Abstract

We find symmetry attractive. It is often an indicator of the deep structure of things, whether they be natural phenomena, or artificial. For example, the most fundamental conservation laws of physics are all based in symmetry. Similarly, the symmetries found in religious art throughout the world are intended to draw attention to deep spiritual truths. Not only do we find symmetry pleasing, but its discovery is often also surprising and illuminating as well. For these reasons, we are inclined to think that symmetries are informative. On the other hand, symmetries represent a kind of invariance under transformation, i.e., redundancies. Redundancy, in turn, implies that the information content of a symmetrical structure or configuration is less than that of a similar nonsymmetrical structure. Symmetry, then, entails a reduction in information content. These considerations present us with somewhat of a paradox. On the one hand, many symmetries that we find in the world are surprising, and surprise indicates informativeness. On the other hand, the surprise value of information arises because it presents us with the unexpected or improbable, but symmetries, far from creating the unexpected, ensure that the known can be extended through invariant transformations. How can this paradox be resolved? Rhythmic entrainment is the formation of regular, predictable patterns in time and/or space through interactions within or between systems (resulting in symmetry). The result of entrainment is a simplification of the entrained system. It is the complement to symmetry breaking. Entrainment can be either forced or spontaneous, with the spontaneous form being uncontrollable. It results from processes that are called self-organising. Interestingly, spontaneous entrainment require much less power to form and maintain. It is also the source of levels in systems. I finish with some observations for social systems