How is "nothing" being represented in the brain?

These have some interesting links embedded in the articles.

Numbers in animals in general:
https://animalstudiesrepository.org/numera/

http://archive.wilsonquarterly.com/in-essence/animal-numeracy

http://www.cccf-fcsge.ca/wp-content/uploads/RS_95-e.pdf

I understand that you are asking about the coding of space but I think that this is closely related. Without special learned mental tricks numeracy seems to depend on perceived size and some concept of grouping. I think that the mental process for concepts involves chunks and relations. The details are not set in stone in my mind and I have gone back and forth on the details as I read different research papers.
The zoo of different representations types (border, head direction, vector & distance, path alignment, place) in the EC/HC seems to grow daily. These are just for the “easy” things you can monitor as a critter moves about. Monkey studies show that relationships of objects on viewed screens seem to call up some sort of representations. I can see that a spatial relationship tied to “air” is a very possible way that this is done. From the links above many animals do know how to code for “nothing.”