10 found
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  1.  10
    Spurious, Emergent Laws in Number Worlds.Cristian S. Calude & Karl Svozil - 2019 - Philosophies 4 (2):17-0.
    We study some aspects of the emergence of _lógos_ from _xáos_ on a basal model of the universe using methods and techniques from algorithmic information and Ramsey theories. Thereby an intrinsic and unusual mixture of meaningful and spurious, emerging laws surfaces. The spurious, emergent laws abound, they can be found almost everywhere. In accord with the ancient Greek theogony one could say that _lógos_, the Gods and the laws of the universe, originate from “the void,„ or from _xáos_, a picture (...)
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  2.  17
    Reflections on Quantum Computing.Michael J. Dinneen, Karl Svozil & Cristian S. Calude - 2000 - Complexity 6 (1):35-37.
  3.  63
    Piron's and Bell's Geometric Lemmas and Gleason's Theorem.Georges Chevalier, Anatolij Dvurečenskij & Karl Svozil - 2000 - Foundations of Physics 30 (10):1737-1755.
    We study the idea of implantation of Piron's and Bell's geometrical lemmas for proving some results concerning measures on finite as well as infinite-dimensional Hilbert spaces, including also measures with infinite values. In addition, we present parabola based proofs of weak Piron's geometrical and Bell's lemmas. These approaches will not used directly Gleason's theorem, which is a highly non-trivial result.
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  4.  51
    Embedding Quantum Universes in Classical Ones.Cristian S. Calude, Peter H. Hertling & Karl Svozil - 1999 - Foundations of Physics 29 (3):349-379.
    Do the partial order and ortholattice operations of a quantum logic correspond to the logical implication and connectives of classical logic? Rephrased, How far might a classical understanding of quantum mechanics be, in principle, possible? A celebrated result of Kochen and Specker answers the above question in the negative. However, this answer is just one among various possible ones, not all negative. It is our aim to discuss the above question in terms of mappings of quantum worlds into classical ones, (...)
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  5.  27
    Strong Determinism Vs. Computability.Cristian Calude, Douglas Campbell, Karl Svozil & Doru Ştefănescu - 1995 - Vienna Circle Institute Yearbook 3:115-131.
    Penrose [40] has discussed a new point of view concerning the nature of physics that might underline conscious thought processes. He has argued that it might be the case that some physical laws are not computable, i.e. they cannot be properly simulated by computer; such laws can most probably arise on the “no-man’s-land” between classical and quantum physics. Furthermore, conscious thinking is a non-algorithmic activity. He is opposing both strong AI , and Searle’s [47] contrary viewpoint mathematical “laws”).
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  6.  46
    The Axiom of Choice in Quantum Theory.Norbert Brunner, Karl Svozil & Matthias Baaz - 1996 - Mathematical Logic Quarterly 42 (1):319-340.
    We construct peculiar Hilbert spaces from counterexamples to the axiom of choice. We identify the intrinsically effective Hamiltonians with those observables of quantum theory which may coexist with such spaces. Here a self adjoint operator is intrinsically effective if and only if the Schrödinger equation of its generated semigroup is soluble by means of eigenfunction series expansions.
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  7. Book and Software Reviews-The Limits of Mathematics.Karl Svozil - 1998 - Complexity 3 (6):63-63.
  8.  9
    One‐to‐One.Karl Svozil - 1998 - Complexity 4 (1):25-29.
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  9.  11
    Towards Fractal Gravity.Karl Svozil - 2020 - Foundations of Science 25 (1):275-280.
    In an extension of speculations that physical space–time is a fractal which might itself be embedded in a high-dimensional continuum, it is hypothesized to “compensate” for local variations of the fractal dimension by instead varying the metric in such as way that the intrinsic dimensionality remains an integer. Thereby, an extrinsic fractal continuum is intrinsically perceived as a classical continuum. Conversely, it is suggested that any variation of the metric from its Euclidean form can be “shifted” to nontrivial fractal topology. (...)
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  10.  9
    The Limits of Mathematics by Gregory J. Chaitin.Karl Svozil - 1998 - Complexity 3 (6):63-63.
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