Comment by ssalazar

I don't have a mathematically rigorous understanding of it but the number of dimensions is basically the number of freely varying inputs to the corresponding functional representation. In a 2d image, x position and y position are mapped to a color, e.g. I(x,y) = C. In a spectrogram, freq and time are mapped to a color (amplitude) e.g. S(f,t) = A. In neither case can you just pick an arbitrary color or amplitude and in general produce a singular x/y or f/t from that.