Now the question arises, What is the nature of this metrical field? Is it merely a name we are giving to the structure of space caused by matter? This view appears impossible, for space of itself, being a mere void, is not amenable to structure. Is the metrical field a direct emanation from matter, a rarefied form of matter? Or again is it a reality of a category differing from matter (call it the ether), which in the absence of matter would be amorphous, and which could only be forced into a structure by the influences due to matter and transmitted from place to place through the ethereal substance? In this case we should again be led to the view that what we commonly call the structure or geometry of real space reduces to the structure of the matter-moulded ether-filling space. Riemann’s exceedingly speculative ideas on the subject of the metrical field were practically ignored in his day, save by the English mathematician Clifford, who translated Riemann’s works, prefacing them to his own discovery of the non-Euclidean Clifford space. Clifford realised the potential importance of the new ideas and suggested that matter itself might be accounted for in terms of these local variations of the non-Euclideanism of space, thus inverting in a certain sense Riemann’s ideas. But in Clifford’s day this belief was mathematically untenable. Furthermore, the physical exploration of space, even in the interior of liquids, seemed to yield unvarying Euclideanism. And here the remarkable irony of the whole situation must be noted. Although experimenters had utilised the most refined apparatus for detecting a possible non-Euclideanism of space and had failed in their efforts, it was reserved for the theoretical investigator Einstein, by a stupendous effort of rational thought, based on a few flimsy empirical clues, to unravel the mystery and to lead Riemann’s ideas to victory.[16] Nor were Clifford’s hopes disappointed, for the varying non-Euclideanism of the continuum was to reveal the mysterious secret of gravitation, and perhaps also of matter, motion and electricity. [Pg 59]