A Theory of the Mechanism of Survival: The Fourth Dimension and Its Applications

by W. Whately Smith

"Two adjacent portions of space, of any dimensionality, are separated by a space of the next lower dimensionality."

The portions AB and BC of the line AC are separated by the point B. (Fig. 11.) The portions ABEF and BCDE of the fig. ACDF are separated by the line EB. The portions ABEFGHIM and BCDEMIKL of the solid ACDFGHKL are separated by the surface BIME.

Fig. 11

Similarly we must suppose that any two adjacent portions of four space are separated by a three space figure.

Or, again, to alter it slightly, "any space is no more than a boundary between two adjacent portions of the next higher space." Whence it follows that the whole of our three space is but the boundary between two adjacent portions of four space.

(5)

"A tesseract, which is the four-dimensional analogue of the cube, is bounded by Eight cubes. It has Twenty-four plane square faces, Thirty-two linear edges, and Sixteen corner points."

This may at first sight seem difficult to grasp.