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Related Experiment Videos

Zipf's Law, unbounded complexity and open-ended evolution.

Bernat Corominas-Murtra1, Luís F Seoane2,3,4, Ricard Solé3,4,5

  • 11 Institute of Science and Technology Austria , Am Campus 1, 3400, Klosterneuburg , Austria.

Journal of the Royal Society, Interface
|April 9, 2019
PubMed
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Open-ended evolution (OEE) drives unbounded complexity increase, linked to combinatorics and Zipf's Law. Statistical information is not conserved in OEE, but non-statistical information resolves this paradox.

Area of Science:

  • Evolutionary Biology
  • Information Theory
  • Complexity Science

Background:

  • Open-ended evolution (OEE) describes unbounded complexity increase in biological and technological systems.
  • OEE is linked to combinatorics and the generative potential of state spaces.
  • Systems exhibiting OEE, like language and proteins, often follow Zipf's Law.

Purpose of the Study:

  • To define open-endedness fundamentally using algorithmic information theory.
  • To explore the relationship between OEE, Zipf's Law, and information conservation.
  • To investigate the suitability of standard information theory for OEE systems.

Main Methods:

  • Application of algorithmic information theory for a fundamental definition of OEE.
  • Utilizing Shannon information theory to analyze the statistical properties of OEE.
Keywords:
Zipf’s Lawalgorithmic complexitycomplexityopen-ended evolution

Related Experiment Videos

  • Mathematical exploration of information conservation within OEE processes.

    • Main Results:

    • A fundamental definition of open-endedness is provided.
    • Zipf's Law emerges as a consequence of OEE within a variational problem framework.
    • Statistical information is shown to be non-conserved in OEE, leading to a paradox.

    Conclusions:

    • OEE's complexity increase challenges standard information conservation principles.
    • A paradox arises where increasing information content effectively erases itself under statistical measures.
    • Non-statistical information forms resolve this paradox, suggesting limitations of Shannon information theory for OEE.