“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"?”

“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.”

“The law of computers is the same as the law of the marketplace. The earth's atmosphere was divided up into a network of cubes, each reducible to a collection of points, and each point the product of a set of calculations. As far as science was concerned, this was the end of clouds, which were but a series of coordinates simulated in a space of greater than three dimensions.”

“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.”

“If our highly pointed triangles of the soldier class are formidable, it may be readily inferred that far more formidable are our women. For if a soldier is a wedge, a women is a needle; being, so to speak, all point, at least at the two extremities. Add to this the power of making herself practically invisible at will, and you will perceive that a female, in Flatland, is a creature by no means to be trifled with.”

“The six squares of our love didn’t add up to a cube. Still, I took the oddly-shaped box down to the post office and tried to mail it into the future, when I’d be more prepared to open it.
”

“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.”