Interesting thought of describing Nothing as non-dimensional. A famous theory "M-theory" also known as string theory predicts that there may exist more spatial dimensions than the 3 observable dimensions (x, y and z) does that mean they're not there? They may exist, it is just that humans are not capable of pursuing them or maybe we are not evolved enough to observe them yet!

Similarly, dimensions of thoughts, feelings and beliefs which are mostly part of consciousness of the brain which we can’t describe mathematically or scientifically yet in full confidence may just be a dimension existing which we aren’t capable of pursuing doesn’t necessarily mean they don’t exist.

It is the curiosity to understand these dimensions of existence make me believe we will crack these mysteries of the Universe sooner or later :)