FLATLAND
BY
EDWIN A. ABBOTT
ABOUT ABBOTT
Edwin A. Abbott: A Journey from Flatland to Infinite Dimensions
Born on December 20, 1838, in Marylebone, London, Edwin Abbott Abbott was not merely a man but a spectrum of vibrant dimensions imprisoned in a seemingly two-dimensional world. His life, although set in Victorian England, transcended the common pathways of his contemporaries, venturing into the fantastical realms that bridged mathematics and literature. A theologian, schoolmaster, and writer, Abbott offered to the world “Flatland,” a masterpiece that intricately wove the threads of spatial dimensions with social satire, which remains acclaimed and relevant to this very day.
Abbott was nurtured in the arms of educational rigor, with his father, Edwin Abbott, serving as the headmaster of the Philological School, Marylebone, and thus established a venerable legacy for the young scholar to trailblaze. Graduating from St. John's College, Cambridge, with honors in classics, Abbott refused to be bound by traditional accolades. His journey spiraled into an eternal exploration of the unchartered territories between theology, education, literature, and geometry.
The day-to-day life of Abbott was steeped in academia, as he took on the mantle of headmaster at the City of London School in 1865. Yet, his mind wandered through realms unseen and unexplored by his peers. His pedagogical practices and philosophies echoed with a resonant understanding of the multifaceted nature of knowledge and learner. He aspired to unravel the tightly knit threads of Victorian society and unweave the intricacies of multiple dimensions through his writings.
“Flatland: A Romance of Many Dimensions” (1884), Abbott’s magnum opus, pivots around a square living in a two-dimensional world, exploring the tangible implications of mathematics and dimensions while satirizing the hierarchical and rigid Victorian society. The protagonist, A. Square, becomes a prophetic voice for Abbott himself, whispering into the ether the possibility of realms beyond comprehension, realms where rigid lines of social structure and spatial dimensions dissolve into an eternal void.
Though tethered to his time and place, Abbott yearned for a utopia that transcended earthly comprehension. His other literary endeavors, such as “Philochristus” (1878) and “Onesimus” (1882), embodied a similar spirit, delving deep into theological and philosophical quandaries with an almost rebellious defiance against the traditionalist ideologies of his epoch.
Abbott’s work blurred the lines between disciplines, creating a unique amalgamation of multifaceted ideas that explored religion, mathematics, and social order. His legacy, albeit punctuated with the immortal “Flatland,” is imbued with a profound, implicit inquiry into the infinite dimensions of understanding that lie beyond our purview. His endeavors continue to pose imperative, unanswered questions, compelling us to peer beyond our confined realities and ponder upon the unfathomable mysteries of the universes that await discovery.
Edwin A. Abbott departed from our earthly dimensions on October 12, 1926, leaving behind a timeless masterpiece that forever echoes through the infinite corridors of metaphysical, mathematical, and societal contemplation. His spirit, undeterred by the limitations of physical existence, forever lingers in the interstices of realms seen and unseen, guiding curious minds towards the perpetual pursuit of knowledge across infinite dimensions.
SUMMARY
"Flatland: A Romance of Many Dimensions," penned by Edwin A. Abbott, is a dazzling voyage into the unseen and unexplored dimensions of existence. Set in a two-dimensional world, it beckons readers to traverse through the life of its protagonist, A. Square, and challenge the very fabric of reality as understood by his flat universe.
In the monochromatic world of Flatland, life is as straightforward as its inhabitants: circles, squares, and other flat shapes moving in a plane, wholly unaware of any world beyond their linear reality. The social hierarchy is rigorously defined by geometrical forms, where the more sides one has, the higher one's status soars. But the serenity of A. Square's existence is shattered when he is visited by a Sphere from a three-dimensional world, known as Spaceland. This Sphere brings with it a revelation that defies not only physics but also the rigidly established social structure of Flatland.
Journey alongside A. Square as he grapples with the seemingly impossible truths unveiled by the Sphere, navigating through the mental tumult of accepting a reality beyond his own, and the ostracism he faces from his own dimension upon attempting to enlighten them. Dive deep into a world where dimensions intertwine with societal satire, and explore the complex, subtle metaphor Abbott intricately weaves, critiquing the Victorian society of his time and perhaps, even our own.
"Flatland" not only charts a physical journey from the second to the third dimension but also an existential one, exploring the confines of perception, belief, and societal rigidity. It invokes us to question, to wonder, and to perpetually seek, asking if we too, like A. Square, are imprisoned in our own “flatland,” blind to the unfathomable dimensions that might lie just a revelation away. This timeless masterpiece dances on the delicate line between mathematical fiction and philosophical allegory, offering not just a story, but an experience that promises to linger, prompting thought and wonderment about the worlds beyond our own.
CHARACTERS LIST
A. Square (Narrator): The protagonist of "Flatland," A. Square is a modestly situated professional residing in a two-dimensional world. His experiences and revelations about higher dimensions serve as the foundation of the narrative.
Sphere: A visitor from the three-dimensional world, Spaceland. Sphere introduces A. Square to the concept of a third dimension, drastically shifting his understanding of reality.
The King of Pointland: An entity that exists in a world of a single point and is completely self-absorbed, as it perceives itself as the entirety of its universe.
The Monarch of Lineland: Ruling a one-dimensional world, the Monarch of Lineland struggles to comprehend A. Square’s explanations of a second dimension, symbolizing the struggle of understanding beyond one's own perspective.
A. Square’s Brother: A character that serves to exhibit the common Flatlander's perspective and disbelief in dimensions beyond their understanding.
A. Square’s Wife: Representing the condition of women in Flatland, A. Square’s Wife is portrayed as simple and line-like, reflecting the limited status and recognition given to women within this society.
A. Square’s Grandson: A curious and open-minded character that displays an initial curiosity towards higher dimensions, indicative of the untainted wonder and receptivity of youth.
The Chief Circle: The leader of Flatland who refuses to accept the reality of higher dimensions, symbolizing the resistance of established hierarchies and regimes to revolutionary ideas.
The Priest: Characters that are part of the ruling elite, embodying the amalgamation of power and dogma to resist new ideas and maintain societal control.
The Irregulars: Shapes that do not conform to the standard geometric norms of Flatland society and thus, face ostracism and persecution, mirroring the societal response to non-conformity.
Hex: The most advanced and powerful character in Flatland, Hex is a key figure in society due to his numerous sides, highlighting the close ties between social status and physical form in Flatland.
The Prosecutor: Representing the oppressive arm of Flatland's regime, the Prosecutor exemplifies the fierce protection of Flatland’s established norms and a rejection of dissenting perspectives.
Contents
Preface To The Second And Revised Edition, 1884
PART 1: THIS WORLD
Section 1. Of The Nature Of Flatland
Section 2. Of The Climate And Houses In Flatland
Section 3. Concerning The Inhabitants Of Flatland
Section 4. Concerning The Women
Section 5. Of Our Methods Of Recognizing One Another
Section 6. Of Recognition By Sight
Section 7. Concerning Irregular Figures
Section 8. Of The Ancient Practice Of Painting
Section 9. Of The Universal Colour Bill
Section 10. Of The Suppression Of The Chromatic Sedition
Section 11. Concerning Our Priests
Section 12. Of The Doctrine Of Our Priests
PART 2: OTHER WORLDS
Section 13. How I Had A Vision Of Lineland
Section 14. How I Vainly Tried To Explain The Nature Of Flatland
Section 15. Concerning A Stranger From Spaceland
Section 16. How The Stranger Vainly Endeavoured To Reveal To Me In Words The Mysteries Of Spaceland
Section 17. How The Sphere, Having In Vain Tried Words, Resorted To Deeds
Section 18. How I Came To Spaceland, And What I Saw There
Section 19. How, Though The Sphere Shewed Me Other Mysteries Of Spaceland, I Still Desired More; And What Came Of It
Section 20. How The Sphere Encouraged Me In A Vision
Section 21. How I Tried To Teach The Theory Of Three Dimensions To My Grandson, And With What Success
Section 22. How I Then Tried To Diffuse The Theory Of Three Dimensions By Other Means, And Of The Result
ToThe Inhabitants of SPACE IN GENERALAnd H. C. IN PARTICULARThis Work is DedicatedBy a Humble Native of FlatlandIn the Hope thatEven as he was Initiated into the MysteriesOf THREE DimensionsHaving been previously conversantWith ONLY TWOSo the Citizens of that Celestial RegionMay aspire yet higher and higherTo the Secrets of FOUR FIVE OR EVEN SIX DimensionsThereby contributingTo the Enlargement of THE IMAGINATIONAnd the possible DevelopmentOf that most rare and excellent Gift of MODESTYAmong the Superior RacesOf SOLID HUMANITY
Preface To The Second And Revised Edition, 1884
By the Editor
If my poor Flatland friend retained the vigour of mind which he enjoyed when he began to compose these Memoirs, I should not now need to represent him in this preface, in which he desires, firstly, to return his thanks to his readers and critics in Spaceland, whose appreciation has, with unexpected celerity, required a second edition of his work; secondly, to apologize for certain errors and misprints (for which, however, he is not entirely responsible); and, thirdly, to explain one or two misconceptions. But he is not the Square he once was. Years of imprisonment, and the still heavier burden of general incredulity and mockery, have combined with the natural decay of old age to erase from his mind many of the thoughts and notions, and much also of the terminology, which he acquired during his short stay in Spaceland. He has, therefore, requested me to reply in his behalf to two special objections, one of an intellectual, the other of a moral nature.
The first objection is, that a Flatlander, seeing a Line, sees something that must be THICK to the eye as well as LONG to the eye (otherwise it would not be visible, if it had not some thickness); and consequently he ought (it is argued) to acknowledge that his countrymen are not only long and broad, but also (though doubtless in a very slight degree) THICK or HIGH. This objection is plausible, and, to Spacelanders, almost irresistible, so that, I confess, when I first heard it, I knew not what to reply. But my poor old friend's answer appears to me completely to meet it.
"I admit," said he—when I mentioned to him this objection—"I admit the truth of your critic's facts, but I deny his conclusions. It is true that we have really in Flatland a Third unrecognized Dimension called 'height', just as it is also true that you have really in Spaceland a Fourth unrecognized Dimension, called by no name at present, but which I will call 'extra-height'. But we can no more take cognizance of our 'height' than you can of your 'extra-height'. Even I—who have been in Spaceland, and have had the privilege of understanding for twenty-four hours the meaning of 'height'—even I cannot now comprehend it, nor realize it by the sense of sight or by any process of reason; I can but apprehend it by faith.
"The reason is obvious. Dimension implies direction, implies measurement, implies the more and the less. Now, all our lines are EQUALLY and INFINITESIMALLY thick (or high, whichever you like); consequently, there is nothing in them to lead our minds to the conception of that Dimension. No 'delicate micrometer'—as has been suggested by one too hasty Spaceland critic—would in the least avail us; for we should not know WHAT TO MEASURE, NOR IN WHAT DIRECTION. When we see a Line, we see something that is long and BRIGHT; BRIGHTNESS, as well as length, is necessary to the existence of a Line; if the brightness vanishes, the Line is extinguished. Hence, all my Flatland friends—when I talk to them about the unrecognized Dimension which is somehow visible in a Line—say, 'Ah, you mean BRIGHTNESS': and when I reply, 'No, I mean a real Dimension', they at once retort, 'Then measure it, or tell us in what direction it extends'; and this silences me, for I can do neither. Only yesterday, when the Chief Circle (in other words our High Priest) came to inspect the State Prison and paid me his seventh annual visit, and when for the seventh time he put me the question, 'Was I any better?' I tried to prove to him that he was 'high', as well as long and broad, although he did not know it. But what was his reply? 'You say I am "high"; measure my "high-ness" and I will believe you.' What could I do? How could I meet his challenge? I was crushed; and he left the room triumphant.
"Does this still seem strange to you? Then put yourself in a similar position. Suppose a person of the Fourth Dimension, condescending to visit you, were to say, 'Whenever you open your eyes, you see a Plane (which is of Two Dimensions) and you INFER a Solid (which is of Three); but in reality you also see (though you do not recognize) a Fourth Dimension, which is not colour nor brightness nor anything of the kind, but a true Dimension, although I cannot point out to you its direction, nor can you possibly measure it.' What would you say to such a visitor? Would not you have him locked up? Well, that is my fate: and it is as natural for us Flatlanders to lock up a Square for preaching the Third Dimension, as it is for you Spacelanders to lock up a Cube for preaching the Fourth. Alas, how strong a family likeness runs through blind and persecuting humanity in all Dimensions! Points, Lines, Squares, Cubes, Extra-Cubes—we are all liable to the same errors, all alike the Slaves of our respective Dimensional prejudices, as one of your Spaceland poets has said—
'One touch of Nature makes all worlds akin'."