Hamlet, sometime Prince of Denmark, warned his friend that there were more things in heaven and earth than dreamed of in his philosophy. Now, both Hamlet and Horatio had absorbed the contemporary wisdom of Wittenberg. And let it be said in passing that their knowledge did not lag behind ours, metaphysically speaking. Nevertheless, Hamlet, if he had lived longer, might have said that no philosophy would ever solve the riddle of the sphinx; that we never know, only name, things. Noah is the supreme symbol of science, he the first namer of the animals in the ark. The world of sensation is our ark and we are one branch of the animal family. We come whence we know not and go where we shall never guess. Standing on this tiny Isle of Error we call the present, we think backward and live forward. Hamlet the sceptical would now demand something more tangible than the Grand Perhaps. My kingdom for a fulcrum! he might cry to Horatio—on which I may rest my lever and pry this too too solid earth up to the starry skies! What the implement? Religion? Remember Hamlet was a Catholic, too sensitive to send unshrived to hell's fire the soul of his uncle. Philosophy? Read Jules Laforgue's Hamlet and realise that if he were alive to-day the melancholy Prince might be a delicate scoffer at all fables. A Hamlet who had read Schopenhauer. What then the escape? We all need more elbow-room in the infinite. The answer is—the Fourth Dimension in Higher Space. Eureka!

After studying Saint Teresa, John of the Cross, Saint Ignatius, or the selections in Vaughan's Hours with the Mystics, even the doubting Thomas is forced to admit that here is no trace of rambling discourse, fugitive ideation, half-stammered enigmas; on the contrary, the true mystic abhors the cloudy, and his vision pierces with crystalline clearness the veil of the visible world. As literary style we find sharp contours and affirmations. Mysticism is not all cobweb lace and opal fire. Remember that we are not stressing the validity of either the vision or its consequent judgments; we only wish to emphasise the absence of muddy thinking in these writings. This quality of precision, allied to an eloquent, persuasive style, we encounter in Claude Bragdon's Four Dimensional Vistas. The author is an architect and has written much of his art and of projective ornament. (He was a Scammon lecturer at the Chicago Art Institute in 1915.) He is a mystic. He is also eminently practical. His contribution to Æsthetics in The Beautiful Necessity is suggestive, and on the purely technical side valuable. But Mr. Bragdon, being both a mathematician and a poet, does not stop at three-dimensional existence. Like the profound English mystic William Blake, he could ask: "How do you know but every bird that cuts the airy way is an immense world of delight, closed by your senses five?"

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.

He calls man a space-eater. Human ambition is to annihilate space. Wars are fought for space, and every step in knowledge is based upon its mastery. What miracles are wireless telegraphy, flying-machines, the Roentgen ray! Astronomy—what ghastly gulfs it shows us in space! Time and space were abolished as sense illusions by the worthy Bishop of Cloyne, George Berkeley; but as we are up to our eyes in quotidian life, which grows over and about us like grass, we cannot shake off the oppression. First thought, and then realised, these marvels are now accepted as matter of fact because mankind has been told the technique of them; as if any explanation can be more than nominal. We shall never know the real nature of the phenomena that crowd in on us from lust to dust. Not even that synthesis of the five senses, the sixth, or sex sense, with its evanescent ecstasy, cuts deeply into the darkness. There may be a seventh sense, a new dimension, intimations of which are setting advanced thinkers on fresh trails. But there is as yet no tangible proof. Philosophers, who, like some singers, bray their brainless convictions to a gaping auditory, ask of us much more credence, and little or no imagination. As that "old mole," working in the ground, gravitation, is defied by aeroplanes, then we should not despair of any hypothesis which permits us a peep through the partly opened door. Plato's cavern and the shadows. Who knows but in this universe there may be a crevice through which filters the light of another life? Emerson, who shed systems yet never organised one, hints at aerial perspectives. A flight through the sky with the sun bathing in the blue jolts one's conception of a rigid finite world. In such perilous altitudes I have enjoyed this experience and felt a liberation of the spirit which has no parallel; not even when listening to Bach or Beethoven or Chopin. Music, indeed, is the nearest approach to psychic freedom.

Mr. Bragdon approvingly quotes Goethe's expression "frozen music," applied to Gothic architecture. (Stendhal appropriated this phrase.) For us the flying buttress is aspiring, and the pointed arch is a fugue. Our author is rich in his analogies, and like Sir Thomas Browne sees "quincunxes" in everything; his particular "quincunx" being Higher Space. The precise patterns in our brain, like those of the ant, bee, and beaver, which enable us to perceive and build the universe (otherwise called innate ideas) are geometrical. Space is the first and final illusion. Time—which is not "a stuff both resistant and substantial," as Henri Bergson declares—is perhaps the Fourth Dimension in the guise of a sequence of states, and not grasped simultaneously, as is the idea of Space. That Time can shrink and expand, opium-eaters, who are not always totally drugged by their dreams, assure us. A second becomes an Æon. And space curvature? Is it any wonder that "Lewis Carroll," who wrote those extraordinary parables for little folk, Through the Looking-Glass and Alice in Wonderland, was a mathematician? A topsy-turvy world; it is even upside down as an optical image. The other side of good and evil may be around the corner. Eternity can lurk in a molecule too tiny to harbour Queen Mab. And we may all live to see the back of our own heads without peering in mirrors. That "astral trunk" once so fervently believed in may prove a reality; it is situated behind the ear and is a long tube that ascends to the planet Saturn, and by its aid we should be enabled to converse with spirits! The pineal gland is the seat of the soul, and miracles fence us in at every step. We fill our belly with the east wind of vain desires. We eat the air promise-crammed. This world is but a point in the universe, and our universe only one of an infinite series. There was no beginning, there is no end. Eternity is now; though death and the tax-gatherer never cease their importunings. All this Mr. Bragdon does not say, though he leans heavily on the arcana of the ancient wisdom. The truth is that the majority of humans are mentally considered vegetables, living in two dimensions. To keep us responsive to spiritual issues, as people were awaked in Swift's Laputa by flappers, is the service performed by such transcendentalists as C. Howard Hinton, author of The Fourth Dimension; Claude Bragdon and Cora Lenore Williams. Their thought is not new; it was hoary with age when the Greeks went to old Egypt for fresh learning; Noah conversed with his wives in the same terminology. But its application is novel, as are the personal nuances. The idea of a fourth spatial dimension may be likened to a fresh lens in the telescope or microscope of speculation. For the present writer the hypothesis is just one more incursion into the fairyland of metaphysics. Without fairies the heart grows old and dusty.

The seven arts are fairy-tales in fascinating shapes. As for the paradise problem, it is horribly sublime for me, this idea of an eternity to be spent in a place which, with its silver, gold, plush, and diamonds, seems like the dream of a retired pawnbroker. The Eternal Recurrence is more consoling. The only excuse for life is its brevity. Why, then, do we yearn for that unending corridor through which in processional rhythms we move, our shoulders bowed by the burden of our chimera—our ego? I confess that I prefer to watch on the edge of some vast promontory the swift approach of a dark sun rushing out from the primordial depths of interstellar spaces to the celestial assignation made at the beginning of Time for our little solar system, whose provinciality, remote from the populous path of the Milky Way, has hitherto escaped colliding with a segment of the infinite. Perhaps in that apocalyptic flare-up—surely a more cosmical and heroic death than stewing in greasy bliss—Higher Space may be manifested and Time and Tri-Dimensional Space be no more. The rest is silence.