, he would find that wherever he stood, a certain mathematical expression (i.e.,
) representative of a length maintained the same invariant value. Something truly objective would have been discovered since, in contrast to visual angle and distance which varied with his position, here was a length which was an absolute since its value transcended his position. He would immediately attribute this absolute to the objective existence of a real rigid pole of length
standing at the point
. In short, the test of objectivity is invariance for all observers, and this illustration has enabled us to separate the absolute length
of the pole from the relative visual angle