and
. Two such durations necessarily intersect and also can neither completely extend over the other.
These diagrams are crude illustrations of some properties of durations and are in many respects misleading as the sequel will show.
The set of moments which inhere in a duration are completely characteristic of that duration, and vice versa. A moment is to be conceived as an abstract of all nature at an instant. No abstractive element can cover a moment except that moment itself. A moment is a route of approximation to all nature which has lost its (essential) temporal extension; thus it is nature under the aspect of a three-dimensional instantaneous space. This is the ideal to which we endeavour to approximate in our exact observations.
[34. Parallelism and Time-Systems]. 34.1 If the Newtonian theory of relativity were true, no pair of durations would lack durations extending over both of them, namely larger durations including both the given durations. But on the electromagnetic theory of relativity this is not necessarily the case, namely some pairs of durations are extended over by a family of durations and some are not. We shall adopt the electromagnetic theory of relativity.
A pair of durations both of which are parts of the same duration are called 'parallel'; and also a pair of moments such that there are durations in which both inhere are called 'parallel.'
Parallelism has the usual properties of transitiveness, symmetry and reflexiveness. Also two durations which do not intersect are parallel; and parallel moments which are not identical never intersect. If two parallel durations intersect there is a duration which is their complete intersection, but there are no durations among the common parts of two durations which are not parallel. Two moments which are not parallel necessarily intersect.
34.2 Two durations which are parallel to the same duration are parallel to each other; thus it is evident that each absolute antiprime and each moment must be composed of parallel durations.