I'd be more interested to know whether there's a practical use of understanding it on this level. I wanted to learn about monads and wrote some smaller Java examples using streams and flatmap. You can see the benefit and understand how it's implemented very easily. However, the academic explanations and notations were not helpful and I'd argue made understanding the concept needlessly complicated.
I'm slowly developing a systematic framework for programming the human brain with foundations in category theory. I've gotten a lot of useful mileage out of what little I've learned about category theory. It contributes to my intuition about how to reprogram my brain. I'm convinced we'll be teaching it to children in the future, once the programming framework is better developed and understood.
What could be more practical than self-improvement?
I'll answer my own question: learning how to apply the same kinds of reasoning to improve how people interact.
I gave some examples in my comment at the bottom of this thread. If you're asking for specific ways I'm using CT in the context, it's mostly as a way to model my experiences and find bits of insight here & there, so specifics are a little hard to come by.
Heh...and as I typed that, I came by some:
The concept of opposite categories is surprisingly useful & gives me comfort when worrying about messing with my mind. If my brain is simply one big personalized category, then anything it can learn can be unlearned.
The concept CT constructions have duals is also really helpful. One thing it suggests to me is anything learned accidentally (and/or temporarily) can be learned intentionally. A specific way this works: synesthesia (cross-wiring of senses, eg. seeing colors in response to hearing music) occurring accidentally, synesthesia temporarily occurring from drugs, and intentionally learning synesthesia. Dualism is a predictive tool in this case.
A way dualism helps me explain some things I've experienced is it suggests mental mechanisms (such as the creation of very different identities beyond the core identity) can fire in functional & dysfunctional ways. I accidentally spawned second & third identities, one of whom is female. It happened through a joyful process, though, and not trauma. The dissociation used is fairly superficial and the goal of creating more is as a continuous process of integrating all of them into a core identity. CT also helps me think about our relationships & how I'm growing through them.
One last example would be the law of composition in CT: if there exists A->B (an arrow from A to B) and B->C, then there exists A->C. Specifically, there exists a way to get from one mental state A to mental state Z that goes through B->...->Y and by experiencing that path, we can learn to shorten it til we can go straight from A to Z. I went through a bit of a path to accidentally create the second identity. The third one was a bit more intentional & took less time to pull off.
If that doesn't answer your question, would you be willing to ask a more specific question in terms of what you'd like to hear examples of?
I really find it difficult as well, and I think it is a lot to do with the nomenclature that surrounds the field. Sometimes I feel it's almost kept obtuse on purpose.
The way I think about is to think of it is if "Design Patterns" helped show how to "engineer" software at the medium scale, category theory is a tool for helping us learn how to compose systems, and not just software.
I wish it were a little more approachable, but it seems like we are getting there.
There are people like Bartosz out there who really want to make it second nature.
THANKS! This is great. I watched the first 3 videos in the series and will finish the rest this week. I love his energy and his ability to explain this stuff.
