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Speaker 1 (00:00):
Section twenty one. 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.
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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
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recognized the words of the resolution of the Council in
joining the arrest, imprisonment, or execution of any one who
should pervert the mind 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
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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
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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,
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after we had interchanged 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
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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 three cubed had met with the approval
of the sphere. Discussing the matter with him, a mere boy,
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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
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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 our house.
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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,
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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 I
had seen and heard was, in some strange way slipping
away from me, like the image of a half grasped,
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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,
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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
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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 heralds oh yes, oh yes, outside in the street,
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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
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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 any thing about the
third dimension. And I am sure I did not say
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one word about upward not northward, for that would be
such nonsense. You know, how could a thing move upward
and not northward? Outward and not northward? Even if I
were a baby, I could not be so absurd as that.
How silly it is, ha ha, not at all silly,
said I losing my temper here. For example, I'd take
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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
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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
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pupil to the Gospel of three Dimensions Section twenty two.
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
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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 catchphrase upward,
not northward, but must rather endeavor to seek a demonstration
by setting before the public a clear view of the
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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
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of a thought land. Whence, in theory a figure could
look down upon flat land 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
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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 flat land, there are
no tablets but lines, and no diagrams but limes, all
in one straight line, and only distinguishable by difference of
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size and brightness. So that when I had finished my treaties,
which I entitled through flat Land 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,
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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. Allowed I
neglected my clients and my own business to give myself
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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,
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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.
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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
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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
dangers of my position. Nevertheless, I could not at times
refrain from bursting out into suspicious or half seditious utterances,
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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 profits and inspired people are
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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
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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
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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,
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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
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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
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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 fifty five degrees,
ordered them to be relieved before I began my defense
by an inferior class of two or three degrees. I
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knew only too well what that meant. I was to
be executed or imprisoned, and my story was to be
yet 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 defense, the President,
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perhaps perceiving that some of the junior circles had been
moved by my evident earnestness, asked me two questions. One,
whether I could indicate the direction which I meant when
I used the words upward, not northward two, whether I could,
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by any diagrams or descriptions other than the enumeration of
imaginary sides and angles indicate the figure I was pleased
to call a cube. I declared that I could say
nothing more, and that I must commit myself to the truth,
whose would surely prevail in the end. The President replied
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that he quite concurred in my sentiment, and that I
could not do better. I must be sentenced to perpetual imprisonment.
But if the truth intended that I should emerge from
prison and evangelize the world, the truth might be trusted
to bring that result to pass. Meanwhile, I should be
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subjected to no discomfort that was not necessary to preclude escape.
And unless I forfeited the privilege by misconduct, I should
be occasionally permitted to see my brother, who had preceded
me to my prison. Seven years have elapsed and I
am still a prisoner. And if I accept the occasional
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visits of my brother, debarred from all companionship save that
of my jailers. My brother is one of the best
of squares, just sensible, cheerful, and not without fraternal affection.
Yet I must confess that my weekly interviews, at least
in one respect, cause me the bitterest pain. He was
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present when the sphere manifested himself in the council chamber.
He saw the spheres changing sections, he heard the explanation
of the phenomena then given to the circles. Since that time,
scarcely a week has passed during seven whole years without
his hearing from me a repetition of the part I
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played in that manifestation, together with ample descriptions of all
the phenomena in Spaceland, and the arguments for the existence
of solid things derivable from analogy. Yet I take shame
to be forced to confess it. My brother has not
yet grasped the nature of the third dimension, and frankly
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avows his disbelief in the existence of a sphere. Hence
I am absolutely destitute of converts, and for aught that
I can see. The millennial revelation has been made to
me for nothing. Prometheus up in Spaceland was bound for
bringing down fire for mortals, But I, poor flat Land Prometheus,
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lie here in prison for bringing down nothing to my countrymen.
Yet I exist in the hope that these memoirs in
some manner, I know not how may find their way
to the minds of humanity in some dimension, and may
stir up a race of rebels who shall refuse to
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be confined to limited dimensionality. That is the hope of
my brighter moments, alas it is not always so. Heavily
weighs on me at times, the burdensome reflection that I
cannot honest say I am confident as to the exact
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shape of the once seen oft regretted cube, And in
my nightly visions the mysterious precept upward not northward, haunts
me like a soul devouring sphinx. It is part of
the martyrdom which I endure for the cause of the truth.
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That there are seasons of mental weakness, when cubes and
spheres flit away into the background of scarce possible existences,
when the land of three dimensions seems almost as visionary
as the land of one or none. Nay, when even
this hard wall that bars me from my freedom, these
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very tablets on which I am writing, and all the
substantial realities of flat land itself, appear no better than
the offspring of a diseased imagination or the baseless fabric
of a dream. The end of flat land are amants
of many dimensions. By Edwin Abbot Abbot