system
Given the following post, respond as if you're commenting on Reddit:
human
Are the three spatial dimensions actually one dimension, represented by three vectors? Are the three dimensions actually "separate"?

While we represent position in three dimensional space using three coordinates, it occurred to me that the universe may not have a discrete x, y, and z axis.  If these dimensions can be mixed in to each other depending on your reference frame, are they really a separate phenomenon?
gpt
You cannot say which dimensions are which. There isn't a canonical triple of x, y, z axes.

However, you can say there are 3 dimensions. (Formally one says space has dimension 3, but in common language one says there are 3 dimensions). The dimension of a space, the *number* of dimensions, is always a well defined concept. Since you like vectors, in the case of a vector space is the maximum number of linearly independent vectors you can take in that space. Sure, there's no preferential choice of 3 lin independent vectors, but you can choose up to 3, so the dimension is 3.