Mythos Lullaby - Kosmos Flatland (Part III)

2023 年 11 月 9 日

Thereby contributing To the Enlargment of THE IMAGINATION (Φαντασία) And the possible Development Of that most and excellent Gift of MODESTY Among the Superior Races Of SOLID HUMANITY

神話的搖籃曲 - 平面神話秩序 英文版

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Gospel Between the Lines

After experiencing a failed attempt at missionary work, A-Square conceived the idea of spreading the gospel through subtle writing. However, he was limited by the two-dimensional realm, and many concepts couldn't be fully translated onto paper.

(§ 22 How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result)

So I devoted several months in privacy to the composition of a treatise on the mysteries of Three Dimensions. Only, with the view of evading the Law, if possible, I spoke not of a physical Dimension, but of a Thoughtland whence, in theory, a Figure could look down upon Flatland and see simultaneously the insides of all things, and where it was possible that there might be supposed to exist a Figure environed, as it were, with six Squares, and containing eight terminal Points. But in writing this book I found myself sadly hampered by the impossibility of drawing such diagrams as were necessary for my purpose: for of course, in our country of Flatland, there are no tablets but Lines, and no diagrams but Lines, all in one straight Line and only distinguishable by difference of size and brightness; so that, when I had finished my treatise (which I entitled, “Through Flatland to Thoughtland”) I could not feel certain that many would understand my meaning.

A-Square repackaged certain three-dimensional concepts using two-dimensional language, presenting them in a way that seemed less risky and easily understandable, yet not completely devoid of their original meaning.

However, A-Square still felt that writing constrained his expression, and he was uncertain if people would accurately grasp some of his intended meanings.

The Zeal

Despite A-Square's intention to maintain a low profile and silently spread the gospel, he inadvertently exposed his dangerous thoughts.

(§ 22 How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result)

And yet at times my spirit was too strong for me, and I gave vent to dangerous utterances.

Already I was considered heterodox if not treasonable, and I was keenly alive to the danger of my position; nevertheless I could not at times refrain from bursting out into suspicious or half-seditious utterances, even among the highest Polygonal or Circular society.

When, for example, the question arose about the treatment of those lunatics who said that they had received the power of seeing the insides of things, I would quote the saying of an ancient Circle, who declared that prophets and inspired people are always considered by the majority to be mad; and I could not help occasionally dropping such expressions as “the eye that discerns the interiors of things,” and “the all-seeing land”; once or twice I even let fall the forbidden terms “the Third and Fourth Dimensions.”

At last, to complete a series of minor indiscretions, at a meeting of our Local Speculative Society held at the palace of the Prefect himself,—some extremely silly person having read an elaborate paper exhibiting the precise reasons why Providence has limited the number of Dimensions to Two, and why the attribute of omnividence is assigned to the Supreme alone—I so far forgot myself as to give an exact account of the whole of my voyage with the Sphere into Space, and to the Assembly Hall in our Metropolis, and then to Space again, and of my return home, and of everything that I had seen and heard in fact or vision.

At first, indeed, I pretended that I was describing the imaginary experiences of a fictitious person; but my enthusiasm soon forced me to throw off all disguise, and finally, in a fervent peroration, I exhorted all my hearers to divest themselves of prejudice and to become believers in the Third Dimension.

And then, as expected, A-Square was imprisoned.

The Memoir

In prison, A-Square encountered his own brother. Despite A-Square's brother witnessing the entire process of the sphere's "coming" and subsequently being silenced and imprisoned, he still doubted everything A-Square said. This caused great anguish for A-Square.

(§ 22 How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result)

My brother is one of the best of Squares, just, sensible, cheerful, and not without fraternal affection; yet I confess that my weekly interviews, at least in one respect, cause me the bitterest pain.

He was present when the Sphere manifested himself in the Council Chamber; he saw the Sphere’s changing sections; he heard the explanation of the phenomena then give to the Circles. Since that time, scarcely a week has passed during seven whole years, without his hearing from me a repetition of the part I played in that manifestation, together with ample descriptions of all the phenomena in Spaceland, and the arguments for the existence of Solid things derivable from Analogy.

Yet—I take shame to be forced to confess it—my brother has not yet grasped the nature of Three Dimensions, and frankly avows his disbelief in the existence of a Sphere.

With no other activities to engage in within the confines of the prison, A-Square began writing his memoir. This memoir is what we know as "Flatland," the book we are familiar with.

(§ 22 How I then tried to diffuse the Theory of Three Dimensions by other means, and of the result)

Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial Revelation has been made to me for nothing.

Prometheus (Προμηθεύς = forethought) up in Spaceland was bound for bringing down fire for mortals, but I—poor Flatland Prometheus—lie here in prison for bringing down nothing to my countrymen. Yet I existing the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.

That is the hope of my brighter moments. Alas, it is not always so. Heavily weights on me at times the burdensome reflection that I cannot honestly say I am confident as to the exact shape of the once-seen, oft-regretted Cube; and in my nightly visions the mysterious precept, “Upward, not Northward,” haunts me like a soul-devouring Sphinx.

It is part of the martyrdom which I endure for the cause of Truth that there are seasons of mental weakness, when Cubes and Spheres flit away into the background of scarce-possible existences; when the Land of Three Dimensions seems almost as visionary as the Land of One or None; nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the substantial realities of Flatland itself, appear no better than the offspring of a diseased imagination, or the baseless fabric of a dream.

Thus concludes A-Square's memoir. This is the story that was published as "Flatland" in 1884.

The traveler snapped out of his reverie and refocused his attention on the elder's narration of the town's past.

The Traveler's Question

Coming back to his senses, the traveler heard the old man say that the girl had grown up. While her mathematical abilities hadn't advanced significantly, her achievements in music and literature had grown increasingly refined. The townspeople adored her singing and piano performances, and the couple, along with their little daughter, experienced a truly blessed time.

Regrettably, shortly after the young girl reached adulthood, her father fell victim to an illness, evoking sympathy from the townspeople who mourned the family's loss.

As the old man carried on recounting the family's history, the traveler couldn't resist interrupting and posing a question that had piqued his curiosity.

Traveler: Excuse me, I am intrigued to learn how that girl eventually pursued a path in mathematics and became a mathematician.

Old man: That girl became a mathematician?

Traveler: Indeed, as it is inscribed on her tombstone. I am genuinely curious about her journey of learning mathematics.

Old man: I'm afraid I have to disappoint you, that girl did not become a mathematician in the end.

Traveler: I'm perplexed. Why would the girl's tombstone bear the inscription "Mathematician Daughter ▲," while her parents' tombstones are marked with "Mathematician's Father ◭" and "Mathematician's Mother ◮"?

Old man: That's a misconception, and it relates to the tragedy that befell the family later on.

The Choice

The old man hesitated briefly, seemingly contemplating where to commence his memory.

The little daughter of that family was optimistic by nature. Besides her love for music and mathematics, she sometimes went to a nearby town to help at an orphanage, where she would teach the children to write, read, and of course, music.

In a certain year, rumors spread of a colossal war, unprecedented in history, which had broken out. Perplexingly, no one beyond the town could offer a clear explanation for its cause.

Some attributed it to a fierce conflict over valuable minerals, while others pointed to a contentious issue of noble inheritance. Yet, there were those who believed that the primary catalyst lay in a religious conflict, as only such a profound dispute could mobilize such a vast number of people.

It was rumored that this war, ignited by factions within the same religion, stemmed from a dispute over the translation of a single word in the scripture. One faction advocated for translating the word as "this," while the opposing faction insisted on translating it as "that." Remarkably, this seemingly innocent word carried a profound connotation of "up."

Neither side could sway the other, and the contentious debate persisted for countless years, accumulating sporadic vendettas and an array of conflicts. Interests clashed, political calculations intertwined, ultimately culminating in the outbreak of a massive war.

Countless lives were lost, fields transformed into desolate wastelands, and cities reduced to ruins.

Fortunately, owing to the town's strategic insignificance, the immediate vicinity remained relatively tranquil and unscathed by the ravages of war, allowing life to continue undisturbed.

The little daughter of that family, as usual, hummed her favorite song to the orphanage to teach the children music.

As the old man recounted this, he let out a sigh and uttered, "Disaster! What a disaster!"

It remains unknown which side's deserters, seeking to exploit the vulnerability of the poorly guarded orphanage, intended to pillage it. Their aim was to steal food, appropriate donations, and even abduct the children to sell them elsewhere. In the face of these thugs, the head of the orphanage bravely confronted them, instructing the girl from that family to lead the children and escape to the nearby town.

The head of the orphanage engaged in a fierce struggle with the deserters, inflicting injuries, but eventually succumbing and falling in a pool of blood, sacrificing his life for the children's sake.

The girl ran alongside the children, urging them not to look back, but to keep running until they reached the safety of the town. Even while fleeing, she valiantly fought back the pursuers with stones strewn along the path.

In her brave defense, she gravely wounded one of the deserters, further enraging the remaining accomplices. Though their anger stemmed not from the impending demise of their comrade, but from the audacity of a seemingly feeble entity daring to resist them. Yet, amidst their fury, they couldn't help but experience a tinge of schadenfreude—relishing the fact that there was now one less person to share their ill-gotten gains.

The pursuers harbored a delusion, believing that chasing after a young girl was an easier path to survival than going to battle, and that it would yield greater rewards. If stones were thrown, surely their unfortunate accomplice would bear the brunt, skillfully dodging any incoming projectiles.

To their astonishment, the stones wielded by the girl proved far more perilous than they had imagined. Each stone followed a destined parabolic trajectory, converging precisely on moving heads, claiming the lives of two more pursuers. In their foolishness, the remaining individuals hastily wrapped whatever they could find around their heads in a futile attempt to shield their most rational part. Panicking and with obstructed vision, they stumbled one after another while giving chase, their pace slowed to a crawl, unable to keep up with the agile girl.

The girl herself sustained injuries, her clothes drenched in blood. When she finally reached the nearby town with the children, her strength waned, her complexion turned ashen, and she collapsed onto the ground, unconscious.

The townspeople who arrived to offer assistance were relieved to find no sign of the pursuing thugs, as they surely would not dare attack a densely populated town.

They did their utmost to save her, staunching her bleeding and keeping a vigil by her bedside. However, before the dawn of the new day, the girl departed from this world.

The Mother's Question

The news of the girl's death spread back to the town where she grew up, leaving behind one mother whose face was constantly wet with tears.

"My daughter! My dear, foolish daughter! My dear, foolish daughter!"

Those who came to offer solace and support could only hear the echoes of this grieving mother's repeated sobs. She had no other words to express her pain, only tears streaming down her face. The separation from her daughter was tormenting her like a heart-wrenching pain, her soul was screaming silently.

For several days, the mother remained immersed in profound grief, barely eating, and surviving on little more than a sip of water. Not sleeping much, most of the time sitting by the window, as if she could still see her little daughter playing spinning under the night sky in front of her, hearing her daughter's piano and singing, sorrow catalyzed the whitening of her hair, the people who came could clearly see her accelerated aging, the whole person seemed to have lost the breath of the soul, the successive deaths of her husband and daughter caused her a heavy blow.

The mother was not just sitting idly, alongside reminiscing about the cherished moments spent with her husband and daughter, she pondered several questions, "The priests spoke of heaven and another world. Are my husband and daughter in heaven? Is my daughter happy there? Can my daughter sing in heaven?"

On one night, after sitting for half a day, the mother finally couldn't withstand the fatigue and closed her eyes to sleep.

In her dream, she saw a point of light, which seemed to be infinitely far away, and was separated from her by a vague human figure. She felt a deep awe.

The mother asked the questions she had been wanting to ask.

The Mother: May I ask if my daughter has arrived in heaven? Is she happy there?

Human Figure: Your daughter is an excellent mathematician. Her soul (ψυχή) beautiful (καλός), logical (λογος), miraculous (θαύμα), happy (ευδαιμονία).

Upon hearing the words of the ethereal figure, she was overcome with ecstasy, weeping and laughing in her dream, as if her soul was no longer torn asunder.

Human figure: Your soul (ψυχή) beautiful (καλός), logical (λογος), happy (ευδαιμονία). You are also a mathematician.

The mother no longer comprehended the figure's words in her dream. She only recalled that her daughter was blissful in heaven, and a profound sense of relief washed over her.

In her understanding, her daughter had reached heaven, and was very happy in heaven. Her dear little daughter even became the mathematician she dreamed of becoming.

The only peculiarity was that the "angel" had referred to her as a mathematician as well. The mother attributed it to her old age and possible confusion, believing that the "angel" had intended to say she was the mother of her beautiful, logical, and happy mathematician daughter.

She harbored no doubt about the reality of her dream. Everything felt vivid and tangible. she firmly believed that her beloved daughter resided in a state of blissful existence within the realms of heaven.

The Tombstone Inscriptions

Following that fateful night, the mother underwent a profound transformation. Gone were the days of sorrow and tears. The very next morning, she hurried to her daughter's tombstone and engraved the words "Mathematician Daughter ▲" beneath her name.

Concern spread among the townsfolk, wondering if she had succumbed to delirium or madness due to overwhelming grief.

She took the time to explain to familiar faces in the town everything she had experienced and witnessed in her dream. She declared, "My daughter has reached heaven and become the mathematician she aspired to be. I am at peace."

Some townspeople chose to believe her, offering heartfelt gratitude to a higher power. "Thank God! Thank God! Thank God!" they exclaimed.

Others harbored doubts, perceiving the elderly woman's mental state as fragile but kindly refrained from disputing her claims.

A few remained skeptical, acknowledging that her daughter's ascension to heaven seemed plausible - after all, she was such a virtuous girl - but doubting that her daughter could become a mathematician. They thought it was probably a kind lie from the "angel".

Still, others thought, "Whether this is true or not, at least this poor woman is no longer washing her face with tears. This is what her husband and daughter would have liked to see."

Now, only the elderly lady remained in the family within the small town. Her other children implored her to leave and reside with them, assuring her of their care. However, she insisted on staying in the familiar surroundings, finding solace in the support of her neighbors. She longed to accompany her husband and young daughter until the end of her days, believing it would lessen the chances of losing her way to heaven and facilitate a joyful reunion. After all, she was an old lady who struggled to navigate by reading maps.

Several more years passed, and eventually, the elderly lady, too, passed away.

In her final moments, those who had been caring for her overheard her whispering, "Am I also a mathematician? Oh, my daughter is the mathematician."

Upon her demise, the townspeople inscribed the tombstones of both her and her husband: "Mathematician's Father ◭" and "Mathematician's Mother ◮."

This is the origin of the inscriptions on those three tombstones, providing the answer the stranger sought to uncover.

Having attentively absorbed the tale of this family, the traveler conveyed his sincerest gratitude to the elderly narrator, leaving behind a meaningful token of appreciation.

Prior to departing the small town, the traveler he offered flowers to the family's tombstone.

His mind drifted to the beginning passage from "Flatland":

To
The Inhabitance of SPACE IN GENERAL
And H.C. IN PARTICULAR
This Work is Dedicated
By a Humble Native of Flatland
In the Hope that
Even as he was Initiated into the Mysteries (Μυστήρια)
Of THREE Dimensions
Having been previously conversant
With ONLY TWO
So the Citizens of that Celestial Region
May aspire yet higher and higher
To the Secrets of FOUR FIVE or EVEN SIX Dimensions
Thereby contributing
To the Enlargment of THE IMAGINATION (Φαντασία)
And the possible Development
Of that most and excellent Gift of MODESTY
Among the Superior Races
Of SOLID HUMANITY