Autonomy: an information theoretic perspective.

We present a tentative proposal for a quantitative measure of autonomy. This is something that, surprisingly, is rarely found in the literature, even though autonomy is considered to be a basic concept in many disciplines, including artificial life. We work in an information theoretic setting for which the distinction between system and environment is the starting point. As a first measure for autonomy, we propose the conditional mutual information between consecutive states of the system conditioned on the history of the environment. This works well when the system cannot influence the environment at all and the environment does not interact synergetically with the system. When, in contrast, the system has full control over its environment, we should instead neglect the environment history and simply take the mutual information between consecutive system states as a measure of autonomy. In the case of mutual interaction between system and environment there remains an ambiguity regarding whether system or environment has caused observed correlations. If the interaction structure of the system is known, we define a "causal" autonomy measure which allows this ambiguity to be resolved. Synergetic interactions still pose a problem since in this case causation cannot be attributed to the system or the environment alone. Moreover, our analysis reveals some subtle facets of the concept of autonomy, in particular with respect to the seemingly innocent system-environment distinction we took for granted, and raises the issue of the attribution of control, i.e. the responsibility for observed effects. To further explore these issues, we evaluate our autonomy measure for simple automata, an agent moving in space, gliders in the game of life, and the tessellation automaton for autopoiesis of Varela et al. [Varela, F.J., Maturana, H.R., Uribe, R., 1974. Autopoiesis: the organization of living systems, its characterization and a model. BioSystems 5, 187-196].