There's an unavoidable duality (An axis is definitionally perpendicular to the lines of constant value) The core of the problem is that the system talks about

There's an unavoidable duality (An axis is definitionally perpendicular to the lines of constant value) The core of the problem is that the system talks about "lines" too much. In regular math, we have axes, but we don't think much about a point being at the "intersection of the x=3 line and the y=5 line", it's just "horizontally 3 and vertically 5". But in GIS we visualize a full grid, with "lines of latitude" instead of "lateral deviation".