The fourth dimension

260 THE FOURTH DIMENSION

intuition of the soul? Can we by the presentation of these hypothetical forms, that are the subject of our present discussion, wake ourselves up to higher intuitions ? And can we explain the world around by a motion that we only know by our souls ?

Apart from all speculation, however, it seems to me that the interest of these four-dimensional shapes and motions is sufficient reason for studying them, and that they are the way by which we can grow into a fuller apprehension of the world as a concrete whole.

Space Names.

If the words written in the squares drawn in fig. 1 are used as the names of the squares in the positions in which they are placed, it is evident that a combination of these names will denote a figure composed of the designated squares. It is found to be most convenient to take as the initial square that marked with an asterisk, so that the directions of progression are towards the observer and to his right. The directions of progression, however, are arbitrary, and can be chosen at will.

Thus et, at, it, an, al will denote a figure in the form of a cross composed of five squares.

Here, by means of the double sequence, ¢,@,7 and m,7,/, it is possible to name a limited collection of space elements.

The system can obviously be extended by using letter sequences of more members.

But, without introducing such a complexity, the principles of a space language can be exhibited, and a nomenclature obtained adequate to all the considerations of the preceding pages.