“As the number of the sides increases, a Polygon approximates to a Circle; and, when the number is very great indeed, say for example three or four hundred, it is extremely difficult for the most delicate touch to feel any polygonal angles. Let me say rather, it WOULD be difficult: for, as I have shown above, Recognition by Feeling is unknown among the highest society, and to FEEL a Circle would be considered a most audacious insult. This habit of abstention from Feeling in the best society enables a Circle the more easily to sustain the veil of mystery in which, from his earliest years, he is wont to enwrap the exact nature of his Perimeter or Circumference.”

— Edwin Abbott Abbott , book Flatland

Source: Flatland: A Romance of Many Dimensions (1884), PART I: THIS WORLD, Chapter 11. Concerning our Priests
Context: p>With us, our Priests are Administrators of all Business, Art, and Science; Directors of Trade, Commerce, Generalship, Architecture, Engineering, Education, Statesmanship, Legislature, Morality, Theology; doing nothing themselves, they are the Causes of everything worth doing, that is done by others.Although popularly everyone called a Circle is deemed a Circle, yet among the better educated Classes it is known that no Circle is really a Circle, but only a Polygon with a very large number of very small sides. As the number of the sides increases, a Polygon approximates to a Circle; and, when the number is very great indeed, say for example three or four hundred, it is extremely difficult for the most delicate touch to feel any polygonal angles. Let me say rather, it WOULD be difficult: for, as I have shown above, Recognition by Feeling is unknown among the highest society, and to FEEL a Circle would be considered a most audacious insult. This habit of abstention from Feeling in the best society enables a Circle the more easily to sustain the veil of mystery in which, from his earliest years, he is wont to enwrap the exact nature of his Perimeter or Circumference.</p

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Edwin Abbott Abbott 87

British theologian and author 1838–1926

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“Assuming her most gracious manner, my Wife advanced towards the Stranger, "Permit me, Madam, to feel and be felt by— " then, suddenly recoiling, "Oh! it is not a Woman, and there are no angles either, not a trace of one. Can it be that I have so misbehaved to a perfect Circle?" "I am indeed, in a certain sense a Circle," replied the Voice, "and a more perfect Circle than any in Flatland; but to speak more accurately, I am many Circles in one."”

Edwin Abbott Abbott book Flatland

</p>
Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 15. Concerning a Stranger from Spaceland

“I’ve learned that waiting is the most difficult bit, and I want to get used to the feeling, knowing that you’re with me, even when you’re not by my side.”

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“It is very difficult for us, placed as we have been from earliest childhood in a condition of training, to say what would have been our feelings had such training never taken place.”

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“There can be an infinite number of polygons, but only five regular solids.”

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Context: There can be an infinite number of polygons, but only five regular solids. Four of the solids were associated with earth, fire, air and water. The cube for example represented earth. These four elements, they thought, make up terrestrial matter. So the fifth solid they mystically associated with the Cosmos. Perhaps it was the substance of the heavens. This fifth solid was called the dodecahedron. Its faces are pentagons, twelve of them. Knowledge of the dodecahedron was considered too dangerous for the public. Ordinary people were to be kept ignorant of the dodecahedron. In love with whole numbers, the Pythagoreans believed that all things could be derived from them. Certainly all other numbers.
So a crisis in doctrine occurred when they discovered that the square root of two was irrational. That is: the square root of two could not be represented as the ratio of two whole numbers, no matter how big they were. "Irrational" originally meant only that. That you can't express a number as a ratio. But for the Pythagoreans it came to mean something else, something threatening, a hint that their world view might not make sense, the other meaning of "irrational".

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Source: Mathematical Thought from Ancient to Modern Times (1972), p. 176

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Sarah Chang (1980) violinist

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Edwin Abbott Abbott 87

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