Related papers: Some Thoughts on Hypercomputation
Beginning with Turing's seminal work in 1950, artificial intelligence proposes that consciousness can be simulated by a Turing machine. This implies a potential theory of everything where the universe is a simulation on a computer, which…
We report a new limitation on the ability of physical systems to perform computation -- one that is based on generalizing the notion of memory, or storage space, available to the system to perform the computation. Roughly, we define memory…
The Turing machine (TM) and the Church thesis have formalized the concept of computable number, this allowed to display non-computable numbers. This paper defines the concept of number "approachable" by a TM and shows that some (if not all)…
Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…
With the great success in simulating many intelligent behaviors using computing devices, there has been an ongoing debate whether all conscious activities are computational processes. In this paper, the answer to this question is shown to…
The Church-Turing Thesis confuses numerical computations with symbolic computations. In particular, any model of computability in which equality is not definable, such as the lambda-models underpinning higher-order programming languages, is…
The quest to understand consciousness, once the purview of philosophers and theologians, is now actively pursued by scientists of many stripes. We examine consciousness from the perspective of theoretical computer science (TCS), a branch of…
A remarkable new definition of a self-delimiting universal Turing machine is presented that is easy to program and runs very quickly. This provides a new foundation for algorithmic information theory. This new universal Turing machine is…
The recent debate on hypercomputation has arisen 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…
The classical simulation of physical processes using standard models of computation is fraught with problems. On the other hand, attempts at modelling real-world computation with the aim of isolating its hypercomputational content have…
Models of computation operating over the real numbers and computing a larger class of functions compared to the class of general recursive functions invariably introduce a non-finite element of infinite information encoded in an arbitrary…
We discuss some claims that certain UCOMP devices can perform hypercomputation (compute Turing-uncomputable functions) or perform super-Turing computation (solve NP-complete problems in polynomial time). We discover that all these claims…
We investigate the Church-Kalm\'ar-Kreisel-Turing Theses concerning theoretical (necessary) limitations of future computers and of deductive sciences, in view of recent results of classical general relativity theory. We argue that (i) there…
The upper limit on what is computable in our universe is unknown, but widely believed to be set by the Turing machine -- with a function being physically computable if and only if it is Turing-computable. I show how this apparently mild…
The theory that all processes in the universe are computational is attractive in its promise to provide an understandable theory of everything. I want to suggest here that this pancomputationalism is not sufficiently clear on which problem…
The Turing machine is one of the simple abstract computational devices that can be used to investigate the limits of computability. In this paper, they are considered from several points of view that emphasize the importance and the…
Can computers overcome human capabilities? This is a paradoxical and controversial question, particularly because there are many hidden assumptions. This article focuses on that issue putting on evidence some misconception related with…
Artificial computing machinery transforms representations through an objective process, to be interpreted subjectively by humans, so the machine and the interpreter are different entities, but in the putative natural computing both…
Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…
The physical Church thesis is a thesis about nature that expresses that all that can be computed by a physical system-a machine-is computable in the sense of computability theory. At a first look, this thesis seems contradictory with the…