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Physical versus Computational Complementarity I
, 1996
"... The dichotomy between endophysical/intrinsic and exophysical/extrinsic perception concerns the question of how a model  mathematical, logical, computational  universe is perceived from inside or from outside, [71, 65, 66, 59, 60, 68, 67]. This distinction goes back in time at least to Archimedes, ..."
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Cited by 20 (19 self)
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The dichotomy between endophysical/intrinsic and exophysical/extrinsic perception concerns the question of how a model  mathematical, logical, computational  universe is perceived from inside or from outside, [71, 65, 66, 59, 60, 68, 67]. This distinction goes back in time at least to Archimedes, reported to have asked for a point outside the world from which one could move the earth. An exophysical perception is realized when the system is laid out and the experimenter peeps at the relevant features without changing the system. The information flows on a oneway road: from the system to the experimenter. An endophysical perception can be realized when the experimenter is part of the system under observation. In such a case one has a twoway informational flow; measurements and entities measured are interchangeable and any attempt to distinguish between them ends up as a convention. The general conception dominating the sciences is that the physical universe is perceivable ...
Quantum randomness and value indefiniteness
 Advanced Science Letters
"... As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable. 1. CONCEPTUALISATION It certainly would be fascinating to pinpoint the time of the emergence of the notion that certain quantum processes, such as the decay of an excited quantum state, occurs pr ..."
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Cited by 13 (6 self)
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As computability implies value definiteness, certain sequences of quantum outcomes cannot be computable. 1. CONCEPTUALISATION It certainly would be fascinating to pinpoint the time of the emergence of the notion that certain quantum processes, such as the decay of an excited quantum state, occurs principally and irreducibly at random; and howlong it took to become the dominant way of thinking about them after almost two centuries of quasirationalistic dominance. Bohr’s and Heisenberg’s influence has been highly recognised and has prevailed, even against the strong rationalistic and philosophic objections raised by, for instance, by Einstein and Schrödinger. 1 � 2 Of course, one of the strongest reasons for this growing acceptance of quantum randomness has been the factual inability to go “beyond ” the quantum in any manner which would encourage new phenomenology and might result in any hope for a progressive quasiclassical research program. 3
Computational universes
 Chaos, Solitons & Fractals
, 2006
"... Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science h ..."
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Cited by 9 (5 self)
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Suspicions that the world might be some sort of a machine or algorithm existing “in the mind ” of some symbolic number cruncher have lingered from antiquity. Although popular at times, the most radical forms of this idea never reached mainstream. Modern developments in physics and computer science have lent support to the thesis, but empirical evidence is needed before it can begin to replace our contemporary world view.
Contexts in quantum, classical and partition logic
 In Handbook of Quantum Logic
, 2006
"... Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud ..."
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Cited by 8 (7 self)
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Contexts are maximal collections of comeasurable observables “bundled together ” to form a “quasiclassical miniuniverse. ” Different notions of contexts are discussed for classical, quantum and generalized urn–automaton systems. PACS numbers: 02.10.v,02.50.Cw,02.10.Ud
Is the Universe Lawful?
, 1996
"... The last 2,500 years have been dominated by the belief, expressed in different forms, that the Universe is lawful, that is, the Universe is a knowable system governed by rules which determine the future uniquely and completely. An extreme way to express this belief is to claim overconfidently that ..."
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Cited by 7 (3 self)
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The last 2,500 years have been dominated by the belief, expressed in different forms, that the Universe is lawful, that is, the Universe is a knowable system governed by rules which determine the future uniquely and completely. An extreme way to express this belief is to claim overconfidently that the study of some branches of science will soon be completed, will soon attend an end. Our aim is to challenge this apocryphal hypothesis by arguing, with complexitytheoretic arguments, that the Universe is lawless, that is, the Universe is lacking any kind of general ordered structure implied by the term "law".
Quantum Information Via State Partitions and the Context Translation Principle
, 2004
"... For manyparticle systems, quantum information in base n can be defined by partitioning the set of states according to the outcomes of nary (joint) observables. Thereby, k particles can carry k nits. With regards to the randomness of single outcomes, a context translation principle is proposed. ..."
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Cited by 6 (6 self)
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For manyparticle systems, quantum information in base n can be defined by partitioning the set of states according to the outcomes of nary (joint) observables. Thereby, k particles can carry k nits. With regards to the randomness of single outcomes, a context translation principle is proposed. Quantum randomness is related to the uncontrollable degrees of freedom of the measurement interface, thereby translating a mismatch between the state prepared and the state measured.
Omega and the time evolution of the Nbody problem
, 2007
"... The series solution of the behavior of a finite number of physical bodies and Chaitin’s Omega number share quasialgorithmic expressions; yet both lack a computable radius of convergence. ..."
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Cited by 4 (4 self)
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The series solution of the behavior of a finite number of physical bodies and Chaitin’s Omega number share quasialgorithmic expressions; yet both lack a computable radius of convergence.
The PoincaréHardy Inequality on the Complement of a Cantor Set
 INTERPOLATION THEORY, SYSTEMS THEORY AND RELATED TOPICS, OPERATOR THEORY: ADVANCES AND APPLICATIONS
, 2000
"... The PoincareHa#63 inequa#g8 y u 2 dist 2 (x, E) dm #K 2 # 2 dm is derived in R3 on the complement ofa Ca# tor set E. We usea specia# selfsimila# tilinga#m a na#inga metric on thespa#1 oftra jectories genera#es bya Ma#956g846218ga# gra#9 which is homeomorphic with thespa#1 of ti ..."
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Cited by 4 (3 self)
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The PoincareHa#63 inequa#g8 y u 2 dist 2 (x, E) dm #K 2 # 2 dm is derived in R3 on the complement ofa Ca# tor set E. We usea specia# selfsimila# tilinga#m a na#inga metric on thespa#1 oftra jectories genera#es bya Ma#956g846218ga# gra#9 which is homeomorphic with thespa#1 of tiles endowed with theEuclidea# dista#ea# A crudeestima#541 of theconsta# t K 2 is 2,100. Twoa#5303g84402 will be briefly discussed. In the la#g one, theconsta# t K 1 # 0.021819 pla ys the role of a#estima#2 for the dimensionlessPla#e consta# t in the correspondinguncerta#4 ty principle.
Reflections on Quantum Computing
, 2000
"... In this rather speculative note three problems pertaining to the power and limits of quantum computing are posed and partially answered: a) when are quantum speedups possible?, b) is fixedpoint computing a better model for quantum computing?, c) can quantum computing trespass the Turing barrier? 1 ..."
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Cited by 2 (0 self)
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In this rather speculative note three problems pertaining to the power and limits of quantum computing are posed and partially answered: a) when are quantum speedups possible?, b) is fixedpoint computing a better model for quantum computing?, c) can quantum computing trespass the Turing barrier? 1 When are quantum speedups possible? This section discusses the possibility that speedups in quantum computing can be achieved only for problems which have a few or even unique solutions [12]. For instance, this includes the computational complexity class UP [15]. Typical examples are Shor's quantum algorithm for prime factoring [18] and Grover's database search algorithm [13] for a single item satisfying a given condition in an unsorted database (see also Gruska [14]). In quantum complexity, one popular class of problems is BQP,whichisthe set of decision problems that can be solved in polynomial time (on a quantum computer) so that the correct answer is obtained with probability at l...