Four Dimensional Vistas by Claude Fayette Bragdon
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8 FOUR-DIMENSIONAL
VISTAS
by
Claude Bragdon
[Illustration]
New York
"_Perception has a destiny_."
_Emerson_.
INTRODUCTION
There are two notable emancipations of the mind from the tyranny of
mere appearances that have received scant attention save from
mathematicians and theoretical physicists.
In 1823 Bolyai 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." The drawing of these lines
led to the concept of the curvature of space, and this to the idea
of _higher_ space.
The recently developed Theory of Relativity has compelled the
revision of the time concept as used in classical physics. One
result of this has been to introduce the notion of _curved_ time.
These two ideas, of curved time and higher space, by their very
nature are bound to profoundly modify human thought. They loosen the
bonds within which advancing knowledge has increasingly labored,
they lighten the dark abysses of consciousness, they reconcile the
discoveries of Western workers with the inspirations of Eastern
dreamers; but best of all, they open vistas, they offer "glimpses
that may make us less forlorn."
CONTENTS
I. THE QUEST OF FREEDOM
The Undiscovered Country--Miracles--The Failure of Common Sense--The
Function of Science--Mathematics--Intuition--Our Sense of Space--The
Subjectivity of Space--The Need of an Enlarged Space-Concept.
II. THE DIMENSIONAL LADDER
Learning to Think in Terms of Spaces--From the Cosmos to the
Corpuscle--And Beyond--Evolution as Space-Conquest--Dimensional
Sequences--Man the Geometer--Higher, and Highest, Space.
III. PHYSICAL PHENOMENA
Looking for the Greater in the Less--Symmetry--Other Allied
Phenomena--Isomerism--The Orbital Motion of Spheres: Cell-Subdivision--
The Electric Current--The Greater Universe--A Hint from Astronomy--
Gravitation--The Ether of Space.
IV. TRANSCENDENTAL PHYSICS
Zoellner--Apparitions--Possession--Clairvoyance in Space--Clairvoyance
in Time--Pisgah Sights of Life's Pageant.
V. CURVED TIME
Time from the Standpoint of Experiment and of Conscious Experience--
Relativity--The Spoon-Man--The Orbital Movement of Time--Materiality
the Mirror of Consciousness--Periodicity.
VI. SLEEP AND DREAMS
Sleep--Dreams--Time in Dreams--The Eastern Teaching in regard to Sleep
and Dreams--Space in Dreams--The Phenomenon of Pause.
VII. THE NIGHT SIDE OF CONSCIOUSNESS
The Field of Psychic Research--Modifying the Past--Karma and
Reincarnation--Colonel De Rochas' Experiments.
VIII. THE EASTERN TEACHING
Oriental Physics and Metaphysics--The Self-Recovered Memory of past
Births--Release.
IX. THE MYSTICS
Hermes Trismegistus--The Page and the Press--The Ship and its
Captain--Direct Vision--Plato's Shadow-Watchers--Swedenborg--Man,
the Space-Eater--The Within and Without--Intuition and Reason--The
Coil of Life.
X. GENIUS
Immanence--Timelessness--Beyond Good and Evil: Beauty--The Daemonic--
"A Dream and a Forgetting"--The Play of Brahm.
XI. THE GIFT OF FREEDOM
Concept and Conduct--Selflessness--Humility--Solidarity--Live Openly--
Non-Resistance to Evil--The Immanent Divine.
FOUR-DIMENSIONAL VISTAS
I THE QUEST OF FREEDOM
THE UNDISCOVERED COUNTRY
Expectancy of freedom is the dominant note of to-day. Amid the crash
of armies and the clash of systems we await some liberating stroke
which shall release us from the old dreary thralldoms. As Nietzsche
says, "It would seem as though we had before us, as a reward for all
our toils, a country still undiscovered, the horizons of which no
one has yet seen, a beyond to every country and every refuge of the
ideal that man has ever known, a world so overflowing with beauty,
strangeness, doubt, terror and divinity, that both our curiosity and
our lust of possession are frantic with eagerness."
Should a name be demanded for this home of freedom, there are those
who would unhesitatingly call it _The Fourth Dimension of Space_.
For such readers as may be ignorant of the amazing content of this
seemingly meaningless phrase, any summary attempt at enlightenment
will lead only to deeper mystification. To the question, where and
what is the fourth dimension, the answer must be, it is here--in us,
and all about us--in a direction toward which we can never point
because at right angles to all the directions that we know. Our
space cannot contain it, because it contains our space. No walls
separate us from this demesne, not even the walls of our fleshly
prison; yet we may not enter, even though we are already "there." It
is the place of dreams, of living dead men: it is _At the Back of
the North Wind_ and _Behind the Looking Glass_.
So might one go on, piling figure upon figure and paradox upon
paradox, to little profit. The effective method is the ordered and
deliberate one; therefore the author asks of his reader the
endurance of his curiosity pending certain necessary preparations of
the mind.
MIRACLES
Could one of our aviators have landed in ancient Athens, doubtless
he would have been given a place in the Greek Pantheon, for the old
idea of a demigod was a man with wings. Why, then, does a flying man
so little amaze us? Because we know about engines, and the smell of
gasoline has dulled our sense of the sublime. The living voice of a
dead man leaves us unterrified if only we can be sure that it comes
from a phonograph; but let that voice speak to us out of vacancy and
we fall a prey to the same order of alarm that is felt by a savage
at the report of a gun that he has never seen.
This illustration very well defines the nature of a miracle: it is a
manifestation of power new to experience, and counter to the current
thought of the time, Miracles are therefore always in order, they
always happen. It is nothing that the sober facts of to-day are more
marvellous than the fictions of Baron Munchausen, so long as we
understand them: it is everything that phenomena are multiplying,
that we are unable to understand. This increasing pressure upon
consciousness _from a new direction_ has created a need to found
belief on something firmer than a bottomless gullibility of mind.
This book is aimed to meet that need by giving the mind the freedom
of new spaces; but before it can even begin to do so, the reader
must be brought to see the fallacy of attempting to measure the
limits of the possible by that faculty known as common sense. And by
common sense is meant, not the appeal to abstract reason, but to
concrete experience.
THE FAILURE OF COMMON SENSE
Common sense had scarce had its laugh at Bell, and its shout of
"I told you so!" at poor Langley, when lo! the telephone became the
world's nervous system, and aeroplanes began to multiply like summer
flies. To common sense the alchemist's dream of transmuting lead
into gold seems preposterous, yet in a hundred laboratories radium
is breaking down into helium, and the new chemistry bids fair to
turn the time-honored jeer at the alchemists completely upside down.
A wife whose mind was oriented in the new direction effectually
silenced her husband's ridicule of what he called her credulity by
reminding him that when wireless telegraphy was first suggested he
had exclaimed, "Ah, that, you know, is one of the things that is not
possible!" He was betrayed by his common sense.
The lessons such things teach us are summed up in the reply of Arago,
the great savant, to the wife of Daguerre. She asked him if he
thought her husband was losing his mind because he was trying to
make permanent the image in a mirror. Arago is said to have answered,
"He who, outside of pure mathematics, says a thing is impossible,
speaks without reason."
Common sense neither leads nor lags, but is ever limited to the
passing moment: the common knowledge of to-day was the mystery and
enchantment of the day before yesterday, and will be the mere
commonplace of the day after to-morrow. If common sense can so
little anticipate the ordinary and orderly advancement of human
knowledge, it is still less able to take that leap into the dark
which is demanded of it now. The course of wisdom is therefore to
place reliance upon reason and intuition, leaving to common sense
the task of guiding the routine affairs of life, and guiding these
alone.
THE FUNCTION OF SCIENCE
In enlisting the aid of reason in our quest for freedom, we shall be
following in the footsteps of mathematicians and theoretical
physicists. In their arduous and unflinching search after truth they
have attained to a conception of the background of phenomena of far
greater breadth and grandeur than that of the average religionist of
to-day. As a mathematician once remarked to a neo-theosophist,
"Your idea of the ether is a more material one than the materialist's
own." Science has, however, imposed upon itself its own limitations,
and in this connection these should be clearly understood.
Science is that knowledge which can be gained by exact observation
and correct thinking. If science makes use of any methods but these
it ceases to be itself. Science has therefore nothing to do with
morals: it gives the suicide his pistol, the surgeon his life-saving
lance, but neither admonishes nor judges them. It has nothing to do
with emotion: it exposes the chemistry of a tear, the mechanism of
laughter; but of sorrow and happiness it has naught to say. It has
nothing to do with beauty: it traces the movements of the stars, and
tells of their constitution; but the fact of their singing together,
and that "such harmony is in immortal souls," it leaves to poet and
philosopher. The timbre, loudness, pitch, of musical tones, is a
concern of science; but for this a Beethoven symphony is no better
than the latest ragtime air from the music halls. In brief, science
deals only with _phenomena_, and its gift to man is power over his
material environment.
MATHEMATICS
The gift of pure mathematics, on the other hand, is primarily to the
mind and spirit: the fact that man uses it to get himself out of his
physical predicaments is more or less by the way. Consider for a
moment this paradox. Mathematics, the very thing common sense swears
by and dotes on, contradicts common sense at every turn. Common
sense balks at the idea of _less than nothing_; yet the _minus_
quantity, which in one sense is less than nothing in that something
must be added to it to make it equal to nothing, is a concept
without which algebra would have to come to a full stop. Again, the
science of quaternions, or more generally, a vector analysis in
which the progress of electrical science is essentially involved,
embraces (explicitly or implicitly) the extensive use of _imaginary_
or _impossible_ quantities of the earlier algebraists. The very
words "imaginary" and "impossible" are eloquent of the defeat of
common sense in dealing with concepts with which it cannot
practically dispense, for even the negative or imaginary solutions
of imaginary quantities almost invariably have some physical
significance. A similar statement might also be made with regard to
_transcendental_ functions.
Mathematics, then, opens up ever new horizons, and its achievements
during the past one hundred years give to thought the very freedom
it seeks. But if science is dispassionate, mathematics is even more
austere and impersonal. It cares not for teeming worlds and hearts
insurgent, so long as in the pure clarity of space, relationships
exist. Indeed, it requires neither time nor space, number nor
quantity. As the mathematician approaches the limits already
achieved by study, the colder and thinner becomes the air and the
fewer the contacts with the affairs of every day. The Promethean
fire of pure mathematics is perhaps the greatest of all in man's
catalogue of gifts; but it is not most itself, but least so, when,
immersed in the manifoldness of phenomenal life, it is made to serve
purely utilitarian ends.
INTUITION
Common sense, immersed in the mere business of living, knows no more
about life than a fish knows about water. The play of reason upon
phenomena dissects life, and translates it in terms of inertia. The
pure logic of mathematics ignores life and disdains its limitations,
leading away into cold, free regions of its own. Now our desire for
freedom is not to vibrate in a vacuum, but to live more abundantly.
_Intuition_ deals with life directly, and introduces us into
life's own domain: it is related to reason as flame is related to
heat. All of the great discoveries in science, all of the great
solutions in mathematics, have been the result of a _flash_ of
intuition, after long brooding in the mind. _Intuition illumines_.
Intuition is therefore the light which must guide us into that
undiscovered country conceded by mathematics, questioned by science,
denied by common sense--_The Fourth Dimension of Space_.
OUR SENSE OF SPACE
Space has been defined as "room to move about." Let us accord to
this definition the utmost liberty of interpretation. Let us
conceive of space not alone as room to move ponderable bodies in,
but as room to think, to feel, to strike out in unimaginable
directions, to overtake felicities and knowledges unguessed by
experience and preposterous to common sense. Space is not measurable:
we attribute dimensionality to space because such is the method of
the mind; and that dimensionality we attribute to space is
progressive because progression is a law of the mind. The so-called
dimensions of space are to space itself as the steps that a climber
cuts in the face of a cliff are to the cliff itself. They are not
necessary to the cliff: they are necessary only to the climber.
Dimensionality is the mind's method of mounting to the idea of the
infinity of space. When we speak of the fourth dimension, what we
mean is the fourth stage in the apprehension of that infinity. We
might as legitimately speak of a fifth dimension, but the
profitlessness of any discussion of a fifth and higher stages lies
in the fact that they can be intelligently approached only through
the fourth, which is still largely unintelligible. The case is like
that of a man promised an increase of wages after he had worked a
month, who asks for his second month's pay before he is entitled to
the first.
THE SUBJECTIVITY OF SPACE
Without going deep into the doctrine of the ideality--that is, the
purely subjective reality--of space, it is easy to show that we have
arrived at our conception of a space of three dimensions by an
intellectual process. The sphere of the senses is two-dimensional:
except for the slight aid afforded by binocular vision, sight gives
us moving pictures _on a plane_, and touch contacts _surfaces_ only.
What circumstances, we may ask, have compelled our intellect to
conceive of _solid_ space? This question has been answered as follows:
"If a child contemplates his hand, he is conscious of its existence
in a double manner--in the first place by its tangibility, the
second by its image on the retina of his eye. By repeated groping
about and touching, the child knows by experience that his hand
retains the same form and extension through all the variations of
distance and position under which it is observed, notwithstanding
that the form and extension of the image on the retina constantly
change with the different position and distance of his hand in
respect to his eye. The problem is thus set to the child's
understanding: how to reconcile to his comprehension the apparently
contradictory facts of the _invariableness_ of the object together
with the _variableness_ of its appearance. This is only possible
within a space of three dimensions, in which, owing to perspective
distortions and changes, these variations of projection can be
reconciled with the constancy of the form of a body."
Thus we have come to the idea of a three-dimensional space in order
to overcome the apparent contradictoriness of facts of sensible
experience. Should we observe in three-dimensional space
contradictory facts our reason would be forced to reconcile these
contradictions, also, and if they could be reconciled by the idea of
a four-dimensional space our reason would accept this idea without
cavil. Furthermore, if from our childhood, phenomena had been of
daily occurrence requiring a space of four or more dimensions for an
explanation conformable to reason, we should feel ourselves native
to a space of four or more dimensions.
Poincare, the great French mathematician and physicist, arrived at
these same conclusions by another route. By a process of
mathematical reasoning of a sort too technical to be appropriately
given here, he discovers an order in which our categories range
themselves naturally, and which corresponds with the points of space;
and that this order presents itself in the form of what he calls a
"three circuit distribution board." "Thus the characteristic property
of space," he says, "that of having three dimensions, is only a
property of our distribution board, _a property residing, so to speak,
in human intelligence_." He concludes that a different association
of ideas would result in a different distribution board, and that
might be sufficient to endow space with a fourth dimension. He
concedes that there may be thinking beings, living in our world,
whose distribution board has four dimensions, and who do
consequently think in hyperspace.
THE NEED OF AN ENLARGED SPACE-CONCEPT
It is the contrariety in phenomena already referred to, that is
forcing advanced minds to entertain the idea of higher space.
Mathematical physicists have found that experimental contradictions
disappear if, instead of referring phenomena to a set of three space
axes and one time axis of reference, they be referred to a set of
four interchangeable axes involving four homogeneous co-ordinates.
In other words, _time_ is made the fourth dimension. Psychic
phenomena indicate that occasionally, in some individuals,
the will is capable of producing physical movements for whose
geometrico-mathematical definition a four-dimensional system of
co-ordinates is necessary. This is only another step along the road
which the human mind has always travelled: our conception of the
cosmos grows more complete and more just at the same time that it
recedes more and more beneath the surface of appearances.
Far from the Higher Space Hypothesis complicating thought, it
simplifies by synthesis and co-ordination in a manner analogous to
that by which plane geometry is simplified when solid geometry
becomes a subject of study. By immersing the mind in the idea of
many dimensions, we emancipate it from the idea of dimensionality.
But the mind moves most readily, as has been said, in ordered
sequence. Frankly submitting ourselves to this limitation, even
while recognizing it as such, let us learn such lessons from it as
we can, serving the illusions that master us until we have made them
our slaves.
II THE DIMENSIONAL LADDER
LEARNING TO THINK IN TERMS OF SPACES
The Reader who is willing to consider the Higher Space Hypothesis
seriously, who would discover, by its aid, new and profound truths
closely related to life and conduct, should first of all endeavor to
arouse in himself a new power of perception. This he will best
accomplish by learning to discern dimensional sequences, not alone
in geometry, but in the cosmos and in the natural world. By so doing
he may erect for himself a veritable Jacob's ladder,
"Pitched between Heaven and Charing Cross."
He should accustom himself to ascend it, step by step, dimension by
dimension. Then he will learn to trust Emerson's dictum, "Nature
geometrizes," even in regions where the senses fail him, and the mind
alone leads on. Much profitable amusement is to be gained by such
exercises as follow. They are in the nature of a running up and down
the scales in order to give strength and flexibility to a new set of
mental fingers. Learning to think in terms of spaces contributes to
our emancipation from the tyranny of space.
FROM THE COSMOS TO THE CORPUSCLE
By way of a beginning, proceed, by successive stages, from the
contemplation of the greatest thing conceivable to the contemplation
of the most minute, and note the space sequences revealed by this
shifting of the point of view.
The greatest thing we can form any conception of is the starry
firmament made familiar to the mind through the study of astronomy.
No limit to this vastitude has ever been assigned. Since the
beginning of recorded time, the earth, together with the other
planets and the sun, has been speeding through interstellar space at
the rate of 300,000,000 miles a year, without meeting or passing a
single star. A ray of light, travelling with a velocity so great as
to be scarcely measurable within the diameter of the earth's orbit,
takes years to reach even the nearest star, centuries to reach those
more distant. Viewed in relation to this universe of suns, our
particular sun and all its satellites--of which the earth is
one--shrinks to a point (a _physical_ point, so to speak--not
geometrical one).
The mind recoils from these immensities: let us forsake them, then,
for more familiar spaces, and consider the earth in its relation to
the sun. Our planet appears as a _moving_ point, tracing out a
_line_--a _one-space_--its path around the sun. Now let us remove
ourselves in imagination only far enough from the earth for human
beings thereon to appear as minute moving things, in the semblance,
let us say, of insects infesting an apple. It is clear that from
this point of view these beings have a freedom of movement in their
"space" (the surface of the earth), of which the larger unit is not
possessed; for while the earth itself can follow only a _line_, its
inhabitants are free to move in the two dimensions of the surface of
the earth.
Abandoning our last coign of vantage, let us descend in imagination
and mingle familiarly among men. We now perceive that these
creatures which from a distance appeared as though flat upon the
earth's surface, are in reality erect at right angles to its plane,
and that they are endowed with the power to move their members in
_three dimensions_. Indeed, man's ability to traverse the surface
of the earth is wholly dependent upon his power of three-dimensional
movement. Observe that with each transfer of our attention from
greater units to smaller, we appear to be dealing with a power of
movement in an additional dimension.
Looking now in thought not _at_ the body of man, but _within_ it, we
apprehend an ordered universe immensely vast in proportion to that
physical ultimate we name the electron, as is the firmament immensely
vast in proportion to a single star. It has been suggested that in
the infinitely minute of organic bodies there is a power of movement
in a _fourth_ dimension. If so, such four-dimensional movement may
be the proximate cause of the phenomenon of _growth_--of those
chemical changes and renewals whereby an organism is enabled to
expand in three-dimensional space, just as by a three-dimensional
power of movement (the act of walking) man is able to traverse his
two-dimensional space--the surface of the earth.
--AND BEYOND
Proceed still further. Behind such organic change--assumed to be
four-dimensional--there is the determination of some _will-to-live_,
which manifests itself to consciousness as thought and as desire.
Into these the idea of space does not enter: we think of them as in
_time_. But if there are developments of other dimensions of space,
thought and emotion may themselves be discovered to have space
relations; that is, they may find expression in the forms of _higher_
spaces. Thus is opened up one of those rich vistas in which the
subject of the fourth dimension abounds, but into which we
can only glance in passing. If there are such higher-dimensional
_thought-forms_, our normal consciousness, limited to a world of
three dimensions, can apprehend only their three-dimensional aspects,
and these not simultaneously, but successively--that is, in _time_.
According to this view, any unified series of _actions_--for example,
the life of an individual, or of a group--would represent the
straining, so to speak, of a thought-form through our _time_, as the
bodies subject to these actions would represent its straining
through our space.
EVOLUTION AS SPACE-CONQUEST
Evolution is a struggle for, and a conquest of, space; for evolution,
as the word implies, is a _drawing out_ of what is inherent from
latency into objective reality, or in other words into spatial--and
temporal--extension.
This struggle for space, by means of which the birth and growth of
organisms is achieved, is the very texture of life, the plot of
every drama. Cells subdivide; micro-organisms war on one another;
plants contend for soil, light, moisture; flowers cunningly suborn
the bee to bring about their nuptials; animals wage deadly warfare
in their rivalry to bring more hungry animals into a space-hungry
world. Man is not exempt from this law of the jungle. Nations
intrigue and fight for land--of which wealth is only the symbol--and
a nation's puissance is measured by its power to push forward into
the territory of its neighbor. The self-same impulse drives the
individual. One measure of the difference between men in the matter
of efficiency is the amount of space each can command: one has a
house and grounds in some locality where every square inch has an
appreciable value; another some fractional part of a lodging house
in the slums. When this bloodless, but none the less deadly, contest
for space becomes acute, as in the congested quarters of great cities,
man's ingenuity is taxed to devise effective ways of augmenting his
_space-potency_, and he expands in a vertical direction. This
third-dimensional extension, typified in the tunnel and in the
skyscraper, is but the latest phase of a conquest of space which
began with the line of the pioneer's trail through an untracked
wilderness.
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