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Updated: May 25, 2025
G. Cantor, and others, which look on our Euclidean space of three dimensions as a special case of the unintuitable yet thinkable analytic concept of a space of n dimensions.
From the latest results of the theory of relativity it is probable that our three-dimensional space is also approximately spherical, that is, that the laws of disposition of rigid bodies in it are not given by Euclidean geometry, but approximately by spherical geometry, if only we consider parts of space which are sufficiently great. Now this is the place where the reader's imagination boggles.
According to one view the development of population, together with the necessity for war which is inextricably mixed up with a developing population, cannot be effected without, as one champion of the doctrine is pleased to put it, "shattering both the structure of Euclidean space and the psychological laws upon which the existence of self-consciousness and human society are conditional."
At the middle of the forehead horizontally subdivide this upper quoin, and then you have two almost equal parts, which before were naturally divided by an internal wall of a thick tendinous substance. *Quoin is not a Euclidean term. It belongs to the pure nautical mathematics. I know not that it has been defined before.
Let us imagine a point S of our space, and a great number of small spheres, L', which can all be brought to coincide with one another. After having gained a vivid mental image of the geometrical behaviour of our L' spheres, let us assume that in our space there are no rigid bodies at all in the sense of Euclidean geometry, but only bodies having the behaviour of our L' spheres.
The first shall be what is called Euclidean geometry, but which is in the main the work of the Pythagorean school of thinkers and social reformers who flourished from the seventh to the fifth centuries B.C. This formed the greater part of the geometrical truth known to mankind until Descartes and the mathematicians recommenced the work in the seventeenth century.
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