Computability as an Evolutionary Context

Ron Cottam, Nils Langloh, Willy Ranson & Roger Vounckx

Abstract

            Chris Langton [1] has argued that one of the major uses of the study of artificial life is as a way of evaluating the feasible resultant footprint of evolutionary development without having to locally assess the implications of all possible adaptive branching processes. The survivability of artificially created life-forms can act as a pointer to significant aspects of the developmental process which would not be necessarily obvious in more advanced living entities, in a way similar to that in which research into low-level animals can show up the importance of behavioural phenomena which remain concealed in the complexities of high-level comportment.

            A second useful strand in this investigation is to evaluate the effects of changes in the descriptive form of the context in which the evolution resulting in naturally viable life-forms has operated. Here the first difficulty is in choosing a modeling base which will support the extension of classically inanimate physics into the diversity of living systems, where the time irreversibility of evolution is a predominant factor. Historically, the most effectively transferrable symbolic model has been that of conventional logic, whose success can be documented through the progressive rise of deterministic science and technology. In this work we have started by formally describing the requirements for environmental-reaction survival computation in a natural temporally-demanding medium [2], and developed this into a more general model of the evolutionary context as a computational machine [3]. The effect of this development is to replace deterministic logic by a modified form which exhibits a continuous range of dimensional fractal diffuseness between the isolation of perfectly ordered localisation and the extended communication associated with nonlocality as represented by pure causal chaos.

            The principal survival criterion for an entity can be described by the relationship between the time-scale of an internal reactive process and that of the external reaction-demanding environment, and evolutionary success becomes primarily a question of ensuring phenomenological computability. This corresponds well with propositions [4] that the critical slowing down associated with phase changes can be attributed to an inability of the constituent media to "compute" sufficiently rapidly their equivalence to the parametric representations implied by the changing states. Survival requires the prioritised objectivisation and identification of dimensions within which an entity is most fragile or most at risk [3]; the evolutionary co-development of a selectively-dimensioned environment [5] brings with it enhanced computability and consequently competitive advantage.

            Timely computation of an entity's reactions to unpredicted environments necessitates the availability of simplified representations of the interaction between an entity and its surroundings in their combined multi-dimensional phase space. Meta-states characterising these objectivisations correspond to regions of the phase space where its contextual description can be reduced reasonably accurately to a small number of parameters, and they are equivalent to the visualisable limited-parametric provisional stages of the evolutionary computation itself. The prime consideration here is that of computability in the face of threat to survival; all other things being equal, he who reacts the fastest lives the longest. The relation between communication and order required for the development of transient trial solutions to environmental problems [3] can be redrawn in terms of computability itself: applicable models must be developed within the time permitted by the context.

            Implementation of these ideas into a mathematically manipulable scheme depends on the extension of current mathematical practice to deal with less than deterministic contexts. It is not sufficient to resort to classical probability or even fuzzy logic; we must model the natural inter-dimensional diffuseness as a way of characterising the emergence of new models from unfamiliar data, as evidenced by the difficulties encountered in maintaining logical correctness in the quantum mechanical treatment of extended systems [6]. In the computability representation of evolution between determinism and chaos, the difference between chance itself and complicated multi-dimensional determinism becomes blurred, and we must replace classical ideas of probability by a more contextually aware formulation closer to that derived by Dempster and Schafer [7, 8] for discrete sets.

References

[1] C. Langton. Technology, Nature, and the Future of Life. In Einstein Meets Magritte, Brussels, Belgium. Vrije Universiteit Brussel, Brussels, 1995.

[2] N. Langloh, R. Cottam, R. Vounckx and J. Cornelis. Towards distributed statistical processing - aquarium: a query and reflection interaction using magic: mathematical algorithms generating interdependent confidences. In S. D. Smith and R. F. Neale, editors, ESPRIT Basic Research Series, Optical Information Technology, pages 303-319. ISBN 3-540-56563-9, Springer-Verlag, Berlin, 1993.

[3] R. Cottam, N. Langloh, W. Ranson and R. Vounckx. Partial Comprehension in a Quasi-Particulate Universe : A Framework for Evolution. In preparation.

[4] see, for example, H. A. Gutowitz and C. G. Langton. Mean field theory of the edge of chaos. Proceedings of Third European Conference on Artificial Life. Universidad de Granada, Spain,1995.

[5] G. Szamosi. The Twin Dimensions: Inventing Time and Space. ISBN 0-07-062646-4, McGraw-Hill, New York, 1986.

[6] I. Antoniou. Extension of the conventional quantum theory and logic for large systems. In Einstein Meets Magritte, Brussels, Belgium. Vrije Universiteit Brussel, Brussels, 1995.

[7] A. P. Dempster. Upper and lower probabilities induced by a multivalued mapping. Annals of Mathematical Statistics, 38, 325-339, 1967.

[8] G. Schafer. A Mathematical Theory of Evidence. Princeton University Press, Princeton, 1976.
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