whose value we shall designate by , marks a date of immense importance in the history of natural philosophy. The fact is that with Einstein’s discoveries such familiar absolutes as lengths, durations and simultaneities were all found to squirm and vary in magnitude when we passed from one Galilean system to another; that is, when we changed the constant magnitude of the relative velocity existing between ourselves as observers and the events observed. On the other hand, here at last was an invariant magnitude , representing the square of the spatial distance covered by a body in any Galilean frame, minus times the square of the duration required for this performance (the duration being measured, of course, by the standard of time of the same frame). It mattered not whether we were situated in this frame or in that one; in every case, if had a definite value when referred to one frame, it still maintained the same value when referred to any other frame. Obviously, we were in the presence of something which, contrary to a distance in space or a duration in time, transcended the idiosyncrasies of our variable points of view. This was the first inkling we had in Einstein’s theory of the existence of a common absolute world underlying the relativity of physical space and time. Minkowski immediately recognised in the mathematical form of this invariant the expression of the square of a distance in a four-dimensional continuum. This distance was termed the Einsteinian interval, or, more simply, the interval. The invariance of all such distances implied the absolute character of the metric relations of this four-dimensional continuum, regardless of our motion, and thereby implied the absolute nature of the continuum itself. The continuum was neither space nor time, but it pertained to both, since a distance between two of its points could be split up into space and time distances in various ways, just as a distance in ordinary space can be split up into length, breadth and height, also in various ways. For these reasons it was called Space-Time, and the interval thus became synonymous with the distance between two points in space-time. [Pg 196] And here certain aspects of the problem must be noted. In the first place, it may appear strange that measurements with clocks can be co-ordinated with measurements with rods or scales. This difficulty, however, need not arrest us; for although is a time which can only be measured with a clock, yet , being the product of a velocity by a time, is a spatial length since it represents the spatial distance covered by light in the time . For this reason we may consider our four-dimensional continuum to possess the qualifications of an extensional space.