The European Physical Journal Special Topics

, Volume 146, Issue 1, pp 205–216 | Cite as

Physics of cognition: Complexity and creativity

  • F. T. ArecchiEmail author


A scientific problem described within a given code is mapped by a corresponding computational problem, We call complexity (algorithmic) the bit length of the shortest instruction that solves the problem. Deterministic chaos in general affects a dynamical system making the corresponding problem experimentally and computationally heavy, since one must reset the initial conditions at a rate higher than that of information loss (Kolmogorov entropy). One can control chaos by adding to the system new degrees of freedom (information swapping: information lost by chaos is replaced by that arising from the new degrees of freedom). This implies a change of code, or a new augmented model. Within a single code, changing hypotheses means fixing different sets of control parameters, each with a different a-priori probability, to be then confirmed and transformed into an a-posteriori probability via Bayes theorem. Sequential application of Bayes rule is nothing else than the Darwinian strategy in evolutionary biology. The sequence is a steepest ascent algorithm, which stops once maximum probability has been reached. At this point the hypothesis exploration stops. By changing code (and hence the set of relevant variables) one can start again to formulate new classes of hypotheses. We call creativity the action of code changing, which is guided by hints not formalized within the previous code, whence not accessible to a computer. We call semantic complexity the number of different scientific codes, or models, that describe a situation. It is however a fuzzy concept, in so far as this number changes due to interaction of the operator with the context. These considerations are illustrated with reference to a cognitive task, starting from synchronization of neuron arrays in a perceptual area and tracing the putative path toward a model building. Since this is a report on work in progress, we skip technicalities in order to stress the gist of the question, and provide references to more detailed work.


European Physical Journal Special Topic Spike Train Information Loss Cognitive Agent Mutual Coupling 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. M.I. Rabinovich, P. Varona, A.I. Selverston, H.D.I. Abarbanel, Rev. Mod. Phys. 78, 1213 (2006) Google Scholar
  2. T.A. Sebeok, Semiotica 1341-4, 61 (2001) Google Scholar
  3. M. Barbieri, The Organic Codes: An Introduction to Semantic Biology (Cambridge University Press, Cambridge, 2003) Google Scholar
  4. H. Simon, Cognitive Sci. 4, 33–46 (1980) Google Scholar
  5. S. Solomon, The Microscopic Representation of Complex Macroscopic Phenomena, Ann. Rev. Comp. Phys. II (World Scientific, 1995), pp. 243–294 Google Scholar
  6. G.J. Chaitin, Algorithmic Information Theory (Cambridge University Press, 1987) Google Scholar
  7. C.H. Bennett, G. Grinstein, Phys. Rev. Lett. 55, 657 (1985) Google Scholar
  8. F.T. Arecchi, A. Farini, Lexicon of Complexity (EC Contract n.PSS*0813) (Studio Editoriale Fiorentino, Firenze, 1996) Google Scholar
  9. F. Rieke et al., Spikes: Exploring the Neuronal Code (MIT Press, Cambridge MA, 1997) Google Scholar
  10. W. Singer, E.C.M. Gray, Annu. Rev. Neurosci. 18, 555 (1995) Google Scholar
  11. C.M. Gray, Neuron 24, 31 (1999) Google Scholar
  12. D. Chawla, E.D. Lumer, K.J. Friston, Neural Comp. 12, 2805 (2000) Google Scholar
  13. F. Duret, F. Shumikhina, S. Molotchnikoff, BMC Neurosci. 7, 72 (2006) Google Scholar
  14. A. Shilnikov, L. Shilnikov, D. Turaev, Int. J. Bif. Chaos 14, 2143 (2004) Google Scholar
  15. F.T. Arecchi, R. Meucci, W. Gadomski, Phys. Rev. Lett. 58, 2205 (1987) Google Scholar
  16. F.T. Arecchi, A. Lapucci, R. Meucci, J.A. Roversi, P. Coullet, Europhys. Lett. 6, 77 (1988) Google Scholar
  17. F.T. Arecchi, W. Gadomski, A. Lapucci, H. Mancini, R. Meucci, J.A. Roversi, JOSA B 5, 1153 (1988) Google Scholar
  18. U. Feudel et al., Chaos 10, 231 (2000) Google Scholar
  19. F.T. Arecchi, Physica A 338, 218 (2004) Google Scholar
  20. E. Allaria, F.T. Arecchi, A. Di Garbo, R. Meucci, Phys. Rev. Lett. 86, 791 (2001) Google Scholar
  21. I. Leyva, E. Allaria, S. Boccaletti, F.T. Arecchi, Phys. Rev. E 68, 066209 (2003) Google Scholar
  22. S. Grossberg, Amer. Scient. 83, 439 (1995) Google Scholar
  23. T. Bayes, Phil. Trans. Royal Soc. Lond. 53, 370 (1763) Google Scholar
  24. F. Varela, E. Thompson, E. Rosch, The Embodied Mind (MIT Press, Cambridge, MA, 1991) Google Scholar
  25. J.J. Hopfield, Proc. Nat. Acad. Sci. USA 79, 2554 (1982) Google Scholar
  26. D.J. Amit, H. Gutfreund, H. Sompolinski, Phys. Rev. A 32, 1007 (1985) Google Scholar
  27. G. Toulouse, S. Dehaene, J.P. Changeux, Proc. Nat. Acad. Sci. USA 83, 1695 (1986) Google Scholar
  28. M. Mezard, G. Parisi, M.A. Virasoro, Spin Glass Theory and Beyond (World Scientific, Singapore, 1987) Google Scholar
  29. K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975) Google Scholar
  30. G. Laurent, M. Stopfer, R.W. Friedrich, M.I. Rabinovich, A. Volkovskii, H.D.I. Abarbanel, Annu. Rev. Neurosci. 24, 263 (2001) Google Scholar
  31. W.J. Freeman, How Brains Make Up Their Minds (Weidenfeld and Nicolson, London, 1999) Google Scholar

Copyright information

© EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2007

Authors and Affiliations

  1. 1.Physics DepartmentUniversity of FlorenceFlorenceItaly

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