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Leibniz was mocked for claiming that we live in the best of all possible worlds. (Voltaire’s Candide asks: “If this is the best, what are the others like?”) In fact, Leibnizian philosophy is really concerned with variety, and in his Monadology Leibniz postulated that the universe is created “with as much variety as possible, but with the greatest order possible”. Strangely, no one seems to have attempted to express this idea in concrete mathematical form before Smolin and I found a realization in the form of various models for which an intrinsic variety can be defined and maximized. Unlike Shannon information, the information content of such models is intrinsic and can be 'read off' directly from them. We initially hoped these models would cast light on the mysteries of quantum mechanics, but, despite several intriguing properties of these models, any direct link to quantum mechanics is clearly still a long way off.
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