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Cristian S. Calude [14]Cristian Calude [8]
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Cristian S. Calude
University of Auckland
  1. The Deluge of Spurious Correlations in Big Data.Cristian S. Calude & Giuseppe Longo - 2017 - Foundations of Science 22 (3):595-612.
    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.  11
    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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  3.  8
    On Partial Randomness.Cristian S. Calude, Ludwig Staiger & Sebastiaan A. Terwijn - 2006 - 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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  4.  17
    Reflections on Quantum Computing.Michael J. Dinneen, Karl Svozil & Cristian S. Calude - 2000 - Complexity 6 (1):35-37.
  5.  9
    Incompleteness and the Halting Problem.Cristian S. Calude - 2021 - Studia Logica 109 (5):1159-1169.
    We present an abstract framework in which we give simple proofs for Gödel’s First and Second Incompleteness Theorems and obtain, as consequences, Davis’, Chaitin’s and Kritchman-Raz’s Theorems.
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  6. On a Theorem of Günter Asser.Cristian S. Calude & Lila Sântean - 1990 - Mathematical Logic Quarterly 36 (2):143-147.
    Recently, G. ASSER has obtained two interesting characterizations of the class of unary primitive recursive string-functions over a fixed alphabet as Robinson algebras. Both characterizations use a somewhat artificial string-function, namely the string-function lexicographically associated with the number-theoretical excess-over-a-square function. Our aim is to offer two new and natural Robinson algebras which are equivalent to ASSER’S algebras.
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  7. WHAT IS. . . A Halting Probability?Cristian S. Calude - 2010 - Notices of the AMS 57:236-237.
    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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  8. Incompleteness, Complexity, Randomness and Beyond.Cristian S. Calude - 2002 - 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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  9.  6
    Computing with Cells and Atoms in a Nutshell.Cristian S. Calude & Gheorghe P.?un - 2000 - Complexity 6 (1):38-48.
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  10.  1
    Discrete Mathematics and Theoretical Computer Science 4th International Conference, Dmtcs 2003, Dijon, France, July 2003, Proceedings. [REVIEW]Cristian Calude, M. J. Dinneen & Vincent Vajnovszki - 2003 - Springer Verlag.
    The fourthDiscrete Mathematics andTheoreticalComputer Science Conference was jointly organized by the Centre for Discrete Mathematics and Theoretical Computer Science of the University of Auckland and the University of Bourgogne in Dijon, France, and took place in Dijon from 7 to12 July2003.Thepreviousconferenceswereheld inAuckland,NewZealand and Constan ̧ ta, Romania. The?ve invited speakers of the conference were: G.J. Chaitin, C. Ding, S. Istrail, M. Margenstein, and T. Walsh. The Programme Committee, consisting of V. Berthe, S. Boza- lidis,C.S.Calude,V.E.Cazanescu, F. Cucker, M. Deza, J. Diaz, (...)
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  11. Real Numbers: From Computable to Random.Cristian S. Calude - 2001 - Studia Philosophica 1.
    A real is computable if it is the limit of a computable, increasing, computably converging sequence of rational...
     
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  12.  30
    Recursive Baire Classification and Speedable Functions.Cristian Calude, Gabriel Istrate & Marius Zimand - 1992 - Mathematical Logic Quarterly 38 (1):169-178.
  13.  28
    Topological Size of Sets of Partial Recursive Functions.Cristian Calude - 1982 - Mathematical Logic Quarterly 28 (27‐32):455-462.
  14.  22
    Are Binary Codings Universal?Cristian Calude & Cezar Câmpeanu - 1996 - Complexity 1 (5):47-50.
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  15.  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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  16.  14
    What is a Random String?Cristian Calude - 1995 - Vienna Circle Institute Yearbook 3:101-113.
    Suppose that persons A and B give us a sequence of 32 bits each, saying that they were obtained from independent coin flips. If A gives the stringu = 01001110100111101001101001110101and B gives the stringv = 00000000000000000000000000000000,then we would tend to believe A and would not believe B: the string u seems to be random, but the string v does not. Further on, if we change the value of a bit in a “random” string, then the result is still a “random” (...)
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  17.  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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  18.  12
    Generalisation of Disjunctive Sequences.Cristian S. Calude - 2005 - 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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  19.  7
    A Genius's Story: Two Books on Gödel.Cristian S. Calude - 1997 - Complexity 3 (2):11-15.
  20.  7
    Deterministic Automata Simulation, Universality and Minimality.Cristian Calude, Elena Calude & Bakhadyr Khoussainov - 1997 - Annals of Pure and Applied Logic 90 (1-3):263-276.
    Finite automata have been recently used as alternative, discrete models in theoretical physics, especially in problems related to the dichotomy between endophysical/intrinsic and exophysical/ extrinsic perception . These studies deal with Moore experiments; the main result states that it is impossible to determine the initial state of an automaton, and, consequently, a discrete model of Heisenberg uncertainty has been suggested. For this aim the classical theory of finite automata — which considers automata with initial states — is not adequate, and (...)
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  21.  7
    Every Computably Enumerable Random Real is Provably Computably Enumerable Random.Cristian Calude & Nicholas Hay - 2009 - Logic Journal of the IGPL 17 (4):351-374.
    We prove that every computably enumerable random real is provable in Peano Arithmetic to be c.e. random. A major step in the proof is to show that the theorem stating that “a real is c.e. and random iff it is the halting probability of a universal prefix-free Turing machine” can be proven in PA. Our proof, which is simpler than the standard one, can also be used for the original theorem. Our positive result can be contrasted with the case of (...)
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  22.  3
    Computing with Cells and Atoms in a Nutshell.Cristian S. Calude & Gheorghe Păun - 2000 - Complexity 6 (1):38-48.
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