Mythos Lullaby - Kosmos Flatland (Part II)

神話的搖籃曲 - 平面神話秩序 英文版

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"The owl of Minerva spreads its wings only with the falling of the dusk" - Hegel

For those who overlook everything from the three-dimensional world, both "Formalism" and "Chromatism (Colorism)" have significant flaws. However, the residents of the two-dimensional plane world have very limited possibilities they can perceive; they can only make choices visible within their field of view.

Although both the "shape-based" and "color-based" philosophies may seem incomplete and destined for disaster, both sides sincerely believe that the philosophy they uphold can solve everything. They fail to realize that both "shape" and "color" are projections of the three-dimensional world onto the two-dimensional plane.

People in the three-dimensional world know that there is something deeper. The simple pursuit of "shape" or "color" cannot solve the ignorance, problems, and conflicts of the two-dimensional world.

Three-dimensional observers wonder why two-dimensional people would fight to the death for such incomplete philosophies. In contrast, the residents of the two-dimensional plane world find the speculations of the three-dimensional inhabitants unbelievable, viewing them as either pure fantasies or the whispers of the devil.

A Square's Visit to the One-Dimensional Linear World

On the penultimate day of 1999, A-Square, the protagonist of "Flatland," had a dream.

In the dream, A Square, being a two-dimensional square, observed a "line space" within an unknown realm. On this "line space," A Square witnessed various line segments.

(§ 13 How I had a Vision of Lineland)

In this one-dimensional linear world, the longest line is the king. In this one-dimensional kingdom, length represents the highest value and serves as the foundation of social order.

Initially, A-Square attempted to have a conversation with the "Line King," but discovered that the "Line King" didn't know where A-Square's voice was coming from. For the king, A-Square's voice originated from an unknown direction (as anything outside the linear space was unknown to the "Line King").

(§ 13 How I had a Vision of Lineland)

It seemed that this poor ignorant Monarch—as he called himself—was persuaded that the Straight Line which he called his Kingdom, and in which he passed his existence, constituted the whole of the world, and indeed the whole of Space. Not being able either to move or to see, save in his Straight Line, he had no conception of anything out of it. Though he had heard my voice when I first addressed him, the sounds had come to him in a manner so contrary to his experience that he had made no answer, “seeing no man,” as he expressed it, “and hearing a voice as it were from my own intestines.”

From the king's perspective, A-Square's voice seemed to be "emanating from within."

For a line, the left end and the right end are considered "sides," while everything between the left and right ends is considered "inside" (εσωτερικός = esoteric = internal). And anything that is neither "side" nor "inside" is considered "outside" (εξωτερικός = exoteric = external).

The king believed that the line space he perceived constituted the entirety of the world.

(§ 13 How I had a Vision of Lineland)

Until the moment when I placed my mouth in his World, he had neither seen me, nor heard anything except confused sounds beating against, what I called his side, but what he called his inside (εσωτερικός = esoteric = internal) or stomach; nor had he even now the least conception of the region from which I had come. Outside his World, or Line, all was a blank to him; nay, not even a blank, for a blank implies Space; say, rather, all was non-existent.

In this one-dimensional linear kingdom, auditory perception is the most important distinguishing sense because everyone can only see a single point, similar to how residents of a two-dimensional world perceive only a line.

(§ 13 How I had a Vision of Lineland)

His subjects—of whom the small Lines were men and the Points Women—were all alike confined in motion and eyesight to that single Straight Line, which was their World. It need scarcely be added that the whole of their horizon was limited to a Point; nor could any one ever see anything but a Point. Man, woman, child, thing—each as a Point to the eye of a Linelander. Only by the sound of the voice could sex or age be distinguished.

In A-Square's eyes, the one-dimensional world appeared quite dull, monotonous, and boring. However, he unexpectedly discovered that the king was full of vitality.

(§ 13 How I had a Vision of Lineland)

Such a life, with all vision limited to a Point, and all motion to a Straight Line, seemed to me inexpressibly dreary; and I was surprised to note that vivacity and cheerfulness of the King. Wondering whether it was possible, amid circumstances so unfavourable to domestic relations, to enjoy the pleasures of conjugal union, I hesitated for some time to question his Royal Highness on so delicate a subject; but at last I plunged into it by abruptly inquiring as to the health of his family. “My wives and children,” he replied, “are well and happy.”

A-Square attempted to explain to the one-dimensional king that in this world, apart from the concepts of north and south, there are also east and west (left and right). However, the one-dimensional king expressed confusion, and their ensuing conversation ended up in communication failure.

(§ 14 How I vainly tried to explain the nature of Flatland)

King: “...though I know not what you mean by ‘right’ and ‘left.’ But I deny that you saw these things. For how could you see the Line, that is to say the inside, of any Man? But you must have heard these things, and then dreamed that you saw them. And let me ask what you mean by those words ‘left’ and ‘right.’ I suppose it is your way of saying Northward and Southward.”

“Not so,” replied I; “besides your motion of Northward and Southward, there is another motion which I call from right to left.”

King: Exhibit to me, if you please, this motion from left to right.

I: Nay, that I cannot do, unless you could step out of your Line altogether.

King: Out of my Line? Do you mean out of the world? Out of Space?

I: Well, yes. Out of your world. Out of your Space. For your Space is not the true Space. True Space is a Plane; but your Space is only a Line.

King: If you cannot indicate this motion from left to right by yourself moving in it, then I beg you to describe it to me in words.

I: If you cannot tell your right side from your left, I fear that no words of mine can make my meaning clearer to you. But surely you cannot be ignorant of so simple a distinction.

King: I do not in the least understand you.

I. Alas! How shall I make it clear? When you move straight on, does it not sometimes occur to you that you could move in some other way, turning your eye round so as to look in the direction towards which your side is now fronting? In other words, instead of always moving in the direction of one of your extremities, do you never feel a desire to move in the direction, so to speak, of your side?

King: Never. And what do you mean? How can a man’s inside “front” in any direction? Or how can a man move in the direction of his inside?

I: Well then, since words cannot explain the matter, I will try deeds, and will move gradually out of Lineland in the direction which I desire to indicate to you.

When it became apparent that language was completely ineffective and their linguistic systems had non-overlapping realms, A-Square decided to persuade the king through action and tangible "phenomena." A-Square planned to "project" himself into the one-dimensional space, allowing the king to "perceive" his true existence.

And A-Square succeeded in making the king perceive his "projection."

(§ 14 How I vainly tried to explain the nature of Flatland)

At the word I began to move my body out of Lineland. As long as any part of me remained in his dominion and in his view, the King kept exclaiming, “I see you, I see you still; you are not moving.”

But when I had at last moved myself out of his Line, he cried in his shrillest voice, “She is vanished; she is dead.”

“I am not dead,” replied I; “I am simply out of Lineland, that is to say, out of the Straight Line which you call Space, and in the true Space, where I can see things as they are. And at this moment I can see your Line, or side—or inside as you are pleased to call it; and I can see also the Men and Women on the North and South of you, whom I will now enumerate, describing their order, their size, and the interval between each.”

When I had done this at great length, I cried triumphantly, “Does that at last convince you?” And, with that, I once more entered Lineland, taking up the same position as before.

A-Square traversing his entire square body along the linear dimension.

From the king's perception, this action appeared as A-Square "suddenly" appearing and then "suddenly" disappearing, as if he had come and died.

A-Square believed that by accomplishing this "miracle," he could make the king believe. However, he didn't anticipate the deep-rooted inertia of the king's worldview. The king simply regarded A-Square as a demon or an evil entity.

The king's "linear rationality" led him to reach a "clear" conclusion: A-Square did not actually move but rather employed magical tricks of disappearance and reappearance. The king believed that the "new world" proclaimed by A-Square did not exist.

Upon hearing this, A-Square became angry.

(§ 14 How I vainly tried to explain the nature of Flatland)

Furious at his perversity, and especially indignant that he professed to be ignorant of my sex, I retorted in no measured terms, “Besotted Being! You think yourself the perfection of existence, while you are in reality the most imperfect and imbecile. You profess to see, whereas you see nothing but a Point! You plume yourself on inferring the existence of a Straight Line; but I can see Straight Lines, and infer the existence of Angles, Triangles, Squares, Pentagons, Hexagons, and even Circles. Why waste more words? Suffice it that I am the completion of your incomplete self. You are a Line, but I am a Line of Lines called in my country a Square: and even I, infinitely superior though I am to you, am of little account among the great nobles of Flatland, whence I have come to visit you, in the hope of enlightening your ignorance.”

A-Square's arrogance successfully provoked the anger of the one-dimensional king, who attempted to attack A-Square.

(§ 14 How I vainly tried to explain the nature of Flatland)

Hearing these words the King advanced towards me with a menacing cry as if to pierce me through the diagonal; and in that same movement there arose from myriads of his subjects a multitudinous war-cry, increasing in vehemence till at last methought it rivalled the roar of an army of a hundred thousand Isosceles, and the artillery of a thousand Pentagons. Spell-bound and motionless, I could neither speak nor move to avert the impending destruction; and still the noise grew louder, and the King came closer, when I awoke to find the breakfast-bell recalling me to the realities of Flatland.

And then A-Square's dream ended.

Visitor from the three-dimensional space

On the day following A-Square's dream visit to the one-dimensional world, he encountered a visitor from the three-dimensional space.

(§ 15 Concerning a Stranger from Spaceland)

It was the last day of our 1999th year of our era. The patterning of the rain had long ago announced nightfall; and I was sitting in the company of my wife, musing on the events of the past and the prospects of the coming year, the coming century, the coming Millennium.

In the house where A-Square resides, a strange sound appeared, along with the appearance of a "person," which greatly frightened A-Square and his wife.

(§ 15 Concerning a Stranger from Spaceland)

My Wife as well as myself heard the words, although she did not understand their meaning, and both of us sprang forward in the direction of the sound. What was our horror when we saw before us a Figure! At the first glance it appeared to be a Woman, seen sideways; but a moment’s observation shewed me that the extremities passed into dimness too rapidly to represent one of the Female Sex; and I should have thought it a Circle, only that it seemed to change its size in a manner impossible for a Circle or for any regular Figure of which I had had experience.

After A-Square asked his wife to leave, he recognized the unfamiliar visitor as a "Circle," one of the most respected entities in his society.

(§ 15 Concerning a Stranger from Spaceland)

then, suddenly recoiling, “Oh! it is not a Woman, and there are no angles either, not a trace of one. Can it be that I have so misbehaved to a perfect Circle?”

The unfamiliar visitor spoke enigmatic words.

(§ 15 Concerning a Stranger from Spaceland)

“I am indeed, in a certain sense a Circle,” replied the Voice, “and a more perfect Circle than any in Flatland; but to speak more accurately, I am many Circles in one.” ...... I glanced at the half-hour glass. The last sands had fallen. The third Millennium had begun.

When this unfamiliar Sphere "descends" into the two-dimensional space where A-Square resides, he perceives it as a Circle based on his experience and knowledge.

The perception of the Circle by A-Square is the two-dimensional cross-section of the "sphere" in the flat plane.

What A-Square's sensory eyes perceive is the one-dimensional projection of this sphere's two-dimensional cross-section.

Through a perceptive interpretation of this one-dimensional projection, A-Square concludes that he sees a two-dimensional "Circle."

(§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland)

There was not the trace of an angle, not the slightest roughness or inequality: never in my life had I met with a more perfect Circle. He remained motionless while I walked around him, beginning from his eye and returning to it again. Circular he was throughout, a perfectly satisfactory Circle; there could not be a doubt of it.

The Revelation of the Three-Dimensional Visitor

A-Square witnessed the appearance of a stranger in his house, and the "roundness" of this unfamiliar individual surpassed any approximations to roundness he had ever encountered. In A-Square's worldview and value system, approaching roundness was synonymous with nobility, leading him to hold deep respect and admiration for the visitor.

(§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland)

Then followed a dialogue, which I will endeavour to set down as near as I can recollect it, omitting only some of my profuse apologies—for I was covered with shame and humiliation that I, a Square, should have been guilty of the impertinence of feeling a Circle. It was commenced by the Stranger with some impatience at the lengthiness of my introductory process.

Stranger. Have you felt me enough by this time? Are you not introduced to me yet?

I. Most illustrious Sir, excuse my awkwardness, which arises not from ignorance of the usages of polite society, but from a little surprise and nervousness, consequent on this somewhat unexpected visit. And I beseech you to reveal my indiscretion to no one, and especially not to my Wife. But before your Lordship enters into further communications, would he deign to satisfy the curiosity of one who would gladly know whence his visitor came?

Stranger. From Space, from Space, Sir: whence else?

I. Pardon me, my Lord, but is not your Lordship already in Space, your Lordship and his humble servant, even at this moment?

Stranger. Pooh! what do you know of Space? Define Space.

I. Space, my Lord, is height and breadth indefinitely prolonged.

Stranger. Exactly: you see you do not even know what Space is. You think it is of Two Dimensions only; but I have come to announce to you a Third—height, breadth, and length.

A-Square and the Three-Dimensional Spherical Visitor repeated, in a certain form, the interaction process A-Square had with the One-Dimensional King the previous day. The Three-Dimensional Visitor attempted to explain the existence of the "third dimension - height" to A-Square, but he couldn't grasp it entirely.

What exactly is "height"?  A-Square remained completely unable to comprehend.

(§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland)

I. Your Lordship is pleased to be merry. We also speak of length and height, or breadth and thickness, thus denoting Two Dimensions by four names.

Stranger. But I mean not only three names, but Three Dimensions.

I. Would your Lordship indicate or explain to me in what direction is the Third Dimension, unknown to me?

Stranger. I came from it. It is up above and down below.

I. My Lord means seemingly that it is Northward and Southward.

Stranger. I mean nothing of the kind. I mean a direction in which you cannot look, because you have no eye in your side.

I. Pardon me, my Lord, a moment’s inspection will convince your Lordship that I have a perfectly luminary at the juncture of my two sides.

Stranger. Yes: but in order to see into Space you ought to have an eye, not on your Perimeter, but on your side, that is, on what you would probably call your inside; but we in Spaceland should call it your side.

I. An eye in my inside! An eye in my stomach! Your Lordship jests.

Stranger. I am in no jesting humour. I tell you that I come from Space, or, since you will not understand what Space means, from the Land of Three Dimensions whence I but lately looked down upon your Plane which you call Space forsooth. From that position of advantage I discerned all that you speak of as solid (by which you mean “enclosed on four sides”), your houses, your churches, your very chests and safes, yes even your insides and stomachs, all lying open and exposed to my view.

The topic of "lateral" and "inside" (εσωτερικός = esoteric = internal) reappeared in a different form during the conversation between A-Square and the Spherical Visitor.

And so, the two continued their futile communication across dimensions.

(§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland)

Stranger. No, indeed. By “height” I mean a Dimension like your length: only, with you, “height” is not so easily perceptible, being extremely small.

I. My Lord, your assertion is easily put to the test. You say I have a Third Dimension, which you call “height.” Now, Dimension implies direction and measurement. Do but measure my “height,” or merely indicate to me the direction in which my “height” extends, and I will become your convert. Otherwise, your Lordship’s own understand must hold me excused.

Just as the "linear rationality" of the one-dimensional king could not understand A-Square's revelation, A-Square's "planar rationality" could not comprehend the revelation of a sphere with a higher dimension than him.

After a round of ineffective persuasion, the Sphere decided to perform a "miracle". The Sphere moved its body to "penetrate" the plane where A Square was located. In A Square's vision, the Sphere "shrunk" and then "disappeared", yet A Square could still hear the Sphere's voice from "inside his body".

(§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland)

But to me, proficient though I was in Flatland Mathematics, it was by no means a simple matter. The rough diagram given above will make it clear to any Spaceland child that the Sphere, ascending in the three positions indicated there, must needs have manifested himself to me, or to any Flatlander, as a Circle, at first of full size, then small, and at last very small indeed, approaching to a Point. But to me, although I saw the facts before me, the causes were as dark as ever. All that I could comprehend was, that the Circle had made himself smaller and vanished, and that he had now re-appeared and was rapidly making himself larger.

After the Sphere demonstrated the "miracle", A-Square was still deeply confused. Therefore, like Socrates, the Sphere performed a round of "geometric knowledge midwifery" on A-Square, starting from a point to deduce a line, from a line to a plane, and then trying to deduce three dimensions from the characteristics of a plane.

But the Sphere failed. A-Square did not believe in the results of mathematical deduction under rational Logic(Λογος). The deduced result was too bizarre, too crazy, too abnormal, and too unacceptable for A-Square. So A-Square went mad.

(§ 16 How the Stranger vainly endeavoured to reveal to me in words the mysteries of Spaceland)

“Monster,” I shrieked, “be thou juggler, enchanter, dream, or devil, no more will I endure thy mockeries. Either thou or I must perish.” And saying these words I precipitated myself upon him.

Then A Square launched an attack on the revealer.

(§ 17 How the Sphere, having in vain tried words, resorted to deeds)

It was in vain. I brought my hardest right angle into violent collision with the Stranger, pressing on him with a force sufficient to have destroyed any ordinary Circle: but I could feel him slowly and unarrestably slipping from my contact; not edging to the right nor to the left, but moving somehow out of the world, and vanishing into nothing.

A Messenger from Heaven Brings the Three-Dimensional Gospel of the Millennium, but the Chosen Apostle Goes Mad

The Sphere felt a sense of disappointment. The Sphere had expected that A-Square, being a relatively fair person and mathematician, would accept the results of its logical deductions despite the limitations in their worldview, flaws, and prejudices. However, A-Square chose to place belief in the one-dimensional projection that his eyes could perceive.

In the three-dimensional society, there is a rule that every 1,000 years, a messenger (άγγελος = angel) is sent to reveal the truth of the three dimensions to the people of the two-dimensional society.

However, as the new millennium began, the path of preaching faced a significant setback. The three-dimensional gospel (ευαγγέλιο = ευ + άγγελος = good news) could not be effectively transmitted.

The chosen apostle (απόστολος = one with a mission), despite possessing the ability for mathematical logic deduction, refused to accept the results of rational deduction.

Upon receiving the revelation, the apostle deemed it a bizarre vision and madly attacked the messenger from "heaven".

(§ 17 How the Sphere, having in vain tried words, resorted to deeds)

Sphere. Why will you refuse to listen to reason? I had hoped to find in you—as being a man of sense and an accomplished mathematician—a fit apostle for the Gospel of the Three Dimensions, which I am allowed to preach once only in a thousand years: but now I know not how to convince you.

The Three-Dimensional Perspective is Not Omniscient

After a series of futile demonstrations of "miracles," the Sphere became desperate. It decided to forcefully "shake" A-Square out of his familiar two-dimensional plane, allowing his eyes to "witness" the "three-dimensional gospel".

(§ 17 How the Sphere, having in vain tried words, resorted to deeds)

“Fool! Madman! Irregular!” I exclaimed; “never will I release thee; thou shalt pay the penalty of thine impostures.”

“Ha! Is it come to this?” thundered the Stranger: “then meet your fate: out of your Plane you go. Once, twice, thrice! ’Tis done!”

Once "shaken" out of the two-dimensional plane, A-Square finally understood the Sphere's Revelation and what the "three-dimensional gospel" meant.

(§ 18 How I came to Spaceland, and what I saw there)

I looked, and, behold, a new world! There stood before me, visibly incorporate, all that I had before inferred, conjectured, dreamed, of perfect Circular beauty. What seemed the centre of the Stranger’s form lay open to my view: yet I could see no heart, lungs, nor arteries, only a beautiful harmonious Something—for which I had no words; but you, my Readers in Spaceland, would call it the surface of the Sphere.

......

Once more I felt myself rising through space. It was even as the Sphere 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 the mines and inmost caverns of the hills, were bared before me.

A-Square thought that witnessing such an incredible spectacle was the manifestation of the "omniscience" and "omnipotence" of "God."

However, A-Square's thoughts were refuted by the Sphere.

(§ 18 How I came to Spaceland, and what I saw there)

Awestruck at the sight of the mysteries (μυστήρια) 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 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 worshipped by your wise men as being Gods: for there is not one of them that does not see as much as you see now. But trust me, your wise men are wrong.”

In the Sphere's view, the vision of the three-dimensional world is neither omniscient nor omnipotent. The vision of the three-dimensional world simply knows more relative to the two-dimensional vision. People in the three-dimensional world can overlook all the details of the two-dimensional plane at any time, but this does not mean that the three-dimensional world is full of good and righteous people. The residents of the three dimensions are just aware of more possibilities.

The vision of the three dimensions does not equate to the Good (ἀγαθός) vision. The three dimensions simply see more than the two dimensions and are aware of more possibilities.

Just as the two dimensions easily see what the one dimension cannot see, it does not mean that A- Square in the two dimensions is a god. However, if A-Square wishes, he can pretend to be a "god" in the one-dimensional world. This is the information advantage of two-dimensional logic over one-dimensional rationality.

(§ 18 How I came to Spaceland, and what I saw there)

I. Then is omnividence the attribute of others besides Gods?

Sphere. I do not know. But, if a pick-pocket or a cut-throat of our country can see everything that is in your country, surely that is no reason why the pick-pocket or cut-throat 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 (δικαιοσύνη) , more merciful, less selfish, more Loving (caritas)? Not in the least. Then how does it make you more Divine (άγιος)?

Order, State, and the Messenger's Predicament

After the Sphere revealed its Revelation to A-Square, it brought A-Square to the political core of the two-dimensional Flatland world.

This was the beginning of the new millennium, the first day of the year 2000, when national leaders were gathered together in a meeting.

At the meeting, the ruler of Flatland announced that at the beginning of every millennium, there would be subjects who fell into illusions, claiming to have received revelations from "heaven" and spreading words about the "existence of a three-dimensional world", "a dimension beyond length and width", and "a new world", thereby bewitching the public, poisoning the minds and souls of young people, corrupting the morals of society, and endangering the order of the state.

Thus, the Circles instructed a strict search for these lost individuals.

After witnessing this, the Sphere, like its predecessors, "descended" to the political core of Flatland and declared the existence of three-dimensional space to the priests.

The Chief Circle and other top rulers were not surprised by the sudden appearance of a stranger, as such things had happened in history and there were records of these events.

(§ 18 How I came to Spaceland, and what I saw there)

“My Lords,” 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.”

The Chief Circle ordered silence and locked up all the lower-ranking individuals present.

A-Square's brother was also present. He was a square clerk, so he was also locked up.

Projection, Analogy, Logic

After the Sphere completed its "descent" and "revelation," it continued to impart knowledge to A-Square about three-dimensional space, including the understanding of light rays, shadows, and perspectives.

Through these teachings, A-Square fell into a kind of intoxicated joy, because he realized that, according to the logic (λόγος) of analogy (αναλογία), above the "three-dimensional space", there might exist a "four-dimensional space".

To A-Square, the Sphere was so learned and capable, a high-dimensional existence, that it must understand his logic and have the ability to show A-Square the grandeur of the four-dimensional space.

Unexpectedly, this move by A-Square angered the Sphere messenger. The Sphere thought that A Square's logic was nonsense, as it had never seen another dimension beyond the three-dimensional space.

After some twists and turns, they visited the zero-dimensional world. In the zero-dimensional world, there is only one point, one existence, and no one else outside of that zero-dimensional existence. It thinks it is the world and doesn't know there is a broader existence.

After visiting the zero dimension, the Sphere admitted to its student that there is indeed the possibility of the existence of four-dimensional space.

The traveler passing through the town remembered that Charles Howard Hinton [19] was the one who named the hypercube as a tesseract, and he wrote a book called The Fourth Dimension [20].

Dionys Burger wrote a book inspired by "Flatland" called "Sphereland" [21].

The Three-Dimensional Gospel of the Two-Dimensional Apostle: Upward, Not Northward!

After experiencing numerous inexplicable revelations, A-Square had the confidence to spread the three-dimensional gospel to every corner of the two-dimensional world.

A-Square condensed the gospel into a single phrase: "Upward, not Northward!" The revelation described a new dimension in a direction called "Up", analogous to the two-dimensional world's "North".

Upon waking up, A-Square overheard the council's proclamation. The council ordered the arrest, imprisonment, or execution of anyone who deceived the people's minds with three-dimensional illusions and claimed to have received revelations from another world.

This alarmed A-Square, and he decided to start his missionary work with those closest to him. He chose his grandson to be his first disciple of the gospel, as his hexagonal grandson was intelligent and had a keen interest in mathematics.

As A-Square began explaining the possible existence of the third dimension to his grandson, he heard a directive from the highest level being transmitted.

(§ 21 How I tried to teach the Theory of Three Dimensions to my Grandson, and with what success)

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, 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.

A-Square's first attempt at missionary work failed.

(Mythos Lullaby - Kosmos Flatland - Part II End)