> which seems to exists as a series of images and animations in my head, call it a "world" model perhaps
This is how most things are in my mental model of almost all higher-order concepts and subject areas. Mostly for math, but also for programming/electronics, biology, chemistry, history, etc.
The thing that usually stops me from forming this kind of picture is missing a fundamental concept, or not being able to conceptualize enough of them in my limited exposure to the subject.
The thing to realize is that this isn't a thing that just happens, it's something you can build yourself as you're learning something. Since the visuospatial parts of your brain are the most powerful, it can be an enormously useful thing to do to fit subjects together and reason about them.
Anecdotally, the "easiest" math/engineering classes I had in college were the ones with robust visual representations (control systems with the transfer function block diagrams and mechanism design with a simple graphical way to design linkages where we learned the math afterward).
This is how most things are in my mental model of almost all higher-order concepts and subject areas. Mostly for math, but also for programming/electronics, biology, chemistry, history, etc.
The thing that usually stops me from forming this kind of picture is missing a fundamental concept, or not being able to conceptualize enough of them in my limited exposure to the subject.
The thing to realize is that this isn't a thing that just happens, it's something you can build yourself as you're learning something. Since the visuospatial parts of your brain are the most powerful, it can be an enormously useful thing to do to fit subjects together and reason about them.
Anecdotally, the "easiest" math/engineering classes I had in college were the ones with robust visual representations (control systems with the transfer function block diagrams and mechanism design with a simple graphical way to design linkages where we learned the math afterward).