Various discussions in various places bring back to mind this thread from early this fall, prompting me to make a try at continuing it. Here’s a series of blog posts where I kept track of a few points along the way:
- Differential Logic, Dynamic Systems, Tangent Functors • 1
- Differential Logic, Dynamic Systems, Tangent Functors • Discussion 1
- Differential Logic, Dynamic Systems, Tangent Functors • Discussion 2
Another thing to keep in mind here is the difference between General Systems Theory, following on Bertalanffy et al., and what is known as Dynamical Systems Theory (DST) or Mathematical Systems Theory (MST). GST spends a lot of time studying part-whole hierarchies while DST/MST deals with the state space of a system and the possible trajectories of the system through it.
Category theory is especially useful in the latter application, abstracting or generalizing as it does the concepts of mathematical objects, functions, and transformations.
For my part I have come to take the DST/MST approach as more fundamental since it starts with fewer assumptions about the anatomy or architecture of the as-yet hypothetical agent, making it one of the first and continuing tasks of the agent to discover its own boundaries, potentials, and structures.
- Differential Logic • Primer
- Differential Logic • Introduction
- Differential Logic and Dynamic Systems