The parts and the whole: inquiring how the interaction of simple subsystems generates complexity
Eduardo Mizraji · International Journal of General Systems · 2006
We approach the general problem of the emergence of complexity in natural, artificial or formal systems, by studying the particular problems that arise during the investigation of elementary cellular automata (ECA). Our objective is to investigate the origin of complex behaviours in the universe of ECA by using a formalism, named “vector logic”, that represents the logical functions in terms of vectors and matrices. This algebraic representation reveals the rich inner structure of the logical functions and provides a new point of view to analyse the laws that govern ECA and their interactions. We show that in this class of automata, the emergence of complexity from completely simple elements does not seem possible, and that complex behaviours result from the coexistence of intrinsic complexities in the elementary laws, together with appropriate initial conditions. “The meaning of words and of expressions, is no longer grasped. An isolated word, or a detail of a design can be understood. But the meaning of the whole escapes. Once we know the number one, we believe that we know the number two because one plus one equals two. We forget that first we must know the meaning of plus”. Comments emitted by computer Alpha 60, in “Alphaville” by Jean-Luc Godard (1965)