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Triangles Quotes

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Triangles Quotes

“We discover the properties of mathematical objects such as triangles. We don’t invent them. This is a crucial point. If we invented the properties of triangles, they would be temporal, contingent entities, subject to incompleteness and inconsistency, and all of our manmade fallacies and errors. In fact, the properties of triangles are the same whether human beings exist or not, and, moreover, these properties are eternally true. Nothing is more astounding than the idea of eternal truths because such truths prove conclusively that mathematics has existed forever, that it’s uncreated and uncaused. Nothing gave rise to mathematics because, in order to do so, it would have to be older than mathematics, and nothing can be older than eternity. Of only one thing can we be sure: eternal things are mathematical things, and not any other kind of thing. “God” would be eternal only if he were mathematical!”

“The Marshall Society talk was doubtless interesting, but probably not altogether pleasant for Hayek. Some forty-odd years later, Joan Robinson in her Ely Lecture talked about how Hayek had “covered the blackboard with his triangles” and about the “pitiful state of confusion” within economics that his talk, in retrospect, represented. In her recounting, Kahn had “asked in a puzzled tone, ‘Is it your view that if I went out tomorrow and bought a new overcoat, that would increase unemployment?’ ‘Yes,’ said Hayek. ‘But,’ pointing to his triangles on the board, ‘it would take a very long mathematical argument to explain why’” (Robinson 1978a [1972], 2–3). In his own reminiscence, Kahn (1984) observed: “It is only fair to Hayek to mention that he had to condense four lectures into one, and that they were written when he had a high temperature” (182).”

“Pearl Harbor is a two-hour movie squeezed into three hours, about how on December 7, 1941, the Japanese staged a surprise attack on an American love triangle. Its centerpiece is 40 minutes of redundant special effects, surrounded by a love story of stunning banality. The film has been directed without grace, vision, or originality, and although you may walk out quoting lines of dialog, it will not be because you admire them.”

“Beingness, doingness and havingness are like a triangle where each side supports the others. They are not in conflict with each other. They all exist simultaneously. Often people attempt to live their lives backwards: They try to have more things, or more money, in order to do more of what they want, so that they will be happier. The way it actually works is the reverse. You must first be who you really are, then do what you need to do, in order to have what you want.”

“A considreable portion of my high school trigonometry course was devoted to the solution of oblique triangles... I have still not had an excuse for using my talents for solving oblique triangles. If a professional mathematician never uses these dull techniques in a highly varied career, why must all high school students devote several weeks to the subject?”

“... fain would I turn back the clock and devote to French or some other language the hours I spent upon algebra, geometry, and trigonometry, of which not one principle remains with me. Stay! There is one theorem painfully drummed into my head which seems to have inhabited some corner of my brain since that early time: "The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides!" There it sticks, but what of it, ye gods, what of it?”

“I ordered a club sandwich, but I'm not even a member. "I like my sandwiches with three pieces of bread." "Well, so do I!" "Then let's form a club." "OK, but we need some more stipulations. Instead of cutting the sandwich once, let's cut it again. Yes, four triangles, arranged in a circle, and in the middle we will dump chips." "How do you feel about frilly toothpicks?" "I'm for 'em!" "Well, this club is formed."”

“If an audience finds themselves paying attention to how you made your film, you're sunk because that means they're unplugged from your story. What matters is what's unfolding on the screen, not how you put it there. It doesn't matter if it's red triangles or million dollar software if the audience doesn't care.”

“Libertarianism is neither of the left nor of the right. It is unique. It is sui generis. It is apart from left and right. The left right political spectrum simply has no room for libertarianism. Think of an equilateral triangle, with libertarianism at one corner, the left at a second corner and the right at the third corner. We are equally distant from both of those misbegotten political economic philosophies. No, better yet, think in terms of an isosceles triangle, with us at the top and the two of them at the bottom, indicating they have more in common with each other than with us.”

“You can see that the care he took defiling the beauty he had forced in them was as precise and clean as his good hands which at night had developed the negatives, floating the sheets in the correct acids and watching the faces and breasts and pubic triangles and sofas emerge. The making and destroying coming from the same source, same lust, same surgery his brain was capable of. (On New Orleans photographer E. J. Bellocq)”