Flatland: A Romance of Many Dimensions
really see a Fourth unrecognized Dimension, not the same as colour, but
existent, though infinitesimal and incapable of measurement?
And besides this, there is the Argument from Analogy of Figures.
SPHERE. Analogy! Nonsense: what analogy?
I. Your Lordship tempts his servant to see whether he remembers the
revelations imparted to him. Trifle not with me, my Lord; I crave, I
thirst, for more knowledge. Doubtless we cannot SEE that other higher
Spaceland now, because we we have no eye in our stomachs. But, just as
there WAS the realm of Flatland, though that poor puny Lineland Monarch
could neither turn to left nor right to discern it, and just as there
WAS close at hand, and touching my frame, the land of Three Dimensions,
though I, blind senseless wretch, had no power to touch it, no eye in
my interior to discern it, so of a surety there is a Fourth Dimension,
which my Lord perceives with the inner eye of thought. And that it
must exist my Lord himself has taught me. Or can he have forgotten
what he himself imparted to his servant?
In One Dimension, did not a moving Point produce a Line with TWO
terminal points?
In Two Dimensions, did not a moving Line produce a Square with FOUR
terminal points?
In Three Dimensions, did not a moving Square produce--did not this eye
of mine behold it--that blessed Being, a Cube, with EIGHT terminal
points?
And in Four Dimensions shall not a moving Cube--alas, for Analogy, and
alas for the Progress of Truth, if it be not so--shall not, I say, the
motion of a divine Cube result in a still more divine Organization with
SIXTEEN terminal points?
Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not
this a Geometrical Progression? Is not this--if I might quote my
Lord's own words--"strictly according to Analogy"?
Again, was I not taught by my Lord that as in a Line there are TWO
bounding Points, and in a Square there are FOUR bounding Lines, so in a
Cube there must be SIX bounding Squares? Behold once more the
confirming Series, 2, 4, 6: is not this an Arithmetical Progression?
And consequently does it not of necessity follow that the more divine
offspring of the divine Cube in the Land of Four Dimensions, must have
8 bounding Cubes: and is not this also, as my Lord has taught me to
believe, "strictly according to Analogy"?
O, my Lord, my Lord, behold, I cast myself in faith upon conjecture,
not knowing the facts; and I appeal to your Lordship to confirm or deny
my logical anticipations. If I am wrong, I yield, and will no longer
demand a fourth Dimension; but, if I am right, my Lord will listen to
reason.
I ask therefore, is it, or is it not, the fact, that ere now your
countrymen also have witnessed the descent of Beings of a higher order
than their own, entering closed rooms, even as your Lordship entered
mine, without the opening of doors or windows, and appearing and
vanishing at will? On the reply to this question I am ready to stake
everything. Deny it, and I am henceforth silent. Only vouchsafe an
answer.
SPHERE. (AFTER A PAUSE). It is reported so. But men are divided in
opinion as to the facts. And even granting the facts, they explain
them in different ways. And in any case, however great may be the
number of different explanations, no one has adopted or suggested the
theory of a Fourth Dimension. Therefore, pray have done with this
trifling, and let us return to business.
I. I was certain of it. I was certain that my anticipations would be
fulfilled. And now have patience with me and answer me yet one more
question, best of Teachers! Those who have thus appeared--no one knows
whence--and have returned--no one knows whither--have they also
contracted their sections and vanished somehow into that more Spacious
Space, whither I now entreat you to conduct me?
SPHERE (MOODILY). They have vanished, certainly--if they ever
appeared. But most people say that these visions arose from the
thought--you will not understand me--from the brain; from the perturbed
angularity of the Seer.
I. Say they so? Oh, believe them not. Or if it indeed be so, that
this other Space is really Thoughtland, then take me to that blessed
Region where I in Thought shall see the insides of all solid things.
There, before my ravished eye, a Cube, moving in some altogether new
direction, but strictly according to Analogy, so as to make every
particle of his interior pass through a new kind of Space, with a wake
of its own--shall create a still more perfect perfection than himself,
with sixteen terminal Extra-solid angles, and Eight solid Cubes for his
Perimeter. And once there, shall we stay our upward course? In that
blessed region of Four Dimensions, shall we linger on the threshold of
the Fifth, and not enter therein? Ah, no! Let us rather resolve that
our ambition shall soar with our corporal ascent. Then, yielding to
our intellectual onset, the gates of the Sixth Dimension shall fly
open; after that a Seventh, and then an Eighth-- How long I should have
continued I know not. In vain did the Sphere, in his voice of thunder,
reiterate his command of silence, and threaten me with the direst
penalties if I persisted. Nothing could stem the flood of my ecstatic
aspirations. Perhaps I was to blame; but indeed I was intoxicated with
the recent draughts of Truth to which he himself had introduced me.
However, the end was not long in coming. My words were cut short by a
crash outside, and a simultaneous crash inside me, which impelled me
through space with a velocity that precluded speech. Down! down! down!
I was rapidly descending; and I knew that return to Flatland was my
doom. One glimpse, one last and never-to-be-forgotten glimpse I had of
that dull level wilderness--which was now to become my Universe
again--spread out before my eye. Then a darkness. Then a final,
all-consummating thunder-peal; and, when I came to myself, I was once
more a common creeping Square, in my Study at home, listening to the
Peace-Cry of my approaching Wife.
Section 20. How the Sphere encouraged me in a Vision
Although I had less than a minute for reflection, I felt, by a kind of
instinct, that I must conceal my experiences from my Wife. Not that I
apprehended, at the moment, any danger from her divulging my secret,
but I knew that to any Woman in Flatland the narrative of my adventures
must needs be unintelligible. So I endeavoured to reassure her by some
story, invented for the occasion, that I had accidentally fallen
through the trap-door of the cellar, and had there lain stunned.
The Southward attraction in our country is so slight that even to a
Woman my tale necessarily appeared extraordinary and well-nigh
incredible; but my Wife, whose good sense far exceeds that of the
average of her Sex, and who perceived that I was unusually excited, did
not argue with me on the subject, but insisted that I was ill and
required repose. I was glad of an excuse for retiring to my chamber to
think quietly over what had happened. When I was at last by myself, a
drowsy sensation fell on me; but before my eyes closed I endeavoured to
reproduce the Third Dimension, and especially the process by which a
Cube is constructed through the motion of a Square. It was not so
clear as I could have wished; but I remembered that it must be "Upward,
and yet not Northward", and I determined steadfastly to retain these
words as the clue which, if firmly grasped, could not fail to guide me
to the solution. So mechanically repeating, like a charm, the words,
"Upward, yet not Northward", I fell into a sound refreshing sleep.
During my slumber I had a dream. I thought I was once more by the side
of the Sphere, whose lustrous hue betokened that he had exchanged his
wrath against me for perfect placability. We were moving together
towards a bright but infinitesimally small Point, to which my Master
directed my attention. As we approached, methought there issued from
it a slight humming noise as from one of your Spaceland bluebottles,
only less resonant by far, so slight indeed that even in the perfect
stillness of the Vacuum through which we soared, the sound reached not
our ears till we checked our flight at a distance from it of something
under twenty human diagonals.
"Look yonder," said my Guide, "in Flatland thou hast lived; of Lineland
thou hast received a vision; thou hast soared with me to the heights of
Spaceland; now, in order to complete the range of thy experience, I
conduct thee downward to the lowest depth of existence, even to the
realm of Pointland, the Abyss of No dimensions.
"Behold yon miserable creature. That Point is a Being like ourselves,
but confined to the non-dimensional Gulf. He is himself his own World,
his own Universe; of any other than himself he can form no conception;
he knows not Length, nor Breadth, nor Height, for he has had no
experience of them; he has no cognizance even of the number Two; nor
has he a thought of Plurality; for he is himself his One and All, being
really Nothing. Yet mark his perfect self-contentment, and hence learn
this lesson, that to be self-contented is to be vile and ignorant, and
that to aspire is better than to be blindly and impotently happy. Now
listen."
He ceased; and there arose from the little buzzing creature a tiny,
low, monotonous, but distinct tinkling, as from one of your Spaceland
phonographs, from which I caught these words, "Infinite beatitude of
existence! It is; and there is none else beside It."
"What," said I, "does the puny creature mean by 'it'?" "He means
himself," said the Sphere: "have you not noticed before now, that
babies and babyish people who cannot distinguish themselves from the
world, speak of themselves in the Third Person? But hush!"
"It fills all Space," continued the little soliloquizing Creature, "and
what It fills, It is. What It thinks, that It utters; and what It
utters, that It hears; and It itself is Thinker, Utterer, Hearer,
Thought, Word, Audition; it is the One, and yet the All in All. Ah,
the happiness ah, the happiness of Being!"
"Can you not startle the little thing out of its complacency?" said I.
"Tell it what it really is, as you told me; reveal to it the narrow
limitations of Pointland, and lead it up to something higher." "That
is no easy task," said my Master; "try you."
Hereon, raising my voice to the uttermost, I addressed the Point as
follows:
"Silence, silence, contemptible Creature. You call yourself the All in
All, but you are the Nothing: your so-called Universe is a mere speck
in a Line, and a Line is a mere shadow as compared with--" "Hush,
hush, you have said enough," interrupted the Sphere, "now listen, and
mark the effect of your harangue on the King of Pointland."
The lustre of the Monarch, who beamed more brightly than ever upon
hearing my words, shewed clearly that he retained his complacency; and
I had hardly ceased when he took up his strain again. "Ah, the joy,
ah, the joy of Thought! What can It not achieve by thinking! Its own
Thought coming to Itself, suggestive of Its disparagement, thereby to
enhance Its happiness! Sweet rebellion stirred up to result in triumph!
Ah, the divine creative power of the All in One! Ah, the joy, the joy
of Being!"
"You see," said my Teacher, "how little your words have done. So far
as the Monarch understands them at all, he accepts them as his own--for
he cannot conceive of any other except himself--and plumes himself upon
the variety of 'Its Thought' as an instance of creative Power. Let us
leave this God of Pointland to the ignorant fruition of his
omnipresence and omniscience: nothing that you or I can do can rescue
him from his self-satisfaction."
After this, as we floated gently back to Flatland, I could hear the