force-field which appertains to levity as the usual central one does to
gravity, we are compelled to revise our conception of space. For in a
space of a kind we are accustomed to conceive, that is, the
three-dimensional, Euclidean space, the existence of such a field with
its characteristic of increasing in strength in the outward direction
is a paradox, contrary to mathematical logic.

This task, which in view of our further observations of the actions of
the levity-gravity polarity in nature we must now tackle, is, however,
by no means insoluble. For in modern mathematics thought-forms are
already present which make it possible to develop a space-concept
adequate to levity. As referred to in Chapter I, it was Rudolf Steiner
who first pointed to the significance in this respect of the branch of
modern mathematics known as Projective Geometry. He showed that
Projective Geometry, if rightly used, carries over the mind from the
customary abstract to a new concrete treatment of mathematical
concepts. The following example will serve to explain, to start with,
what we mean by saying that mathematics has hitherto been used
abstractly.

One of the reasons why the world-picture developed by Einstein in his
Theory of Relativity deserves to be acknowledged as a step forward in
comparison with the picture drawn by classical physics, lies in the
fact that the old conception of three-dimensional space as a kind of
'cosmic container', extending in all directions into infinity and
filled, as it were, with the content of the physical universe, is
replaced by a conception in which the structure of space results from
the laws interrelating this content. Our further discussion will show
that this indeed is the way along which, to-day, mathematical thought
must move in order to cope with universal reality.