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Beyond Turing Machines
"... In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are present ..."
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Cited by 32 (4 self)
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In this paper we describe and analyze models of problem solving and computation going beyond Turing Machines. Three principles of extending the Turing Machine's expressiveness are identified, namely, by interaction, evolution and infinity. Several models utilizing the above principles are presented. Other
Gödeltype Spacetimes: History and New Developments Visualizing ideas about Gödeltype rotating universes
"... Abstract. This paper consists mostly of pictures visualizing ideas leading to Gödel’s rotating cosmological model. The pictures are constructed according to concrete metric tensor fields. The main aim is to visualize ideas. Some kinds of physical theories describe what our universe looks like. Other ..."
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Abstract. This paper consists mostly of pictures visualizing ideas leading to Gödel’s rotating cosmological model. The pictures are constructed according to concrete metric tensor fields. The main aim is to visualize ideas. Some kinds of physical theories describe what our universe looks like. Other kinds of physical theories describe instead what the universe could be like independently of the properties of the actual universe. This second kind aims for the “basic laws of physics ” in some sense which we will not make precise here (but cf. e.g. Malament [Mal84, pp.98–99]). The present paper belongs to the second kind. Moreover, it is even more abstract than this, namely it aims for visualizing or grasping some mathematical or logical aspects of what the universe could be like. The first few pages of this material are of a “sciencepopularizing ” character in the sense that first we recall a spacetime diagram from Hawking–Ellis [HE73] as “Godgiven truth”, i.e. we do not explain why the reader should believe that diagram. Then we derive in an easily understandable visual manner an exciting, exotic consequence of that diagram: timetravel. This applies to the first few pages.
Description of the free motion with momentums in Gödel’s universe ∗
, 2008
"... We study the geodesic motion in Gödel’s universe, using conserved quantities. We give a necessary and sufficient condition for curves to be geodesic curves in terms of conserved quantities, which can be computed from the initial values of the curve. We check our result with numerical simulations too ..."
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We study the geodesic motion in Gödel’s universe, using conserved quantities. We give a necessary and sufficient condition for curves to be geodesic curves in terms of conserved quantities, which can be computed from the initial values of the curve. We check our result with numerical simulations too. 1