The fourth dimension

CHAPTER VII THE EVIDENCES FOR A FOURTH DIMENSION

THE method necessarily to be employed in the search for the evidences of a fourth dimension, consists primarily in the formation of the conceptions of four-dimensional shapes and motions. When we are in possession of these it is possible to call in the aid of observation, without them we may have been all our lives in the familiar presence of a four-dimensional phenomenon without ever recognising its nature.

To take one of the conceptions we have already formed, the turning of a real thing into its mirror image would be an occurrence which it would be hard to explain, except on the assumption of a fourth dimension.

We know of no such turning. But there exist a multitude of forms which show a certain relation to a plane, a relation of symmetry, which indicates more than an accidental juxtaposition of parts. In organic life the universal type is of right- and left-handed symmetry, there is a plane on each side of which the parts correspond. Now we have seen that in four dimensions a plane takes the place ofa line in three dimensions. In our space, rotation about an axis is the type of rotation, and the origin of bodies symmetrical about a line as the earth is symmetrical about an axis can easily be explained. But where there issymmetry about a plane no simple physical motion, such as we

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