Again nonsensical body-experience argument. Do you need to see 11 dimensional world in order to invent math to deal with string theory? Do physicist see those extra dimensions in their eyes?
11 dimensional vector calculus is a pretty clear example of recogniting generality between 1, 2 and 3 dimensions we can experience, and extending it to an arbitrary number.
While humans, in their mind, do construct things they did not experience, we develop tools to do that based on what we do (even things like axiom of parallelism: we experience "intersections" or lack of them, so we can ask ourselves "what if two parallel lines do intersect?").
Mathematics has really become abstract in the last 2 centuries, and was pretty tied to physical reality up to that point.
And you are required to see 11 dimension to stand for your body experienceism. You are not allowed to extend linear algebra from 3D to arbitrary dimensions.