Archive for the ‘Mathematics and Logic’ Category

Explanatory gap

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The Computational Explanatory Gap James Reggia, Derek Monner & Jared Sylvester :: Journal of Consciousness Studies, 21, No. 9&10, 2014, pp. 153-78 :: www.imprint.co.uk/jcs.html Summary and review of the above paper INTRODUCTION: The durability of the explanatory gap between neural processing and consciousness is seen as surprising given the successes of neuroscience in recent decades. Models of cognitive processing still require external direction, which is exactly what the conscious Read more […]

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Chaos theory and Turing’s oracle computer

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Know it all Michael Brooks, based on Emmett Redd & Steven Younger, Missouri State University New Scientist, 19 July 2014 www.newscientist.com/ Summary and review of the above article INTRODUCTION: The proposal for a computer based on a whole range of inputs between fully off and fully on, which could exceed the limitations of the Gödel theorem by operating in an unpredictable and chaotic manner, may throw light on consciousness in the brain. Alan Turing appreciated that the Read more […]

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Donald Hoffman’s Consciousness Theory

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In this conference Donald Hoffman discussed why qualia are more relevant than Dennett had tried to argue in the 1990s. Another highlight was the exchange between Hameroff and Tegmark, where Tegmark took a surprisingly casual view of his much vaunted 2000 Paper.

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Our Mathematical Universe

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Our Mathematical Universe Max Tegmark (2014) Summary and review of the above book The first part of this book is a readable guide to understanding physics and cosmology. Where it goes wrong is that the author gets out of his depth in trying to extend to non-consensual areas such as time, reality and consciousness. The discussion here starts well in identifying that the brain constructs a model of reality, which is consciousness, helped by the integrative brain hub scheme developed by neuroscientists Read more […]

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Penrose, Godel & artificial intelligence

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A refutation of Penrose’s Godelian case against artificial intelligence Selmer Bringsjord & Hong Xiao Dept. of Philosophy & Cognitive Science Dept. of Computer Science Rensselaer Polytechnic Institute February 2000 This paper is sometimes glibly quoted as a complete refutation of the arguments relative to the Godel theorem and the brain, but in reality the opinions of the authors are much more mixed. The authors emphasise the distinction between ‘Strong Artificial Intelligence’ Read more […]

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Godel’s theorem

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Godel’s first incompleteness theorem Summarised from various sources Godel’s first incompleteness theorem is the starting point for Penrose’s approach to an explanation of the nature of mathematical understanding. In the later development of Penrose’s ideas by Stuart Hameroff mathematical understanding has been enlarged to mean consciousness, presumably on the argument that we need to consciously feel or appreciate the truth of a mathematical statement that is not provable by the immediately Read more […]

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Godel & Turing

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Godel & Turing Chaitin Godel showed that the connection between proof  and truth was shaky. In mathematics and in other formal systems statements can be true but unprovable. Some mathematical propositions might be undecidable, and this demolishes the idea of a closed consistent body of rules, and replaces it with incompleteness. Chaitin discusses randomness. Something is random if there is no pattern or abbrevaited description. Then there is no algorithm shorter than the thing itself. Read more […]

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Consciousness in mathematical cognition

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The Essential role of consciousness in mathematical cognition Robert Hadley, Simon Fraser University Journal of Consciousness Studies, 17, No. 1-2, 2010, pp. 27-46 http://ingentaconnect.com/journals/browse/imp/jcs Hadley puts forward alternative possibilities to Penrose’s argument from the Godel theorem, in order to reach a Penrose-type conclusion about brains and computers. He argues that a system that lacked consciousness would be incapable of certain concepts and certain proofs. Hadley Read more […]

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Computable universe

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Foreword to A Computable Universe: Understanding computation and exploring nature as computation Roger Penrose World Scientific 2012 Penrose’s argues that Gödel’s incompleteness theorem provides a strong case for human understanding being non-computable. This relates to our ability to demonstrate the truth of certain mathematical propositions. These are described as π1 sentences. These sentences assert that a particular computation, such as Lagrange’s theorem which asserts that every natural Read more […]

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Neurons and logic gates

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Neurons and logic gates from the webmaster The idea that the brain is a computer has been popular since the invention of the latter, and this remains a mainstream consensus. The feeling of many others that there is an essential difference between computers and humans has tended to be pushed aside as an uneducated delusion. However, although much brain processing can be accepted as being analagous to computing, it may be that there is a fairly easy to detect structural difference between Read more […]

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