Such was the
essence of the difficulty with which we were confronted in Section
23.
But the considerations of Sections 25 and 26 show us the way to
surmount this difficulty. We refer the fourdimensional space-time
continuum in an arbitrary manner to Gauss co-ordinates. We assign to
every point of the continuum (event) four numbers, x[1], x[2], x[3],
x[4] (co-ordinates), which have not the least direct physical
significance, but only serve the purpose of numbering the points of
the continuum in a definite but arbitrary manner. This arrangement
does not even need to be of such a kind that we must regard x[1],
x[2], x[3], as "space" co-ordinates and x[4], as a " time "
co-ordinate.
The reader may think that such a description of the world would be
quite inadequate. What does it mean to assign to an event the
particular co-ordinates x[1], x[2], x[3], x[4], if in themselves these
co-ordinates have no significance ? More careful consideration shows,
however, that this anxiety is unfounded. Let us consider, for
instance, a material point with any kind of motion. If this point had
only a momentary existence without duration, then it would to
described in space-time by a single system of values x[1], x[2], x[3],
x[4].
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