*

We know from our previous studies that the concept of polarity is not
exhausted by conceiving the world as being constituted by polarities of
one order only. Besides primary polarities, there are secondary ones,
the outcome of interaction between the primary poles. Having conceived
of Point and Plane as a geometrical polarity of the first order, we
have therefore to ask what formative elements there are in geometry
which represent the corresponding polarity of the second order. The
following considerations will show that these are the radius, which
arises from the point becoming related to the plane, and the
spherically bent surface (for which we have no other name than that
again of the sphere), arising from the plane becoming related to the
point.

In Euclidean geometry the sphere is defined as 'the locus of all points
which are equidistant from a given point'. To define the sphere in this
way is in accord with our post-natal, gravity-bound consciousness. For
in this state our mind can do no more than envisage the surface of the
sphere point by point from its centre and recognize the equal distance
of all these points from the centre. Seen thus, the sphere arises as
the sum-total of the end-points of all the straight lines of equal
length which emerge from the centre-point in all directions. Fig. 8
indicates this schematically. Here the radius, a straight line, is
clearly the determining factor.

We now move to the other pole of the primary polarity, that is to the
plane, and let the sphere arise by imagining the plane approaching an
infinitely distant point evenly from all sides. We view the process