One problem with the regularities framework is that, like other frameworks, it is an interlocking set of conceptual intuitions and hypotheses that do not lead to an easy definition. It is almost OK to say that regularities are not definable but we know one when we see one. I don’t quite agree with that conclusion, but let us first see if we can agree about some phenomena being regularities, so that we can at least say that we know one when we see one. Here are a few examples of what I would call regularities:
The size of an animal predicts the pitch of it’s voice. Mice squeak and lions roar and not vice versa
Clouds are puffy while water is runny.
More controversially, the size of an animal predicts how smart it is. A bacterium can never be as smart as a dophin.
These three examples are all related to each other though not in any obvious way. The underlying mechanisms for mice squeaking, clouds puffing and dolphins thinking are all different. Even the evolutionary histories are different. However, at a thermodynamic level, we can see that all of them have to do with how energy and information flow through the respective systems. Physicists talk about “universality” i.e., that the macroscopic properties of a system can often be independent of it’s microscopic origins. The regularity approach takes this one step further, that the regularities of a system are not only independent of the underlying mechanism or causal features, they are the real thing. Especially when it comes to biological processes we can hypothesize that it is regularities and their graspability that is being selected for in natural selection, not the underlying mechanism. I see this as a biologically grounded version of the hardware/software distinction well known in AI and cognitive science. Just as an earlier generation of theorists argued that the same software can be instantiated in different hardware, we can argue that the same regularity can be instantiated via different mechanisms while remaining the same.