"Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in the… - Edwin A. Abbott

"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."

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About Edwin A. Abbott

Edwin Abbott Abbott (20 December 1838 – 12 October 1926) was an English schoolmaster and theologian, most famous as the author of the social satire Flatland (1884), widely noted for its use of mathematical dimensions in religious and political allegories.

Biography information from Wikiquote

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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.

Additional quotes by Edwin A. Abbott

"Only is often used ambiguously for alone. "The rest help me to revenge myself; you only advise me to wait." This ought to mean, "you only advise, instead of helping;" but in similar sentences "you only" is often used for "you alone.

Well, then, if a Point by moving three inches, makes a Line of three inches represented by 3; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by 32; 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 33.” “Go to bed,” said I, a little ruffled by his interruption: “if you would talk less nonsense, you would remember more sense.” So

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