, Volume 181, Issue 2, pp 255–275 | Cite as

Self-organisation in dynamical systems: a limiting result



There is presently considerable interest in the phenomenon of “self-organisation” in dynamical systems. The rough idea of self-organisation is that a structure appears “by itself” in a dynamical system, with reasonably high probability, in a reasonably short time, with no help from a special initial state, or interaction with an external system. What is often missed, however, is that the standard evolutionary account of the origin of multi-cellular life fits this definition, so that higher living organisms are also products of self-organisation. Very few kinds of object can self-organise, and the question of what such objects are like is a suitable mathematical problem. Extending the familiar notion of algorithmic complexity into the context of dynamical systems, we obtain a notion of “dynamical complexity”. A simple theorem then shows that only objects of very low dynamical complexity can self organise, so that living organisms must be of low dynamical complexity. On the other hand, symmetry considerations suggest that living organisms are highly complex, relative to the dynamical laws, due to their large size and high degree of irregularity. In particular, it is shown that since dynamical laws operate locally, and do not vary across space and time, they cannot produce any specific large and irregular structure with high probability in a short time. These arguments suggest that standard evolutionary theories of the origin of higher organisms are incomplete.


Self organisation Complexity Information Evolution Limitative Symmetry Irregularity Dynamics 


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  1. Blazis D. E. J. (2002) Introduction. Biological Bulletin 202(3): 245–246Google Scholar
  2. Chaitin G. (1982) Gödel’s theorem and information. International Journal of Theoretical Physics 21: 941–954CrossRefGoogle Scholar
  3. Dawkins, R. (1986). The blind watchmaker. Reprinted by Penguin (1988).Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  1. 1.Department of PhilosophyUniversity of British ColumbiaVancouverCanada

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