Zeno machines and hypercomputation

This paper reviews the Church-Turing Thesis (or rather, theses) with reference to their origin and application and considers some models of "hypercomputation", concentrating on perhaps the most straight-forward option: Zeno machines (Turing machines with accelerating clock). The halting problem is briefly discussed in a general context and the suggestion that it is an inevitable companion of any reasonable computational model is emphasised. It is hinted that claims to have "broken the Turing barrier" could be toned down and that the important and well-founded role of Turing computability in the mathematical sciences stands unchallenged.Comment: 11 pages. First submitted in December 2004, substantially revised in July and in November 2005. To appear in Theoretical Computer Scienc

Water and energy in South Africa – managing scarcity

In this paper we examine the nexus of water an energy scarcity in South Africa. The fresh water resources of the country are close to exhaustion (Business Day, 2009; Turton, 2008)⁠, yet safe drinking water is not yet universally available to all in the country – in spite of a government policy to provide water for basic needs, taken to be 25ℓ per person per day (Coovadia, Jewkes, Barron, Sanders, & McIntyre, 2009)⁠. A growing economy and a population now close to 50 million have also put considerable strain on the electricity supply and distribution system, including wide-spread residential power outages in the main economic centers and, since January 2008, mandatory cuts for industrial users (Patel, 2008)⁠. The paper provides an overview of the current system in South Africa for supplying and managing water and electricity – for residential, industrial and for agricultural use – with a special emphasis on the energy requirements for delivering water as well as the water required in generating electric power. Finally we consider the example of Australia, another country with severe water shortages and one with a comparable demand for electricity, and attempt to draw lessons for South Africa from Australia’s more market-driven approach to energy and water.Water; energy; South Africa

Universality and programmability of quantum computers

Manin, Feynman, and Deutsch have viewed quantum computing as a kind of universal physical simulation procedure. Much of the writing about quantum logic circuits and quantum Turing machines has shown how these machines can simulate an arbitrary unitary transformation on a finite number of qubits. The problem of universality has been addressed most famously in a paper by Deutsch, and later by Bernstein and Vazirani as well as Kitaev and Solovay. The quantum logic circuit model, developed by Feynman and Deutsch, has been more prominent in the research literature than Deutsch's quantum Turing machines. Quantum Turing machines form a class closely related to deterministic and probabilistic Turing machines and one might hope to find a universal machine in this class. A universal machine is the basis of a notion of programmability. The extent to which universality has in fact been established by the pioneers in the field is examined and this key notion in theoretical computer science is scrutinised in quantum computing by distinguishing various connotations and concomitant results and problems.Comment: 17 pages, expands on arXiv:0705.3077v1 [quant-ph

Water and energy in South Africa – managing scarcity

In this paper we examine the nexus of water an energy scarcity in South Africa. The fresh water resources of the country are close to exhaustion (Business Day, 2009; Turton, 2008)⁠, yet safe drinking water is not yet universally available to all in the country – in spite of a government policy to provide water for basic needs, taken to be 25ℓ per person per day (Coovadia, Jewkes, Barron, Sanders, & McIntyre, 2009)⁠. A growing economy and a population now close to 50 million have also put considerable strain on the electricity supply and distribution system, including wide-spread residential power outages in the main economic centers and, since January 2008, mandatory cuts for industrial users (Patel, 2008)⁠. The paper provides an overview of the current system in South Africa for supplying and managing water and electricity – for residential, industrial and for agricultural use – with a special emphasis on the energy requirements for delivering water as well as the water required in generating electric power. Finally we consider the example of Australia, another country with severe water shortages and one with a comparable demand for electricity, and attempt to draw lessons for South Africa from Australia’s more market-driven approach to energy and water

Is Economics Entering its Post-Witchcraft Era?

Recently, an awareness is emerging in economics about the fact that important problems are not solvable algorithmically, that is, by any finite number of steps. This statement can be made mathematically exact and this paper reviews the contributions that have been made in this regard, related to standard topics in economics

Is Economics Entering its Post-Witchcraft Era?

Recently, an awareness is emerging in economics about the fact that important problems are not solvable algorithmically, that is, by any finite number of steps. This statement can be made mathematically exact and this paper reviews the contributions that have been made in this regard, related to standard topics in economics

Is Economics Entering its Post-Witchcraft Era?

Recently, an awareness is emerging in economics about the fact that important problems are not solvable algorithmically, that is, by any finite number of steps. This statement can be made mathematically exact and this paper reviews the contributions that have been made in this regard, related to standard topics in economics