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Set Theory and Physics
 FOUNDATIONS OF PHYSICS, VOL. 25, NO. 11
, 1995
"... Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of soli ..."
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Cited by 8 (7 self)
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Inasmuch as physical theories are formalizable, set theory provides a framework for theoretical physics. Four speculations about the relevance of set theoretical modeling for physics are presented: the role of transcendental set theory (i) hr chaos theory, (ii) for paradoxical decompositions of solid threedimensional objects, (iii) in the theory of effective computability (ChurchTurhrg thesis) related to the possible "solution of supertasks," and (iv) for weak solutions. Several approaches to set theory and their advantages and disadvatages for" physical applications are discussed: Cantorian "naive" (i.e., nonaxiomatic) set theory, contructivism, and operationalism, hr the arrthor's ophrion, an attitude of "suspended attention" (a term borrowed from psychoanalysis) seems most promising for progress. Physical and set theoretical entities must be operationalized wherever possible. At the same thne, physicists shouM be open to "bizarre" or "mindboggling" new formalisms, which treed not be operationalizable or testable at the thne of their " creation, but which may successfully lead to novel fields of phenomenology and technology.
Debugging the Universe
"... The first great age of automata began at the close of the medieval period and lasted into the 17th century[31]. The technological marvels of that era were clockwork confections machined from brass and iron—intricate assemblies of gears, cranks, levers, escapements and ratchets. The clocks of ..."
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Cited by 1 (0 self)
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The first great age of automata began at the close of the medieval period and lasted into the 17th century[31]. The technological marvels of that era were clockwork confections machined from brass and iron—intricate assemblies of gears, cranks, levers, escapements and ratchets. The clocks of
International Journal of Theoretical Physics, VoL 21, Nos. 3/4, 1982 Conservative Logic 1
"... Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certain additit, e quantities (among which energy plays a distinguished role). Because it more c ..."
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Conservative logic is a comprehensive model of computation which explicitly reflects a number of fundamental principles of physics, such as the reversibility of the dynamical laws and the conservation of certain additit, e quantities (among which energy plays a distinguished role). Because it more closely mirrors physics than traditional models of computation, conservative logic is in a better position to provide indications concerning the realization of highperformance computing systems, i.e., of systems that make very efficient use of the "computing resources" actually offered by nature. In particular, conservative logic shows that it is ideally possible to build sequential circuits with zero internal power dissipation. After establishing a general framework, we discuss two specific models of computation. The first uses binary, variables and is the conservativelogic counterpart of switching theory; this model proves that universal computing capabilities are compatible with the reversibility and conservation constraints. The second model, which is a refinement of the first, constitutes a substantial breakthrough in establishing a correspondence between computation and physics. In fact, this model is based on elastic collisions of identical "balls, " and thus is formally identical with the atomic model that underlies the (classical) kinetic theory of perfect gases. Quite literally, the functional behavior of a generalpurpose digital computer can be reproduced by a perfect gas placed in a suitably shaped container and given appropriate initial conditions. 1.
unknown title
, 2009
"... Existence of biological uncertainty principle implies that we can never find ’THE ’ measure for biological complexity. ..."
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Existence of biological uncertainty principle implies that we can never find ’THE ’ measure for biological complexity.
1 Quantum algorithmic information theory
, 2008
"... The agenda of quantum algorithmic information theory, ordered ‘topdown, ’ is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits ..."
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The agenda of quantum algorithmic information theory, ordered ‘topdown, ’ is the quantum halting amplitude, followed by the quantum algorithmic information content, which in turn requires the theory of quantum computation. The fundamental atoms processed by quantum computation are the quantum bits which are dealt with in quantum information theory. The theory of quantum computation will be based upon a model of universal quantum computer whose elementary unit is a twoport interferometer capable of arbitrary U(2) transformations. Basic to all these considerations is quantum theory, in particular Hilbert space quantum mechanics. 1 Information is physical, so is computation qait.tex The reasoning in constructive mathematics [17, 18, 19] and recursion theory, at least insofar as their applicability to worldly things is concerned, makes implicit assumptions about the operationalizability of the entities of discourse. It is this postulated correspondence between practical and theoretical objects, subsumed by the ChurchTuring thesis, which confers power to the formal methods. Therefore, any finding in physics concerns the formal sciences; at least insofar as
Contents
, 2008
"... Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the nbody problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unk ..."
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Different types of physical unknowables are discussed. Provable unknowables are derived from reduction to problems which are known to be recursively unsolvable. Recent series solutions to the nbody problem and related to it, chaotic systems, may have no computable radius of convergence. Quantum unknowables include the random occurrence of single events, complementarity and value indefiniteness.
Contents
, 2011
"... In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While their interrelations are examined closely, these four facets ..."
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In contemporary theoretical physics, the powerful notion of symmetry stands for a web of intricate meanings among which I identify four clusters associated with the notion of transformation, comprehension, invariance and projection. While their interrelations are examined closely, these four facets of symmetry are scrutinised one after the other in great detail. This decomposition allows us to examine closely the multiple different roles symmetry plays in many places in physics. Furthermore, some connections with others disciplines like neurobiology, epistemology, cognitive sciences and, not least, philosophy are proposed in an attempt to show that symmetry can be an organising principle also in these fields. pacs: 11.30.j, 11.30.Qc, 01.70.+w,