FOUR DIMENSIONAL VISTAS
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 aesthetics 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 aeon. 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.