Results 1 
9 of
9
Beyond The Universal Turing Machine
, 1998
"... We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a phi ..."
Abstract

Cited by 32 (2 self)
 Add to MetaCart
We describe an emerging field, that of nonclassical computability and nonclassical computing machinery. According to the nonclassicist, the set of welldefined computations is not exhausted by the computations that can be carried out by a Turing machine. We provide an overview of the field and a philosophical defence of its foundations.
Computations via experiments with kinematic systems
, 2004
"... Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be des ..."
Abstract

Cited by 15 (4 self)
 Add to MetaCart
(Show Context)
Consider the idea of computing functions using experiments with kinematic systems. We prove that for any set A of natural numbers there exists a 2dimensional kinematic system BA with a single particle P whose observable behaviour decides n ∈ A for all n ∈ N. The system is a bagatelle and can be designed to operate under (a) Newtonian mechanics or (b) Relativistic mechanics. The theorem proves that valid models of mechanical systems can compute all possible functions on discrete data. The proofs show how any information (coded by some A) can be embedded in the structure of a simple kinematic system and retrieved by simple observations of its behaviour. We reflect on this undesirable situation and argue that mechanics must be extended to include a formal theory for performing experiments, which includes the construction of systems. We conjecture that in such an extended mechanics the functions computed by experiments are precisely those computed by algorithms. We set these theorems and ideas in the context of the literature on the general problem “Is physical behaviour computable? ” and state some open problems.
The Broad Conception Of Computation
 American Behavioral Scientist
, 1997
"... A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine  a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, ..."
Abstract

Cited by 15 (3 self)
 Add to MetaCart
(Show Context)
A myth has arisen concerning Turing's paper of 1936, namely that Turing set forth a fundamental principle concerning the limits of what can be computed by machine  a myth that has passed into cognitive science and the philosophy of mind, to wide and pernicious effect. This supposed principle, sometimes incorrectly termed the 'ChurchTuring thesis', is the claim that the class of functions that can be computed by machines is identical to the class of functions that can be computed by Turing machines. In point of fact Turing himself nowhere endorses, nor even states, this claim (nor does Church). I describe a number of notional machines, both analogue and digital, that can compute more than a universal Turing machine. These machines are exemplars of the class of nonclassical computing machines. Nothing known at present rules out the possibility that machines in this class will one day be built, nor that the brain itself is such a machine. These theoretical considerations undercut a numb...
Hypercomputation
, 2002
"... A survey of the field of hypercomputation, including discussion of a variety of objections. ..."
Abstract

Cited by 11 (0 self)
 Add to MetaCart
A survey of the field of hypercomputation, including discussion of a variety of objections.
Computational Analysis of Human Thinking Processes
, 2004
"... Human creative thinking is analyzed, in particular through the principle of multiple knowledge. It is claimed that current digital computers, however fast, cannot achieve true humanlevel intelligence, and that the ChurchTuring thesis might be inadequate to encapsulate top human thinking mechan ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Human creative thinking is analyzed, in particular through the principle of multiple knowledge. It is claimed that current digital computers, however fast, cannot achieve true humanlevel intelligence, and that the ChurchTuring thesis might be inadequate to encapsulate top human thinking mechanisms. We try to show this by introducing and analyzing a two and oneprocessing entity. Formally, we want to compare performance of a single program/process performed by a Turing machine, and two programs/processes performed by two interaction Turing machines that can dynamically change each others programs based on dynamic unconstrained input. c #2003 Yang's Scientific Research Institute, LLC. All rights reserved.
Comparative Analysis of Hypercomputational Systems
, 2006
"... In the 1930s, Turing suggested his abstract model for a practical computer, hypothetically visualizing the digital programmable computer long before it was actually invented. His model formed the foundation for every computer made today. The past few years have seen a change in ideas where philosoph ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
In the 1930s, Turing suggested his abstract model for a practical computer, hypothetically visualizing the digital programmable computer long before it was actually invented. His model formed the foundation for every computer made today. The past few years have seen a change in ideas where philosophers and scientists are suggesting models of hypothetical computing devices which can outperform the Turing machine, performing some calculations the latter is unable to. The ChurchTuring Thesis, which the Turing machine model embodies, has raised discussions on whether it could be possible to solve undecidable problems which Turing’s model is unable to. Models which could solve these problems, have gone further to claim abilities relating to quantum computing, relativity theory, even the modeling of natural biological laws themselves. These so called ‘hypermachines’ use hypercomputational abilities to make the impossible possible. Various models belonging to different disciplines of physics, mathematics and philosophy, have been suggested for these theories. My (primarily researchoriented) project is based on the study and review of these different hypercomputational models and attempts to compare the different models in terms of computational power. The project focuses on the ability to compare these models of different disciplines on similar grounds and
Turing's Omachines, Searle, Penrose and the Brain
"... In his PhD thesis (1938) Turing introduced what he described as 'a new kind of machine'. He called these 'Omachines'. The present paper employs Turing's concept against a number of currently fashionable positions in the philosophy of mind. ..."
Abstract
 Add to MetaCart
In his PhD thesis (1938) Turing introduced what he described as 'a new kind of machine'. He called these 'Omachines'. The present paper employs Turing's concept against a number of currently fashionable positions in the philosophy of mind.
Some Key Remarks by Turing Bibliography Other Internet Resources Related Entries
, 1997
"... There are various equivalent formulations of the ChurchTuring thesis. A common one is that every effective computation can be carried out by a Turing machine. The ChurchTuring thesis is often misunderstood, particularly in recent writing in the philosophy of mind. ..."
Abstract
 Add to MetaCart
There are various equivalent formulations of the ChurchTuring thesis. A common one is that every effective computation can be carried out by a Turing machine. The ChurchTuring thesis is often misunderstood, particularly in recent writing in the philosophy of mind.
Invited Article The ChurchTuring Thesis
, 1303
"... There are various equivalent formulations of the ChurchTuring thesis. A common one is that every effective computation can be carried out by a Turing machine. The ChurchTuring thesis is often misunderstood, particularly in recent writing in the ..."
Abstract
 Add to MetaCart
There are various equivalent formulations of the ChurchTuring thesis. A common one is that every effective computation can be carried out by a Turing machine. The ChurchTuring thesis is often misunderstood, particularly in recent writing in the