What is the Fourth Dimension? A subtle transposition of precious essences from the earthly to the spiritual plane. We live in a world of three dimensions, the symbols of which are length, breadth, thickness. A species of triangular world, a prison for certain souls who see in the category of Time an escape from that other imperative, Space (however, not the Categorical Imperative of Kant and its acid moral convention). Helmholtz and many mathematicians employed the "n" dimension as a working hypothesis. It is useful in some analytical problems, but it is not apprehended by the grosser senses. Pascal, great thinker and mathematician, had his "Abyss"; it was his Fourth Dimension, and he never walked abroad without the consciousness of it at his side. This illusion or obsession was the result of a severe mental shock early in his life. Many of us are like the French philosopher. We have our "abyss," mystic or real. Mr. Bragdon quotes from the mathematician Bolyai, who in 1823 "declared with regard to Euclid's so-called axiom of parallels, 'I will draw two lines through a given point both of which will be parallel to a given line.'" Space, then, may be curved in another dimension. Mr. Bragdon believes that it is, though he does not attempt to prove it, as that would be impossible; but he gives his readers the chief points in the hypothesis. The "n" dimension may be employed as a lever to the imagination. Even revealed religion demands our faith, and imagination is the prime agent in the interpretation of the universe, according to the gospel of mystic mathematics.
Nature geometrises, said Emerson, and it is interesting to note the imagery of transcendentalism through the ages. It is invariably geometrical. Spheres, planes, cones, circles, spirals, tetragrams, pentagrams, ellipses, and what-not. A cubistic universe. Xenophanes said that God is a sphere. And then there are the geometrical patterns made by birds on the wing. Heaven in any religion is another sphere. Swedenborg offers a series of planes, many mansions for the soul at its various stages of existence. The Bible, the mystical teachings of Mother Church--why evoke familiar witnesses? We are hemmed in by riddles, and the magnificent and mysterious tumult of life asks for the eye of imagination, which is also the eye of faith. The cold fire and dark light of the mystics must not repel us by their strangeness. Not knowledge but perception is power, and the psychic is the sign-post of the future. What do all these words mean: matter, energy, spirit, cells, molecules, electrons, but the same old thing? I am a colony of cells, yet that fact does not get me closer to the core of the soul. What will? A fourth spatial dimension, answers Claude Bragdon. Truly a poetic concept.