In connection with the subject of higher space there is a
remark which is sometimes made, a question which is put--"If
there are four dimensions, then there may be five and six, and
so on up to any number?"
This question is one, I own, which it would never have occurred
to me to ask. Still it often happens that a line of thought which
is most foreign and unattractive does repay investigation. And
so let us follow the ready algebraist, to whom it is as easy
to write down five as four, and n as five. Let us see what it
is reasonable to think on the subject.
If we take four-dimensional shapes and examine them, we find
that there is in them a peculiarity of the same kind which led
us to be sure of the reality of a four-dimensional existence
from the inspection of these dimensional shapes. In four dimensions
we can have two figures which are precisely similar in all their
parts, and which yet will not move so that one shall occupy the
place of the other.
And the same observation can be made with regard to five-dimensional
Hence it would seem that there is an indication of a higher
and higher reality. And if we suppose that the same fact of absolute
similarity, without the possibility of superposition, were found
again and a gain, then we should be compelled to recognize the
existence of higher and still higher space, and we should have
to admit the existence of an indefinite number of dimensions.
But let us turn away from this direct inquiry. Let us ask
what the phrase an infinite number of dimensions" denotes.
The question reminds me so forcibly of an Eastern story that
I must digress fur a moment.
For it is said that once, in the cool of the morning, beneath
the spreading branches of a great palm the master stood. And
round him were gathered three or four with whom he spent the
hours of his quiet life.
And not for long had they gathered together.
One was a warrior, and long ago he had come to the master,
asking him what he should do, and had received for answer--"Go
back and serve your commander. The day will come when you will
have fulfilled your life, and the voice within you will speak
And the soldier had returned to the life of camps and marches
and combats, till at length, at the close of a hard-fought day,
he threw down his weapons, and passing through the enemy's land,
came to where the master taught.
And his comrades, seeking long for their leader, at last buried
with honor a corpse unrecognizable for wounds.
He now sat on a bare stone listening. Beside him stood a younger
man. He had been a merchant, travelling over the whole earth
in search of gain, and in restlessness of curiosity. And when
in wonder he had begged the master what he should do, he had
been told--"Wander over the earth, and visit every part;
when thy eagerness for change is satisfied, an inward voice will
And he had travelled far, till, even, in the course of his
wanderings, he had come to the most distant lands, and gained
great riches by what he bought and sold.
But when his stores were full, and his possessions had increased
beyond his dreams, he left them all, and, seeking that hillside,
lived obediently to the master's words.
Half lying upon the ground was one whose countenance hardly
bespoke him--fitting companion for the others. And, indeed, he
had been that one, whose life had afforded the master the most
interest of all of them.
For he had not, like the others, been immersed in an active
and adventurous life, but had been a slave to the wants of his
own body. And seeing amidst his vices that the master had words
for others, he had besought him to tell him too what to do.
And the master had told him first one thing and then another,
but always he fell back, unable to withdraw himself, even for
a short while, from his bodily cravings, hut, gratifying them
with drink and Sloth, he passed his days in brutishness.
Then at length the master, hailing him as a friend, had said
to him--I will not seek to withdraw you any longer, for is not
your body like the rain-clouds, and the sky a part of the changing
show that hangs before our faces? Gaze, therefore, earnestly
on your body, attend to it the more intently, for this is your
vocation; and when you see the flimsy veil it is, come to me.
And this man had sat for ten years contemplating the middle
portion of his body, till his frame had grown so cramped that
he could not rise. At last he had bidden his fellows carry him
to the master; and now he too listened to the words that fell
on welcome ears.
And many days they had spoken together, and retiring each
to his hut of reeds at nightfall, had pondered over the master's
words. And on each of them had come a change.
Into the soldier's face, hard and stern set, had come the
dawn of gentleness. The quick, observant gaze of the traveller
now at times changed almost into such an expression as one would
wear who looks at the wide fields that lie above the countries
of the earth. And in the dull, inexpressive countenance of him
who had sat absorbed in the contemplation of his body, had come
the kindling light of intelligence.
And on this day the master opened his lips, and began to instruct
them about the universe.
He told them much that made them wonder. He told them of the
mysterious currents of life that passed away from the bodies
and frames which they could see, and that, spreading into the
minutest particles of the earth, collected again, and eddying
back through seed and leaf and fruit, participated anew with
the soul, which also in its turn had gone through many vicissitudes,
in that mingling ground of various principles which we call a
And seeing their wonder and interest, and feeling that they
were desirous to know, and since, moreover, he saw no harm in
gratifying their wish, he began to explain to them the deepest
facts of their physical being. And talking of the universe, which
contained all that they saw and knew, from the beneficent stars
to the humblest blade of grass, he said--"The world rests
upon an elephant." And then he paused.
The warrior did not speak. He who had been absorbed in the
contemplation of his body did not open his lips--or if he had
it would not have mattered; for with the instinctive and right
attitude of the half-cultured mind to the proximate object which
is the last to come before its intelligence, he would have said
if he had spoken, "worship the elephant;" and the master
would have greeted this remark with a kindly smile, and proceeded
with his discourse.
But just as he was about to take up the thread of his speech,
there came from the traveller, who had been listening eagerly,
a hurried question.
For, alas, in his wanderings, this one had traversed the greater
part of the globe, and in the course of them had come to the
West, where even at this early period a habit of mind reigned,
very unlike that which characterized the calm, deep, contemplative
souls of the East.
Moved by this restless and questioning spirit, he cried out--"And
on what does the elephant rest?"
"Upon a tortoise," the holy man replied. And had
he not been beyond all human passions, his tone would have been
one of mockery.
He taught them no more. Why should he tell them of these things?
Was it not better rather to dwell in the daily perfectionment
of brotherly love, and in the ministering offices of devoted
And yet one cannot help wishing that unlucky question had
not been put. If only the unfortunate disciple had but said,
"Let us investigate the elephant," or, better still,
had said nothing--what should we not have known now!
And if then such a question sealed the fount of sacred wisdom
at that remote epoch, what must not the effect of our modern
For now such a disciple would not simply ask, "Upon what
does the elephant rest?" but he would have glibly asked,
all in one breath--"Upon what does the elephant rest, and
upon what does the support of the elephant rest, and on what
the support of that? and so on, ad infinitum; do tell me."
And so too, even on the rivulet from the fount of wisdom that
trickles sparingly through our own minds, is there not a checking
effect coming from this mental attitude of ever asking what is
behind and behind and behind, seeking formal causes always, instead
of living apprehension of the proximate?
Indeed, that question was a misfortune if the possession of
fact knowledge is a boon. For what could have been a more apt
description of this all-supporting elastic solid ether than the
broad arching back of the largest animal known on earth--the
created being that could bear the most, and of all not-human
creatures, the most intelligent and responsive?
The master knew how all the worlds were held together--and
how much more!
And, indeed, does not this feeling come upon us strongly with
regard to those of the Eastern world, with whom we have the privilege
For my own part, however much I have learnt in the intervals
of my speaking with them, there they still hover on the weather-bow
of my knowledge--they, or those from whom they learn, are in
the possession of knowledge of which all my powers are but secondary
instances or applications.
What it is I know not, nor do they ever approach to tell me.
Yet with them I feel an inward sympathy, for I too, as they,
have an inward communion and delight, with a source lying above
all points and turns and proofs--an inward companion, whose presence
in my mind for one half-hour is worth more to me than all the
cosmogonies that I have ever read of, and of which all the thoughts
I have ever thought are but minutest fragments, mixed up with
ignorance and error. What their secret is I know not, mine is
humble enough--the inward apprehension of space.
And I have often thought, travelling by railway, when between
the dark underground stations the lads and errand boys bend over
the scraps of badly printed paper, reading fearful tales--I have
often thought how much better it would be if they were doing
that which I may call "communing with space." 'Twould
be of infinite delight, romance, and interest; far more than
are those creased tawdry papers, with no form in themselves or
in their contents.
And yet, looking at the same printed papers, being curious,
and looking deeper and deeper into them with a microscope, I
have seen that in splodgy ink stroke and dull fibrous texture,
each part was definite, exact, absolutely so far and no farther,
punctiliously correct; and deeper and deeper lying a wealth of
form, a rich variety and amplitude of shapes, that in a moment
leapt higher than my wildest dreams could conceive.
And then I have felt as one would do if the dark waters of
a manufacturing town were suddenly to part, and from them, in
them, and through them, were to uprise Aphrodite, radiant, undimmed,
flashing her way to the blue beyond the smoke; for there, in
these crabbed marks and crumpled paper, there, if you but look,
is space herself, in all her infinite determinations of form.
Thus the reverent and true attitude is, not to put formal
questions, but to press that which we know of into living contact
with our minds.
And so the next step, when we would pass beyond the knowledge
of the things about us in the world, is to acquire a sense and
living apprehension of four-dimensional space.
But the question does come to many minds. "What lies
beyond?" And, although our knowledge is not ripe enough
to answer this question, still, hurrying on before, we may ask--not
what does lie beyond, but what is it natural for us in our present
state of knowledge to think about the many dimensions of space?
Let us drop for a moment into the most common sense mode of
looking at it. Why do we think of space at all? To explain what
goes on. If everything followed uniformly, we should not need
to think of three, or even two dimensions--one would do. But
problems come up, practical problems, which need to be reconciled.
Things get "behind" one another, are hidden, and disappear.
So we find that one variable will not suffice. If we were in
a line looking at only one thing, its gradual changes of distance
from us would be all our experience. We should not call this
"distance"; it would be the one fact of our experience;
and if we treated it mathematically, we should express it as
the variation of one variable. So we may consider as identical,
one-dimensional space, and the variation of one variable. Now
plane space requires two variables. May not plane space then
be defined as our knowledge of the variation of two variables?
The being in plane space requires two variables to account for
his experience. He lives, we say, in a space of two dimensions.
Now why should we not identify these, and say that that which
he calls space is the organized mass of knowledge of the relations
of two variables that has grown up in his mind?
We talk of distance and size as if each were something known
in itself. But suppose a percipient soul subjected to a series
of changes depending on two independent causes, which always
operated together, and which were each of them continuous in
their increase and diminution, would not this percipient soul
form an idea of space of two dimensions? Would he not say that
he lived in a space of two dimensions? His apprehension of the
number of variables by which he was able to account for his experience
would project itself into a feeling of being in space; and the
kind of space would depend on the number of variables he habitually
Now we have become habituated to use, for practical thought,
three variables; these explain the greater part of our daily
life. Is that which we call space simply the organized knowledge
of the relations of these variables? Without pledging ourselves
to this view, let us adopt it and note its consequences.
Then it is evident that as we come into the presence of more
and more independent causes--I mean, as we find that these are
in nature working independently of one or more in number than
three--we shall have to study the general aspect of events which
turn up from the combinations in varying intensity of these four
or more principles, or causes of our sensation. Then we shall
get a mental organization capable of dealing readily and rapidly
with the combinations of these causes. And this mental organization
will be indicated in our consciousness by the feeling of being
in four-dimensional (or more-dimensional) space.
It seems strange to talk of there being three independent
causes, or of some such limited number, for in the events that
happen around us we see a vast variety of causes. There is the
tendency to fall, there is the motion of the wind, there are
the actions of human beings, each of them producing effects,
and besides these many other causes.
But if we look at them, we find that they are not all independent
one of the other, but may be different forms of the same cause.
Indeed, if we suppose that we live in three-dimensional space,
and that every change and occurrence is the result of the movements
of the small particles of matter, there would ultimately be only
three independent causes--the three independent movements, namely,
which a particle could go through.
Thus it would appear that, since no one would deny that there
are an infinite number of perfectly independent causes in nature,
the formation of a sense of higher and higher kinds of space
was simply necessary as, our knowledge becoming deeper, we came
into contact with more and more of these causes.
It might be said that these causes might be very diverse from
each other; one might be apprehended as love, another as color,
another as distance. But this view is hardly tenable, for to
apprehend a cause it must be congruent with the others which
we already apprehend. If it is known at all it must work uniformly
in with the rest of our experience. No doubt there are an infinite
number of causes, which give that richness to experience of which
the intellect can take hold only by a small part.
But when the intellect does take hold of a part, it takes
hold of it by seeing how it comes in, modifying each of the already
existing possibilities and producing a new variety, out of which
the actual experience is a selection. Thus, if a being having
an experience derived from two causes, and so living in a space
of two dimensions, were to be affected by a third cause, he would
first of all find that there were many things which he would
say could not be explained by space relations. Then he would
gradually arrive at the idea of a three-dimensional space. Space
being due then not to anything in the nature of the causes themselves,
but to the number of them.
Then, to us, when mentally we come into the comprehension
of any new independent cause, we must acquire the sense of a
new dimension, and the question of space and space relation is
altogether independent of the nature of these causes--the real
and systematic apprehension of them necessitating an enlargement
of our sense of space. Now the unknown comes to us generally
in the properties of the minute particles of matter which make
the different "kinds." Hence as we study matter closer
and closer we shall find that we need more and more dimensions.
And the molecular forces in one kind of space will be the physical
forces of the next higher.
That is to say, when in our space we have explained all that
we can explain by the supposition of particles moving in our
space, we shall find that there is a residuum, and this residuum
will be explained by the four-dimensional movement of the minutest
particles. The large movements are simply movements in three-dimensional
space, but to explain the residual phenomenon a higher kind of
space will be requisite.
Still, this all seems to me a barren view, and I am convinced
that it is far truer to think of space, as indeed we can hardly
help doing, as a beneficent being, supporting us all looking
at us in every lovely leafy bough, and bending towards us in
the forms of those we know.
And, moreover, there is one very valid objection to the conclusion
that we have explained anything, or made any step by using the
It will be found that such a notion as a continuously varying
quantity is a mere verbal expression. All that we can conceive
or understand are definite steps, definite units. We can conceive
a great many definite magnitudes, but not continuous magnitude.
The idea of continuity is one which we use and apply; but to
think men have explained anything by speaking of continuous variables,
is really to lose ourselves in words.
But, although we dismiss the previous supposition, still we
see that, even if it were true, the practical thing to do is
to acquire the sense of a higher dimensional space.
And, indeed, what a field is here! Take a single example. The
idea of magnitude is one dimensional simply adding and adding
on in a straight line.
The idea of rotation, or twisting, in its very nature involves
the idea of two dimensions--for it is the passage from one dimension
to another--it is an idea which, in its essence, has two dimensions.
If we think of a twist, it is the change from one direction
to another. It cannot be thought without the two directions being
present to the mind--the direction from which and the direction
to which the change takes place.
In our space we have nothing more than this rotation. If a
ball is twisting, and a blow is given to it, which tends to set
up a twist in a new direction, the old twist and the new one
combine together into a single twist about a new axis.
But in four-dimensional space there is such a thing as a twist
of a twist--a rotation of a rotation--bearing to a simple rotation
the same relation that an area does to a line. Perfectly independent
rotations may exist in a four-dimensional body.
And again, evidently if there is an idea which in its essence
involves two dimensions, may there not be an idea which, of its
very nature, includes three dimensions?
What that idea is, we do not know now; but some time, when the
knowledge of space is more highly developed, that idea will become
as familiar to us as the idea of a twist is now.
And, indeed, space is wonderful. We all know that space is
infinite in magnitude--stretching on endlessly.
And when we look quietly at space, she shows us at once that
she has infinite dimensions.
And yet, both in magnitudes and dimensions there is something
To measure, we must begin somewhere, but in space there is
no "somewhere" marked out for us to begin at. This
measuring is something, after all, foreign to space, introduced
by us for our convenience.
And as to dimensions, in order to enumerate and realize the
different dimensions, we must fix on a particular line to begin
with, and then draw other lines at right angles to this one.
But the first straight line we take can be drawn in an infinite
number of directions. Why should we take any particular one?
If we take any particular line, we do something arbitrary,
of our own will and decision, not given to us naturally by space.
No wonder then that if we take such a course we are committed
to an endless task.
We feel that all these efforts, necessary as they are to us
to apprehend space, have nothing to do with space herself. We
introduce something of our own, and are lost in the complexities
which this brings about.
May we not compare ourselves to those Egyptian priests who,
worshipping a veiled divinity, laid on her and wrapped her about
ever with richer garments, and decked her with fairer raiment.
So we wrap round space our garments of magnitude and vesture
of many dimensions.
Till suddenly, to us as to them, as with a forward tilt of
the shoulders, the divinity moves, and the raiment and robes
fall to the ground, leaving the divinity herself, revealed, but
invisible; not seen, but somehow felt to be there.
And these are not empty words. For the one space which is
not this form or that form, not this figure or that figure, but
which is to be known by us whenever we regard the least details
of the visible world--this space can be apprehended. It is not
the shapes and things we know, but space is to be apprehended
The true apprehension and worship of space lies in the grasp
of varied details of shape and form, all of which, in their exactness
and precision, pass into the one great apprehension.
And we must remember that this apprehension does not lie in
the talking about it. It cannot be conveyed in description.
We must beware of the attitude of standing open-mouthed just
because there is so much mechanics which we do not understand.
Surely there is no mechanics which we do not understand, but
geometry and mathematics only spring up there where we, in our
imperfect way, introducing our own limitations, tend towards
the knowledge of inscrutable nature.
If we want to pass on and on till magnitude and dimensions
disappear, is it not done for us already? That reality, where
magnitudes and dimensions are not, is simple and about us. For
passing thus on and on we lose ourselves, but find the clue again
in the apprehension of the simplest acts of human goodness, in
the most rudimentary recognition of another human soul wherein
is neither magnitude nor dimension, and yet all is real.
The answer to this is twofold. In order to live, self knowledge
is necessary. That knowledge of self which is distinctly a matter
of ethical inquiry, is altogether foreign to these pages.
But there is a no less important branch of self knowledge
which !seems altogether like a research into the external world.
In this we pass into a closer and closer contemplation of material
things and relations, till suddenly we find that what we thought
was certain and solid thought is really a vast and over-arching
crust, whose limitlessness to us was but our conformity to its
limits a shell out of which and beyond which we may at any time
But if we do so pass, we do not leave behind us the idea of
matter. All that we thus attain is a different material conception
In ancient times there was no well-defined line between physics
and metaphysics. And our present physical notions are derived
from amongst the mass of metaphysical notions. Metaphysics is
so uncertain, because when any one of its doctrines becomes certain,
it takes a place in physics.
And the exploration of the facts of higher space is the practical
execution of the great vision of Kant. He turned thought in an
entirely new direction. And where he turned, all seemed blank--all
positive assertions fell away, as he looked into the blackness
of pure thought.
But out of this absence can come any amount of physical knowledge.
It is like an invisible stuff out of which visible garments can
But, indeed, many would say: What is the use of these speculations?
Does not the contemplation of space leave the mind cold, the
heart untouched? Not altogether.
Is not our life very much a matter of fact, concerned with
events? All our feelings are bound up with things which we do
And thus a right conception of the possibilities of action
in our world, and in i higher world, must have some influence
Then also there is a path through which we can pass, leading
from the most complete materialism to something very different
from the first form in which it presents itself.
Any one, who will try, can find that, by passing deeper and
deeper into absolute observation of matter, and familiarity with
it, that which he first felt as real passes away--though still
there, it passes away, and becomes but the outward sign of realities
Thus there springs before the mind an idealism which is more
real than matter; a glimpse of a higher world, which is no abstraction,
or fancy, or thought, but of which our realities are the appearances.
And with this there comes overpoweringly upon the mind of
one, who thinks on higher space, the certainty that all we think,
or do, or imagine, lies open.
In that large world our secrets lie as clear as the secrets
of a plane being lie to an eye above the plane. For howsoever
closely a being living on a plane may hide from his fellows,
he has nothing secret from an eye that gazes down upon his plane.
The very idea that he can put forward to such a one any false
pretenses, is absurd.
And so we lie palpable, open. There is no such thing as secrecy.
And as I have said before, the difference between the moral
life and the animal life, in a world of any dimensions, lies
in this--that the animal life consists of actions which are those
natural to the possibilities of space of that world; the moral
life (viewed as exhibited in physical arrangements) lies in the
striving, by modification and restraint of the natural actions,
towards those actions and modes of existence which are natural
in a higher space world.
It has been shown how plane beings could only pass each other
by courtesy and mutual forbearance. And the great effort wherein
the higher spirit most plainlyshows itself, apart from convenience,
or profit, or any obvious physical good, is in one very simple
and obvious tendency towards a higher-dimensional existence.
For, as to a higher space being no secrets of ours are hidden--nothing
is unknown, so, in making towards one another our limited lives
open and manifest, we treat each other in the service of truth,
as if we were each members of that higher world.
It is often said and felt, that all our actions do in the
course of time impress their effect on the world. Nothing is
lost. And if we, being limited, know that this is so, how much
the more apparent is it when we realize our higher being. We
know that, as animal frames moving and acting in the world, the
effect of every movement passes on and on.
And with this effort corruption and evil fall. Space is so
large that no interior can be hidden from the vivifying breath
of the universe; no part can be cut off, however foul, from direct
contact with the purifying winds which traverse space higher
As conscious minds, we realize the oneness of past and future
in our open communication one with another. We attain a mental
consciousness of the higher fact. Whether we represent it to
ourselves as a day wherein all that ever has been done will be
told, or as an omnipresent and all-knowing mind, it is the same.
Truth is nothing but an aspiration to our higher being. And
the first sign of love towards individuals, as towards the world
as distinguished from the easy and yielding good nature which
always tries to please that which is nearest at the moment--is
veracity. This is the secret of the mysterious effect of science
on our emotions--the simple description of fact, apart from our
own conditions and prejudices. And also in the material world
around us, this is the secret of the beauty of the crystal and
of still water. For in them the near and the far are brought
together; in their translucency they give an emblem of the one
vision wherein a higher being grasps every part of the solid
matter, of which we can only see outside and surface.
The acceptance of the rule of the great master of empiric
religion, Comte--"Live openly"--is really to imitate
in our world, and make ourselves conscious of our true existence
in a higher world.
There are two sides of religion--the inductive and the deductive.
To the realm of deduction belongs theology, with its central
assertion and its manifold consequences. But inductive religion
consists in grasping, amidst the puzzling facts of life, those
greater existences in which the individual organizations are
bound up, and which they serve, passing, as in every science,
from the details to the whole. And the connecting link between
materialism and the conduct of life, lies in the doctrine of
the limited nature of our present space perceptions. For, with
the elevation of our notion of space to its true place, the antagonism
between our present materialistic and our present idealistic
views of life falls away.
Uncle Taz Library
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