Algorithmic information theory for physicists and natural scientists /

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"Version: 20200601"--Title page verso.Includes bibliographical references.1. Introduction -- 1.1. Brief outline of the book -- 1.2. What are complex systems? -- 1.3. Some approaches to complex or organised systems -- 1.4. Algorithmic information theory (AIT) -- 1.5. Algorithmic information theory and mathematics -- 1.6. Real-world systems2. Computation and algorithmic information theory -- 2.1. The computational requirements for workable algorithms -- 2.2. The Turing machine -- 2.3. Measure theory3. AIT and algorithmic complexity -- 3.1. Shorter algorithms imply order -- 3.2. Machine dependence and the invariance theorem -- 3.3. Self-delimiting coding and the Kraft inequality -- 3.4. Optimum coding and Shannon's noiseless coding theorem -- 3.5. Entropy relative to the common framework -- 3.6. Entropy and probability -- 3.7. The fountain of all knowledge : Chaitin's Omega -- 3.8. G?odel's theorem and formal axiomatic systems -- 3.9. The algorithmic entropy, the universal semi-measure and inference4. The algorithmic entropy of strings with structure and variation -- 4.1. Identical algorithmic approaches to strings with variation -- 4.2. The provisional entropy -- 4.3. The specification by a probability distribution -- 4.4. How to specify noisy data -- 4.5. The non-typical state and the thermodynamic entropy5. Modelling and the minimum description length -- 5.1. Introduction -- 5.2. The algorithmic entropy approach to modelling -- 5.3. The minimum description length approach6. The non-typical string and randomness -- 6.1. Outline on perspectives on randomness -- 6.2. Martin-L?of test of randomness7. Order and entropy -- 7.1. The meaning of order -- 7.2. Algorithmic entropy and the traditional entropy8. Reversibility, and Landauer's principle -- 8.1. Introduction -- 8.2. Landauer's principle -- 8.3. Outline of Landauer's argument -- 8.4. The simulation of a reversible real-world computation -- 8.5. The algorithmic entropy as a function of state -- 8.6. External interventions to restore a degraded system9. The algorithmic equivalent of the second law of thermodynamics -- 9.1. The meaning of 'equilibrium' -- 9.2. The increase in thermodynamic entropy as a system trends to the most probable set of states -- 9.3. The relationship between algorithmic entropy and the thermodynamic entropy of a macrostate10. How replication processes maintain a system far from the most probable set of states -- 10.1. Maintaining a system distant from the equilibrium -- 10.2. Examples of the computational issues around the degradation of simple systems -- 10.3. Entropy balances in a reversible system -- 10.4. Homeostasis and second law evolution -- 10.5. Replication processes generate order to counter the second law of thermodynamics -- 10.6. Simple illustrative examples of replication -- 10.7. The algorithmic entropy cost of replica variations -- 10.8. A replicating living system -- 10.9. Selection processes to sustain a natural system -- 10.10. Summary of system regulation and AIT11. Sustainability requirements of a viable economy distant from equilibrium -- 11.1. Introduction -- 11.2. A reminder of the principles of AIT -- 11.3. An economy seen as a replicating system -- 11.4. Order creation through the know-how of economic agents -- 11.5. A narrative to capture economic development -- 11.6. Are there resource limits to economic growth? -- 11.7. Order and GDP -- 11.8. Complementary approaches to human systems -- 11.9. Implications of the algorithmic approach -- 11.10. Conclusions for economic systems12. AIT and philosophical issues -- 12.1. Algorithmic descriptions, learning and artificial intelligence -- 12.2. The mathematical implications of algorithmic information theory -- 12.3. How can we understand the Universe? -- 12.4. Closing thoughts.Algorithmic information theory (AIT), or Kolmogorov complexity as it is known to mathematicians, can provide a useful tool for scientists to look at natural systems, however some critical conceptual issues need to be understood and the advances already made collated and put in a form accessible to scientists. This book has been written in the hope that readers will be able to absorb the key ideas behind AIT so that they are in a better position to access the mathematical developments and to apply the ideas to their own areas of interest. The theoretical underpinning of AIT is outlined in the earlier chapters, while later chapters focus on the applications, drawing attention to the thermodynamic commonality between ordered physical systems such as the alignment of magnetic spins, the maintenance of a laser distant from equilibrium, and ordered living systems such as bacterial systems, an ecology, and an economy.Also available in print.Mode of access: World Wide Web.System requirements: Adobe Acrobat Reader, EPUB reader, or Kindle reader.Sean Devine obtained a PhD in physics from the University of Canterbury, New Zealand and, after three years overseas, spent 20 years as a research physicist, in what was the New Zealand Department of Scientific and Industrial Research, before returning to university to study economics. Sean has since served as manager of the Public Good Science Fund and as Executive Director of The Association of Crown Research Institutes. He has also been a director of one technological company and later become chairperson of another, Robinson Seismic, before acting as its CEO during a global expansion phase. In 2002 Sean returned to university research and undertook systems research in innovation systems, sustainability and complexity theory while doing some postgraduate teaching before recently retiring.Title from PDF title page (viewed on July 9, 2020).

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: .,

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1 online resource (various pagings) :illustrations (some color).

Language

English

ISBN/ISSN

9780750326407

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510

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Subject(s)

Kolmogorov complexity.
Information theory.
COMPUTERS / Information Theory.

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Sean D. Devine.

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