Theorems Of Parallelogram Quotes

The paraphrase of Gödel's Theorem says that for any record player, there are records which it cannot play because they will cause its indirect self-destruction. ~ Douglas R. Hofstadter

The Mean Value Theorem is the midwife of calculus - not very important or glamorous by itself, but often helping to deliver other theorems that are of major significance. ~ Edward Mills Purcell

Credit expansion results in the recurrence of economic crisis and periods of depression. Inflation makes the prices of all commodities and services soar. The attempts to enforce wage rates higher than those the unhampered market would have determined produce mass unemployment prolonged year after year. Price ceilings result in a drop in the supply of commodities affected. The economists have proved these theorems in an irrefutable way. No ~ Ludwig Von Mises

It is my dearest hope that one day I shall be the one to discover the GUT-the Grand Unified Tale, the one which will bind together all our Theorems and Laws, leaving out not one Orphan Girl or Youngest Son or Cup of Life and Death. Not one Descent or Ascent, not one Riddle or Puzzle or Trick. One perfect golden map that can guide any soul to its desire and back again. I will be the one to do it, I know it. I hope I know it. I know I hope it. ~ Catherynne M Valente

Humanism ... is not a single hypothesis or theorem, and it dwells on no new facts. It is rather a slow shifting in the philosophic perspective, making things appear as from a new centre of interest or point of sight. ~ William James

The theory of numbers, more than any other branch of mathematics, began by being an experimental science. Its most famous theorems have all been conjectured, sometimes a hundred years or more before they were proved; and they have been suggested by the evidence of a mass of computations. ~ G.H. Hardy

Murphy's Law, that brash proletarian restatement of Godel's Theorem ... ~ Thomas Pynchon

The centre of gravity of any parallelogram lies on the straight line joining the middle points of opposite sides. ~ Archimedes

Imagine a life-form whose brainpower is to ours as ours is to a chimpanzee's. To such a species, our highest mental achievements would be trivial. Their toddlers, instead of learning their ABCs on Sesame Street, would learn multivariable calculus on Boolean Boulevard. Our most complex theorems, our deepest philosophies, the cherished works of our most creative artists, would be projects their schoolkids bring home for Mom and Dad to display on the refrigerator door. ~ Neil DeGrasse Tyson

One of the most important lessons, perhaps, is the fact that SOFTWARE IS HARD. From now on I shall have significantly greater respect for every successful software tool that I encounter. During the past decade I was surprised to learn that the writing of programs for TeX and Metafont proved to be much more difficult than all the other things I had done (like proving theorems or writing books). The creation of good software demand a significiantly higher standard of accuracy than those other things do, and it requires a longer attention span than other intellectual tasks. ~ Donald Knuth

Wars and chaoses and paradoxes ago, two mathematicians between them ended an age d began another for our hosts, our ghosts called Man. One was Einstein, who with his Theory of Relativity defined the limits of man's perception by expressing mathematically just how far the condition of the observer influences the thing he perceives.
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The other was Goedel, a contemporary of Eintstein, who was the first to bring back a mathematically precise statement about the vaster realm beyond the limits Einstein had defined: In any closed mathematical system--you may read 'the real world with its immutable laws of logic'--there are an infinite number of true theorems--you may read 'perceivable, measurable phenomena'--which, though contained in the original system, can not be deduced from it--read 'proven with ordinary or extraordinary logic.' Which is to say, there are more things in heaven and Earth than are dreamed of in your philosophy, Horatio. There are an infinite number of true things in the world with no way of ascertaining their truth. Einstein defined the extent of the rational. Goedel stuck a pin into the irrational and fixed it to the wall of the universe so that it held still long enough for people to know it was there.
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The visible effects of Einstein's theory leaped up on a convex curve, its production huge in the first century after its discovery, then leveling off. The production of Goedel's law crept up on a concave curve, microscopic at first, th ~ Samuel R. Delany

If I am happy in spite of my deprivations, if my happiness is so deep that it is a faith, so thoughtful that it becomes a philosophy of life. If, in short, I am an optimist, my testimony to the creed of optimism is worth hearing. ~ Helen Keller

The hedonistic conception of man is that of a lightning calculator of pleasures and pains, who oscillates like a homogeneous globule of desire of happiness under the impulse of stimuli that shift him about the area but leave him intact ...
He is an isolated, definitive human datum, in stable equilibrium except for the buffets of the impinging forces that displace him in one direction or another. Self-poised in elemental space, he spins symmetrically about his own spiritual axis until the parallelogram of forces bears down on him, whereupon he follows he line of the resultant ~ Thorstein Veblen

It is a matter for considerable regret that Fermat, who cultivated the theory of numbers with so much success, did not leave us with the proofs of the theorems he discovered. In truth, Messrs Euler and Lagrange, who have not disdained this kind of research, have proved most of these theorems, and have even substituted extensive theories for the isolated propositions of Fermat. But there are several proofs which have resisted their efforts. ~ Adrien-Marie Legendre

To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well. ~ Albert Camus

Which is to say that culture is not a reflex of political economy, but
that society is now a reflex of key shifts in music theory and practice ...
[Sampladelia is] the sound made by those early-twentieth-century discoveries
in particle physics and relativiity theory, the projection of the minds of
Einstein, Heisenbery, and Bohr, their fateful explorations of liquid time,
curving space, uncertainty fields and relativity theorems, into densely
configured and fully ambivalent android music tracks ~ Arthur Kroker

The most probable of all my theorems, is that life is ordered by the principles of some religion so peculiar and obscure it has no followers, and none may fathom it, nor know the rituals by which to court its favour. ~ Alan Moore

An axiomatic system comprises axioms and theorems and requires a certain amount of hand-eye coordination before it works. A formal system comprises an explicit list of symbols, an explicit set of rules governing their cohabitation, an explicit list of axioms, and, above all, an explicit list of rules explicitly governing the steps that the mathematician may take in going from assumptions to conclusions. No appeal to meaning nor to intuition. Symbols lose their referential powers; inferences become mechanical. ~ David Berlinski

God has the Big Book, the beautiful proofs of mathematical theorems are listed here. ~ Paul Erdos

One can be enlightened about proofs as well as theorems. Without enlightenment, one is merely reduced to memorizing proofs. With enlightenment about a proof, its flow becomes clear and it can become an item of astonishing beauty. In addition, the need to memorize disappears because the proof has become part of your soul. ~ Herbert S. Gaskill

Humans like to think of themselves as unusual. We've got big brains that make it possible for us to think, and we think that we have free will and that our behavior can't be described by some mechanistic set of theorems or ideas. But even in terms of much of our behavior, we really aren't very different from other animals. ~ Mark Pagel

A reply to Olbers' attempt in 1816 to entice him to work on Fermat's Theorem. I confess that Fermat's Theorem as an isolated proposition has very little interest for me, because I could easily lay down a multitude of such propositions, which one could neither prove nor dispose of. [] ~ Carl Friedrich Gauss

The combination of Bayes and Markov Chain Monte Carlo has been called "arguably the most powerful mechanism ever created for processing data and knowledge."
Almost instantaneously MCMC and Gibbs sampling changed statisticians' entire method of attacking problems. In the words of Thomas Kuhn, it was a paradigm shift. MCMC solved real problems, used computer algorithms instead of theorems, and led statisticians and scientists into a worked where "exact" meant "simulated" and repetitive computer operations replaced mathematical equations. It was a quantum leap in statistics. ~ Sharon Bertsch McGrayne

There is a theorem that colloquially translates, You cannot comb the hair on a bowling ball ... Clearly, none of these mathematicians had Afros, because to comb an Afro is to pick it straight away from the scalp. If bowling balls had Afros, then yes, they could be combed without violation of mathematical theorems. ~ Neil DeGrasse Tyson

I am persuaded that this method [for calculating the volume of a sphere] will be of no little service to mathematics. For I foresee that once it is understood and established, it will be used to discover other theorems which have not yet occurred to me, by other mathematicians, now living or yet unborn. ~ Archimedes

Did chemistry theorems exist? No: therefore you had to go further, not be satisfied with the quia, go back to the origins, to mathematics and physics. The origins of chemistry were ignoble, or at least equivocal: the dens of the alchemists, their abominable hodgepodge of ideas and language, their confessed interest in gold, their Levantine swindles typical of charlatans and magicians; instead, at the origin of physics lay the strenuous clarity of the West-Archimedes and Euclid. ~ Primo Levi

One may characterize physics as the doctrine of the repeatable, be it a succession in time or the co-existence in space. The validity of physical theorems is founded on this repeatability. ~ Friedrich Hund

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. ~ Christopher Zeeman

I was a capable boy, intelligent, well-liked, but powerfully afraid. And I felt, vaguely, wordlessly, that for a child to be marked off for such a life, to be forced to live in fear was a great injustice. And what was the source of this fear? What was hiding behind the smoke screen of streets and schools? And what did it mean that number 2 pencils, conjugations without context, Pythagorean theorems, handshakes, and head nods were the difference between life and death, were the curtains drawing down between the world and me? ~ Ta-Nehisi Coates

But my shift to the serious study of economics gradually weakened my belief in Major Douglas's A+B theorem, which was replaced in my thought by the expression MV = PT. ~ James Meade

No matter how correct a mathematical theorem may appear to be, one ought never to be satisfied that there was not something imperfect about it until it also gives the impression of being beautiful. ~ George Boole

Q7. The total output of all the mathematicians who have ever lived, together with the output of all the human mathematicians of the next (say) thousand years is finite and could be contained in the memory banks of an appropriate computer. Surely this particular computer could, therefore, simulate this output and thus behave (externally) in the same way as a human mathematician-whatever the Godel argument might appear to tell us to the contrary?

While this is presumably true, it ignores the essential issue, which is how we (or computers) know which mathematical statements are true and which are false. (In any case, the mere storage of mathematical statements is something that could be achieved by a system much less sophisticated than a general purpose computer, e.g. photographically.) The way that the computer is being employed in Q7 totally ignores the critical issue of truth judgment. One could equally well envisage computers that contain nothing but lists of totally false mathematical 'theorems', or lists containing random jumbles of truths and falsehoods. How are we to tell which computer to trust? The arguments that I am trying to make here do not say that an effective simulation of the output of conscious human activity (here mathematics) is impossible, since purely by chance the computer might 'happen' to get it right-even without any understanding whatsoever. But the odds against this are absurdly enormous, and the issues that are being addressed here, namel ~ Roger Penrose

The elegance of a mathematical theorem is directly proportional to the number of independent ideas one can see in the theorem and inversely proportional to the effort it takes to see them. ~ George Polya

To many, mathematics is a collection of theorems. For me, mathematics is a collection of examples; a theorem is a statement about a collection of examples and the purpose of proving theorems is to classify and explain the examples ... ~ John B. Conway