Flatland: A Romance of Many Dimensions

“...learn this lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy..”

“Upward, not Northward”

“Behold yon miserable creature. That Point is a Being like ourselves, 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; 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 that to aspire is better than to be blindly and impotently happy.”

“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 your eye once again and try to look steadily.”

“I have actually known a case where a Woman has exterminated her whole household, and half an hour afterwards, when her rage was over and the fragments swept away, has asked what has become of her husband and her children.”

“Like all great art, it defies the tyrant Time.”

“Distress not yourself if you cannot at first understand the deeper mysteries of Spaceland. By degrees they will dawn upon you.”

“In One Dimensions, did not a moving Point produce a Line with two terminal points?In two Dimensions, did not a moving Line produce a Square wit four terminal points?In Three Dimensions, did not a moving Square produce - did not the eyes of mine behold it - that blessed being, 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 result in a still more divine organization with sixteen terminal points?Behold the infallible confirmation of the Series, 2, 4, 8, 16: is not this a Geometrical Progression? Is not this - if I might qupte my Lord's own words - "Strictly according to Analogy"?Again, was I not taught by my Lord that as in a Line there are two bonding 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: 2, 4, 6: is not this an 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 me to believe, "strictly according to analogy"?”

“I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.”

“Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe:" but now my mind has been opened to higher views of things. In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate.”

“Doubtless, the life of an Irregular is hard; but the interests of the Greater Number require that it shall be hard.”

“It fills all Space, 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 is the One, and yet the All in All. Ah, the happiness, ah, the happiness of Being!”

“All this very plausible reasoning does not convince me, as it has not convinced the wisest of our Statesmen, that our ancestors erred in laying it down as an axiom of policy that the toleration of Irregularity is incompatible with the safety of the State.”

“Doubtless we cannot see that other higher Spaceland now, because we have no eye in our stomachs.”

“Moreover a blunt and stolid regard for literal truth indisposes them to make those lavish promises by which the more judicious Circle can in a moment pacify his consort. The result is massacre;”

“Few are the hearts whose happy lot it is at once to recognize in each other's voices the partner intended for them by Providence, and to fly into a reciprocal and perfectly harmonious embrace. With most of us the courtship is of long duration.”

“For why should the thirst for knowledge be aroused, only to be disappointed and punished?”

“My Lord, you 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 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 Flatland and see the inside of all things, so of a certainly there is yet above us some higher, purer region, whither thou dost surely purpose to lead me - O Thou Whome 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 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 whome so much has already been vouchsafed.”

“This can never be,” and on the other hand, “It must needs be precisely thus, and we know all about it.”

“¡Oh ser ignorante y obstinado! Os creéis la perfección de la existencia y sois en realidad el más imperfecto y estúpido de todos los seres. ¡Os ufanáis de ver, cuando no podéis ver, más que un punto! Os vanagloráis de deducir la existencia de una línea recta; pero yo puedo ver líneas rectas y deducir la existencia de ángulos, triángulos, cuadrados, pentágonos, hexágonos e incluso círculos. ¿Por qué desperdiciar más palabras? Basta con decir que soy la plenitud de vuestro yo incompleto. Vois sois una línea, pero yo soy una línea de líneas, lo que en mi país se llama un cuadrado: e incluso yo, pese a ser infinitamente superior a vos, soy poca cosa entre los grandes nobles de Planilandia, de donde he venido a visitaros, con la esperanza de iluminar vuestra ignorancia.”

“Once a Woman, always a Woman" is a Decree of Nature; and the very Laws of Evolution seem suspended in her disfavour. Yet at least we can admire the wise Prearrangement which has ordained that, as they have no hopes, so they shall have no memory to recall, and no forethought to anticipate, the miseries and humiliations which are at once a necessity of their existence and the basis of the constitution of Flatland.”

“Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows—only hard with luminous edges—and you will then have a pretty correct notion of my country and countrymen.”

“I looked, and, behold, a new world!”

“so that even a Woman in reasonable health can journey several furlongs northward without much difficulty—”

“[S]uddenly the course of events was completely changed by one of those picturesque incidents which Statesmen ought never to neglect, often to anticipate, and sometimes perhaps to originate, because of the absurdly disproportionate power with which they appeal to the sympathies of the populace.”

“the birth of children is too important a matter to have been allowed to depend upon such an accident as proximity.”

“The little Hexagon meditated on this a while and then said to me; "But you have been teaching me to raise numbers to the third power: I suppose three-to-the-third must mean something in Geometry; what does it mean?" "Nothing at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to shew the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by three; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which may be represented by three-to-the-second. xxx Upon this, my Grandson, again returning to his former suggestion, took me up rather suddenly and exclaimed, "Well, then, if a Point by moving three inches, makes a Line of three inches represented by three; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by three-to-the-second; it must be that a Square of three inches every way, moving somehow parallel to itself (but I don't see how) must make Something else (but I don't see what) of three inches every way—and this must be represented by three-to-the-third.""Go to bed," said I, a little ruffled by this interruption: "if you would talk less nonsense, you would remember more sense.”

“Behold yon miserable creature. That Point is a Being like ourselves, 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; 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 his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy. Now listen.”

“I neglected my clients and my own business to give myself to the contemplation of the mysteries which I had once beheld, yet which I could impart to no one, and found daily more difficult to reproduce even before my own mental vision.”

“[W]alking sometimes in a perfectly desolate plain where there have been no houses nor trees to guide me, I have been occasionally compelled to remain stationary for hours together, waiting till the rain came before continuing my journey.”