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THE MEANING OF FOUR-DIMENSIONAL SPACE.

The main line of thought developed in these pages has no claims to originality. Professor Zöllner of Leipsic was an ardent exponent of the theory in the "seventies" and some authors hold that even the ancient writings of the East contain attempts to express Four-Dimensional concepts.

Whether this is actually so is open to doubt but it must be remembered that in the days when these writings were produced mathematical knowledge was itself in its infancy and that there was, therefore, no terminology available in which the Higher Space concepts could be suitably expressed even supposing that the ancient philosophers had them in mind.

It is only through accumulated knowledge, especially the work of Gauss, Lobatschewsky, Bolyai, Riemann, and others that modern mathematicians are able to deal easily with space of more than three dimensions.

It may be noted that Kant says:

"If it be possible that there are developments of other dimensions of space, it is very probable that God has somewhere produced them. For His works have all the grandeur and glory that can be comprised."