Flatland: A Romance of Many Dimensions
mild voice of my Companion pointing the moral of my vision, and
stimulating me to aspire, and to teach others to aspire. He had been
angered at first--he confessed--by my ambition to soar to Dimensions
above the Third; but, since then, he had received fresh insight, and he
was not too proud to acknowledge his error to a Pupil. Then he
proceeded to initiate me into mysteries yet higher than those I had
witnessed, shewing me how to construct Extra-Solids by the motion of
Solids, and Double Extra-Solids by the motion of Extra-Solids, and all
"strictly according to Analogy", all by methods so simple, so easy, as
to be patent even to the Female Sex.
Section 21. How I tried to teach the Theory of Three Dimensions
to my Grandson, and with what success
I awoke rejoicing, and began to reflect on the glorious career before
me. I would go forth, methought, at once, and evangelize the whole of
Flatland. Even to Women and Soldiers should the Gospel of Three
Dimensions be proclaimed. I would begin with my Wife.
Just as I had decided on the plan of my operations, I heard the sound
of many voices in the street commanding silence. Then followed a
louder voice. It was a herald's proclamation. Listening attentively,
I recognized the words of the Resolution of the Council, enjoining the
arrest, imprisonment, or execution of any one who should pervert the
minds of the people by delusions, and by professing to have received
revelations from another World.
I reflected. This danger was not to be trifled with. It would be
better to avoid it by omitting all mention of my Revelation, and by
proceeding on the path of Demonstration--which after all, seemed so
simple and so conclusive that nothing would be lost by discarding the
former means. "Upward, not Northward"--was the clue to the whole
proof. It had seemed to me fairly clear before I fell asleep; and when
I first awoke, fresh from my dream, it had appeared as patent as
Arithmetic; but somehow it did not seem to me quite so obvious now.
Though my Wife entered the room opportunely just at that moment, I
decided, after we had exchanged a few words of commonplace
conversation, not to begin with her.
My Pentagonal Sons were men of character and standing, and physicians
of no mean reputation, but not great in mathematics, and, in that
respect, unfit for my purpose. But it occurred to me that a young and
docile Hexagon, with a mathematical turn, would be a most suitable
pupil. Why therefore not make my first experiment with my little
precocious Grandson, whose casual remarks on the meaning of 3^3 had met
with the approval of the Sphere? Discussing the matter with him, a
mere boy, I should be in perfect safety; for he would know nothing of
the Proclamation of the Council; whereas I could not feel sure that my
Sons--so greatly did their patriotism and reverence for the Circles
predominate over mere blind affection--might not feel compelled to hand
me over to the Prefect, if they found me seriously maintaining the
seditious heresy of the Third Dimension.
But the first thing to be done was to satisfy in some way the curiosity
of my Wife, who naturally wished to know something of the reasons for
which the Circle had desired that mysterious interview, and of the
means by which he had entered the house. Without entering into the
details of the elaborate account I gave her,--an account, I fear, not
quite so consistent with truth as my Readers in Spaceland might
desire,--I must be content with saying that I succeeded at last in
persuading her to return quietly to her household duties without
eliciting from me any reference to the World of Three Dimensions. This
done, I immediately sent for my Grandson; for, to confess the truth, I
felt that all that I had seen and heard was in some strange way
slipping away from me, like the image of a half-grasped, tantalizing
dream, and I longed to essay my skill in making a first disciple.
When my Grandson entered the room I carefully secured the door. Then,
sitting down by his side and taking our mathematical tablets,--or, as
you would call them, Lines--I told him we would resume the lesson of
yesterday. I taught him once more how a Point by motion in One
Dimension produces a Line, and how a straight Line in Two Dimensions
produces a Square. After this, forcing a laugh, I said, "And now, you
scamp, you wanted to make me believe that a Square may in the same way
by motion 'Upward, not Northward' produce another figure, a sort of
extra Square in Three Dimensions. Say that again, you young rascal."
At this moment we heard once more the herald's "O yes! O yes!" outside
in the street proclaiming the Resolution of the Council. Young though
he was, my Grandson--who was unusually intelligent for his age, and
bred up in perfect reverence for the authority of the Circles--took in
the situation with an acuteness for which I was quite unprepared. He
remained silent till the last words of the Proclamation had died away,
and then, bursting into tears, "Dear Grandpapa," he said, "that was
only my fun, and of course I meant nothing at all by it; and we did not
know anything then about the new Law; and I don't think I said anything
about the Third Dimension; and I am sure I did not say one word about
'Upward, not Northward', for that would be such nonsense, you know.
How could a thing move Upward, and not Northward? Upward and not
Northward! Even if I were a baby, I could not be so absurd as that.
How silly it is! Ha! ha! ha!"
"Not at all silly," said I, losing my temper; "here for example, I take
this Square," and, at the word, I grasped a moveable Square, which was
lying at hand--"and I move it, you see, not Northward but--yes, I move
it Upward--that is to say, not Northward, but I move it somewhere--not
exactly like this, but somehow--" Here I brought my sentence to an
inane conclusion, shaking the Square about in a purposeless manner,
much to the amusement of my Grandson, who burst out laughing louder
than ever, and declared that I was not teaching him, but joking with
him; and so saying he unlocked the door and ran out of the room. Thus
ended my first attempt to convert a pupil to the Gospel of Three
Dimensions.
Section 22. How I then tried to diffuse the Theory
of Three Dimensions by other means, and of the result
My failure with my Grandson did not encourage me to communicate my
secret to others of my household; yet neither was I led by it to
despair of success. Only I saw that I must not wholly rely on the
catch-phrase, "Upward, not Northward", but must rather endeavour to
seek a demonstration by setting before the public a clear view of the
whole subject; and for this purpose it seemed necessary to resort to
writing.
So I devoted several months in privacy to the composition of a treatise
on the mysteries of Three Dimensions. Only, with the view of evading
the Law, if possible, I spoke not of a physical Dimension, but of a
Thoughtland whence, in theory, a Figure could look down upon Flatland
and see simultaneously the insides of all things, and where it was
possible that there might be supposed to exist a Figure environed, as
it were, with six Squares, and containing eight terminal Points. But
in writing this book I found myself sadly hampered by the impossibility
of drawing such diagrams as were necessary for my purpose; for of
course, in our country of Flatland, there are no tablets but Lines, and
no diagrams but Lines, all in one straight Line and only
distinguishable by difference of size and brightness; so that, when I
had finished my treatise (which I entitled, "Through Flatland to
Thoughtland") I could not feel certain that many would understand my
meaning.
Meanwhile my life was under a cloud. All pleasures palled upon me; all
sights tantalized and tempted me to outspoken treason, because I could
not but compare what I saw in Two Dimensions with what it really was if
seen in Three, and could hardly refrain from making my comparisons
aloud. I neglected my clients and my own business to give myself to
the contemplation of the mysteries which I had once beheld, yet which I
could impart to no one, and found daily more difficult to reproduce
even before my own mental vision.
One day, about eleven months after my return from Spaceland, I tried to
see a Cube with my eye closed, but failed; and though I succeeded
afterwards, I was not then quite certain (nor have I been ever
afterwards) that I had exactly realized the original. This made me
more melancholy than before, and determined me to take some step; yet
what, I knew not. I felt that I would have been willing to sacrifice
my life for the Cause, if thereby I could have produced conviction.
But if I could not convince my Grandson, how could I convince the
highest and most developed Circles in the land?
And yet at times my spirit was too strong for me, and I gave vent to
dangerous utterances. Already I was considered heterodox if not
treasonable, and I was keenly alive to the danger of my position;
nevertheless I could not at times refrain from bursting out into
suspicious or half-seditious utterances, even among the highest
Polygonal and Circular society. When, for example, the question arose
about the treatment of those lunatics who said that they had received
the power of seeing the insides of things, I would quote the saying of
an ancient Circle, who declared that prophets and inspired people are
always considered by the majority to be mad; and I could not help
occasionally dropping such expressions as "the eye that discerns the
interiors of things", and "the all-seeing land"; once or twice I even
let fall the forbidden terms "the Third and Fourth Dimensions". At
last, to complete a series of minor indiscretions, at a meeting of our
Local Speculative Society held at the palace of the Prefect
himself,--some extremely silly person having read an elaborate paper
exhibiting the precise reasons why Providence has limited the number of
Dimensions to Two, and why the attribute of omnividence is assigned to
the Supreme alone--I so far forgot myself as to give an exact account
of the whole of my voyage with the Sphere into Space, and to the
Assembly Hall in our Metropolis, and then to Space again, and of my
return home, and of everything that I had seen and heard in fact or
vision. At first, indeed, I pretended that I was describing the
imaginary experiences of a fictitious person; but my enthusiasm soon
forced me to throw off all disguise, and finally, in a fervent
peroration, I exhorted all my hearers to divest themselves of prejudice
and to become believers in the Third Dimension.
Need I say that I was at once arrested and taken before the Council?
Next morning, standing in the very place where but a very few months
ago the Sphere had stood in my company, I was allowed to begin and to
continue my narration unquestioned and uninterrupted. But from the
first I foresaw my fate; for the President, noting that a guard of the
better sort of Policemen was in attendance, of angularity little, if at
all, under 55 degrees, ordered them to be relieved before I began my
defence, by an inferior class of 2 or 3 degrees. I knew only too well
what that meant. I was to be executed or imprisoned, and my story was
to be kept secret from the world by the simultaneous destruction of the
officials who had heard it; and, this being the case, the President
desired to substitute the cheaper for the more expensive victims.
After I had concluded my defence, the President, perhaps perceiving
that some of the junior Circles had been moved by my evident
earnestness, asked me two questions:--
1. Whether I could indicate the direction which I meant when I used
the words "Upward, not Northward"?