Related papers: Uncomputability and free will
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…
In a previous paper (arXiv:1008.3661v1[quant-ph] 21 Aug 2010), we have given a purely logical proof of the Conway and Kochen Free Will theorem in QM: the freedom of the observer implies the freedom of the observed particle. Here we show…
The 20th century has revealed two important limitations of scientific knowledge. On the one hand, the combination of Poincar\'e's nonlinear dynamics and Heisenberg's uncertainty principle leads to a world picture where physical reality is,…
We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that…
Defeasible logic is a rule-based nonmonotonic logic, with both strict and defeasible rules, and a priority relation on rules. We show that inference in the propositional form of the logic can be performed in linear time. This contrasts…
Any complete theory of physical reality must allow for the ubiquitous phenomenon of subjective experience at some level, or risk being conceptually incoherent. However, as long as the ontological status of subjectivity itself remains…
There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…
An account of determinism and indeterminism in physics, addressed to non-physicist readers, leading up to proposals for how to understand statements about the future and single-event probability, motivated by quantum mechanics.
I discuss some of the main interpretations given to explain the indeterministic nature of quantum measurements and show that all has some loopholes in one corner or another. I propose an alternative interpretation based on the notion of…
Recently, origins of non-deterministic behavior and free will in living systems obtain growing interest (see, e.g. Maye A, Hsieh C, Sugihara G, Brembs B (2007) Order in Spontaneous Behavior. PLoS ONE 2(5): e443.…
Utilizing operational dynamic modeling [Phys. Rev. Lett. 109, 190403 (2012); arXiv:1105.4014], we demonstrate that any finite-dimensional representation of quantum and classical dynamics violates the Ehrenfest theorems. Other peculiarities…
The aim of this paper is to argue that the (alleged) indeterminism of quantum mechanics, claimed by adherents of the Copenhagen interpretation since Born (1926), can be proved from Chaitin's follow-up to Goedel's (first) incompleteness…
The quantum mechanical measurement process is considered. A hypothetical concept of irrational dynamical variables is proposed. A possible definition of measurement is discussed along with a mathematical method to calculate experimental…
Decision problems in physics have been an active field of research for quite a few decades resulting in some interesting findings in recent years. However, such research investigations are based on a priori knowledge of theoretical computer…
The human mind is endowed with innate primordial perceptions such as space, distance, motion, change, flow of time, matter. The field of cognitive science argues that the abstract concepts of mathematics are not Platonic, but are built in…
Modal logics are widely used in computer science. The complexity of their satisfiability problems has been an active field of research since the 1970s. We prove that even very "simple" modal logics can be undecidable: We show that there is…
Computational complexity is examined using the principle of increasing entropy. To consider computation as a physical process from an initial instance to the final acceptance is motivated because many natural processes have been recognized…
For over a decade, the hypercomputation movement has produced computational models that in theory solve the algorithmically unsolvable, but they are not physically realizable according to currently accepted physical theories. While…
A mechanical system is presented exhibiting a non-deterministic singularity, that is, a point in an otherwise deterministic system where forward time trajectories become non-unique. A Coulomb friction force applies linear and angular forces…
I argue that scientific determinism is not supported by facts, but results from the elegance of the mathematical language physicists use, in particular from the so-called real numbers and their infinite series of digits. Classical physics…