeno-machines falls into a dilemma: either they are (...) specified such that they do not have output states, or they are specified such that they do have output states, but involve contradiction. Repairs though non-effective methods or special rules for semi-decidable problems are sought, but not found. The paper concludes that hypercomputing supertasks are impossible in the actual world and thus no reason for rejection of the Church-Turing thesis in its traditional interpretation. (shrink)

A Geometrical Approach to Quantum Information.

A number of examples have been given of physical systems (both classical and quantum mechanical) which when provided with a (continuously variable) computable input will give a non-computable output. It has been suggested that these systems might allow one to design analogue machines which would calculate the values of some number-theoretic non-computable function. Analysis of the examples show that the suggestion is wrong. In Section 4 I claim that given a reasonable definition of analogue machine it will always be wrong. (...) The claim is to be read not so much as a dogmatic assertion, but rather as a challenge. -/- In Sections 1 and 2 I discuss analogue machines, and lay down some conditions which I believe they must satisfy. In Section I discuss the particular forms which a paradigm undecidable problem (or non-computable function) may take. In Sections 5 and 6 I justify any claim for two particular examples lying within the range of classical physics, and in Section 7 I justify it for two (closely connected) examples from quantum mechanics, and discuss, very briefly, other possible quantum mechanical situations. Section 8 contains various remarks and comments. In Section 9 I consider the suggestion made by Penrose that a (future) theory of quantum gravity may predict non-locally-determined, and perhaps non-computable patterns of growth for microsopic structures. My conclusion is that such a theory will have to have non-computability built into it. (shrink)

Recent work on hypercomputation has raised new objections against the Church–Turing Thesis. In this paper, I focus on the challenge posed by a particular kind of hypercomputer, namely, SAD computers. I first consider deterministic and probabilistic barriers to the physical possibility of SAD computation. These suggest several ways to defend a Physical version of the Church–Turing Thesis. I then argue against Hogarth's analogy between non-Turing computability and non-Euclidean geometry, showing that it is a non-sequitur. I conclude that the Effective version (...) of the Church–Turing Thesis is unaffected by SAD computation. (shrink)

This paper develops my (BJPS 2009) criticisms of the philosophical significance of a certain sort of infinitary computational process, a hyperloop. I start by considering whether hyperloops suggest that "effectively computable" is vague (in some sense). I then consider and criticise two arguments by Hogarth, who maintains that hyperloops undermine the very idea of effective computability. I conclude that hyperloops, on their own, cannot threaten the notion of an effective procedure.

The recent debate on hypercomputation has raised new questions both on the computational abilities of quantum systems and the Church-Turing Thesis role in Physics.We propose here the idea of “effective physical process” as the essentially physical notion of computation. By using the Bohm and Hiley active information concept we analyze the differences between the standard form (quantum gates) and the non-standard one (adiabatic and morphogenetic) of Quantum Computing, and we point out how its Super-Turing potentialities derive from an incomputable information (...) source in accordance with Bell’s constraints. On condition that we give up the formal concept of “universality”, the possibility to realize quantum oracles is reachable. In this way computation is led back to the logic of physical world. (shrink)

Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermadynamics and (...) its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinsim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology. (shrink)

'Computationalism' is a relatively vague term used to describe attempts to apply Turing's model of computation to phenomena outside its original purview: in modelling the human mind, in physics, mathematics, etc. Early versions of computationalism faced strong objections from many (and varied) quarters, from philosophers to practitioners of the aforementioned disciplines. Here we will not address the fundamental question of whether computational models are appropriate for describing some or all of the wide range of processes that they have been applied (...) to, but will focus instead on whether `renovated' versions of the \textit{new computationalism} shed any new light on or resolve previous tensions between proponents and skeptics. We find this, however, not to be the case, because the 'new computationalism' falls short by using limited versions of "traditional computation", or proposing computational models that easily fall within the scope of Turing's original model, or else proffering versions of hypercomputation with its many pitfalls. (shrink)

Black holes are extremely relativistic objects. Physical processes around them occur in a regime where the gravitational field is extremely intense. Under such conditions, our representations of space, time, gravity, and thermodynamics are pushed to their limits. In such a situation philosophical issues naturally arise. In this chapter I review some philosophical questions related to black holes. In particular, the relevance of black holes for the metaphysical dispute between presentists and eternalists, the origin of the second law of thermodynamics and (...) its relation to black holes, the problem of information, black holes and hypercomputing, the nature of determinisim, and the breakdown of predictability in black hole space-times. I maintain that black hole physics can be used to illuminate some important problems in the border between science and philosophy, either epistemology and ontology. (shrink)