Quantum Cellular Automata

Quantum cellular automata (QCA) are reviewed, including early and more recent proposals. QCA are a generalization of (classical) cellular automata (CA) and in particular of reversible CA. The latter are reviewed shortly. An overview is given over early attempts by various authors to define one-dimensional QCA. These turned out to have serious shortcomings which are discussed as well. Various proposals subsequently put forward by a number of authors for a general definition of one- and higher-dimensional QCA are reviewed and their properties such as universality and reversibility are discussed.Comment: 12 pages, 3 figures. To appear in the Springer Encyclopedia of Complexity and Systems Scienc

Scale-invariant cellular automata and self-similar Petri nets

Two novel computing models based on an infinite tessellation of space-time are introduced. They consist of recursively coupled primitive building blocks. The first model is a scale-invariant generalization of cellular automata, whereas the second one utilizes self-similar Petri nets. Both models are capable of hypercomputations and can, for instance, "solve" the halting problem for Turing machines. These two models are closely related, as they exhibit a step-by-step equivalence for finite computations. On the other hand, they differ greatly for computations that involve an infinite number of building blocks: the first one shows indeterministic behavior whereas the second one halts. Both models are capable of challenging our understanding of computability, causality, and space-time.Comment: 35 pages, 5 figure

Automation of play:theorizing self-playing games and post-human ludic agents

This article offers a critical reflection on automation of play and its significance for the theoretical inquiries into digital games and play. Automation has become an ever more noticeable phenomenon in the domain of video games, expressed by self-playing game worlds, self-acting characters, and non-human agents traversing multiplayer spaces. On the following pages, the author explores various instances of automated non-human play and proposes a post-human theoretical lens, which may help to create a new framework for the understanding of videogames, renegotiate the current theories of interaction prevalent in game studies, and rethink the relationship between human players and digital games

Impartial games emulating one-dimensional cellular automata and undecidability

We study two-player \emph{take-away} games whose outcomes emulate two-state one-dimensional cellular automata, such as Wolfram's rules 60 and 110. Given an initial string consisting of a central data pattern and periodic left and right patterns, the rule 110 cellular automaton was recently proved Turing-complete by Matthew Cook. Hence, many questions regarding its behavior are algorithmically undecidable. We show that similar questions are undecidable for our \emph{rule 110} game.Comment: 22 pages, 11 figure

The Implications of Interactions for Science and Philosophy

Reductionism has dominated science and philosophy for centuries. Complexity has recently shown that interactions---which reductionism neglects---are relevant for understanding phenomena. When interactions are considered, reductionism becomes limited in several aspects. In this paper, I argue that interactions imply non-reductionism, non-materialism, non-predictability, non-Platonism, and non-nihilism. As alternatives to each of these, holism, informism, adaptation, contextuality, and meaningfulness are put forward, respectively. A worldview that includes interactions not only describes better our world, but can help to solve many open scientific, philosophical, and social problems caused by implications of reductionism.Comment: 12 pages, 2 figure

Philosophical Aspects of Quantum Information Theory

Quantum information theory represents a rich subject of discussion for those interested in the philosphical and foundational issues surrounding quantum mechanics for a simple reason: one can cast its central concerns in terms of a long-familiar question: How does the quantum world differ from the classical one? Moreover, deployment of the concepts of information and computation in novel contexts hints at new (or better) means of understanding quantum mechanics, and perhaps even invites re-assessment of traditional material conceptions of the basic nature of the physical world. In this paper I review some of these philosophical aspects of quantum information theory, begining with an elementary survey of the theory, seeking to highlight some of the principles and heuristics involved. We move on to a discussion of the nature and definition of quantum information and deploy the findings in discussing the puzzles surrounding teleportation. The final two sections discuss, respectively, what one might learn from the development of quantum computation (both about the nature of quantum systems and about the nature of computation) and consider the impact of quantum information theory on the traditional foundational questions of quantum mechanics (treating of the views of Zeilinger, Bub and Fuchs, amongst others).Comment: LaTeX; 55pp; 3 figs. Forthcoming in Rickles (ed.) The Ashgate Companion to the New Philosophy of Physic

Indeterminism and Undecidability

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 theorem. In comparison, Bell's (1964) theorem as well as the so-called free will theorem-originally due to Heywood and Redhead (1983)-left two loopholes for deterministic hidden variable theories, namely giving up either locality (more precisely: local contextuality, as in Bohmian mechanics) or free choice (i.e. uncorrelated measurement settings, as in 't Hooft's cellular automaton interpretation of quantum mechanics). The main point is that Bell and others did not exploit the full empirical content of quantum mechanics, which consists of long series of outcomes of repeated measurements (idealized as infinite binary sequences): their arguments only used the long-run relative frequencies derived from such series, and hence merely asked hidden variable theories to reproduce single-case Born probabilities defined by certain entangled bipartite states. If we idealize binary outcome strings of a fair quantum coin flip as infinite sequences, quantum mechanics predicts that these typically (i.e.\ almost surely) have a property called 1-randomness in logic, which is much stronger than uncomputability. This is the key to my claim, which is admittedly based on a stronger (yet compelling) notion of determinism than what is common in the literature on hidden variable theories.Comment: 24 pages, v2 was major revision (doubled in size), v3 adds crucial clarifying footnote 24 and corrects a few typo

Mindedness: On the minimal conditions for possessing a mind

This thesis explores the grounds for justifying the ascription of mentality to non-human agents. In the first part, I set my research within the framework of scientific naturalism and the computational theory of mind. Then I argue that while the behaviour of certain agents demands a computational explanation, there is no justification for attributing mentality to them. I use these examples to backup my claim that some authors indulge in unnecessary ascription of mentality to certain animals (e.g. insects) on the main grounds that they possess computational capacities. The second part of my thesis takes up recent literature exploring the line that divides computational agents with and without mentality. More precisely, I criticise the proposals put forward by Fodor, Dretske, Burge, Bermúdez and Carruthers. My main argument takes the form of a reductio ad absurdum by showing that their criteria apply to artefacts to which the attribution of mentality is unjustified. Overall, I conclude that even though the views advanced by the mentioned authors help to elucidate the computational grounds that could make the emergence of a mind possible, they do not offer a satisfactory criterion for the ascription of mentality to some computational agents but not others. In the final part I develop my own proposal for grounding the attribution of mentality. My strategy consists in drawing upon the distinction between personal and subpersonal levels of explanation, according to which properly psychological descriptions have whole-agents as their subject matter, use a distinctive theoretical vocabulary, and are constrained by norms of rationality. After showing that the personal-subpersonal distinction is compatible with a naturalistic framework, I adapt the distinction so that it can be applied to non-human agents, and conclude that it imposes constraints in cognitive architecture that point in the direction of cognitive access, generality and integration