March 25, 2025
Today, I was the test subject of an exercise to clearly explain categorical systems theory and double categorical systems theory. I was presented with a single clause and could "double click" any phrase, that is, ask a question regarding any phrase to try and understand what was going on.
It was super useful and I started of by asking definition-type questions and then later asking for clarity on the assumptions that I'd made as the activity went on. I think learning how to think, write, and talk clearly about your work is very important. In fact, it's at the root of building knowledge and disseminating it—what any researcher aims to do.
The following is the outcome of the activity: a summary of the concepts I'd learned.
We make simulations to represent complex systems. Representing systems simulationally is useful because we can interact with them in a lower-dimensional way. Simply sharing an exact-copy replica doesn't mean that you're sharing the right things. Categorical systems theory is a way of simulating systems with grammar. This means that if I know the grammar I can 1) rebuild the original state of the system (which is valuable to be able to do) from the lower-dim model, and 2) can understand any system that uses the grammar. Just like in natural language, you can combine thoughts into new ideas, you can do the same thing with models and thereby build new systems and worlds (which is great).
CST is a theory with two variants: one is operadic, where you model a system by capturing the whole state and can show how the state is different by looking at the graphical differences in the different captures; the second is procedural, where you model a system by capturing the transformations of the objects within it. These two variants convey different information, and each would reconstruct the original state differently.
DCST unifies the two variants into a harmonized grammar that can generalize to more simulations and helps us reconstruct original states with more confidence (as there's a single grammar that we could add to a manual to then refer to).