A Primer of Higher Space (The Fourth Dimension)

the mathematician as are the elements of the cube whence it is derived.*

Again return, and for the third time. Arithmetically, it is possible to raise a number to any given power; that is, to multiply it by itself any number of times. There is a known spatial correlative of the second power of a number, the square; and of its third power, the cube; but we have no direct or sensory knowledge of that analogous form, the tesseract, which would correspond to the fourth power of a number, nor of the four-dimensional space in which alone its development would be possible. With the geometry of such a space, mathematicians have long been familiar, but is there such a space—is there any body for this mathematical soul?

THE REASONABLENESS OF THE HIGHER SPACE HYPOTHESIS

Before dismissing such an idea as absurd, let it be remembered that the mathematician is today the scout of science. Of this fact, the discovery of Neptune is a classic example. A French mathematician computed and announced the place of a hypothetical body exterior to Uranus. A German astronomer pointed his telescope toward the designated quarter of the heavens and found an object with a planetary disc not plotted on the map of stars. It was the sought-for world. May not the preoccupation of mathematicians with problems involving a hypothetical space of four dimensions anticipate the discovery and conquest, not of a new world, but of a new space?

*The hyper-cube has 16 corners, 32 edges, 24 square faces, and 8 bounding cubes.