Understanding the measurements was also difficult because the mathematical and physical concepts had not yet been developed – in particular, the concept of a vector field that associates a vector with each point in space. The Earth's field is generally represented by field lines that run from pole to pole; the field at any point is parallel to a field line but does not have to point at either pole. As late as the eighteenth century, however, a natural philosopher would believe that a magnet had to be pointing directly at something.