rinsic character. Accordingly we can think of rects and levels as
merely loci of event-particles. In so doing we are also cutting out
those abstractive elements which cover sets of event-particles, without
these elements being event-particles themselves. There are classes of
these abstractive elements which are of great importance. I will
consider them later on in this and in other lectures. Meanwhile we will
ignore them. Also I will always speak of 'event-particles' in preference
to 'puncts,' the latter being an artificial word for which I have no
great affection.

Parallelism among rects and levels is now explicable.

Consider the instantaneous space belonging to a moment A, and let A
belong to the temporal series of moments which I will call {alpha}.
Consider any other temporal series of moments which I will call {beta}.
The moments of {beta} do not intersect each other and they intersect the
moment A in a family of levels. None of these levels can intersect, and
they form a family of parallel instantaneous planes in the instantaneous
space of moment A. Thus the parallelism of moments in a temporal series
begets the parallelism of levels in an instantaneous space, and
thence--as it is easy to see--the parallelism of rects. Accordingly the
Euclidean property of space arises from the parabolic property of time.
It may be that there is reason to adopt a hyperbolic theory of time and
a corresponding hyperbolic theory of space. Such a theory has not been
worked out, so it is not possible to judge as to the character of the
evidence which could be brought forward in its favour.

The theory of order in an instantaneous space is immediately derived
from time-order. For consider the space of a moment M. Let {alpha} be
the name of a time-system to which M does not belong. Let A_1, A_2, A_3
etc. be moments of {alpha} in the order of their occurrences. Then A_1,
A_2, A_3, etc. intersect M in parallel levels l_1, l_2, l_3, etc. Then
the relative order of the parallel levels in the space of M is the same
as the relative order of the corresponding moments in the time-system
{alpha}. Any rect in M which intersects all these levels in its set of
puncts, thereby receives for its puncts an order of position on it. So
spatial order is derivative from temporal order. Furthermore there are
alternative time-systems, but there is only one definite spatial order
in each instantaneous space. Accordingly the various modes of deriving
spatial