August 8, 2025 • 43 mins
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Episode Transcript
Available transcripts are automatically generated. Complete accuracy is not guaranteed.
Speaker 1 (00:00):
Part two, Section eighteen. How I came to Spaceland and
what I saw there? An unspeakable horror seized me. There
was a darkness, then a dizzy, sickening sensation of sight
that was not like seeing. I saw a line that
was no line, space that was not space. I was
(00:23):
myself and not myself. When I could find voice, I
shrieked aloud in agony. Either this is madness or it
is hell. It is neither, calmly replied the voice of
the sphere. It is knowledge. It is three dimensions. Open
(00:44):
your eye once again and try to look steadily. I looked,
and behold a new world. There stood before me, visibly
incorporate all that I had before inferred, conjectured, dreamed of
(01:04):
perfect circular beauty. What seemed the center of the Stranger's
form lay open to my view. Yet I could see
no heart, nor lungs, nor arteries, only a beautiful, harmonious
something for which I had no words. But you, my
(01:26):
readers in Spaceland, would call it the surface of the sphere.
Prostrating myself mentally before my guide, I cried, how is
it o divine ideal of consumate loveliness and wisdom that
I see thy inside, and yet cannot discern thy heart,
(01:47):
thy lungs, thy arteries, thy liver. What you think you see,
you see not, he replied. It is not given to you,
nor to any other being, to behold my internal parts.
I am of a different order of beings from those
in Flatland. Were I a circle, you could discern my intestines.
(02:10):
But I am a being composed, as I told you before,
of many circles, the many in the one called in
this country a sphere. And just as the outside of
a cube is a square, so the outside of a
sphere presents the appearance of a circle. Bewildered though I
(02:32):
was by my teacher's enigmatic utterance, I no longer chafed
against it, but worshiped him in silent adoration. He continued,
with more mildness in his voice. Distress not yourself. If
you cannot at first understand the deeper mysteries of spaceland,
by degrees, they will dawn upon you. Let us begin
(02:55):
by casting back a glance at the region whence you came.
Return with me awhile to the plains of flat Land,
and I will show you that which you have so
often reasoned and thought about, but never seen with the
sense of sight. A visible angle impossible, I cried, But
(03:18):
the sphere leading the way, I followed, as if in
a dream, till once more his voice arrested me. Look yonder,
and behold your own pentagonal house and all its inmates.
Reader's note. The following paragraph refers to a detailed diagram.
The diagram shows the points of the compass, with north
(03:39):
at the top. Next to this, there is a large
equal sided pentagon sitting on a horizontal base. Centrally placed
on the lower left edge of the pentagon, there is
an opening labeled men's door, the size of the opening
being about a quarter of the length of that edge.
(04:00):
This door leads into a large central space labeled the hall,
which is otherwise surrounded by rooms. The position of these
rooms will now be described clockwise from the northern point.
The upper right edge is divided equally between two rooms
labeled in order, my study and my Bedroom. The left
(04:24):
hand wall of the study runs vertically down from the
northern point, and the right hand wall is parallel to
the lower right edge of the pentagon. The study has
a door into the hall, and there is Isosceles triangle
inside labeled the page. Sharing a wall with the study
(04:44):
is my rhomboid shaped bedroom, the right hand wall of
which is the top quarter of the lower right hand
edge of the pentagon. It shares a wall and communicating
door with the room to the south labeled my my
Wife's Apartment. About three tenths down the lower right edge,
(05:06):
there is a narrow opening labeled Women's door. This leads
into a long, narrow room labeled my Wife's apartment. This
room has doorways into my bedroom above, into the hall
to the left, and into the room to the south,
also long and narrow, where a straight line is marked
(05:28):
my daughter. The only door from my Daughter's room is
into my wife's apartment. Continuing clockwise down the lower right
edge of the pentagon, the next room is a long
and wide room with two openings into the hall. Inside
are three isosceles triangles of varying acuteness. The uppermost and
(05:52):
most acute is labeled the scullion, the next and middle
sized is labeled the Footman, and the lowerest and least
acute is labeled the Butler. At the bottom right point
of the pentagon, a large corner room is labeled the
cellar and has a door into the hall. Along the
(06:14):
left half of the bottom or southern edge, there are
two small rooms, each with a door into the hall,
and each with a hexagon inside labeled my grandson's. Continuing
clockwise up the left side of the pentagon, between the
men's door and the northern point, there are four small rooms.
(06:36):
Each of these rooms, labeled my sons, has a pentagon
inside it and a door into the hall. In the
middle of the central hall is a straight line labeled
my wife. Outside the pentagon one At each end of
the bottom or southern edge, are two very acute Isosceles triangles,
(06:57):
each labeled Policeman. End of reader's note. I looked below
and saw with my physical eye all that domestic individuality
which I had hitherto merely inferred with the understanding, And
how poor and shadowy was the inferred conjecture in comparison
(07:18):
with the reality which I now beheld. My four sons
calmly asleep in the northwestern rooms, my two orphan grandsons
to the south, the servants, the butler, my daughter, all
in their several apartments. Only my affectionate wife, alarmed by
(07:39):
my continued absence, had quitted her room, and was roving
up and down in the hall, anxiously awaiting my return. Also,
the page, aroused by my cries, had left his room,
and under pretext of ascertaining whether I had fallen somewhere
in a faint, was prying into the cabinet in my study.
(08:00):
All this I could now see not merely infer and
as we came nearer and nearer, I could discern even
the contents of my cabinet, and the two chests of gold,
and the tablets of which the Sphere had made mention.
Touched by my wife's distress, I would have sprung downward
(08:21):
to reassure her, but I found myself incapable of motion.
Trouble not yourself about your wife, said my guide. She
will not be long left in anxiety. Meantime, let us
take a survey of flat land. Once more, I felt
myself rising through space. It was even as the Sphere
(08:43):
had said. The further we receded from the object we beheld,
the larger became the field of vision. My native city,
with the interior of every house and every creature therein
lay open to my view. In miniature, we mounted higher
and lo the secrets of the earth, the depths of mines,
(09:07):
and inmost caverns of the hills were bared before me.
AWE struck at the sight of the mysteries of the
earth thus unveiled before my unworthy eye. I said to
my companion, Behold, I am become as a god. For
the wise men in our country say that to see
all things, or as they express it, omnividence is the
(09:31):
attribute of God alone. There was something of scorn in
the voice of my teacher as he made answer, Is
it so? Indeed? Then the very pick pockets and cut
throats of my country are to be worshiped by your
wise men as being gods. For there is not one
of them that does not see as much as you
(09:53):
see now. But trust me, your wise men are wrong.
I is omnividence the attribute of others beside God's sphere?
I do not know. But if a pickpocket or a
cutthroat of our country can see everything that is in
your country, surely that is no reason whether pickpocket or
(10:17):
cutthroat should be accepted by you as a god. This omnividence,
as you call it, it is not a common word
in spaceland. Does it make you more just? More merciful,
less selfish, more loving. Not in the least, then, how
does it make you more divine? I more merciful, more loving.
(10:41):
But these are the qualities of women. And we know
that a circle is a higher being than a straight line,
in so far as knowledge and wisdom are more to
be esteemed than mere affection. Sphere, it is not for
me to classify human faculties. According to merit, many of
the best and wisest in spaceland think more of the
(11:03):
affections than of the understanding, more of your despised straight
lines than of your belauded circles. But enough of this,
Look yonder? Do you know that building? I looked, and
afar off I saw an immense polygonal structure, in which
I recognized the General Assembly Hall of the States of Flatland,
(11:26):
surrounded by dense lines of pentagonal buildings at right angles
to each other, which I knew to be streets. And
I perceived that I was approaching the great metropolis. Here
we descend, said my guide. It was now morning, the
first hour of the first day of the two thousandth
year of our era. Acting as was there wont in
(11:49):
strict accordance with precedent, the highest circles of the Realm
were meeting in solemn conclave, as they had met on
the first hour of the first day of the year
one thousand, and also on the first hour of the
first day of the year nought. The minutes of the
previous meetings were now read by one whom I at
(12:10):
once recognized as my brother, a perfectly symmetrical square, and
the Chief Clerk of the High Council. It was found
recorded on each occasion that whereas the states had been
troubled by divers ill intentioned persons, pretending to have received
revelations from another world, and professing to produce demonstrations, whereby
(12:33):
they had instigated to frenzy both themselves and others, it
had been for this cause unanimously resolved by the Grand
Council that on the first day of each millinery, special
injunctions be sent to the prefects in the several districts
of Flatland to make strict search for such misguided persons,
(12:54):
and without formality of mathematical examination, to destroy all such
as were I soosceles of any degree, to scourge and
imprison any regular triangle, to cause any square or pentagon
to be sent to the district asylum, and to arrest
any one of higher rank, sending him straightway to the
capital to be examined and judged by the council. You
(13:19):
hear your fate, said the sphere to me, while the
council was passing for the third time, the formal resolution
death or imprisonment awaits the apostle of the Gospel of
three Dimensions. Not so, replied I. The matter is now
so clear to me, the nature of real space so palpable,
(13:40):
that methinks I could make a child understand it. Permit
me but to descend at this moment and enlighten them?
Not yet, said my guide. The time will come for that.
Meantime I must perform my mission. Stay thou there in
thy place. Saying these words, he leapt with great dexterity
(14:01):
into the sea. If I may say, call it a
flat land. Right in the midst of the ring of councilors,
I come, cried he to proclaim that there is a
land of three dimensions. I could see many of the
younger councilors start back in manifest horror as the Sphere's
circular section widened before them. But on a sign from
(14:26):
the presiding circle, who showed not the slightest alarm or surprise.
Six Isosceles of a lone type, from six different quarters
rushed upon the sphere. We have him, they cried, No, yes,
we have him. Still he's going. He's gone, my lords,
(14:47):
said the President to the junior circles of the Council.
There is not the slightest need for surprise. The secret archives,
to which I alone have access, tell me that a
similar occurrence happened on the last two millennial commencements. You will,
of course, say nothing of these trifles outside the cabinet.
(15:08):
Raising his voice, he now summoned the guard, arrest the policeman,
gag them. You know your duty. After he had consigned
to their fate the wretched policeman, ill fated and unwilling
witnesses of a state secret which they were not to
be permitted to reveal, he again addressed to counselors, my lords,
(15:31):
the business of the Council being concluded, I have only
to wish you a happy new year. Before departing, he
expressed at some lengths to the Clerk, my excellent but
most unfortunate brother, his sincere regret that in accordance with precedent,
and for the sake of secrecy, he must condemn him
(15:52):
to perpetual imprisonment, but added his satisfaction that unless some
mention were made by him of that day's incident, his
life would be spared Section nineteen. How though the sphere
showed me other mysteries of spaceland, I still desired more,
(16:14):
and what came of it? When I saw my poor
brother led away to imprisonment. I attempted to leap down
into the council chamber, desiring to intercede on his behalf,
or at least bid him farewell. But I found that
I had no motion of my own. I absolutely depended
on the volition of my guide, who said, in gloomy tones,
(16:37):
heed not thy brother, haply, thou shalt have ample time
hereafter to condole with him. Follow me Reader's note. The
following paragraph makes reference to a diagram. Diagram one shows
a three dimensional cube with visible edges drawn and hidden
(16:58):
edges dotted, giving it a three dimensional appearance. Horizontal shading
makes it appear that the cube is made up of
many layers. Diagram two shows the same figure, but all
lines indicating perspective are missing. With the effect that it
no longer appears to be solid, but looks like a
(17:21):
two dimensional irregular hexagonal figure. End of reader's note. Once more,
we ascended into space. Hitherto, said the sphere. I have
shown you nought save plain figures and their interiors. Now
I must introduce you to solids, and reveal to you
(17:41):
the plan upon which they are constructed. Behold this multitude
of moveable square cards. See I put one on another,
not as you supposed northward of the other, but on
the other now as second, now a third. See I
am building up a solid by a multitude of squares
(18:03):
parallel to one another. Now the solid is complete, being
as high as it is long and broad, and we
call it a cube. Pardon me, my lord, replied I,
But to my eye, the appearance is as of an
irregular figure whose inside is laid open to the view.
(18:23):
In other words, methinks I see no solid, but a plain,
such as we infer in flat land, only of an
irregularity which betokens some monstrous criminal, so that the very
sight of it is painful to my eyes. True, said
the sphere. It appears to you a plane because you
(18:44):
are not accustomed to light and shade and perspective, just
as in flat land a hexagon would appear a straight
line to one who has not the art of sight recognition,
but in reality it is a solid. Shall learn by
the sense of feeling. He then introduced me to the cube,
(19:05):
and I found that this marvelous being was indeed no plane,
but a solid, and that he was endowed with six
plain sides and eight terminal points called solid angles. And
I remembered the saying of the sphere that just such
a creature as this would be formed by a square
(19:26):
moving in space parallel to himself. And I rejoiced to
think that so insignificant a creature as I could, in
some sense be called the progenitor of so illustrious an offspring.
But still I could not fully understand the meaning of
what my teacher had told me concerning light and shade
(19:50):
and perspective, and I did not hesitate to put my
difficulties before him. Were I to give the spheres explain
nation of these matters, succinct and clear though it was,
it would be tedious to an inhabitant of space who
knows these things already. Suffice it that, by his lucid
(20:12):
statements and by changing the position of objects and lights,
and by allowing me to feel the several objects and
even his own sacred person, he at last made all
things clear to me, so that I could now readily
distinguish between a circle and a sphere, a plain figure
(20:33):
and a solid This was the climax, the paradise of
my strange, eventful history. Henceforth I have to relate the
story of my miserable fall, most miserable, yet surely most undeserved.
For why should the thirst for knowledge be aroused only
(20:55):
to be disappointed and punished. My volition shrinks from the
painful task of recalling my humiliation. Yet, like a second Prometheus,
I will endure this and worse. If by any means
I may arouse in the interiors of plain and solid
humanity a spirit of rebellion against the conceit which would
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limit our dimensions to two or three, or any number
short of infinity away, then with all personal considerations, let
me continue to the end as I began, without further
digressions or anticipations, pursuing the plain path of dispassionate history.
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The exact facts, the exact words, and they are burnt
in upon my brain shall be set down without alteration
of an iota, and let my readers judge between me
and destiny. The sphere would willingly have continued his lessons
by indoctrinating me in the confirmation of all regular solids, cylinders, cones, pyramids, pentahedrons, hexahedrons, dodecahedrons,
(22:11):
and spheres. But I ventured to interrupt him, not that
I was wearied of knowledge. On the contrary, I thirsted
for yet deeper and fuller drafts than he was offering
to me. Pardon me, said I, O, thou whom I
must no longer addresses the perfection of all beauty? But
(22:35):
let me beg THEE to vouchsafe thy servant a sight
of thine interior sphere. My what I thine interior, thy stomach,
thy intestines sphere? Whence this ill timed, impertinent request? Then
(22:55):
what mean you by saying that I am no longer
the perfection of all beauty? I, my Lord, your own
wisdom has taught me to aspire to one even more great,
more beautiful, and more closely approximate to perfection than yourself.
As you, yourself superior to all flatland forms, combine many
(23:19):
circles in one. So doubtless there is one above you
who combines many spheres in one supreme existence, surpassing even
the solids of spaceland. And even as we who are
now in space look down on flat land and see
the insides of all things, so of a certainty there
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is yet above us, some higher, purer region, whither thou
dost surely purpose to lead me. O thou, whom I
shall always call everywhere and in all dimensions, my priest
philosopher and friend, some yet more spacious space, some more
dimensionable dimensionality, from the vantage ground of which we shall
(24:06):
look down together upon the revealed insides of solid things,
and where thine own intestines and those of thy kindred
spheres will lie exposed to the view of the poor
wandering exile from flatland, to whom so much has already
been vouchsafed. Sphere, woof stuff. Enough of this trifling. The
(24:30):
time is short, and much remains to be done before
you are fit to proclaim the Gospel of three dimensions
to your blind, benighted countrymen in flatland. I nay, gracious teacher,
deny me not what I know. It is in thy
power to perform, grant me but one glimpse of Thine interior,
(24:52):
and I am satisfied forever remaining henceforth, thy docile pupil,
thy unemancipable slave, ready to receive all thy teachings, and
to feed upon the words that fall from thy lips.
Sphere well, then to content and silence. You let me
say at once, I would show you what you wish
(25:13):
if I could, But I cannot. Would you have me
turn my stomach inside out to oblige you? I, but
my Lord has shown me the intestines of all my
countrymen in the land of two dimensions, by taking me
with him into the land of three. What therefore more
easy than now to take his servant on a second
(25:36):
journey into the blessed region of the fourth dimension, where
I shall look down with him once more upon this
land of three dimensions, and see the inside of every
three dimensioned house, the secrets of the solid earth, the
treasures of the minds in spaceland, and the intestines of
every solid living creature, even of the noble and adorables sphere.
(26:03):
But where is this land of four dimensions? I I
know not, But doubtless my teacher knows sere not I
there is no such land. The very idea of it
is utterly inconceivable. I your lordship tempts his servant to
(26:24):
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 have no eye in our stomachs. But just
as there was the realm of flat land, though that poor,
(26:47):
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
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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
(27:32):
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
(27:54):
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
(28:15):
result in a still more divine organization with sixteen terminal points.
Behold the infallible confirmation of the series two, four, eight, sixteen.
Is not this a geometrical progression? Is not this if
I might quote my Lord's own words strictly according to analogy? Again,
(28:42):
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 to two U for six. Is not this an
(29:03):
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 eight bounding cubes?
And is not this also, as my Lord has taught
(29:23):
me to believe strictly according to analogy? Oh 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,
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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,
(30:08):
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 that safe an answer sphere after a pause,
(30:33):
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,
(30:58):
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
(31:20):
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.
(31:43):
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, who
believe them not? Or if it indeed be so that
this other space is really thought land, then take me
(32:06):
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
(32:28):
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
(32:51):
the fifth and not enter therein? Ah? No, Let us
rather resolve that our ambition shall soar with our corporal assent. 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
(33:15):
not in vain did the Sphere, in his voice of thunder,
reiterate his commands 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 drafts of truth
(33:40):
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,
(34:01):
I was rapidly descending, and I knew that return to
flat land 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,
(34:25):
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 twenty. How the sphere encouraged me in
(34:47):
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 flat land,
(35:08):
the narrative of my adventures must needs be unintelligible. So
I endeavored 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 Laan stunned. The
southward attraction in our country is so slight that even
(35:28):
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
(35:52):
to my chamber to think quietly over what had happened.
When I was at last by myself, a drows sensation
fell on me. But before my eyes closed, I endeavored
to reproduce the third dimension, and especially the process by
which a cube is constructed through the motion of a square.
(36:14):
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
(36:35):
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
(36:59):
were moving together hither 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 blue bottles, only less resonant
by far. So slight, indeed, that even in the perfect
(37:22):
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 flat Land. Thou hast
lived of line Land. Thou hast received a vision. Thou
(37:43):
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 depths of existence, even
to the realm of point Land, the abyss of no dimensions.
Behold yon miserable creature. That point is a being like ourselves,
(38:08):
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.
(38:30):
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
(38:54):
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 space and phonographs, from which
(39:15):
I caught these words.
Speaker 2 (39:17):
Infinite beatitude of existence. It is, and there is none
else beside it?
Speaker 1 (39:26):
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 soliloquising creature.
(39:53):
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
(40:13):
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.
(40:34):
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 pointer as follows. Silence, silence,
(40:55):
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, harsh. You have said
enough interrupted the sphere. Now listen and mark the effect
(41:17):
of your harangue on the King of Pointland. The luster
of the monarch, who beamed more brightly than ever upon
hearing my words, showed clearly that he retained his complacency,
and I had hardly ceased when he took up his
strain again.
Speaker 2 (41:35):
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
(41:58):
divine creative power of the all in one, Ah, their 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,
(42:20):
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.
(42:41):
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 mild voice of
my companion, pointing the moral of my vision and stimulating
me to aspire and to teach others to aspire. He
(43:04):
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
(43:25):
I had witnessed, showing 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. End of Section twenty
Part two, Section eighteen. How I came to Spaceland and
what I saw there? An unspeakable horror seized me. There
was a darkness, then a dizzy, sickening sensation of sight
that was not like seeing. I saw a line that
was no line, space that was not space. I was
(00:23):
myself and not myself. When I could find voice, I
shrieked aloud in agony. Either this is madness or it
is hell. It is neither, calmly replied the voice of
the sphere. It is knowledge. It is three dimensions. Open
(00:44):
your eye once again and try to look steadily. I looked,
and behold a new world. There stood before me, visibly
incorporate all that I had before inferred, conjectured, dreamed of
(01:04):
perfect circular beauty. What seemed the center of the Stranger's
form lay open to my view. Yet I could see
no heart, nor lungs, nor arteries, only a beautiful, harmonious
something for which I had no words. But you, my
(01:26):
readers in Spaceland, would call it the surface of the sphere.
Prostrating myself mentally before my guide, I cried, how is
it o divine ideal of consumate loveliness and wisdom that
I see thy inside, and yet cannot discern thy heart,
(01:47):
thy lungs, thy arteries, thy liver. What you think you see,
you see not, he replied. It is not given to you,
nor to any other being, to behold my internal parts.
I am of a different order of beings from those
in Flatland. Were I a circle, you could discern my intestines.
(02:10):
But I am a being composed, as I told you before,
of many circles, the many in the one called in
this country a sphere. And just as the outside of
a cube is a square, so the outside of a
sphere presents the appearance of a circle. Bewildered though I
(02:32):
was by my teacher's enigmatic utterance, I no longer chafed
against it, but worshiped him in silent adoration. He continued,
with more mildness in his voice. Distress not yourself. If
you cannot at first understand the deeper mysteries of spaceland,
by degrees, they will dawn upon you. Let us begin
(02:55):
by casting back a glance at the region whence you came.
Return with me awhile to the plains of flat Land,
and I will show you that which you have so
often reasoned and thought about, but never seen with the
sense of sight. A visible angle impossible, I cried, But
(03:18):
the sphere leading the way, I followed, as if in
a dream, till once more his voice arrested me. Look yonder,
and behold your own pentagonal house and all its inmates.
Reader's note. The following paragraph refers to a detailed diagram.
The diagram shows the points of the compass, with north
(03:39):
at the top. Next to this, there is a large
equal sided pentagon sitting on a horizontal base. Centrally placed
on the lower left edge of the pentagon, there is
an opening labeled men's door, the size of the opening
being about a quarter of the length of that edge.
(04:00):
This door leads into a large central space labeled the hall,
which is otherwise surrounded by rooms. The position of these
rooms will now be described clockwise from the northern point.
The upper right edge is divided equally between two rooms
labeled in order, my study and my Bedroom. The left
(04:24):
hand wall of the study runs vertically down from the
northern point, and the right hand wall is parallel to
the lower right edge of the pentagon. The study has
a door into the hall, and there is Isosceles triangle
inside labeled the page. Sharing a wall with the study
(04:44):
is my rhomboid shaped bedroom, the right hand wall of
which is the top quarter of the lower right hand
edge of the pentagon. It shares a wall and communicating
door with the room to the south labeled my my
Wife's Apartment. About three tenths down the lower right edge,
(05:06):
there is a narrow opening labeled Women's door. This leads
into a long, narrow room labeled my Wife's apartment. This
room has doorways into my bedroom above, into the hall
to the left, and into the room to the south,
also long and narrow, where a straight line is marked
(05:28):
my daughter. The only door from my Daughter's room is
into my wife's apartment. Continuing clockwise down the lower right
edge of the pentagon, the next room is a long
and wide room with two openings into the hall. Inside
are three isosceles triangles of varying acuteness. The uppermost and
(05:52):
most acute is labeled the scullion, the next and middle
sized is labeled the Footman, and the lowerest and least
acute is labeled the Butler. At the bottom right point
of the pentagon, a large corner room is labeled the
cellar and has a door into the hall. Along the
(06:14):
left half of the bottom or southern edge, there are
two small rooms, each with a door into the hall,
and each with a hexagon inside labeled my grandson's. Continuing
clockwise up the left side of the pentagon, between the
men's door and the northern point, there are four small rooms.
(06:36):
Each of these rooms, labeled my sons, has a pentagon
inside it and a door into the hall. In the
middle of the central hall is a straight line labeled
my wife. Outside the pentagon one At each end of
the bottom or southern edge, are two very acute Isosceles triangles,
(06:57):
each labeled Policeman. End of reader's note. I looked below
and saw with my physical eye all that domestic individuality
which I had hitherto merely inferred with the understanding, And
how poor and shadowy was the inferred conjecture in comparison
(07:18):
with the reality which I now beheld. My four sons
calmly asleep in the northwestern rooms, my two orphan grandsons
to the south, the servants, the butler, my daughter, all
in their several apartments. Only my affectionate wife, alarmed by
(07:39):
my continued absence, had quitted her room, and was roving
up and down in the hall, anxiously awaiting my return. Also,
the page, aroused by my cries, had left his room,
and under pretext of ascertaining whether I had fallen somewhere
in a faint, was prying into the cabinet in my study.
(08:00):
All this I could now see not merely infer and
as we came nearer and nearer, I could discern even
the contents of my cabinet, and the two chests of gold,
and the tablets of which the Sphere had made mention.
Touched by my wife's distress, I would have sprung downward
(08:21):
to reassure her, but I found myself incapable of motion.
Trouble not yourself about your wife, said my guide. She
will not be long left in anxiety. Meantime, let us
take a survey of flat land. Once more, I felt
myself rising through space. It was even as the Sphere
(08:43):
had said. The further we receded from the object we beheld,
the larger became the field of vision. My native city,
with the interior of every house and every creature therein
lay open to my view. In miniature, we mounted higher
and lo the secrets of the earth, the depths of mines,
(09:07):
and inmost caverns of the hills were bared before me.
AWE struck at the sight of the mysteries of the
earth thus unveiled before my unworthy eye. I said to
my companion, Behold, I am become as a god. For
the wise men in our country say that to see
all things, or as they express it, omnividence is the
(09:31):
attribute of God alone. There was something of scorn in
the voice of my teacher as he made answer, Is
it so? Indeed? Then the very pick pockets and cut
throats of my country are to be worshiped by your
wise men as being gods. For there is not one
of them that does not see as much as you
(09:53):
see now. But trust me, your wise men are wrong.
I is omnividence the attribute of others beside God's sphere?
I do not know. But if a pickpocket or a
cutthroat of our country can see everything that is in
your country, surely that is no reason whether pickpocket or
(10:17):
cutthroat should be accepted by you as a god. This omnividence,
as you call it, it is not a common word
in spaceland. Does it make you more just? More merciful,
less selfish, more loving. Not in the least, then, how
does it make you more divine? I more merciful, more loving.
(10:41):
But these are the qualities of women. And we know
that a circle is a higher being than a straight line,
in so far as knowledge and wisdom are more to
be esteemed than mere affection. Sphere, it is not for
me to classify human faculties. According to merit, many of
the best and wisest in spaceland think more of the
(11:03):
affections than of the understanding, more of your despised straight
lines than of your belauded circles. But enough of this,
Look yonder? Do you know that building? I looked, and
afar off I saw an immense polygonal structure, in which
I recognized the General Assembly Hall of the States of Flatland,
(11:26):
surrounded by dense lines of pentagonal buildings at right angles
to each other, which I knew to be streets. And
I perceived that I was approaching the great metropolis. Here
we descend, said my guide. It was now morning, the
first hour of the first day of the two thousandth
year of our era. Acting as was there wont in
(11:49):
strict accordance with precedent, the highest circles of the Realm
were meeting in solemn conclave, as they had met on
the first hour of the first day of the year
one thousand, and also on the first hour of the
first day of the year nought. The minutes of the
previous meetings were now read by one whom I at
(12:10):
once recognized as my brother, a perfectly symmetrical square, and
the Chief Clerk of the High Council. It was found
recorded on each occasion that whereas the states had been
troubled by divers ill intentioned persons, pretending to have received
revelations from another world, and professing to produce demonstrations, whereby
(12:33):
they had instigated to frenzy both themselves and others, it
had been for this cause unanimously resolved by the Grand
Council that on the first day of each millinery, special
injunctions be sent to the prefects in the several districts
of Flatland to make strict search for such misguided persons,
(12:54):
and without formality of mathematical examination, to destroy all such
as were I soosceles of any degree, to scourge and
imprison any regular triangle, to cause any square or pentagon
to be sent to the district asylum, and to arrest
any one of higher rank, sending him straightway to the
capital to be examined and judged by the council. You
(13:19):
hear your fate, said the sphere to me, while the
council was passing for the third time, the formal resolution
death or imprisonment awaits the apostle of the Gospel of
three Dimensions. Not so, replied I. The matter is now
so clear to me, the nature of real space so palpable,
(13:40):
that methinks I could make a child understand it. Permit
me but to descend at this moment and enlighten them?
Not yet, said my guide. The time will come for that.
Meantime I must perform my mission. Stay thou there in
thy place. Saying these words, he leapt with great dexterity
(14:01):
into the sea. If I may say, call it a
flat land. Right in the midst of the ring of councilors,
I come, cried he to proclaim that there is a
land of three dimensions. I could see many of the
younger councilors start back in manifest horror as the Sphere's
circular section widened before them. But on a sign from
(14:26):
the presiding circle, who showed not the slightest alarm or surprise.
Six Isosceles of a lone type, from six different quarters
rushed upon the sphere. We have him, they cried, No, yes,
we have him. Still he's going. He's gone, my lords,
(14:47):
said the President to the junior circles of the Council.
There is not the slightest need for surprise. The secret archives,
to which I alone have access, tell me that a
similar occurrence happened on the last two millennial commencements. You will,
of course, say nothing of these trifles outside the cabinet.
(15:08):
Raising his voice, he now summoned the guard, arrest the policeman,
gag them. You know your duty. After he had consigned
to their fate the wretched policeman, ill fated and unwilling
witnesses of a state secret which they were not to
be permitted to reveal, he again addressed to counselors, my lords,
(15:31):
the business of the Council being concluded, I have only
to wish you a happy new year. Before departing, he
expressed at some lengths to the Clerk, my excellent but
most unfortunate brother, his sincere regret that in accordance with precedent,
and for the sake of secrecy, he must condemn him
(15:52):
to perpetual imprisonment, but added his satisfaction that unless some
mention were made by him of that day's incident, his
life would be spared Section nineteen. How though the sphere
showed me other mysteries of spaceland, I still desired more,
(16:14):
and what came of it? When I saw my poor
brother led away to imprisonment. I attempted to leap down
into the council chamber, desiring to intercede on his behalf,
or at least bid him farewell. But I found that
I had no motion of my own. I absolutely depended
on the volition of my guide, who said, in gloomy tones,
(16:37):
heed not thy brother, haply, thou shalt have ample time
hereafter to condole with him. Follow me Reader's note. The
following paragraph makes reference to a diagram. Diagram one shows
a three dimensional cube with visible edges drawn and hidden
(16:58):
edges dotted, giving it a three dimensional appearance. Horizontal shading
makes it appear that the cube is made up of
many layers. Diagram two shows the same figure, but all
lines indicating perspective are missing. With the effect that it
no longer appears to be solid, but looks like a
(17:21):
two dimensional irregular hexagonal figure. End of reader's note. Once more,
we ascended into space. Hitherto, said the sphere. I have
shown you nought save plain figures and their interiors. Now
I must introduce you to solids, and reveal to you
(17:41):
the plan upon which they are constructed. Behold this multitude
of moveable square cards. See I put one on another,
not as you supposed northward of the other, but on
the other now as second, now a third. See I
am building up a solid by a multitude of squares
(18:03):
parallel to one another. Now the solid is complete, being
as high as it is long and broad, and we
call it a cube. Pardon me, my lord, replied I,
But to my eye, the appearance is as of an
irregular figure whose inside is laid open to the view.
(18:23):
In other words, methinks I see no solid, but a plain,
such as we infer in flat land, only of an
irregularity which betokens some monstrous criminal, so that the very
sight of it is painful to my eyes. True, said
the sphere. It appears to you a plane because you
(18:44):
are not accustomed to light and shade and perspective, just
as in flat land a hexagon would appear a straight
line to one who has not the art of sight recognition,
but in reality it is a solid. Shall learn by
the sense of feeling. He then introduced me to the cube,
(19:05):
and I found that this marvelous being was indeed no plane,
but a solid, and that he was endowed with six
plain sides and eight terminal points called solid angles. And
I remembered the saying of the sphere that just such
a creature as this would be formed by a square
(19:26):
moving in space parallel to himself. And I rejoiced to
think that so insignificant a creature as I could, in
some sense be called the progenitor of so illustrious an offspring.
But still I could not fully understand the meaning of
what my teacher had told me concerning light and shade
(19:50):
and perspective, and I did not hesitate to put my
difficulties before him. Were I to give the spheres explain
nation of these matters, succinct and clear though it was,
it would be tedious to an inhabitant of space who
knows these things already. Suffice it that, by his lucid
(20:12):
statements and by changing the position of objects and lights,
and by allowing me to feel the several objects and
even his own sacred person, he at last made all
things clear to me, so that I could now readily
distinguish between a circle and a sphere, a plain figure
(20:33):
and a solid This was the climax, the paradise of
my strange, eventful history. Henceforth I have to relate the
story of my miserable fall, most miserable, yet surely most undeserved.
For why should the thirst for knowledge be aroused only
(20:55):
to be disappointed and punished. My volition shrinks from the
painful task of recalling my humiliation. Yet, like a second Prometheus,
I will endure this and worse. If by any means
I may arouse in the interiors of plain and solid
humanity a spirit of rebellion against the conceit which would
(21:18):
limit our dimensions to two or three, or any number
short of infinity away, then with all personal considerations, let
me continue to the end as I began, without further
digressions or anticipations, pursuing the plain path of dispassionate history.
(21:40):
The exact facts, the exact words, and they are burnt
in upon my brain shall be set down without alteration
of an iota, and let my readers judge between me
and destiny. The sphere would willingly have continued his lessons
by indoctrinating me in the confirmation of all regular solids, cylinders, cones, pyramids, pentahedrons, hexahedrons, dodecahedrons,
(22:11):
and spheres. But I ventured to interrupt him, not that
I was wearied of knowledge. On the contrary, I thirsted
for yet deeper and fuller drafts than he was offering
to me. Pardon me, said I, O, thou whom I
must no longer addresses the perfection of all beauty? But
(22:35):
let me beg THEE to vouchsafe thy servant a sight
of thine interior sphere. My what I thine interior, thy stomach,
thy intestines sphere? Whence this ill timed, impertinent request? Then
(22:55):
what mean you by saying that I am no longer
the perfection of all beauty? I, my Lord, your own
wisdom has taught me to aspire to one even more great,
more beautiful, and more closely approximate to perfection than yourself.
As you, yourself superior to all flatland forms, combine many
(23:19):
circles in one. So doubtless there is one above you
who combines many spheres in one supreme existence, surpassing even
the solids of spaceland. And even as we who are
now in space look down on flat land and see
the insides of all things, so of a certainty there
(23:42):
is yet above us, some higher, purer region, whither thou
dost surely purpose to lead me. O thou, whom I
shall always call everywhere and in all dimensions, my priest
philosopher and friend, some yet more spacious space, some more
dimensionable dimensionality, from the vantage ground of which we shall
(24:06):
look down together upon the revealed insides of solid things,
and where thine own intestines and those of thy kindred
spheres will lie exposed to the view of the poor
wandering exile from flatland, to whom so much has already
been vouchsafed. Sphere, woof stuff. Enough of this trifling. The
(24:30):
time is short, and much remains to be done before
you are fit to proclaim the Gospel of three dimensions
to your blind, benighted countrymen in flatland. I nay, gracious teacher,
deny me not what I know. It is in thy
power to perform, grant me but one glimpse of Thine interior,
(24:52):
and I am satisfied forever remaining henceforth, thy docile pupil,
thy unemancipable slave, ready to receive all thy teachings, and
to feed upon the words that fall from thy lips.
Sphere well, then to content and silence. You let me
say at once, I would show you what you wish
(25:13):
if I could, But I cannot. Would you have me
turn my stomach inside out to oblige you? I, but
my Lord has shown me the intestines of all my
countrymen in the land of two dimensions, by taking me
with him into the land of three. What therefore more
easy than now to take his servant on a second
(25:36):
journey into the blessed region of the fourth dimension, where
I shall look down with him once more upon this
land of three dimensions, and see the inside of every
three dimensioned house, the secrets of the solid earth, the
treasures of the minds in spaceland, and the intestines of
every solid living creature, even of the noble and adorables sphere.
(26:03):
But where is this land of four dimensions? I I
know not, But doubtless my teacher knows sere not I
there is no such land. The very idea of it
is utterly inconceivable. I your lordship tempts his servant to
(26:24):
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 have no eye in our stomachs. But just
as there was the realm of flat land, though that poor,
(26:47):
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
(27:09):
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
(27:32):
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
(27:54):
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
(28:15):
result in a still more divine organization with sixteen terminal points.
Behold the infallible confirmation of the series two, four, eight, sixteen.
Is not this a geometrical progression? Is not this if
I might quote my Lord's own words strictly according to analogy? Again,
(28:42):
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 to two U for six. Is not this an
(29:03):
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 eight bounding cubes?
And is not this also, as my Lord has taught
(29:23):
me to believe strictly according to analogy? Oh 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,
(29:46):
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,
(30:08):
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 that safe an answer sphere after a pause,
(30:33):
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,
(30:58):
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
(31:20):
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.
(31:43):
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, who
believe them not? Or if it indeed be so that
this other space is really thought land, then take me
(32:06):
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
(32:28):
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
(32:51):
the fifth and not enter therein? Ah? No, Let us
rather resolve that our ambition shall soar with our corporal assent. 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
(33:15):
not in vain did the Sphere, in his voice of thunder,
reiterate his commands 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 drafts of truth
(33:40):
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,
(34:01):
I was rapidly descending, and I knew that return to
flat land 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,
(34:25):
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 twenty. How the sphere encouraged me in
(34:47):
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 flat land,
(35:08):
the narrative of my adventures must needs be unintelligible. So
I endeavored 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 Laan stunned. The
southward attraction in our country is so slight that even
(35:28):
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
(35:52):
to my chamber to think quietly over what had happened.
When I was at last by myself, a drows sensation
fell on me. But before my eyes closed, I endeavored
to reproduce the third dimension, and especially the process by
which a cube is constructed through the motion of a square.
(36:14):
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
(36:35):
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
(36:59):
were moving together hither 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 blue bottles, only less resonant
by far. So slight, indeed, that even in the perfect
(37:22):
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 flat Land. Thou hast
lived of line Land. Thou hast received a vision. Thou
(37:43):
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 depths of existence, even
to the realm of point Land, the abyss of no dimensions.
Behold yon miserable creature. That point is a being like ourselves,
(38:08):
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.
(38:30):
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
(38:54):
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 space and phonographs, from which
(39:15):
I caught these words.
Speaker 2 (39:17):
Infinite beatitude of existence. It is, and there is none
else beside it?
Speaker 1 (39:26):
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 soliloquising creature.
(39:53):
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
(40:13):
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.
(40:34):
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 pointer as follows. Silence, silence,
(40:55):
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, harsh. You have said
enough interrupted the sphere. Now listen and mark the effect
(41:17):
of your harangue on the King of Pointland. The luster
of the monarch, who beamed more brightly than ever upon
hearing my words, showed clearly that he retained his complacency,
and I had hardly ceased when he took up his
strain again.
Speaker 2 (41:35):
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
(41:58):
divine creative power of the all in one, Ah, their 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,
(42:20):
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.
(42:41):
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 mild voice of
my companion, pointing the moral of my vision and stimulating
me to aspire and to teach others to aspire. He
(43:04):
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
(43:25):
I had witnessed, showing 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. End of Section twenty
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