,
,
, preserves its form for all systems moving uniformly and rectilinearly with respect to one another.
[19]A continuous manifold may be defined as any continuum of elements such that a single element is defined by
continuously variable magnitudes.
Interpreted geometrically this means that the transformation is conformal in imaginary space of four dimensions. Moreover, the time-co-ordinate enters into physical laws in exactly the same way as the three space-co-ordinates, i.e. we may regard time spatially as a fourth dimension of space. This has been very beautifully worked out by Minkowski, whose premature loss is deeply to be regretted. It may be fitting here to recall some remarks of Bergson in his "Time and Free Will." He there states that "time is the medium in which conscious states form discrete series: this time is nothing but space, and pure duration is something different." Again, "what we call measuring time is nothing but counting simultaneities; owing to the fact that our consciousness has organized the oscillations of a pendulum as a whole in memory, they are first preserved and afterwards disposed in a series: in a word, we create for them a fourth dimension of space, which we call homogeneous time, and which enables the movement of the pendulum, although taking place at one spot, to be continually set in juxtaposition to itself. Duration thus assumes the illusory form of a homogeneous medium and the connecting link between these two terms, space and duration, is simultaneity, which might be defined as the intersection of time and space." Minkowski calls the space-time-manifold "world" and each point (event) "world-point."