Conceptually I understand phase space and it is indeed one of my favorite things. I don’t do the math but since I was a teenager, I’ve been fascinated by these “gravity” -type things where the center is never quite pinpointed, along with other metaphorical connections social and such.
My 10th grade vail deane report was on black holes and when I first heard about strange attractors in 1990 at Hampshire (recreationally as I didn’t take any math classes but I bent the ear of a professor or two in their off time), I could see the connection to the experience of gravity.
I know it’s a little different than phase but I’m thinking in terms of gravity’s center – visualizing it its shape changing depending on what’s around it and the things around it being changed by the changes in gravity and their relationship to one another.
I also find few-bodied systems in gravity fascinating… and that we can’t precisely predict the moon’s future positions even now, although our estimates are pretty close.