Abstract
Since the origins of civilisation, computation methods adopted in various cultures could be roughly subdivided into two types.
One relied upon a system of notation, initially only for numbers, and rules of performing arithmetical operations on these notations. I will refer to this type as the linguistic one. Gradually it developed into algebra where generic or specific names could be ascribed to other mathematical objects, and then to operations on them as well.
Keynote talk at the 2014 Interdisciplinary Symposium on Complex Systems (ISCS’14), University of Florence, September 15–18, 2014.
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References
Aaronson, S.: NP–complete problems and physical reality, 23. arXiv:quant–ph/0502072
Aaronson, S.: Why philosophers should care about computational complexity, 58. arXiv:1108.1791
Dehaene, S., Mehler, J.: Cross–linguistic regularities in the frequency of number words. Cognition 43, 1–29 (1992)
Delahaye, J.–P.: Les entiers ne naissent pas égaux. Pour la Science (421), 80–85 (2012)
Huang, S.-M., Yen, D.C., Yang, L.-W., Hua, J.-S.: An investigation of Zipf’s Law for fraud detection. Decision Support Systems 46, 70–83 (2008)
Levin, L.A.: Various measures of complexity for finite objects (axiomatic description). Soviet Math. Dokl. 17(2), 522–526 (1976)
Levin, L.A.: Randomness conservation inequalities: information and independence in mathematical theories. Information and Control 61, 15–37 (1984)
Li, M., Vitányi, P.: An introduction to Kolmogorov complexity and its applications. Springer (1993)
Mandelbrot, B.: An information theory of the statistical structure of languages. In: Jackson, W. (ed.) Communication Theory, pp. 486–502. Butterworth, Woburn (1953)
Manin, D.Y.: Zipf’s Law and Avoidance of Excessive Synonymy. Cognitive Science 32(7), 1075–1078 (2008), arXiv:0710.0105
Manin, D.Y.: Mandelbrot’s model for Zipf’s Law. Can Mandelbrot’s model explain Zipf’s Law for language? Journ of Quantitative Linguistics 16(3), 274–285 (2009)
Manin, Y.I.: A Course in Mathematical Logic for Mathematicians, 2nd edn. Graduate Texts in Mathematics. Springer (2010)
Manin, Y.I.: A computability challenge: Asymptotic bounds and isolated error-correcting codes. In: Dinneen, M.J., Khoussainov, B., Nies, A. (eds.) WTCS 2012 (Calude Festschrift). LNCS, vol. 7160, pp. 174–182. Springer, Heidelberg (2012)
Manin, Y.I.: Classical computing, quantum computing, and Shor’s factoring algorithm, Séminaire Bourbaki, no. 862, vol. 266, pp. 375–404. Astérisque (June 1999/2000), arXiv: quant-ph/9903008
Manin, Y.I.: Renormalization and computation I. Motivation and background. In: Loday, J., Vallette, B. (eds.) Proceedings OPERADS 2009. Séminaires et Congrès, vol. 26, pp. 181–223. Soc. Math. de France (2012), math.QA/0904.492
Manin, Y.I.: Renormalization and computation II: Time cut–off and the Halting Problem. Math. Struct. in Comp. Science 22, 729–751 (2012), Special issue, Cambridge UP. math.QA/0908.3430
Manin, Y.I.: Kolmogorov complexity as a hidden factor of scientific discourse: From Newton’s law to data mining. In: Talk at the Plenary Session of the Pontifical Academy of Sciences on Complexity and Analogy in Science: Theoretical, Methodological and Epistemological Aspects, Vatican, November 5–7 (2012) arXiv:1301.0081
Manin, Y.I.: Zipf’s law and L. Levin’s probability distributions. Functional Analysis and its Applications, Vol. 48(2) (2014), arXiv:1301.0427
Manin, Y., Marcoll, M.: Kolmogorov complexity and the asymptotic bound for error-correcting codes. Journ. of Diff. Geometry (to appear in 2014), arXiv:1203.0653
Manin, Y., Marcolli, M.: Big Bang, Blow Up, and Modular Curves: Algebraic Geometry in Cosmology. arXiv:1402.2158
Manin, Y., Marcolli, M.: Error–correcting codes and phase transitions. Math. in Comp. Science 5, 133–170 (2011), arXiv:mat.QA/0910.5135
Murtra, B.C., Solé, R.: On the Universality of Zipf’s Law. Phys. Rev. E 82 (2010)
Piantadosi, S.T.: Zipf’s word frequency law in natural language: A critical review and future directions, http://colala.bcs.rochester.edu/papers/piantadosi2014zipfs.pdf
Smith, R.: Investigation of the Zipf–plot of the extinct Meroitic language. Glottometrics 15, 53–61 (2007)
Tversky, A., Kahneman, D.: Availability; A Heuristic for Judging Frequency and Probability. Cognitive Psychology 5, 207–232 (1973)
Todd, L.: Veldhuizen. Software Libraries and Their Reuse: Entropy, Kolmogorov Complexity, and Zipf’s Law. arXiv:cs/0508023
Vladut, S.G., Nogin, D.Y., Tsfasman, M.A.: Algebraic geometric codes: Basic notions. Mathematical Surveys and Monographs. American Mathematical Society, Providence (2007)
Zipf, G.K.: The psycho–biology of language. Routledge, London (1936)
Zipf, G.K.: Human behavior and the principle of least effort. Addison–Wesley (1949)
Zvonkin, A.K., Levin, L.A.: The complexity of finite objects and the basing of the concepts of information and randomness on the theory of algorithms. Uspehi Mat. Nauk 25(6(156)), 8–127 (1970), (Russian)
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Manin, Y.I. (2015). Physics in the World of Ideas: Complexity as Energy. In: Sanayei, A., E. Rössler, O., Zelinka, I. (eds) ISCS 2014: Interdisciplinary Symposium on Complex Systems. Emergence, Complexity and Computation, vol 14. Springer, Cham. https://doi.org/10.1007/978-3-319-10759-2_1
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