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.
1838 – 1926
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.
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لو كنت رجلاً منطقيا - مع أنني أرتاب بعض الشيء في كونكـ رجلا – لأنكـ تمتلكـ فيما يبدو صوتا واحدا، ولكن لو كانت لديكـ ذرة من المنطق، لاستمعت إلى صوت العقل، أنت تطلب مني أن أصدق أن هناكـ نوعا أخر من الحركة غير تلكـ التي أراها كل يوم ، و أنا بدوري أطلب منكـ أن تصف بالكلمات أو تبين عن طريق الحركة ذلكـ الخط الآخر الذي تتحدث عنهـ، ولكنكـ بدلاً من أن تتحرك تمارس نوعا من الحيل السحريّة للاختفاء ومعاودة الظهور مرة أخرى، وبدلاً من أن تقدم لي صورة واضحة لعالمكـ الجديد، تخبرني فقط بأطوال نحو أربعين من حاشيتي، وهي حقائق يعرفها أي طفل في عاصمتنا، هل هناكـ ما هو أكثر جنوناً أو وقاحة من ذلكـ؟ اعترف بحماقتكـ أو ارحل عن أرضي..
"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."
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.
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
"All faults or defects, from the slightest misconduct to the most flagitious crime, Pantocyclus attributed to some deviation from perfect Regularity in the bodily figure, caused perhaps (if not congenital) by some collision in a crowd; by neglect to take exercise, or by taking too much of it; or even by a sudden change of temperature, resulting in a shrinkage or expansion in some too susceptible part of the frame. Therefore, concluded that illustrious Philosopher, neither good conduct nor bad conduct is a fit subject, in any sober estimation, for either praise or blame. For why should you praise, for example, the integrity of a Square who faithfully defends the interests of his client, when you ought in reality rather to admire the exact precision of his right angles? Or again, why blame a lying, thievish Isosceles when you ought rather to deplore the incurable inequality of his sides?
Theoretically, this doctrine is unquestionable; but it has practical drawbacks. In dealing with an Isosceles, if a rascal pleads that he cannot help stealing because of his unevenness, you reply that for that very reason, because he cannot help being a nuisance to his neighbours, you, the Magistrate, cannot help sentencing him to be consumed - and there's an end of the matter. But in little domestic difficulties, where the penalty of consumption, or death, is out of the question, this theory of Configuration sometimes comes in awkwardly; and I must confess that occasionally when one of my own Hexagonal Grandsons pleads as an excuse for his disobedience that a sudden change of the temperature has been too much for his perimeter, and that I ought to lay the blame not on him but on his Configuration, which can only be strengthened by abundance of the choicest sweetmeats, I neither see my way logically to reject, nor practically to accept, his conclusions.
For my own part, I find it best to assume that a good sound scolding or castigation has some latent and strengthening influence on m
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.