I recently posted on Assembly Theory. I’ve read up on it some more since then and found this review of the theory by philosopher Johannes Jäger helpful.
Recursivity makes the dynamics of the model historically contingent. In the end, the kinds of objects that you actually can assemble are not only restricted by the rules of your universe, but also by the starting point and trajectory you actually chose to take […] You don’t have to deal with all possible combinations of building blocks, just the ones that are actually present in whatever “world” (a mix or “ensemble” of different objects) that you are simulating or observing.
Here’s Jaeger on the definition of the Assembly Index, the measure central to AT:
You can consider such a system a kind of a null model: given your basic building blocks and the assembly rules you defined, you can calculate how many steps you need to take before a specific composite object can arise. That minimal path to construct a composite object is called its assembly index.
Jaeger also points to the less helpful aspects of AT as defined by Cronin et al, including their confusing definition (for an evolutionary biologist) of selection.
The controversial 2023 Nature paper on AT is here.
Nehaveigur 