I was writing it mathematically as I thought you would appreciate how your intuitive grasp of what n-dimensions is described mathematically.

The terminology (gibberish) I used is nothing more than a convenient but very precise shorthand for communicating abstractions. The reason these particular abstractions are given special names by mathematicians is that they occur over and over again. There is a lot of conceptual leverage to be gained if you are able to see the same patterns in seemingly unrelated problems.

As Poincaré put it, "Mathematics is the art of giving the same name to different things". I'd argue it's worth knowing some of those names.