In 1981, Richard Feynman gave a talk at a conference hosted by the MIT Information Mechanics Group. This talk was entitled "Simulating Physics with Computers," and is reproduced in this volume. In this talk Feynman asked whether it is possible that, at some extremely microscopic scale, nature may operate exactly like discrete computer-logic. In particular, he discussed whether crystalline arrays of logic called Cellular Automata (CA) might be able to simulate our known laws of physics in a direct fashion. This question had been the subject of long and heated debates between him and his good friend Edward Fredkin (the head of the MIT Group) who has long maintained that some sort of discrete classicalinformation model will eventually replace continuous different

We consider models of emergence, adding downward causation to conventional models where causation permeates from low-level elements to high-level behaviour. We describe an architecture and prototype simulation medium for tagging and modelling emergent features in CA-like systems. This is part of ongoing work on engineering emergence.

The traditional computational devices and models, such as the von Neumann architecture or the Turing machine, are strongly influenced by concepts of central control and perfection. The standard models of computation seem to cover the reality of computation only partially and lack, in particular, in the ability to describe more natural forms of computation. In this paper we propose the concept of embodied computation, a straight forward advancement of well known concepts such as amorphous computing, emergent phenomena and embodied cognitive science. Many embodied microscopic computational devices form a single macroscopic device of embodied computation. The solution to computational problems emerges from a huge amount of local interactions. The system’s memory is the sum of the positional information and possibly of the internal states. Such systems are very robust and allow different methodologies to analyze computation. To back this theoretic concept some results based on simulations are given and potential benefits of this approach are discussed.

related. I am confident that at their interface great discoveries await those who seek them. ” (L.Adleman, [3]) 1. FOREWORD Natural computing is the field of research that investigates models and computational techniques inspired by nature and, dually, attempts to understand the world around us in terms of information processing. It is a highly interdisciplinary field that connects the natural sciences with computing science, both at the level of information technology and at the level of fundamental research, [98]. As a matter of fact, natural computing areas and topics come in many flavours, including pure theoretical research, algorithms and software applications, as well as biology, chemistry and physics experimental laboratory research. In this review we describe computing paradigms abstracted

Introduction Physical modelling is the process of finding a mathematical description that is consistent with observations of the physical world. Many models, from the heat equation to the Schrodinger equation, are formulated in the continuous language of di#erential equations. Space and time are thought of as a continuum, hence the models potentially specify detail down to arbitrarily fine scales. Discrete physical models are an attractive alternative to continuous models such as partial di#erential equations. In discrete models, space is treated as a lattice, and time is discrete. Physical processes are modelled by rules that typically depend on a small number of nearby locations. From a theoretical standpoint, such models have the advantage that they do not have infinitely many locations per unit volume. From a practical standpoint, they correspond to the discrete structure of digital computing machines, and this makes them natural for simulation. Formulations in which space and t

. The genotype-phenotype relation for the 256 elementary cellular automata is studied using neural networks. Neural network are trained to learn the mapping from each genotype rule to its corresponding Li-Packard phenotype class. By investigating learning curves and networks pruned with Optimal Brain Damage on all 256 rules, we find that there is a correspondence between the complexity of the phenotype class and the complexity (net size needed and test error) of the net trained on the class. For Li-Packard Class A (null rules) it is possible to extract a simple logical relation from the pruned network. The observation that some rules are harder for the networks to classify leads to an investigation of rule 73 and its conjugate rule 109. Experiments reveal 3-cycles in magnetization in agreement with observations in higher dimensional cellular automata systems. 1

The Matrix presents a version of an old philosophical fable: the brain in a vat. A disembodied brain is floating in a vat, inside a scientist’s laboratory. The scientist has arranged that the brain will be stimulated with the same sort of inputs that a normal embodied brain receives. To do this, the brain is connected to a giant computer simulation of a world. The simulation determines which inputs the brain receives. When the brain produces outputs, these are fed back into the simulation. The internal state of the brain is just like that of a normal brain, despite the fact that it lacks a body. From the brain’s point of view, things seem very much as they seem to you and me. The brain is massively deluded, it seems. It has all sorts of false beliefs about the world. It believes that it has a body, but it has no body. It believes that it is walking outside in the sunlight, but in fact it is inside a dark lab. It believes it is one place, when in fact it may be

Abstract. We consider models of emergence, adding downward causation to conventional models where causation permeates from low-level elements to high-level behaviour. We describe an architecture and prototype simulation medium for tagging and modelling emergent features in CA-like systems. This is part of ongoing work on engineering emergence.

In [1] we have shown a strong argument in support of the "Universe as a computer " idea. In the current work, we continue our exposition by showing more arguments that reveal why our Universe is not only "some kind of computer", but also a concrete computational model known as a "cellular automaton".

As computational devices continue to advance, there are reasons to examine their foundations a little more deeply, and to ask whether there may not be something more to be found. The fundamental manner in which hardware and software interact is poorly understood, and yet there is little indication in the literature that this is being discussed or explored. In spite of our technological achievements, we are at a loss to precisely define the boundaries between hardware and software, and to describe the nature of their interface. This paper aims to raise some of the major issues and questions, to propose a hardware-information duality, and to suggest directions in which further research might be pursued. 1.