ashion, effect measurements of
the greatest complication. Furthermore, according to the relativistic
doctrine, the operation of time-measurement on earth will not correspond
quite exactly to any time-measurement on Mars.

I have discussed this example in order to make you realise that in
thinking of the possibilities of measurement in the space-time manifold,
we must not confine ourselves merely to those minor variations which
might seem natural to human beings on the earth. Let us make therefore
the general statement that four measurements, respectively of
independent types (such as measurements of lengths in three directions
and a time), can be found such that a definite event-particle is
determined by them in its relations to other parts of the manifold.

If (p_1, p_2, p_3, p_4) be a set of measurements of this system, then
the event-particle which is thus determined will be said to have p_1,
p_2, p_3, p_4 as its co-ordinates in this system of measurement. Suppose
that we name it the p-system of measurement. Then in the same p-system
by properly varying (p_1, p_2, p_3, p_4) every event-particle that has
been, or will be, or instantaneously is now, can be indicated.
Furthermore, according to any system of measurement that is natural to
us, three of the co-ordinates will be measurements of space and one will
be a measurement of time. Let us always take the last co-ordinate to
represent the time-measurement. Then we should naturally say that (p_1,
p_2, p_3) determined a point in space and that the event-particle
happened at that point at the time p_4. But we must not make the mistake
of thinking that there is a space in addition to the space-time
manifold. That manifold is all that there is for the determination of
the meaning of space and time. We have got to determine the meaning of a
space-point in terms of the event-particles of the four-dimensional
manifold. There is only one way to do this. Note that if we vary the
time and take times with the same three space co-ordinates, then the
event-particles, thus indicated, are all at the same point. But seeing
that there is nothing else except the event-particles, this can only
mean that the point (p_1, p_2, p_3) of the space in the p-system is
merely the collection of event-particles (p_1, p_2, p_3, [p_4]), where
p_4 is varied and (p_1, p_2, p_3) is kept fixed. It is rather
disconcerting to find that a point in space is not a simple entity; but
it is a conclusion which