The Computability-Theoretic Content of Emergence

In dealing with emergent phenomena, a common task is to identify useful descriptions of them in terms of the underlying atomic processes, and to extract enough computational content from these descriptions to enable predictions to be made. Generally, the underlying atomic processes are quite well understood, and (with important exceptions) captured by mathematics from which it is relatively easy to extract algorithmic con- tent. A widespread view is that the difficulty in describing transitions from algorithmic activity to the emergence associated with chaotic situations is a simple case of complexity outstripping computational resources and human ingenuity. Or, on the other hand, that phenomena transcending the standard Turing model of computation, if they exist, must necessarily lie outside the domain of classical computability theory. In this article we suggest that much of the current confusion arises from conceptual gaps and the lack of a suitably fundamental model within which to situate emergence. We examine the potential for placing emer- gent relations in a familiar context based on Turing's 1939 model for interactive computation over structures described in terms of reals. The explanatory power of this model is explored, formalising informal descrip- tions in terms of mathematical definability and invariance, and relating a range of basic scientific puzzles to results and intractable problems in computability theory

A Survey on Continuous Time Computations

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature

Towards Autopoietic Computing

A key challenge in modern computing is to develop systems that address complex, dynamic problems in a scalable and efficient way, because the increasing complexity of software makes designing and maintaining efficient and flexible systems increasingly difficult. Biological systems are thought to possess robust, scalable processing paradigms that can automatically manage complex, dynamic problem spaces, possessing several properties that may be useful in computer systems. The biological properties of self-organisation, self-replication, self-management, and scalability are addressed in an interesting way by autopoiesis, a descriptive theory of the cell founded on the concept of a system's circular organisation to define its boundary with its environment. In this paper, therefore, we review the main concepts of autopoiesis and then discuss how they could be related to fundamental concepts and theories of computation. The paper is conceptual in nature and the emphasis is on the review of other people's work in this area as part of a longer-term strategy to develop a formal theory of autopoietic computing.Comment: 10 Pages, 3 figure

What Makes a Computation Unconventional?

A coherent mathematical overview of computation and its generalisations is described. This conceptual framework is sufficient to comfortably host a wide range of contemporary thinking on embodied computation and its models.Comment: Based on an invited lecture for the 'Symposium on Natural/Unconventional Computing and Its Philosophical Significance' at the AISB/IACAP World Congress 2012, University of Birmingham, July 2-6, 201

On the Computability of Solomonoff Induction and Knowledge-Seeking

Solomonoff induction is held as a gold standard for learning, but it is known to be incomputable. We quantify its incomputability by placing various flavors of Solomonoff's prior M in the arithmetical hierarchy. We also derive computability bounds for knowledge-seeking agents, and give a limit-computable weakly asymptotically optimal reinforcement learning agent.Comment: ALT 201

On the possible Computational Power of the Human Mind

The aim of this paper is to address the question: Can an artificial neural network (ANN) model be used as a possible characterization of the power of the human mind? We will discuss what might be the relationship between such a model and its natural counterpart. A possible characterization of the different power capabilities of the mind is suggested in terms of the information contained (in its computational complexity) or achievable by it. Such characterization takes advantage of recent results based on natural neural networks (NNN) and the computational power of arbitrary artificial neural networks (ANN). The possible acceptance of neural networks as the model of the human mind's operation makes the aforementioned quite relevant.Comment: Complexity, Science and Society Conference, 2005, University of Liverpool, UK. 23 page

Information Processing, Computation and Cognition

Computation and information processing are among the most fundamental notions in cognitive science. They are also among the most imprecisely discussed. Many cognitive scientists take it for granted that cognition involves computation, information processing, or both – although others disagree vehemently. Yet different cognitive scientists use ‘computation’ and ‘information processing’ to mean different things, sometimes without realizing that they do. In addition, computation and information processing are surrounded by several myths; first and foremost, that they are the same thing. In this paper, we address this unsatisfactory state of affairs by presenting a general and theory-neutral account of computation and information processing. We also apply our framework by analyzing the relations between computation and information processing on one hand and classicism and connectionism/computational neuroscience on the other. We defend the relevance to cognitive science of both computation, at least in a generic sense, and information processing, in three important senses of the term. Our account advances several foundational debates in cognitive science by untangling some of their conceptual knots in a theory-neutral way. By leveling the playing field, we pave the way for the future resolution of the debates’ empirical aspects