CHAPTER IX
SUMMARY AND CONCLUSION
I will bring this work to a close by a brief recapitulation of its more salient points.
A dimension is defined as "an independent direction in space." A flat surface is two-dimensional and the space we know is three-dimensional. The direction of the fourth dimension must be at right angles to every direction which can be drawn in our space and four-dimensional space is such that through any point in it, four, and only four, lines can be drawn mutually at right angles.
From every point in our space a line can be drawn running off in the direction of four space.
Consequently every point in our space is absolutely accessible from the direction of the fourth dimension.
The best way of drawing conclusions as to the properties of four space is by means of the analogy of the two-dimensional world; since four space is to three space as the latter is to two space.
The fact that we cannot perceive four space, or picture its nature to ourselves, is no proof that it is non-existent.