Congruence arithmetic Quotes

“A goal of this book has been to tear down in some small part these barriers to understanding by attempting to shatter the “divinity of arithmetic,” through showing that even the methods, which we now take most for granted, were not given to us from on high, but were actually the result of centuries of scientific efforts on the part of our predecessors. p. 269”

“Mathematicians call it “the arithmetic of congruences.” You can think of it as clock arithmetic. Temporarily replace the 12 on a clock face with 0. The 12 hours of the clock now read 0, 1, 2, 3, … up to 11. If the time is eight o’clock, and you add 9 hours, what do you get? Well, you get five o’clock. So in this arithmetic, 8 + 9 = 5; or, as mathematicians say, 8 + 9 ≡ 5 (mod 12), pronounced “eight plus nine is congruent to five, modulo twelve.”

“Seven Rules Formulated for Teaching Arithmetic:1) Consider the situation the pupils faces.2) Consider the response you wish to connect with.3) Form the bond; do not expect it to come by miracle.4) Other things being equal, form no bond that will have to be broken.5) Other things being equal, do not form two or three bonds when one will serve.6) Other things being equal, form bonds in the way that they are required later to act.7) Favor, therefore, the situations which life itself will offer, and the responses which life itself will demand. (p. 101)”

“It's completely logical," explained the Dodecahedron. "The more you want, the less you get, and the less you get, the more you have. Simple arithmetic, that's all. Suppose you had something and added something to it. What would that make?""More," said Milo quickly."Quite correct," he nodded. "Now suppose you had something and added nothing to it. What would you have?""The same," he answered again, without much conviction. "Splendid," cried the Dodecahedron. "And suppose you had something and added less than nothing to it. What would you have then?""FAMINE!" roared the anguished Humbug, who suddenly realized that that was exactly what he'd eaten twenty-three bowls of.”

“The ground for the necessity of Christian schools lies in this very thing, that no fact can be known unless it be known in its relationship to God. And once this point is clearly seen, the doubt as to the value of teaching arithmetic in Christian schools falls out of the picture. Of course arithmetic must be taught in a Christian school. It cannot be taught anywhere else.”

“If scientific reasoning were limited to the logical processes of arithmetic, we should not get very far in our understanding of the physical world. One might as well attempt to grasp the game of poker entirely by the use of the mathematics of probability.”

“Mathematics is not arithmetic. Though mathematics may have arisen from the practices of counting and measuring it really deals with logical reasoning in which theorems—general and specific statements—can be deduced from the starting assumptions. It is, perhaps, the purest and most rigorous of intellectual activities, and is often thought of as queen of the sciences.”

“I know perfectly well that it is impossible, according to arithmetic and scholarly books, to live in a far valley off a handful of ewes and two low yield cows. But we live, I say. You children all lived; your sisters now have sturdy children in far-off districts. And what you are now carrying under your heart will also live and be welcome, little one, despite arithmetic and scholarly books.”

“If we do not laugh, we will cry. Crying will only make us hotter and sweatier. We Jews like to joke about death because what you laugh at and make familiar can no longer frighten you. Besides, Chayaleh, what else is there to do?”