Our brains can work with verbal paths as well as visualization. It does not mean we have to stay with the words or visuals, especially forever. These are just to help. Importantly, without knowing where we are about faculties, activities, or states, we could be only repeating formulas after other people.
We can envision our grammar journey as traveling in an abstract dimension. However, we can think about the Cartesian coordinates, just as in our natural, three-dimensional realities.