Maximal variety as a new fundamental principle of dynamics

Abstract

It is suggested, following a proposal made recently by Smolin, that the most fundamental law of the universe takes this form: Among the set of all possible universes compatible with an irreducibly minimal set of structural constraints, the actually realized universe is the one which maximizes a mathematically well-defined number (the variety) that measures the structural variety of the universe (in the totality of its history). This gives expression to Leibniz's idea that the actual universe gives “the greatest variety possible, but with the greatest possible order.” Two models are proposed in which the idea can be realized and its consequences tested; both are discrete in nature and satisfy highly nonlocal laws. In such a scheme a unique (finite) universe is called into being by the fundamental requirement of maximal variety (for given definition of the variety), which it is conjectured could have such a powerful ordering effect that space, time, the currently known laws of physics, and the observed structure of the universe could all appear as emergent consequences of the single underlying law.