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8bb48e8 My first feeling was that there was no way to continue. Writing isn't like math;in math, two plus two always equals four no matter what your mood is like. With writing, the way you feel changes everything. writing sadness mathematics Stephenie Meyer
94d01a4 I couldn't claim that I was smarter than sixty-five other guys--but the average of sixty-five other guys, certainly! humor intelligence statistics mathematics Richard P. Feynman
9e406b4 Ideas that require people to reorganize their picture of the world provoke hostility. science life philosophy paradigm-shift thomas-kuhn chaos-theory paradigm mathematics physics James Gleick
7164e66 Physics depends on a universe infinitely centred on an equals sign. equilibrium metaphysics harmony mathematics physics Mark Z. Danielewski
5d39de2 We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it. science mathematics physics Roger Penrose
1d9d8ff "When Republicans recently charged the President with promoting 'class warfare,' he answered it was 'just math.' But it's more than math. It's a matter of morality. morality politics class-warfare conservatism republican-party-united-states united-states economics liberalism society mathematics Robert B. Reich
fa4159a The study of mathematics is apt to commence in disappointment... We are told that by its aid the stars are weighed and the billions of molecules in a drop of water are counted. Yet, like the ghost of Hamlet's father, this great science eludes the efforts of our mental weapons to grasp it. shakespeare stars science grasp molecules mental study ghost math mathematics hamlet william-shakespeare Alfred North Whitehead
d617314 "People enjoy inventing slogans which violate basic arithmetic but which illustrate "deeper" truths, such as "1 and 1 make 1" (for lovers), or "1 plus 1 plus 1 equals 1" (the Trinity). You can easily pick holes in those slogans, showing why, for instance, using the plus-sign is inappropriate in both cases. But such cases proliferate. Two raindrops running down a window-pane merge; does one plus one make one? A cloud breaks up into two clouds -more evidence of the same? It is not at all easy to draw a sharp line between cases where what is happening could be called "addition", and where some other word is wanted. If you think about the question, you will probably come up with some criterion involving separation of the objects in space, and making sure each one is clearly distinguishable from all the others. But then how could one count ideas? Or the number of gases comprising the atmosphere? Somewhere, if you try to look it up, you can probably fin a statement such as, "There are 17 languages in India, and 462 dialects." There is something strange about the precise statements like that, when the concepts "language" and "dialect" are themselves fuzzy." truth mathematics Douglas R. Hofstadter
c863cfb No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through. hate love teacher math mathematics school Roger Penrose
dde5d87 Mathematicians deal with large numbers sometimes, but never in their income. pithy maths mathematics Isaac Asimov
197cfc6 [...] provability is a weaker notion than truth truth gödel-s-incompleteness-theorem mat proof mathematics Douglas R. Hofstadter
6176984 "...I guess I can put two and two together." "Sometimes the answer's four," I said, "and sometimes it's twenty-two..." humor smartass mathematics Dashiell Hammett
a25372f was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years' worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics. tragedy history science srinivasa-ramanujan strange math mathematics Michio Kaku
144d3ae Of course, reading novels was just another form of escape. As soon as he closed their pages he had to come back to the real world. But at some point Tengo noticed that returning to reality from the world of a novel was not as devastating a blow as returning from the world of mathematics. Why should that have been? After much deep thought, he reached a conclusion. No matter how clear the relationships of things might become in the forest of story, there was never a clear-cut solution. That was how it differed from math. The role of a story was, in the broadest terms, to transpose a single problem into another form. Depending on the nature and direction of the problem, a solution could be suggested in the narrative. Tengo would return to the real world with that suggestion in hand. It was like a piece of paper bearing the indecipherable text of a magic spell. At times it lacked coherence and served no immediate practical purpose. But it would contain a possibility. Someday he might be able to decipher the spell. That possibility would gently warm his heart from within. reading novels mathematics Haruki Murakami
2337f8a "Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..." Klapaucius thought, and thought some more. Finally he nodded and said: "Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit." "Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming: Come, let us hasten to a higher plane, Where dyads tread the fairy fields of Venn, Their indices bedecked from one to n, Commingled in an endless Markov chain! Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers of a more ergodic zone. In Reimann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our asymptotes no longer out of phase, We shall encounter, counting, face to face. I'll grant thee random access to my heart, Thou'lt tell me all the constants of thy love; And so we two shall all love's lemmas prove, And in bound partition never part. For what did Cauchy know, or Christoffel, Or Fourier, or any Boole or Euler, Wielding their compasses, their pens and rulers, Of thy supernal sinusoidal spell? Cancel me not--for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain. Ellipse of bliss, converge, O lips divine! The product of our scalars is defined! Cyberiad draws nigh, and the skew mind Cuts capers like a happy haversine. I see the eigenvalue in thine eye, I hear the tender tensor in thy sigh. Bernoulli would have been content to die, Had he but known such a^2 cos 2 phi!" poetry mathematics Stanisław Lem
91c2998 Existe una opinion generalizada segun la cual la matematica es la ciencia mas dificil cuando en realidad es la mas simple de todas. La causa de esta paradoja reside en el hecho de que, precisamente por su simplicidad, los razonamientos matematicos equivocados quedan a la vista. En una compleja cuestion de politica o arte, hay tantos factores en juego y tantos desconocidos e inaparentes, que es muy dificil distinguir lo verdadero de lo falso. El resultado es que cualquier tonto se cree en condiciones de discutir sobre politica y arte -y en verdad lo hace- mientras que mira la matematica desde una respetuosa distancia. science matemáticas mathematics Ernesto Sabato
ddd84fe He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixteens. The numbers formed up and marched past his brain in terrified obedience. Division and multiplication were discovered. Algebra was invented and provided an interesting diversion for a minute or two. And then he felt the fog of numbers drift away, and looked up and saw the sparkling, distant mountains of calculus. math mathematics Terry Pratchett
219e0d6 "But that can never be," said Milo, jumping to his feet. "Don't be too sure," said the child patiently, "for one of the nicest things about mathematics, or anything else you might care to learn, is that many of the things which can never be, often are. You see," he went on, "it's very much like your trying to reach Infinity. You know that it's there, but you just don't know where -- but just because you can never reach it doesn't mean that it's not worth looking for." mathematics Norton Juster
d6c1d52 Music was not so very different from mathematics. It was all just patterns and sequences. The only difference was that they hung in the air instead of on a piece of paper. Dancing was a grand equation. One side was sound, the other movement. The dancer's job was to make them equal. music dancer dancing math mathematics Julia Quinn
fe1b286 Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that ascertained the true position of the earth and accounted for all celestial phenomena; that discovered his three laws--discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that , , , and , almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of , , and , of , and and of all the pioneers of progress--that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that and , , and , and , and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God? discoveries progress tragedy libraries poets shakespeare india light writer fiction books inspiration bible science songs intelligence alessandro-volta benjamin-franklin beranger bonaventura-cavalieri bonaventura-francesco-cavalieri burns cavalieri chemistry china copernicus descartes euclid experiments franklin fulton galileo galileo-galilei galvani gottfried-leibniz gottfried-von-leibniz gottfried-wilhelm-leibniz gottfried-wilhelm-von-leibniz greece hydrostatics inventions isaac-newton james-watt johann-von-goethe johannes-kepler kepler laws-of-motion leibniz luigi-aloisio-galvani luigi-galvani math mathematics morse newton nicolaus-copernicus optics pentateuch pierre-jean-de-béranger pioneers pneumatics rene-descartes richard-trevithick robert-burns robert-fulton rome samuel-finley-breese-morse samuel-morse schiller the-bible theory-of-gravity theory-of-universal-gravitation trevethick volta watt Æschylus johann-wolfgang-von-goethe goethe egypt william-shakespeare Robert G. Ingersoll
45498e5 "Is everyone with one face called a Milo?" "Oh no," Milo replied; "some are called Henry or George or Robert or John or lots of other things." "How terribly confusing," he cried. "Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless." "I never thought of it that way," Milo admitted. "Then I suggest you begin at once," admonished the Dodecahedron from his admonishing face, "for here in Digitopolis everything is quite precise." names mathematics Norton Juster
df92fed "Most people would have probably lost count around seven. This was, Harry knew from his extensive reading on logic and arithmetic, the largest number that most people could visually appreciate. Put seven dots on a page, and most people can take a quick glance and declare, "Seven." Switch to eight, and the majority of humanity was lost." humanity numbers seven mathematics Julia Quinn
5e6c4f8 To return to the general analysis of the Rosicrucian outlook. Magic was a dominating factor, working as a mathematics-mechanics in the lower world, as celestial mathematics in the celestial world, and as angelic conjuration in the supercelestial world. One cannot leave out the angels in this world view, however much it may have been advancing towards the scientific revolution. The religious outlook is bound up with the idea that penetration has been made into higher angelic spheres in which all religions were seen as one; and it is the angels who are believed to illuminate man's intellectual activities. In the earlier Renaissance, the magi had been careful to use only the forms of magic operating in the elemental or celestial spheres, using talismans and various rituals to draw down favourable influences from the stars. The magic of a bold operator like Dee, aims beyond the stars, aims at doing the supercelestial mathematical magic, the angel-conjuring magic. Dee firmly believed that he had gained contact with good angels from whom he learned advancement in knowledge. This sense of close contact with angels or spiritual beings is the hallmark of the Rosicrucian. It is this which infuses his technology, however practical and successful and entirely rational in its new understanding of mathematical techniques, with an unearthly air, and makes him suspect as possibly in contact, not with angels, but with devils. john-dee occultism mathematics Frances A. Yates
37c2f9c Magic is like a lot of other disciplines that people have recently begun developing, in historic terms. Working with magic is a way of understanding the universe and how it functions. You can approach it from a lot of different angles, applying a lot of different theories and mental models to it. You can get to the same place through a lot of different lines of theory and reasoning, kind of like really advanced mathematics. There's no truly right or wrong way to get there, either--there are just ways, some more or less useful than others for a given application. And new vistas of thought, theory, and application open up on a pretty regular basis, as the Art develops and expands through the participation of multiple brilliant minds. But that said, once you have a good grounding in it,you get a pretty solid idea of what's possible and what isn't. No matter how much circumlocution you do with your formulae, two plus two doesn't equal five. (Except maybe very, very rarely, sometimes, in extremely specific and highly unlikely circumstances.) magic mathematics Jim Butcher
8954bdb Schools were started to train human talents... The Guild... emphasizes almost pure mathematics. Bene Gesserit performs... politics. The original Bene Gesserit school was directed by those who saw the need of a thread of continuity in human affairs. They saw there count be no such continuity without separating human stock from animal stock - for breeding purposes. humanity politics mathematics Frank Herbert
7eddaf9 The oldest problem in economic education is how to exclude the incompetent. A certain glib mastery of verbiage-the ability to speak portentously and sententiously about the relation of money supply to the price level-is easy for the unlearned and may even be aided by a mildly enfeebled intellect. The requirement that there be ability to master difficult models, including ones for which mathematical competence is required, is a highly useful screening device. mathematics John Kenneth Galbraith
61cd893 Take this neat little equation here. It tells me all the ways an electron can make itself comfortable in or around an atom. That's the logic of it. The poetry of it is that the equation tells me how shiny gold is, how come rocks are hard, what makes grass green, and why you can't see the wind. And a million other things besides, about the way nature works. nature feynman fine-structure-constant mathematics physics Richard Feynman
72707a2 Like Moliere's M. Jourdain, who spoke prose all his life without knowing it, mathematicians have been reasoning for at least two millennia without being aware of all the principles underlying what they were doing. The real nature of the tools of their craft has become evident only within recent times A renaissance of logical studies in modern times begins with the publication in 1847 of George Boole's 'The Mathematical Analysis of Logic'. nature science study george-boole jean-baptiste-poquelin m-jourdain molière reasoning logic math mathematics Ernest Nagel
b0a43ed The truth, he thought, has never been of any real value to any human being- it is a symbol for mathematicians and philosophers to pursue. I human relations kindness and lies are worth a thousand truths. lies philosophy truth mathematics Graham Greene
9d2a5c1 A certain elementary training in statistical method is becoming as necessary for everyone living in this world of today as reading and writing. statistics mathematics H.G. Wells
17f999d A remarkably consistent finding, starting with elementary school students, is that males are better at math than females. While the difference is minor when it comes to considering average scores, there is a huge difference when it comes to math stars at the upper extreme of the distribution. For example, in 1983, for every girl scoring in the highest percentile in the math SAT, there were 11 boys. Why the difference? There have always been suggestions that testosterone is central. During development, testosterone fuels the growth of a brain region involved in mathematical thinking and giving adults testosterone enhances their math skills. Oh, okay, it's biological. But consider a paper published in science in 2008. The authors examined the relationship between math scores and sexual equality in 40 countries based on economic, educational and political indices of gender equality. The worst was Turkey, United States was middling, and naturally, the Scandinavians were tops. Low and behold, the more gender equal the country, the less of a discrepancy in math scores. By the time you get to the Scandinavian countries it's statistically insignificant. And by the time you examine the most gender equal country on earth at the time, Iceland, girls are better at math than boys. Footnote, note that the other reliable sex difference in cognition, namely better reading performance by girls than by boys doesn't disappear in more gender equal societies. It gets bigger. In other words, culture matters. We carry it with us wherever we go. genetics gender mathematics Robert M. Sapolsky
e08dcfd In the field of Egyptian mathematics Professor Karpinski of the University of Michigan has long insisted that surviving mathematical papyri clearly demonstrate the Egyptians' scientific interest in pure mathematics for its own sake. I have now no doubt that Professor Karpinski is right, for the evidence of interest in pure science, as such, is perfectly conclusive in the Edwin Smith Surgical Papyrus. science pure-research university-of-michigan mathematics James Henry Breasted
ab09405 Lots of people wrote to the magazine to say that Marilyn vos Savant was wrong, even when she explained very carefully why she was right. Of the letters she got about the problem, 92% said that she was wrong and lots of these were from mathematicians and scientists. Here are some of the things they said: 'I'm very concerned with the general public's lack of mathematical skills. Please help by confessing your error.' -Robert Sachs, Ph.D., George Mason University ... 'I am sure you will receive many letters from high school and college students. Perhaps you should keep a few addresses for future columns.' -W. Robert Smith, Ph.D., Georgia State University... 'If all those Ph.D.'s were wrong, the country would be in very serious trouble.' -Everett Harman, Ph.D., U.S. Army Research Institute irony mathematics Mark Haddon
3887757 I don't deny that it was more than a coincidence which made things turn out as they did, it was a whole train of coincidences. But what has providence to do with it? I don't need any mystical explanation for the occurrence of the improbable; mathematics explains it adequately, as far as I'm concerned. Mathematically speaking, the probable (that in 6,000,000,000 throws with a regular six-sided die the one will come up approximately 1,000,000,000 times) and the improbable (that in six throws with the same die the one will come up six times) are not different in kind, but only in frequency, whereby the more frequent appears a priori more probable. But the occasional occurrence of the improbable does not imply the intervention of a higher power, something in the nature of a miracle, as the layman is so ready to assume. The term probability includes improbability at the extreme limits of probability, and when the improbable does occur this is no cause for surprise, bewilderment or mystification. providence mathematics Max Frisch
5b43cd4 See appendix A for a proof that Winston Churchill was a carrot. mathematics Charles Seife
d421324 I liked numbers because they were solid, invariant; they stood unmoved in a chaotic world. There was in numbers and their relation something absolute, certain, not to be questioned, beyond doubt. science mathematics Oliver Sacks
b740012 Outside the port, the slashed rock of the unnamed asteroid tumbled and spun in dynamics known only to the gods of chaos mathematics. god dynamics gods-of-chaos chaos mathematics Dan Simmons
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