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NonBoolean Descriptions for MindMatter Problems
"... A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmat ..."
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A framework for the mindmatter problem in a holistic universe which has no parts is outlined. The conceptual structure of modern quantum theory suggests to use complementary Boolean descriptions as elements for a more comprehensive nonBoolean description of a world without an apriorigiven mindmatter distinction. Such a description in terms of a locally Boolean but globally nonBoolean structure makes allowance for the fact that Boolean descriptions play a privileged role in science. If we accept the insight that there are no ultimate building blocks, the existence of holistic correlations between contextually chosen parts is a natural consequence. The main problem of a genuinely nonBoolean description is to find an appropriate partition of the universe of discourse. If we adopt the idea that all fundamental laws of physics are invariant under time translations, then we can consider a partition of the world into a tenseless and a tensed domain. In the sense of a regulative principle, the material domain is defined as the tenseless domain with its homogeneous time. The tensed domain contains the mental domain with a tensed time characterized by a privileged position, the Now. Since this partition refers to two complementary descriptions which are not given apriori,wehavetoexpectcorrelations between these two domains. In physics it corresponds to Newton’s separation of universal laws of nature and contingent initial conditions. Both descriptions have a nonBoolean structure and can be encompassed into a single nonBoolean description. Tensed and tenseless time can be synchronized by holistic correlations. 1.
Truth and Light: Physical Algorithmic Randomness
, 2005
"... This thesis examines some problems related to Chaitin's Ω number. In the first section, we describe several new minimalist prefixfree machines suitable for the study of concrete algorithmic information theory; the halting probabilities of these machines are all Ω numbers. In the second part, we s ..."
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This thesis examines some problems related to Chaitin's Ω number. In the first section, we describe several new minimalist prefixfree machines suitable for the study of concrete algorithmic information theory; the halting probabilities of these machines are all Ω numbers. In the second part, we show that when such a sequence is the result given by a measurement of a system, the system itself can be shown to satisfy an uncertainty principle equivalent to Heisenberg's uncertainty principle. This uncertainty principle also implies Chaitin's strongest form of incompleteness. In the last part, we show that Ω can be written as an infinite product over halting programs; that there exists a "natural," or basefree formulation that does not (directly) depend on the alphabet of the universal prefixfree machine; that Tadaki's generalized halting probability is welldefined even for arbitrary univeral Turing machines and the plain complexity; and finally, that the natural generalized halting probability can be written as an infinite product over primes and has the form of a zeta function whose zeros encode halting information. We conclude with some speculation about physical systems in which partial randomness could arise, and identify many open problems.
How to acknowledge hypercomputation?
, 2007
"... We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models. ..."
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We discuss the question of how to operationally validate whether or not a “hypercomputer” performs better than the known discrete computational models.
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, 712
"... We discuss the question of how to operationally validate whether or not a “hypercomputer ” performs better than the known discrete computational models. 1 ..."
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We discuss the question of how to operationally validate whether or not a “hypercomputer ” performs better than the known discrete computational models. 1