Results 1 
6 of
6
Physical Hypercomputation and the Church–Turing Thesis
, 2003
"... We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy’s thesis.
On the Inherent Incompleteness of Scientific Theories
, 2005
"... We examine the question of whether scientific theories can ever be complete. For two closely related reasons, we will argue that they cannot. The first reason is the inability to determine what are “valid empirical observations”, a result that is based on a selfreference Gödel/Tarskilike proof. Th ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
We examine the question of whether scientific theories can ever be complete. For two closely related reasons, we will argue that they cannot. The first reason is the inability to determine what are “valid empirical observations”, a result that is based on a selfreference Gödel/Tarskilike proof. The second reason is the existence of “metaempirical ” evidence of the inherent incompleteness of observations. These reasons, along with theoretical incompleteness, are intimately connected to the notion of belief and to theses within the philosophy of science: the QuineDuhem (and underdetermination) thesis and the observational/theoretical distinction failure. Some puzzling aspects of the philosophical theses will become clearer in light of these connections. Other results that follow are: no absolute measure of the informational content of empirical data, no absolute measure of the entropy of physical systems, and no complete computer simulation of the natural world are possible. The connections with the mathematical theorems of Gödel and Tarski reveal the existence of other connections between scientific and mathematical incompleteness: computational irreducibility, complexity, infinity, arbitrariness and selfreference. Finally, suggestions will be offered of where a more rigorous (or formal) “proof ” of scientific incompleteness can be found.
Physical Hypercomputation and the Church–Turing
"... Abstract. We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or c ..."
Abstract
 Add to MetaCart
Abstract. We describe a possible physical device that computes a function that cannot be computed by a Turing machine. The device is physical in the sense that it is compatible with General Relativity. We discuss some objections, focusing on those which deny that the device is either a computer or computes a function that is not Turing computable. Finally, we argue that the existence of the device does not refute the Church–Turing thesis, but nevertheless may be a counterexample to Gandy’s thesis. Key words: Church–Turing thesis, effective computation, Gandy’s thesis, physical hypercomputation, supertasks A hypercomputer is a physical or an abstract system that computes functions that cannot be computed by a universal Turing machine. Turing (1939) was perhaps the first to introduce hypercomputers. He called them omachines, for machines with oracles. Other examples of hypercomputers are described in Copeland and Sylvan (1999). In what follows we describe a possible physical device that computes a nonTuring computable function. This physical hypercomputer is a version of the devices introduced by Pitowsky (1990) and Hogarth (1992, 1994). We consider
Hamiltonian Systems as Machines Over the Reals
"... Abstract. I explain how to associate computations with physical systems such as finite degree of freedom hamiltonian systems, and thus show why we should consider such systems as real number machines. I make a few comparisons between these real number machines of those and Blum, Shub and Smale (the ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract. I explain how to associate computations with physical systems such as finite degree of freedom hamiltonian systems, and thus show why we should consider such systems as real number machines. I make a few comparisons between these real number machines of those and Blum, Shub and Smale (the question of equivalence is still open), and also make some general comments on complexity in physics. 1.
Undecidability of the Imitation Game
"... This paper considers the concept of computability in the original version of the imitation game proposed by Alan M. Turing, the socalled Turing test. In the Turing test, a man, an imitating machine, and an interrogator are the players of an imitation game. In our version of the Turing test, the imi ..."
Abstract
 Add to MetaCart
This paper considers the concept of computability in the original version of the imitation game proposed by Alan M. Turing, the socalled Turing test. In the Turing test, a man, an imitating machine, and an interrogator are the players of an imitation game. In our version of the Turing test, the imitator and the interrogator are formalized as Turing machines, allowing us to derive some impossibility results concerning the capabilities of the interrogator. This is the key issue; the validity of the Turing test is not attributed to the capability of man nor the imitator but rather to the capability of the interrogator. In particular, it is shown that no formalized interrogator exists who can perfectly distinguish man from imitating machines. 1 Introduction We consider the manmachine problem raised in the imitation game with respect to the computability. The imitation game was proposed by A. M. Turing (1950); It is played with three people, a man (A), a woman (B), and an interrogator (C...