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Epistemology as information theory: from Leibniz to Omega, Collapse 1
 European Computing and Philosophy Conference, Västeraas
, 2006
"... In 1686 in his Discours de métaphysique, Leibniz points out that if an arbitrarily complex theory is permitted then the notion of “theory” becomes vacuous because there is always a theory. This idea is developed in the modern theory of algorithmic information, which deals with the size of computer p ..."
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In 1686 in his Discours de métaphysique, Leibniz points out that if an arbitrarily complex theory is permitted then the notion of “theory” becomes vacuous because there is always a theory. This idea is developed in the modern theory of algorithmic information, which deals with the size of computer programs and provides a new view of Gödel’s work on incompleteness and Turing’s work on uncomputability. Of particular interest is the halting probability Ω, whose bits are irreducible, i.e., maximally unknowable mathematical facts. More generally, these ideas constitute a kind of “digital philosophy ” related to recent attempts of Edward Fredkin, Stephen Wolfram and others to view the world as a giant computer. There are also connections with recent “digital physics ” speculations that the universe might actually be discrete, not continuous. This système du monde is presented as a coherent whole in my book Meta Math!, which will be published this fall.
Gödel on computability
"... Around 1950, both Gödel and Turing wrote papers for broader audiences. 1 Gödel drew in his 1951 dramatic philosophical conclusions from the general formulation of his second incompleteness theorem. These conclusions concerned the nature of mathematics and the human mind. The general formulation of t ..."
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Around 1950, both Gödel and Turing wrote papers for broader audiences. 1 Gödel drew in his 1951 dramatic philosophical conclusions from the general formulation of his second incompleteness theorem. These conclusions concerned the nature of mathematics and the human mind. The general formulation of the second theorem was explicitly based on Turing’s 1936 reduction of finite procedures to machine computations. Turing gave in his 1954 an understated analysis of finite procedures in terms of Post production systems. This analysis, prima facie quite different from that given in 1936, served as the basis for an exposition of various unsolvable problems. Turing had addressed issues of mentality and intelligence in contemporaneous essays, the best known of which is of course Computing machinery and intelligence. Gödel’s and Turing’s considerations from this period intersect through their attempt, on the one hand, to analyze finite, mechanical procedures and, on the other hand, to approach mental phenomena in a scientific way. Neuroscience or brain science was an important component of the latter for both: Gödel’s remarks in the Gibbs Lecture as well as in his later conversations with Wang and Turing’s Intelligent Machinery can serve as clear evidence for that. 2 Both men were convinced that some mental processes are not mechanical, in the sense that Turing machines cannot mimic them. For Gödel, such processes were to be found in mathematical experience and he was led to the conclusion that mind is separate from matter. Turing simply noted that for a machine or a brain it is not enough to be converted into a universal (Turing) machine in order to become intelligent: “discipline”, the characteristic
Alan Turing and the Mathematical Objection
 Minds and Machines 13(1
, 2003
"... Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet accord ..."
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Abstract. This paper concerns Alan Turing’s ideas about machines, mathematical methods of proof, and intelligence. By the late 1930s, Kurt Gödel and other logicians, including Turing himself, had shown that no finite set of rules could be used to generate all true mathematical statements. Yet according to Turing, there was no upper bound to the number of mathematical truths provable by intelligent human beings, for they could invent new rules and methods of proof. So, the output of a human mathematician, for Turing, was not a computable sequence (i.e., one that could be generated by a Turing machine). Since computers only contained a finite number of instructions (or programs), one might argue, they could not reproduce human intelligence. Turing called this the “mathematical objection ” to his view that machines can think. Logicomathematical reasons, stemming from his own work, helped to convince Turing that it should be possible to reproduce human intelligence, and eventually compete with it, by developing the appropriate kind of digital computer. He felt it should be possible to program a computer so that it could learn or discover new rules, overcoming the limitations imposed by the incompleteness and undecidability results in the same way that human mathematicians presumably do. Key words: artificial intelligence, ChurchTuring thesis, computability, effective procedure, incompleteness, machine, mathematical objection, ordinal logics, Turing, undecidability The ‘skin of an onion ’ analogy is also helpful. In considering the functions of the mind or the brain we find certain operations which we can express in purely mechanical terms. This we say does not correspond to the real mind: it is a sort of skin which we must strip off if we are to find the real mind. But then in what remains, we find a further skin to be stripped off, and so on. Proceeding in this way, do we ever come to the ‘real ’ mind, or do we eventually come to the skin which has nothing in it? In the latter case, the whole mind is mechanical (Turing, 1950, p. 454–455). 1.
On Dynamical Genetic Programming: Simple Boolean Networks in Learning Classifier Systems
, 2008
"... Abstract. Many representations have been presented to enable the effective evolution of computer programs. Turing was perhaps the first to present a general scheme by which to achieve this end. Significantly, Turing proposed a form of discrete dynamical system and yet dynamical representations remai ..."
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Abstract. Many representations have been presented to enable the effective evolution of computer programs. Turing was perhaps the first to present a general scheme by which to achieve this end. Significantly, Turing proposed a form of discrete dynamical system and yet dynamical representations remain almost unexplored within conventional genetic programming. This paper presents results from an initial investigation into using simple dynamical genetic programming representations within a Learning Classifier System. It is shown possible to evolve ensembles of dynamical Boolean function networks to solve versions of the wellknown multiplexer problem. Both synchronous and asynchronous systems are considered.
Geometry for a Brain. Optimal Control in a Network of Adaptive Memristors
"... Copyright © 2013 Germano Resconi and Ignazio Licata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the brain the relations betwe ..."
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Copyright © 2013 Germano Resconi and Ignazio Licata. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In the brain the relations between free neurons and the conditioned ones establish the constraints for the informational neural processes. These constraints reflect the systemenvironment state, i.e. the dynamics of homeocognitive activities. The constraints allow us to define the cost function in the phase space of free neurons so as to trace the trajectories of the possible configurations at minimal cost while respecting the constraints imposed. Since the space of the free states is a manifold or a non orthogonal space, the minimum distance is not a straight line but a geodesic. The minimum condition is expressed by a set of ordinary differential equation ( ODE) that in general are not linear. In the brain there is not an algorithm or a physical field that regulates the computation, then we must consider an emergent process coming out of the neural collective behavior triggered by synaptic variability. We define the neural computation as the study of the classes of trajectories on a
Is the Turing test good enough? The fallacy of resourceunbounded intelligence.
"... This goal of this paper is to defend the plausibility of the argument that passing the Turing test is a sufficient condition for the presence of intelligence. To this effect, we put forth new objections to two famous counterarguments: Searle’s ”Chinese Room ” and Block’s ”Aunt Bertha. ” We take Sea ..."
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This goal of this paper is to defend the plausibility of the argument that passing the Turing test is a sufficient condition for the presence of intelligence. To this effect, we put forth new objections to two famous counterarguments: Searle’s ”Chinese Room ” and Block’s ”Aunt Bertha. ” We take Searle’s argument to consist of two points: 1) intelligence is not merely an ability to manipulate formal symbols; it is also the ability of relating those symbols to a multisensory realworld experience; and 2) intelligence presupposes an internal capacity for generalization. On the first point, while we concede that multisensory realworld experience is not captured by the test, we show that intuitions about the relevance of this experience to intelligence are not clearcut. Therefore, it is not obvious that the Turing test should be dismissed on this basis alone. On the second point, we strongly disagree with the notion that the test cannot distinguish a machine with internal capacity for generalization from a machine which has no such capacity. This view is best captured by Ned Block, who argues that a sufficiently large lookup table is capable of passing any Turing test of finite length. We claim that, contrary to Block’s assumption, it is impossible to construct such a table, and show that it is possible to ensure that a machine relying solely on such table will fail an appropriately constructed Turing test. 1
ACCELERATING MACHINES
, 2006
"... This paper presents an overview of accelerating machines. We begin by exploring the history of the accelerating machine model and the potential power that it provides. We look at some of the problems that could be solved with an accelerating machine, and review some of the possible implementation me ..."
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This paper presents an overview of accelerating machines. We begin by exploring the history of the accelerating machine model and the potential power that it provides. We look at some of the problems that could be solved with an accelerating machine, and review some of the possible implementation methods that have been presented. Finally, we expose the limitations of accelerating machines and conclude by posing some problems for further research.
The Turing OMachine and the DIME Network Architecture: Injecting the Architectural Resiliency into Distributed Computing
"... Turing’s omachine discussed in his PhD thesis can perform all of the usual operations of a Turing machine and in addition, when it is in a certain internal state, can also query an oracle for an answer to a specific question that dictates its further evolution. In his thesis, Turing said 'We s ..."
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Turing’s omachine discussed in his PhD thesis can perform all of the usual operations of a Turing machine and in addition, when it is in a certain internal state, can also query an oracle for an answer to a specific question that dictates its further evolution. In his thesis, Turing said 'We shall not go any further into the nature of this oracle apart from saying that it cannot be a machine. ’ There is a host of literature discussing the role of the oracle in AI, modeling brain, computing, and hypercomputing machines. In this paper, we take a broader view of the oracle machine inspired by the genetic computing model of cellular organisms and the selforganizing fractal theory. We describe a specific software architecture implementation that circumvents the halting and undecidability problems in a process workflow computation to introduce the architectural resiliency found in cellular organisms into distributed computing machines. A DIME (Distributed Intelligent Computing Element), recently introduced as the building block of the DIME computing model, exploits the concepts from Turing’s oracle machine and extends them to implement a recursive managed distributed computing network, which can be viewed as an interconnected group of such specialized oracle machines, referred to as a DIME network. The DIME network architecture provides the architectural resiliency through autofailover; autoscaling; livemigration; and endtoend transaction security assurance in a distributed system. We demonstrate these characteristics using prototypes without the complexity introduced by hypervisors, virtual machines and other layers of adhoc management software in today’s distributed computing environments.
Discrete Quantum Walks and Quantum Image Processing
, 2005
"... ... Processing. Our work is a contribution within the field of quantum computation from the perspective of a computer scientist. With the purpose of finding new techniques to develop quantum algorithms, there has been an increasing interest in studying Quantum Walks, the quantum counterparts of clas ..."
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... Processing. Our work is a contribution within the field of quantum computation from the perspective of a computer scientist. With the purpose of finding new techniques to develop quantum algorithms, there has been an increasing interest in studying Quantum Walks, the quantum counterparts of classical random walks. Our work in quantum walks begins with a critical and comprehensive assessment of those elements of classical random walks and discrete quantum walks on undirected graphs relevant to algorithm development. We propose a model of discrete quantum walks on an infinite line using pairs of quantum coins under different degrees of entanglement, as well as quantum walkers in different initial state configurations, including superpositions of corresponding basis states. We have found that the probability distributions of such quantum walks have particular forms which are different from the probability distributions of classical random walks. Also, our numerical results show that the symmetry properties of quantum walks with entangled coins have a nontrivial relationship with corresponding initial states and evolution operators. In addition, we have studied the properties of the entanglement generated between walkers, in a
TOWARDS COMMONSENSE REASONING VIA CONDITIONAL SIMULATION: LEGACIES OF TURING IN ARTIFICIAL INTELLIGENCE
"... Abstract. The problem of replicating the flexibility of human commonsense reasoning has captured the imagination of computer scientists since the early days of Alan Turing’s foundational work on computation and the philosophy of artificial intelligence. In the intervening years, the idea of cogniti ..."
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Abstract. The problem of replicating the flexibility of human commonsense reasoning has captured the imagination of computer scientists since the early days of Alan Turing’s foundational work on computation and the philosophy of artificial intelligence. In the intervening years, the idea of cognition as computation has emerged as a fundamental tenet of Artificial Intelligence (AI) and cognitive science. But what kind of computation is cognition? We describe a computational formalism centered around a probabilistic Turing machine called QUERY, which captures the operation of probabilistic conditioning via conditional simulation. Through several examples and analyses, we demonstrate how the QUERY abstraction can be used to cast commonsense reasoning as probabilistic inference in a statistical model of our observations and the uncertain structure of the world that generated that experience. This formulation is a recent synthesis of several research programs in AI and cognitive science, but it also represents a surprising convergence of several of Turing’s pioneering insights in AI, the foundations of computation, and statistics.