I just realized that the reason perpendicularities are called perpendicularities us because you're literally traveling on a path perpendendicular to our 3 dimensions.
Think about it, a straight line that's perpendicular to 2 other lines (that are not parallel) has to extend into the third dimension, entering another plane. So the perpendicularities are points where these perpendicular lines extending into a 4th dimension intersect- hence perpendicularities

















