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  1.  19
    Cristian S. Calude & Giuseppe Longo (forthcoming). The Deluge of Spurious Correlations in Big Data. Foundations of Science:1-18.
    Very large databases are a major opportunity for science and data analytics is a remarkable new field of investigation in computer science. The effectiveness of these tools is used to support a “philosophy” against the scientific method as developed throughout history. According to this view, computer-discovered correlations should replace understanding and guide prediction and action. Consequently, there will be no need to give scientific meaning to phenomena, by proposing, say, causal relations, since regularities in very large databases are enough: “with (...)
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  2.  3
    Cristian S. Calude, Ludwig Staiger & Sebastiaan A. Terwijn (2006). On Partial Randomness. Annals of Pure and Applied Logic 138 (1):20-30.
    If is a random sequence, then the sequence is clearly not random; however, seems to be “about half random”. L. Staiger [Kolmogorov complexity and Hausdorff dimension, Inform. and Comput. 103 159–194 and A tight upper bound on Kolmogorov complexity and uniformly optimal prediction, Theory Comput. Syst. 31 215–229] and K. Tadaki [A generalisation of Chaitin’s halting probability Ω and halting self-similar sets, Hokkaido Math. J. 31 219–253] have studied the degree of randomness of sequences or reals by measuring their “degree (...)
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  3.  45
    Cristian S. Calude, Peter H. Hertling & Karl Svozil (1999). Embedding Quantum Universes in Classical Ones. 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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  4. Cristian S. Calude, WHAT IS. . . A Halting Probability?
    Turing’s famous 1936 paper “On computable numbers, with an application to the Entscheidungsproblem” defines a computable real number and uses Cantor’s diagonal argument to exhibit an uncomputable real. Roughly speaking, a computable real is one that one can calculate digit by digit, that there is an algorithm for approximating as closely as one may wish. All the reals one normally encounters in analysis are computable, like π, √2 and e. But they are much scarcer than the uncomputable reals because, as (...)
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  5.  30
    Cristian S. Calude (2002). Incompleteness, Complexity, Randomness and Beyond. Minds and Machines 12 (4):503-517.
    Gödel's Incompleteness Theorems have the same scientific status as Einstein's principle of relativity, Heisenberg's uncertainty principle, and Watson and Crick's double helix model of DNA. Our aim is to discuss some new faces of the incompleteness phenomenon unveiled by an information-theoretic approach to randomness and recent developments in quantum computing.
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  6.  3
    Cristian S. Calude (1997). A Genius's Story: Two Books on Gödel. Complexity 3 (2):11-15.
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  7.  2
    Cristian S. Calude & Gheorghe P.?un (2000). Computing with Cells and Atoms in a Nutshell. Complexity 6 (1):38-48.
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  8.  1
    Cristian S. Calude & Gheorghe Păun (2000). Computing with Cells and Atoms in a Nutshell. Complexity 6 (1):38-48.
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  9.  2
    Cristian S. Calude (2005). Generalisation of Disjunctive Sequences. Mathematical Logic Quarterly 51 (2):120.
    The present paper proposes a generalisation of the notion of disjunctive sequence, that is, of an infinite sequence of letters having each finite sequence as a subword. Our aim is to give a reasonable notion of disjunctiveness relative to a given set of sequences F. We show that a definition like “every subword which occurs at infinitely many different positions in sequences in F has to occur infinitely often in the sequence” fulfils properties similar to the original unrelativised notion of (...)
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