Advertisement

Mathematical Foundations of Anticipatory Systems

  • A. H. LouieEmail author
Living reference work entry

Abstract

A natural system is an anticipatory system if it contains an internal predictive model of itself and its environment, and in accordance with the model’s predictions, antecedent actions are taken. An organism is the very example of an anticipatory system. Deep system-theoretic homologies allow the possibility of obtaining insights into anticipatory processes in the human and social sciences from the understanding of biological anticipation. To this end, a comprehensive theory of anticipatory systems is the means. The present chapter is an exposition on the mathematical foundations of such a theory.

Keywords

Robert Rosen Relational biology Anticipatory system Modelling relation Encoding Decoding Causality Inference Commutativity Category theory Functor Simulation Model Analogue Conjugacy Surrogacy Internal predictive model Antecedent actions Transducer Feedforth 

Notes

Acknowledgments

I began writing this chapter when I was a resident Fellow at the Stellenbosch Institiute for Advanced Study (stiαs), South Africa, in February-April 2016. I thank stiαs for its hospitality and my contemporary Fellows for their engaging dialogues.

References

  1. Brown, R., & Glazebrook, J. F. (2013). A career of unyielding exploration: In memory of Ion C. Baianu (1947–2013). Quanta, 2, 1–6.CrossRefGoogle Scholar
  2. Hertz, H. (1899). The principles of mechanics presented in a new form (Trans. D. E. Jones & J. T. Walley). London: Macmillan.Google Scholar
  3. Louie, A. H. (2009). More than life itself: A synthetic continuation in relation biology. Frankfurt: ontos.CrossRefGoogle Scholar
  4. Louie, A. H. (2010). Robert Rosen’s anticipatory systems. In: R. Miller & R. Poli (Eds.) Special issue: Anticipatory systems and the philosophical foundations of futures studies. Foresight 12(3), 18–29.Google Scholar
  5. Louie, A. H. (2013). The reflection of life: Functional entailment and imminence in relational biology. New York: Springer.CrossRefGoogle Scholar
  6. Louie, A. H. (2015). A metabolism–repair theory of by-products and side-effects. International Journal of General Systems, 44, 26–54.CrossRefGoogle Scholar
  7. Louie, A. H. (2017). Intangible life: Functorial connections in relational biology. New York: Springer.Google Scholar
  8. Mac Lane, S. (1997). Categories for the working mathematician (2nd ed.). New York: Springer.Google Scholar
  9. Rosen, R. (1974). Planning, management, policies and strategies: Four fuzzy concepts. International Journal of General Systems, 1, 245–252.CrossRefGoogle Scholar
  10. Rosen, R. (1980). Ergodic approximations and specificity. Mathematical Modelling, 1, 91–97.CrossRefGoogle Scholar
  11. Rosen, R. (1985a). [AS] Anticipatory systems: Philosophical, mathematical, and methodological foundations. Oxford: Pergamon; (2012) 2nd ed., New York: Springer.Google Scholar
  12. Rosen, R. (1985b). Organisms as causal systems which are not mechanisms: An essay into the nature of complexity. In R. Rosen (Ed.), Theoretical biology and complexity: Three essays on the natural philosophy of complex systems (pp. 165–203). Orlando: Academic.CrossRefGoogle Scholar
  13. Rosen, R. (1991). Life itself: A comprehensive inquiry into the nature, origin, and fabrication of life. New York: Columbia University Press.Google Scholar
  14. Rosen, R. (2000). Essays on life itself. New York: Columbia University Press.Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.OttawaCanada
  2. 2.Stellenbosch Institute for Advanced Study (stiαs), Wallenberg Research Centre at Stellenbosch UniversityStellenbosch 7600South Africa

Personalised recommendations