Whenever our discussions have turned to talking about dimensions, it’s pretty easy to derail them over the issue of nomenclature and definitions. This is probably because there’s a rather arbitrary explanation or understanding that has been agreed upon with regard to the use of certain words. As most experts already understand, dimensions can be different things (both conceptually and mathematically) depending on the application.
The way that it’s mathematically expressed, space actually comprises a set of three 2D planes, arranged orthogonally. In this usage, each individual “dimension” is actually a plane, or a set of two perpendicular directions, where each direction is also called a “dimension.” The x and y dimensions combine to form the xy-plane which is perpendicular (normal) to the z axis; it is the direction of the z axis and not the location of the z axis that is the thing which is perpendicular to the x direction and the y direction. For these reasons, it would be more meaningful (less confusing or less arbitrary) to specify our mathematical treatment of space as 2D3 rather than 3D. It’s the reason why our mathematical treatment of Euclidean 3-space has octants… 2x2x2=8.