From the Closed Classical Algorithmic Universe to an Open World of Algorithmic Constellations

  • Mark Burgin
  • Gordana Dodig-Crnkovic
Part of the Studies in Applied Philosophy, Epistemology and Rational Ethics book series (SAPERE, volume 7)


In this paper we analyze methodological and philosophical implications of algorithmic aspects of unconventional computation. At first, we describe how the classical algorithmic universe developed and analyze why it became closed in the conventional approach to computation. Then we explain how new models of algorithms turned the classical closed algorithmic universe into the open world of algorithmic constellations, allowing higher flexibility and expressive power, supporting constructivism and creativity in mathematical modeling. As Gödel’s undecidability theorems demonstrate, the closed algorithmic universe restricts essential forms of mathematical cognition. In contrast, the open algorithmic universe, and even more the open world of algorithmic constellations, remove such restrictions and enable new, richer understanding of computation.


Unconventional algorithms unconventional computing algorithmic constellations Computing beyond Turing machine model 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Dept. of MathematicsUCLALos AngelesUSA
  2. 2.Department of Computer Science and Networks, School of Innovation, Design and EngineeringMälardalen UniversityVästeråsSweden

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