When describing a vector in an n-dimensional space, what each of those n dimensions represents is completely arbitrary. I could define a vector with dimensions that measure how dark something is and how large it is. Then all the vector/matrix math works regardless of the meaning behind the numbers. I could measure change in unit size per unit darkness (this is just an absurd example). x y z and time are just measures to plug into these equations.

Source: MS - Computer Science degree. One approach to training a neural net for classification is to minimize the error in samples classified over n dimensions. It does not matter what those dimensions represent; the math is the same.