“Visualizing just about anything” isn’t helpful if you want to learn from the visualization, though. (c.f the /r/dataisbeautiful subreddit nowadays: https://www.reddit.com/r/dataisbeautiful/top/?sort=top&t=mon...)

That’s not to say that a purely artistic data visualization has no value, but it’s not academic. (I admit I am guilty of that at times)

Data visualization is only a part of it. I'm talking about visualizing concepts.

Structure is data

I feel like visualizations rely too much on the existence of a meaningful isomorphism. That is, once a problem is visualized effectively it becomes trivial and though applicable to future similar problems the isomorphism itself is too domain specific to be generalized. It feels like trying to find an analogy that will help you find all future analogies.

I do agree with this sentiment very much but at the same time I do feel like no one has really given it a good shake.

Isn't that what category theory is about, on the meta level, and in the result in case of specific isomorphisms, too?

edit: at that I still have John C. Baez, Mike Stay - "Physics, Topology, Logic and Computation: A Rosetta Stone" on my reading list https://arxiv.org/abs/0903.0340