A minimal event occupies a finite region in space-time. Let us take
time alone for purposes of illustration. The event in question may
overlap in time with each of two others, although the first of these
others wholly precedes the second; for example, you may hear a long
note on the violin while you hear two short notes on the piano. (It
is not necessary to suppose that these are really minimal events; I
merely want to illustrate what is meant.) I assume that every event
is contemporaneous with events that are not contemporaneous with each
other; this is what is meant by saying that every event lasts for a
finite time, as the reader can easily convince himself if he remembers
that time is wholly relational. If we look away from the world of
physics for a moment, and confine ourselves to the world of one man’s
experience, we can easily define an “instant” in his life. It will be
a group of events, all belonging to his experience, and having the
following two properties: (1) any two of the events overlap; (2) no
event outside the group overlaps with every member of the group. By
a slightly more complicated but essentially similar method, we can
define a point-instant in space-time as a group of events having two
properties analogous to those used just now in defining an “instant”
in one biography.[13] Thus the “points” (or point-instants) that
the mathematician needs are not simple, but are structures composed
of events, made up for the convenience of the mathematician. There
will be many “points” of which a given minimal event is a member;
all these together make up the region of space-time occupied by that
event. Space-time order, as well as space-time points, results from the
relations between events.
[13] See _The Analysis of Matter_, by the present author,
chap. xxviii.
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