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The Quantum Coin Toss  Testing Microphysical Undecidability
, 1990
"... A critical review of randomness criteria shows that nogo theorems severely restrict the validity of actual "proofs" of undecidability. It is suggested to test microphysical undecidability by physical processes with low extrinsic complexity, such as polarized laser light. The publication and distrib ..."
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Cited by 20 (16 self)
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A critical review of randomness criteria shows that nogo theorems severely restrict the validity of actual "proofs" of undecidability. It is suggested to test microphysical undecidability by physical processes with low extrinsic complexity, such as polarized laser light. The publication and distribution of a sequence of pointer readings generated by such methods is proposed. Unlike any pseudorandom sequence generated by finite deterministic automata, the postulate of microscopic randomness implies that this sequence can be safely applied for all purposes requireing stochasticity and high complexity.
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.
The Complexity of Proving Chaoticity and the ChurchTuring Thesis
, 2010
"... Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may “compute the hard or even the incomputable” by measuring observables which correspond to computationa ..."
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Cited by 2 (1 self)
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Proving the chaoticity of some dynamical systems is equivalent to solving the hardest problems in mathematics. Conversely, one argues that it is not unconceivable that classical physical systems may “compute the hard or even the incomputable” by measuring observables which correspond to computationally hard or even incomputable problems.
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.
Czechoslovak Academy of Sciences Prague
"... On the length of proofs of finitistic consistency statements in first order theories t ..."
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On the length of proofs of finitistic consistency statements in first order theories t