servers. It is this
possibility which makes the fundamental distinction between the new way
of conceiving the universe and the old way. The secret of understanding
relativity is to understand this. It is of no use rushing in with
picturesque paradoxes, such as 'Space caught bending,' if you have not
mastered this fundamental conception which underlies the whole theory.
When I say that it underlies the whole theory, I mean that in my opinion
it ought to underlie it, though I may confess some doubts as to how far
all expositions of the theory have really understood its implications
and its premises.

Our measurements when they are expressed in terms of an ideal accuracy
are measurements which express properties of the space-time manifold.
Now there are measurements of different sorts. You can measure lengths,
or angles, or areas, or volumes, or times. There are also other sorts of
measures such as measurements of intensity of illumination, but I will
disregard these for the moment and will confine attention to those
measurements which particularly interest us as being measurements of
space or of time. It is easy to see that four such measurements of the
proper characters are necessary to determine the position of an
event-particle in the space-time manifold in its relation to the rest of
the manifold. For example, in a rectangular field you start from one
corner at a given time, you measure a definite distance along one side,
you then strike out into the field at right angles, and then measure a
definite distance parallel to the other pair of sides, you then rise
vertically a definite height and take the time. At the point and at the
time which you thus reach there is occurring a definite instantaneous
point-flash of nature. In other words, your four measurements have
determined a definite event-particle belonging to the four-dimension
space-time manifold. These measurements have appeared to be very simple
to the land-surveyor and raise in his mind no philosophic difficulties.
But suppose there are beings on Mars sufficiently advanced in
scientific invention to be able to watch in detail the operations of
this survey on earth. Suppose that they construe the operations of the
English land-surveyors in reference to the space natural to a being on
Mars, namely a Martio-centric space in which that planet is fixed. The
earth is moving relatively to Mars and is rotating. To the beings on
Mars the operations, construed in this f