The idea of a primeval order or design is central to Indo European cultures — it is there in the Rig-Vedic corpus in the notion of Rta, and it is there in Plato when he talks about ideas. Someone like Thomas McEvilley would argue that these notions have circulated within the ancient world for a long time. I think much of what we call logic, design and model come from elaborations upon this primal vision of a cosmic order. Regularities are nothing but a modern manifestation of this rather old insight.
The primeval intuition of a cosmic order has bequeathed many investigations, some in the abstract sphere and others in the concrete sphere. As far as I know, the most influential abstract technical treatment of the notion of order is in one of the following two sequences:
(a) Patterns of reasoning > logic > algorithms > computer programs.
(b) Patterns of motion > Calculus > Science of Mechanics > Unified Theory of Matter
Nevertheless, the older notion of order/Rta is both metaphysically and historically prior as well as being conceptually and aesthetically richer. In regularity theory I am interested in recovering some of the lost meanings of ‘order.’ Part of my motive is to bring about a closer relation between ethics, science and aesthetics. This too has a traditional grounding — especially in the Indian traditions where Rta is tied to Dharma: the early Buddhists use the term dhamma/dharma for both the causal and the ethical order. The other motive is empirical and scientific — I think that human life in particular and organismic life in general is regular but it is not mechanical. I see the older conception of order and regularity as our best hope of breaking away from mechanical thinking.
Now that we have this primeval notion of order in the back of our heads, we need to move to a more operational understanding of regularities in the context of living beings. For my purposes, a regularity in the living world can be defined as:
A regularity is a way of being with which we repeatedly engage the world
Some orders are wholesome, while others might be pathological. According to some parts of the Indian tradition, the pathology might run rather deep. It might be part of the human condition (our being-in-samsara so to speak) to propagate an unwholesome order. In this view, human beings have a tendency to reify something impermanent and incomplete into something permanent and complete.