A Primer of Higher Space (The Fourth Dimension)

its three dimensions. This is clear, even axiomatic, and the case must be the same if space has more than three dimensions. Whatever the number of dimensions in space, everything must have that number of dimensions, too. If there are more than three dimensions in space and we perceive only three in the objects around us, then we are forced to the conclusion that we perceive things only partially. All the dimensions beyond the third are for us nonexistent, but our lack of perceptive power does not in any way affect the objects themselves.

Notwithstanding this self-evident fact (that the number of dimensions in an object must be co-equal with the number of dimensions in space itself), there is a sense in which such expressions as a "one-dimensional" or a "two-dimensional" body have quite sufficient validity. They may be used to designate, first, a cross-section, limit, or boundary—the edge of a razor would be one-dimensional in this sense, and the surface of a table two-dimensional—and second, to designate something in which the given number of dimensions is patent, and any dimensions beyond these latent; or in which the constituent particles have, or appear to have, free movement or power of transmission in the designated number of dimensions, and restricted movement in all directions above and beyond that number. Understood in this way, a nerve, a hair, the stem of a leaf—the trunk of a tree, even—might properly be called one-dimensional; a leaf, a handkerchief, a piece of paper, two-dimensional; and any solid of our space three-dimensional. For there is a perfectly appreciable difference, based upon extension in space, between