“
Poems are rough notations for the music we are.
”
”
Jalal ad-Din Muhammad ar-Rumi
“
It will take all your heart, it will take all your breath
It will be short, it will not be simple
”
”
Adrienne Rich
“
The reason it's worth standing up for punctuation is not that it's an arbitrary system of notation known only to an over-sensitive elite who have attacks of the vapours when they see it misapplied. The reason to stand up for punctuation is that without it there is no reliable way of communicating meaning.
”
”
Lynne Truss (Eats, Shoots & Leaves: The Zero Tolerance Approach to Punctuation)
“
the whole purport of literature...is the notation of the heart. Style is but the faintly contemptible vessel in which the bitter liquid is recommended to the world.
”
”
Thornton Wilder (The Bridge of San Luis Rey)
“
Because Music is a language that lives in the spiritual realms, we can hear it, we can notate it and create it, but we cannot hold it in our hands
”
”
Joy Harjo
“
Who would sup with the mighty must climb the path of daggers.
-Anonymous notation found inked in the margin of a manuscript history (believed to date to the time of Arthur Hawkwing) of the last days of the Tovan Conclaves
”
”
Robert Jordan (The Path of Daggers (The Wheel of Time, #8))
“
The process of writing has something infinite about it. Even though it is interrupted each night, it is one single notation, and it seems most true when it eschews artistic devices of any sort.
”
”
Elias Canetti (The Secret Heart of the Clock)
“
I asked him what, if anything, got him down about teaching. He said he didn't think that anything about it got him exactly down, but there was one thing, he thought, that frightened him: reading the pencilled notations in the margins of books in the college library.
”
”
J.D. Salinger (Raise High the Roof Beam, Carpenters & Seymour: An Introduction)
“
Notation on Quark Manipulation as Applied to the Time/Space Continuum.
”
”
Gabriel F.W. Koch (Steel Blood)
“
FINAL NOTATIONS
it will not be simple, it will not be long
it will take little time, it will take all your thought
it will take all your heart, it will take all your breath
it will be short, it will not be simple
it will touch you through your ribs, it will take all your heart
it will not be long, it will occupy your thought
as a city is occupied, as a bed is occupied
it will take all your flesh, it will not be simple
you are coming into us who cannot withstand you
you are coming into us who never wanted to withstand you
you are taking parts of us into places never planned
you are going far away with pieces of our lives
it will be short, it will take all your breath
it will not be simple, it will become your will
”
”
Adrienne Rich (An Atlas of the Difficult World)
“
There is no pattern the human mind can devise that does not exist already within the bounds of nature...Everything we do, see, write, notate, all are an echo of the deep seams of the universe. Music is the invisible world made visible through sound.
”
”
Kate Mosse (Sepulchre (Languedoc, #2))
“
Codes and patterns are very different from each other,” Langdon said. “And a lot of people confuse the two. In my field, it’s crucial to understand their fundamental difference.”
“That being?”
Langdon stopped walking and turned to her. “A pattern is any distinctly organized sequence. Patterns occur everywhere in nature—the spiraling seeds of a sunflower, the hexagonal cells of a honeycomb, the circular ripples on a pond when a fish jumps, et cetera.”
“Okay. And codes?”
“Codes are special,” Langdon said, his tone rising. “Codes, by definition, must carry information. They must do more than simply form a pattern—codes must transmit data and convey meaning. Examples of codes include written language, musical notation, mathematical equations, computer language, and even simple symbols like the crucifix. All of these examples can transmit meaning or information in a way that spiraling sunflowers cannot.
”
”
Dan Brown (Origin (Robert Langdon, #5))
“
What was a zero anyway? A zero signified nothing, all it did was tell you nothing about nothing. Still, wasn't zero also something meaningful, a number in and of itself? In jianpu notation, zero indicated a caesura, a pause or rest of indeterminate length. Did time that went uncounted, unrecorded, still qualify as time? If zero was both everything and nothing, did an empty life have exactly the same weight as a full life? Was zero like the desert, both finite and infinite?
”
”
Madeleine Thien (Do Not Say We Have Nothing)
“
Luna luase aspectul unui cap de înger cu aureolă și trup de nori. Treptat, norii s-au îndepărtat, lăsând-o golașă pe cerul albastru. Încet-încet se stingea... Lumina îmi strângea sufletul, mototolindu-l ca pe o hârtie pe care mi-am notat greșit sentimentele, aruncând-o în gunoiul zilei.
”
”
Carmen Stoian (korsakoff - doar inceputul)
“
As long as we are engaged in this orgy of unnecessary terminology and notation…
”
”
David J. Griffiths (Introduction to Electrodynamics)
“
My husband is my most ruthless critic... sometimes he will say, 'It's been said better before.' Of course it has. It's all been said better before. If I thought I had to say it better than anybody else, I'd never start. Better or worse is immaterial. The thing is that it has to be said; by me; ontologically. We each have to say it, to say it our own way. Not of our own will, but as it comes out through us. Good or bad, great or little: that isn't what human creation is about. It is that we have to try; to put it down in pigment, or words, or musical notations, or we die.
”
”
Madeleine L'Engle
“
both you and paintings are layered… first, ephemera and notations on the back of the canvas. Labels indicate gallery shows, museum shows, footprints in the snow, so to speak. Then pencil scribbles on the stretcher, usually by the artist, usually a title or date. Next the stretcher itself. Pine or something. Wooden triangles in the corners so the picture can be tapped tighter when the canvas becomes loose. Nails in the wood securing the picture to the stretcher. Next, a canvas: linen, muslin, sometimes a panel; then the gesso - a primary coat, always white. A layer of underpaint, usually a pastel color, then, the miracle, where the secrets are: the paint itself, swished around, roughly, gently, layer on layer, thick or thin, not more than a quarter of an inch ever -- God can happen in that quarter of an inch -- the occasional brush hair left embedded, colors mixed over each other, tones showing through, sometimes the weave of the linen revealing itself. The signature on top of the entire goulash. Then varnish is swabbed over the whole. Finally, the frame, translucent gilt or carved wood. The whole thing is done.
”
”
Steve Martin (An Object of Beauty)
“
Music expresses feeling, that is to say, gives shape and habitation to feeling, not in space but in time. To the extent that music has a history that is more than a history of its formal evolution, our feelings must have a history too. Perhaps certain qualities of feeling that found expression in music can be recorded by being notated on paper, have become so remote that we can no longer inhabit them as feelings, can get a grasp of them only after long training in the history and philosophy of music, the philosophical history of music, the history of music as a history of the feeling soul.
”
”
J.M. Coetzee (Diary of a Bad Year)
“
In the smoky firelight the two old men nodded off like a pair of ancient kings passing the aeons in their tumuli. Made a musical notation of their snores. Elgar is to be played by a bass tuba, Ayrs a bassoon.
”
”
David Mitchell (Cloud Atlas)
“
Language is music. Written words are musical notation. The music of a piece of fiction establishes the way in which it is to be read, and, in the largest sense, what it means. It is essential to remember that characters have a music as well, a pitch and tempo, just as real people do. To make them believable, you must always be aware of what they would or would not say, where stresses would or would not fall.
”
”
Marilynne Robinson (When I Was a Child I Read Books)
“
She was in herself, like a woman near term,
and did not think of the man, going on ahead,
or the path, climbing upwards towards life.
She was in herself. And her being-dead
filled her with abundance.
As a fruit with sweetness and darkness,
so she was full with her vast death.
”
”
Rainer Maria Rilke (ORPHEUS. EURYDICE. HERMES. NOTATIONS ON A LANDSCAPE.)
“
We could, of course, use any notation we want; do not laugh at notations; invent them, they are powerful. In fact,mathematics is, to a large extent, invention of better notations.
”
”
Richard P. Feynman (The Feynman Lectures on Physics Vol 1)
“
..by honouring the demands of our bleeding, our blood gives us something in return. The crazed bitch from irritation hell recedes. In her place arises a side of ourselves with whom we may not-at first- be comfortable. She is a vulnerable, highly perceptive genius who can ponder a given issue and take her world by storm. When we're quiet and bleeding, we stumble upon solutions to dilemmas that've been bugging us all month. Inspiration hits and moments of epiphany rumba 'cross de tundra of our senses. In this mode of existence one does not feel antipathy towards a bodily ritual that so profoundly and reinforces our cuntpower.
”
”
Inga Muscio (Cunt: A Declaration of Independence)
“
Obsession is, in any case, the premonition of the existence of an individual language, an irreproducible language through the attentive use of which we will be able to uncover the truth. We must follow this premonition into regions that to others might seem absurd and mad. I don’t know why this language of truth sounds angelic to some, while to others it changes into mathematical signs or notations. But there are also those to whose whim it speaks in a very strange way.
”
”
Olga Tokarczuk (Flights)
“
I'm not givin' in an inch to fear.
”
”
David Crosby (The Best of Crosby, Stills, Nash & Young for Guitar: Includes Super TAB Notation (The Best of... for Guitar Series))
“
I needed another basis for musical structure. This I found in sound's duration parameter, sound's only parameter which is present even when no sound is intended.
”
”
John Cage (M: Writings '67–'72)
“
Literature is the notation of the heart.
”
”
Thornton Wilder
“
From this time on, my life would be written in headlines, but I am not concerned with them. It was the marginal notations of the heart that were most important to the man within.
”
”
Carlos P. Romulo (I Walked With Heroes)
“
Early, I indentured myself to the five horizontal lines where black notes were written on a sheet of music. It is a place of world of signs and notations that speaks to me with perfect clarity. It is a place of time signatures, fermatas, ledger lines, grace notes, and demisemiquavers that are the common tongue and heritage of musicians all over the world. . . . It is something I cannot imagine being without. For without music, life is a journey through a desert that has not ever heard the rumor of God. In music’s sweet harmony, I had all the proof I needed of a God who held the earth together between the staffs, where the heavens lay. Here, he marked all the lines and spaces with notes so perfect that they praised all of his creation with their beauty.
”
”
Pat Conroy (Beach Music)
“
So a)To what extent might human relationships be expressed in a mathematical or logical formula? And b) If so, what signs might be placed between the integers? Plus and minus, self- evidently; sometimes multiplication, and yes. division. But these signs are limited. Thus an entirely failed relationship might be expressed in terms of both loss/minus and division/ reduction, showing a total zero; whereas an entirely successful one can be represented by both addition and multiplication. But what of most relationships? Do they not require to be expressed in notations which are logically insoluble?
”
”
Julian Barnes (The Sense of an Ending)
“
Freiherr Hugo Reiss made a notation on his pad. Broach subject with SS General Otto Skorzeny, or better yet Otto Ohlendorf at Amt III of the Reichssicherheitshauptamt. Didn’t Ohlendorf head Einsatzgruppe D?
”
”
Philip K. Dick (The Man in the High Castle)
“
There is much more to playing the clavier than playing written music. Do you realize with accompanying there is often nothing written out but the bass line--the left hand? There might be a few notations as to a suggested harmony, but it is up to me to fill in the music, at the proper volume, style, and harmony for the soloist--often instantly. I've heard it said that Bach questioned wether the soloist or the accompanist deserves the greatest glory.
”
”
Nancy Moser (Mozart's Sister (Ladies of History, #1))
“
We, the garden of technology. We, undecidable.
”
”
John Cage (I–VI: MethodStructureIntentionDisciplineNotationIndeterminacyInterpenetrationImitationDevotionCircumstancesVariableStructureNonunderstandingContingencyInconsistencyPerformance)
“
In any book, it is impossible to avoid some mistakes, some confusion,
some incorrectness of language, and some misuse of notation. If you find
any such things in the present book, then correct them or improve them for
yourself, or write your own book.
”
”
Serge Lang (Basic Mathematics)
“
I spent a few more minutes puzzling over the timeline before turning my attention to the notebook’s first page, which contained a pencil drawing of an old-school coin-operated arcade game—one I didn’t recognize. Its control panel featured a single joystick and one unlabeled white button, and its cabinet was entirely black, with no side art or other markings anywhere on it, save for the game’s strange title, which was printed in all capital green letters across its jet black marquee: POLYBIUS. Below his drawing of the game, my father had made the following notations: No copyright or manufacturer info anywhere on game cabinet. Reportedly only seen for 1–2 weeks in July 1981 at MGP. Gameplay was similar to Tempest. Vector graphics. Ten levels? Higher levels caused players to have seizures, hallucinations, and nightmares. In some cases, subject committed murder and/or suicide. “Men in Black” would download scores from the game each night. Possible early military prototype created to train gamers for war? Created by same covert op behind Bradley Trainer?
”
”
Ernest Cline (Armada)
“
The difference between the detailed plans he drew up and the house itself when finished, so filled with raked sea light, is the difference between the body and the soul, between musical notation and a song, between the idea for a drawing and the actual drawing itself.
”
”
Colm Tóibín (A Guest at the Feast)
“
. Maybe postmodern writers like me all have post-atomic poetic feet & that’s what makes them ugly to the pre-atomic eye & difficult to notate. Maybe this is THE ATTACK OF THE MUTANT POST-ATOMIC FEET! Maybe this is why we’re always saying the words: ‘take me to your reader.
”
”
bpNichol
“
I know the impossibility of the hickey, whose urge is not ultimately to mark or to be marked, but to possess and be possessed. I cannot render anything precisely in words, as I cannot crush my lover's body inside of mine. All I can do is leave a mark--the notation of my effort, a symbol for the thing. That is the endless pleasure and frustration of the writer and the lover: to reach and reach and never become.
”
”
Melissa Febos (Abandon Me: Memoirs)
“
sightseeing, an activity that delights the truly idle because it seems so much like scholarship, gawping and eavesdropping on antiquity, flattering oneself with the notion that one is discovering the past when really one is inventing it, using a guidebook as a scenario of swift notations.
”
”
Paul Theroux (The Great Railway Bazaar: By Train Through Asia)
“
To the right collector, the Witchfinder Army’s library would have been worth millions. The right collector would have to have been very rich, and not have minded gravy stains, cigarette burns, marginal notations, or the late Witchfinder Lance Corporal Wotling’s passion for drawing mustaches
”
”
Terry Pratchett (Good Omens: The Nice and Accurate Prophecies of Agnes Nutter, Witch)
“
All right,” he said. “Since you asked, Webmind is an emergent quantum-computational system based on a stable null-sigma condensate that resists decoherence thanks to constructive feedback loops.” He turned to the blackboard, scooped up a piece of chalk, and began writing rapidly. “See,” he said, “using Dirac notation, if we let Webmind’s default conscious state be represented by a bra of phi and a ket of psi, then this would be the einselected basis.” His chalk flew across the board again. “Now, we can get the vector basis of the total combined Webmind alpha-state consciousness...
”
”
Robert J. Sawyer (WWW: Watch (WWW, #2))
“
The twinkle that softens the review; the martyr's super-logic and the child's intuition; the fact that a fragment of moss can pull back into the memory a whole forest – these are proofs that there is reality in the imponderable, and not only notation but connotation is a part of the proper study of mankind.
”
”
Beatrice Warde
“
There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the want of an appropriate notation for expressing the conditions of a dynamical problem, and the general principles by which its solution must be obtained. By the labours of LaGrange, the motions of a disturbed planet are reduced with all their complication and variety to a purely mathematical question. It then ceases to be a physical problem; the disturbed and disturbing planet are alike vanished: the ideas of time and force are at an end; the very elements of the orbit have disappeared, or only exist as arbitrary characters in a mathematical formula.
”
”
George Boole
“
Technology, for instance, has become a kind of imposter for connection, making us believe we’re connected when we’re really not—at least not in the ways we need to be.
”
”
Brené Brown (The Gifts of Imperfection: Let Go of Who You Think You're Supposed to Be and Embrace Who You Are)
“
I paint to rest from the phenomena of the external world - to pronounce it -- and to make notations of its essences with which to verify the inner eye.
”
”
Morris Graves
“
Jewish Law is like musical notation; it gives meaning to the stuff of life by regulating it in time. The Sabbath is its most sacred interval
”
”
Judith Shulevitz
“
Come, my dear. This has been far too much excitement for me this morning. Feel an irresistible urge to stare at some roses and make notations.
”
”
Cindy Anstey (Love, Lies and Spies)
“
For the biographer, the final clue to character lies in the yet unread - the scribbled note, the diary page, a notation in the margin of a draft - until the day when even the most devoted portraitist of the dead says, "Enough!" Working in the service of the dead, biographers quit their labors only when the sole remaining task is the impossible - resurrection.
”
”
Laura Furman (The Mother Who Stayed: Stories)
“
Writing is, like gender or dominatricing, a kind of performance. But the craft of writing is primarily an art of making decisions. I often like to terrorize my students by insisting that every single notation—every piece of punctuation, every word, every paragraph break—in a piece of writing is a decision. You know when something is done, I tell them (they always want to know how to know when something is done), when you know the argument for every single choice, when not a single apostrophe has slipped by uninterrogated, when every word has been swapped for its synonym and then recovered. I don’t mean to take the fun out of creation, or even to impose my own laborious process on them, but I actually believe this. Not in the first draft, or even the fifth, but by the end, I want to have stripped as many tics and defaults, as many blind choices as is in my power. I want to be awake to all my choices.
”
”
Melissa Febos (Body Work: The Radical Power of Personal Narrative)
“
the scientific advances made by early Middle Eastern cultures, one of them being our modern numbering system, whose advantages over Roman numerals included ‘positional notation’ and the invention of the number zero. Of course, Langdon always ended this lecture with a reminder that Arab culture had also given mankind the word al-kuhl—the favorite beverage of Harvard freshmen—known as alcohol.
”
”
Dan Brown (The Lost Symbol (Robert Langdon, #3))
“
Jenny’s admonition had the desired effect. Ned drew a deep breath and thrust his arm gingerly into the bag, his mouth puckered in distaste. The expression on his face flickered from queasy horror to confusion. From there, it
flew headlong into outright bafflement. Shaking his head, he pulled his fist from the bag and turned his hand palm up.
For a long moment, the two men stared at the offending lump. It was brightly colored. It was round. It was—
“An orange?” Lord Blakely rubbed his forehead. “Not quite what I expected.” He scribbled another notation.
“We live in enlightened times,” Jenny murmured.
”
”
Courtney Milan (Proof by Seduction (Carhart, #1))
“
His work was just barely passing by academic standards at this time, but this wasn’t because he wasn’t working or thinking. He was thinking too hard, and the harder you think in this high country of the mind the slower you go. Phaedrus read in a scientific way rather than a literary way, testing each sentence as he went along, noting doubts and questions to be resolved later, and I’m fortunate in having a whole trunkful of volumes of these notations
”
”
Robert M. Pirsig (Zen and the Art of Motorcycle Maintenance)
“
Hopper would later gain fame both as a teacher and as a pioneer in the development of high-level programming languages. Yet perhaps her best-known contribution came in the summer of 1945, when she and her colleagues were tracking down a glitch in the Mark II and discovered a large moth that had gotten crushed by one of the relay switches and shorted it out. She taped the dead moth into the logbook with the notation “First case of an actual bug being found.
”
”
M. Mitchell Waldrop (The Dream Machine)
“
The Strategic Bombing Survey estimates that “probably more persons lost their lives by fire at Tokyo in a 6-hour period than at any [equivalent period of] time in the history of man.” The fire storm at Dresden may have killed more people but not in so short a space of time. More than 100,000 men, women and children died in Tokyo on the night of March 9-10, 1945; a million were injured, at least 41,000 seriously; a million in all lost their homes. Two thousand tons of incendiaries delivered that punishment—in the modern notation, two kilotons. But the wind, not the weight of bombs alone, created the conflagration, and therefore the efficiency of the slaughter was in some sense still in part an act of God.
”
”
Richard Rhodes (The Making of the Atomic Bomb: 25th Anniversary Edition)
“
Finding patterns and structure in information is how our brains extract meaning from the world, and putting words to music and rhyme are a way of adding extra levels of pattern and structure to language. It’s the reason Homeric bards sang their epic oral poems, the reason that the Torah is marked up with little musical notations, and the reason we teach kids the alphabet in a song and not as twenty-six individual letters. Song is the ultimate structuring device for language.
”
”
Joshua Foer (Moonwalking with Einstein: The Art and Science of Remembering Everything)
“
Unlike musical notation, paint or clay, language is inside every one of us. For free. We are all proficient at it. We already have the palette, the paints and the instruments. We don’t have to go and buy any reserved materials. Poetry is made of the same stuff you are reading now, the same stuff you use to order pizza over the phone, the same stuff you yell at your parents and children, whisper in your lover’s ear and shove into an e-mail, text or birthday card. It is common to us all.
”
”
Stephen Fry (The Ode Less Travelled: Unlocking the Poet Within)
“
In fact, they didn’t even keep track of birth dates here. Instead, they used a traditional method of counting a person’s age. Newborn babies were “one year old,” and became one year older at the start of the new year. As for the reason it didn’t start at zero... I was briefly afraid I’d discover they didn’t yet have the concepts of zero or place-value notation. In fact, they had both. Newborn babies being “one” was just a holdover from previous times, before the numeral “zero” existed within their culture. Old
”
”
Kanata Yanagino (The Faraway Paladin: Volume 1: The Boy in the City of the Dead)
“
Sometimes he wrote equations, or musical notation, sometimes he wrote in Latin; he refused to tell her what it was about. "Nothing," he said. "I have nothing important or original to say, yet I feel compelled to express myself, so I just write it down and let it go.
”
”
Gwendolen Gross (When She Was Gone)
“
We know that our language is incapable of recalling even the pale reflection of those strange and perished states. The same would be true of this entire journal if it had to be the notation of what I was. I shall therefore make it clear that it is meant to indicate what I am today, as I write it. It is not a quest of time gone by, but a work of art whose pretext−subject is my former life. It will be a present fixed with the help of the past, and not vice versa. Let it be therefore understood that the facts were what I say they were, but the interpretation that I give them is what I am—now.
”
”
Jean Genet (The Thief's Journal)
“
n tempo sembravano puttane. Adesso somigliavano a studentesse universitarie. Volevano tutte sembrare studentesse. Perché non ci andavano davvero, all’università, allora? Non avrebbero avuto niente di diverso dalle altre. Nessuno le avrebbe mai notate. Cristo, che maniera assurda di stare al mondo.
”
”
William Lindsay Gresham (Nightmare Alley)
“
Un tempo sembravano puttane. Adesso somigliavano a studentesse universitarie. Volevano tutte sembrare studentesse. Perché non ci andavano davvero, all’università, allora? Non avrebbero avuto niente di diverso dalle altre. Nessuno le avrebbe mai notate. Cristo, che maniera assurda di stare al mondo.
”
”
William Lindsay Gresham (Nightmare Alley)
“
The Industrial Revolution was based on two grand concepts that were profound in their simplicity. Innovators came up with ways to simplify endeavors by breaking them into easy, small tasks that could be accomplished on assembly lines. Then, beginning in the textile industry, inventors found ways to mechanize steps so that they could be performed by machines, many of them powered by steam engines. Babbage, building on ideas from Pascal and Leibniz, tried to apply these two processes to the production of computations, creating a mechanical precursor to the modern computer. His most significant conceptual leap was that such machines did not have to be set to do only one process, but instead could be programmed and reprogrammed through the use of punch cards. Ada saw the beauty and significance of that enchanting notion, and she also described an even more exciting idea that derived from it: such machines could process not only numbers but anything that could be notated in symbols.
”
”
Walter Isaacson (The Innovators: How a Group of Hackers, Geniuses and Geeks Created the Digital Revolution)
“
The U.S. Air Force Academy likewise sought racial “diversity” through double standards. A 1982 memorandum on Air Force Academy stationery, with the notation “for your eyes only,” listed different cut-off scores to use when identifying possible candidates for the Academy from different racial ethnic groups. Composite SAT scores as low as 520 were acceptable for blacks, though Hispanics and American Indians had to do somewhat better, and Asian Americans had to meet the general standards. For athletes “lower cut-offs” were permissible.52 Given that composite SAT scores begin at 400 (out of a possible 1600) a requirement of 520 is really a requirement to earn only 120 points out of a possible 1200 points earned.
”
”
Thomas Sowell (Inside American Education)
“
Ahlakın bahtsızlığı : her şeyi daha iyi bilmesi ve bu yüzden de hiçbir şey öğrenememesi.
”
”
Elias Canetti (The Agony of Flies: Notes and Notations)
“
Typically, preachers in our work-oriented society teach that God rested to provide humanity with a precedent for rest, an example for our good. Seldom have I heard mention of the other meaning for rest, the one used in musical notation. This meaning refers to cessation rather than recovery from weariness. Our enjoyment of music owes much to these brief pauses.
”
”
Hugh Ross (Hidden Treasures in the Book of Job (Reasons to Believe): How the Oldest Book in the Bible Answers Today's Scientific Questions)
“
5.4 The question of accumulation. If life is a wager, what form does it take? At the racetrack, an accumulator is a bet which rolls on profits from the success of one of the horse to engross the stake on the next one.
5.5 So a) To what extent might human relationships be expressed in a mathematical or logical formula? And b) If so, what signs might be placed between the integers?Plus and minus, self-evidently; sometimes multiplication, and yes, division. But these sings are limited. Thus an entirely failed relationship might be expressed in terms of both loss/minus and division/ reduction, showing a total of zero; whereas an entirely successful one can be represented by both addition and multiplication. But what of most relationships? Do they not require to be expressed in notations which are logically improbable and mathematically insoluble?
5.6 Thus how might you express an accumulation containing the integers b, b, a (to the first), a (to the second), s, v?
B = s - v (*/+) a (to the first)
Or
a (to the second) + v + a (to the first) x s = b
5.7 Or is that the wrong way to put the question and express the accumulation? Is the application of logic to the human condition in and of itself self-defeating? What becomes of a chain of argument when the links are made of different metals, each with a separate frangibility?
5.8 Or is "link" a false metaphor?
5.9 But allowing that is not, if a link breaks, wherein lies the responsibility for such breaking? On the links immediately on the other side, or on the whole chain? But what do you mean by "the whole chain"? How far do the limits of responsibility extend?
6.0 Or we might try to draw the responsibility more narrowly and apportion it more exactly. And not use equations and integers but instead express matters in the traditional narrative terminology. So, for instance, if...." - Adrian Finn
”
”
Julian Barnes (The Sense of an Ending)
“
When angry at a colleague, Lincoln would fling off what he called a “hot” letter, releasing all his pent wrath. He would then put the letter aside until he cooled down and could attend the matter with a clearer eye. When Lincoln’s papers were opened at the turn of the twentieth century, historians discovered a raft of such letters, with Lincoln’s notation underneath; “never sent and never signed.” Such forbearance set an example for the team. One evening, Lincoln listened as Stanton worked himself into a fury against one of the generals. “I would like to tell him what I think of him,” Stanton stormed. “Why don’t you,” suggested Lincoln. “Write it all down.” When Stanton finished the letter, he returned and read it to the president. “Capital,” Lincoln said. “Now, Stanton, what are you going to do about it?” “Why, send it of course!” “I wouldn’t,” said the president. “Throw it in the waste-paper basket.” “But it took me two days to write.” “Yes, yes and it did you ever so much good. You feel better now. That is all that is necessary. Just throw it in the basket.” And after some additional grumbling, Stanton did just that.
”
”
Doris Kearns Goodwin (Leadership: In Turbulent Times)
“
Whatever you want," he said. "Will you please come here now?"
I slipped a piece of protective tissue over my drawing and flipped the book closed. A piece of blue scratch paper slid out, the line I'd copied from Edward;s poetry book. "Hey. Translate for me, Monsieur Bainbridge."
I set the sketchbook on my stool and joined him on the chaise. He tugged me onto his lap and read over his head. "'Qu'ieu sui avinen, leu lo sai.' 'That I am handsome, I know."
"Verry funny."
"Very true." He grinned. "The translation. That's what it says. Old-fashionedly."
I thought of Edward's notation on the page, the reminder to read the poem to Diana in bed, and rolled my eyes. You're so vain.I bet you think this song is about you..."Boy and their egos."
Alex cupped my face in his hands. "Que tu est belle, tu le sais."
"Oh,I am not-"
"Shh," he shushed me, and leaned in.
The first bell came way too soon. I reluctantly loosened my grip on his shirt and ran my hands over my hair. He prompty thrust both hands in and messed it up again. "Stop," I scolded, but without much force.
"I have physics," he told me. "We're studying weak interaction."
I sandwiched his open hand between mine. "You know absolutely nothing about that."
"Don't be so quick to accept the obvious," he mock-scolded me. "Weak interaction can actually change the flavor of quarks."
The flavor of quirks, I thought, and vaguely remembered something about being charmed. I'd sat through a term of introductory physics before switching to basic biology. I'd forgotten most of that as soon as I'd been tested on it,too.
"I gotta go." Alex pushed me to my feet and followed. "Last person to get to class always gets the first question, and I didn't do the reading."
"Go," I told him. "I have history. By definition, we get to history late."
"Ha-ha. I'll talk to you later." He kissed me again, then walked out, closing the door quietly behind him.
”
”
Melissa Jensen (The Fine Art of Truth or Dare)
“
So we are all reincarnations—though short-lived ones. When we die our atoms will disassemble and move off to find new uses elsewhere—as part of a leaf or other human being or drop of dew. Atoms, however, go on practically forever. Nobody actually knows how long an atom can survive, but according to Martin Rees it is probably about 1035 years—a number so big that even I am happy to express it in notation.
”
”
Bill Bryson (A Short History of Nearly Everything)
“
that there is no agreement on what a programming language really is and what its main purpose is supposed to be. Is a programming language a tool for instructing machines? A means of communicating between programmers? A vehicle for expressing high-level designs? A notation for algorithms? A way of expressing relationships between concepts? A tool for experimentation? A means of controlling computerized devices
”
”
Anonymous
“
Here, then, is the genesis of two of the most important historical premises of Western science. The first is that there is a law of nature, an order of things and events awaiting our discovery, and that this order can be formulated in thought, that is, in words or in some type of notation. The second is that the law of nature is universal, a premise deriving from monotheism, from the idea of one God ruling the whole world.
”
”
Alan W. Watts (Nature, Man and Woman)
“
A second technician gauges Werner’s eye color against a chromatic scale on which sixty or so shades of blue are displayed. Werner’s color is himmelblau, sky blue. To assess his hair color, the man snips a lock of hair from Werner’s head and compares it to thirty or so other locks clipped to a board, arrayed darkest to lightest. “Schnee,” the man mutters, and makes a notation. Snow. Werner’s hair is lighter than the lightest color on the board.
”
”
Anthony Doerr (All the Light We Cannot See)
“
Dispersal was a conscious strategy of the plunderers. Only by destroying these collections could they build up new ones. Many of these libraries were the results of decades, sometimes centuries, of careful collecting. There had been generations of learned collectors and readers. The books also said something about the people who owned and treasured them: what they read and what they thought and what they dreamed. Sometimes they left traces in the form of underlined passages, notations, notes in the margins, or short comments. The beautiful and personally designed ex librises that many readers had made for their books demonstrate the care and pride they took in their libraries. Each collection in its own right took form in a unique culture, a depiction of its creator's world, which was lost when the library was broken up. The books are fragments of a library, of a world that once existed.
”
”
Anders Rydell (The Book Thieves: The Nazi Looting of Europe's Libraries and the Race to Return a Literary Inheritance)
“
I have been giving the best of my advice to this project since 1975. At first I was extremely hopeful. The original objectives of the language included reliability, readability of programs, formality of language definition, and even simplicity. Gradually these objectives have been sacrificed in favor of power, supposedly achieved by a plethora of features and notational conventions, many of them unnecessary and some of them, like exception handling, even dangerous. ...
It is not too late! I believe that by careful pruning of the ADA language, it is still possible to select a very powerful subset that would be reliable and efficient in implementation and safe and economic in use. The sponsors of the language have declared unequivocally, however, that there shall be no subsets. This is the strangest paradox of the whole strange project. If you want a language with no subsets, you must make it small.
”
”
C.A.R. Hoare
“
It’s all been said better before. If I thought I had to say it better than anybody else, I’d never start. Better or worse is immaterial. The thing is that it has to be said; by me; ontologically. We each have to say it, to say it our own way. Not of our own will, but as it comes out through us. Good or bad, great or little: that isn’t what human creation is about. It is that we have to try; to put it down in pigment, or words, or musical notations, or we die.
”
”
Madeleine L'Engle (The Crosswicks Journals: A Circle of Quiet, The Summer of the Great-Grandmother, The Irrational Season, and Two-Part Invention)
“
Upon finding the letter, I had one of those out of body experiences that come only after poring over archival material for nine hours straight, most of it dull as dust, but then something like this appears and you look around at the two or three other glaze-eyed researchers and want to go around the room and give everyone a high-five, but instead you just get up and quietly go to the water fountain, then make a notation for photocopy, and crack the next folder.
”
”
Jay Kirk (Kingdom Under Glass: A Tale of Obsession, Adventure, and One Man's Quest to Preserve the World's Great Animals)
“
It is safe to say that the message spoke of a common shape to all the processes of the world, and insisted there was a unity to all explanations. It confirmed that all phenomena are expressions of a single phenomenon, and while all droplets consider themselves independent, they are nonetheless still ocean through and through.
In that message the great suspicions were vindicated and the old cliches were jettisoned. The hymn of the world was notated and an invitation to join the choir extended. The shape of Being was outlined in all its myriad forms and the whole was expressed in the part.
With the right ears even a lesser creature can hear the song. It is sung constantly, from the heart of each atom and star.
The galaxies hum of shape and form in their essence. That is their secret.
The particles whisper of the nature of proper interactions. That is their game.
And during a storm, in the forest, on the right night, it is no secret that the leaves all sing of God.
”
”
Exurb1a (The Fifth Science)
“
But the figures,” he said, tapping the writing board. “You said they were erratic, and they still are.” “Yes,” she said, narrowing her eyes at the flamespren. “But I can predict when they will be erratic and when they won’t be.” He looked at her, frowning. “The spren change when I measure them, Ashir,” she said. “Before I measure, they dance and vary in size, luminosity, and shape. But when I make a notation, they immediately freeze in their current state. Then they remain that way permanently, so far as I can tell.
”
”
Brandon Sanderson (The Way of Kings (The Stormlight Archive, #1))
“
Notice that if , then and , whereas if
, then and .
(a) If is absolutely convergent, show that both of the
series and are convergent.
(b) If is conditionally convergent, show that both of the
series and are divergent.
44. Prove that if is a conditionally convergent series and
is any real number, then there is a rearrangement of
whose sum is . [Hints: Use the notation of Exercise 43.
an an
0 a
n
an
0
an an
0 an
0
an
an
an
a
n
an
an
a
n
an
r
an
r
Take just enough positive terms so that their sum is greater
than . Then add just enough negative terms so that the
cumulative sum is less than . Continue in this manner and use
Theorem 11.2.6.]
45. Suppose the series is conditionally convergent.
(a) Prove that the series is divergent.
(b) Conditional convergence of is not enough to determine whether is convergent. Show this by giving an
example of a conditionally convergent series such that
converges and an example where diverges.
r an
r
an
n
2
an
an
nan
nan
nan
an
We now have several ways of testing a series for convergence
”
”
James Stewart (Calculus: Early Transcendentals)
“
Again as during fetal development, synapses that underlie cognitive and other abilities stick around if they’re used but wither if they’re not. The systematic elimination of unused synapses, and thus unused circuits, presumably results in greater efficiency for the neural networks that are stimulated—the networks that support, in other words, behaviors in which the adolescent is actively engaged. Just as early childhood seems to be a time of exquisite sensitivity to the environment (remember the babies who dedicate auditory circuits only to the sounds of their native language, eliminating those for phonemes that they do not hear), so may adolescence. The teen years are, then, a second chance to consolidate circuits that are used and prune back those that are not—to hard-wire an ability to hit a curve ball, juggle numbers mentally, or turn musical notation into finger movements almost unconsciously. Says Giedd, “Teens have the power to determine their own brain development, to determine which connections survive and which don’t, [by] whether they do art, or music, or sports, or videogames.
”
”
Jeffrey M. Schwartz (The Mind & The Brain: Neuroplasticity and the Power of Mental Force)
“
I spoke off the record to a database consultant who was working with a company in Italy. They had a lot of clients, and their database would generate a client ID for each one by using something like the current year, the first letter of the client company name and then an index number to make sure each ID was unique. For some reason their database was losing companies whose names started with the letter E. It was because they were using Excel and it was converting those client IDs to be a scientific notation number, which was no longer recognized as an ID.
”
”
Matt Parker (Humble Pi: When Math Goes Wrong in the Real World)
“
There is no "religious language" or "scientific language". There is rather the international notation of mathematics and logic; and English, French, Spanish and the like. In short, "religious discourse" and "scientific discourse" are part of the same overall conceptual structure. Moreover, in that conceptual structure there is a large amount of discourse, which is neither religious nor scientific, that is constantly being utilized by both the religious man and the scientist when they make religious and scientific claims. In short, they share a number of key categories.
”
”
Kai Nielsen (An Introduction to the Philosophy of Religion)
“
What governs what we choose to notice? The first (which we shall have to qualify later) is whatever seems advantageous or disadvantageous for our survival, our social status, and the security of our egos. The second, again working simultaneously with the first, is the pattern and the logic of all the notation symbols which we have learned from others, from our society and our culture. It is hard indeed to notice anything for which the languages available to us (whether verbal, mathematical, or musical) have no description. This is why we borrow words from foreign languages.
”
”
Alan W. Watts
“
It is tempting to look upon England as a sort of musical Australia, an island culture inhabited by, and sustaining, its own insular fauna – musical kangaroos, koalas, and platypuses. That, however, would be very much to exaggerate England's musical isolation or independence. It is also a considerable exaggeration to view the English preference for thirds as something altogether alien or opposed to continental practice, as if only in remote geographical corners (and behind closed doors, among consenting adults) could harmonies unsanctioned by Pythagoras or the Musica enchiriadis be furtively enjoyed.
”
”
Richard Taruskin (Music from the Earliest Notations to the Sixteenth Century)
“
Only a simple black pencil will do for making a notation of a benchmark. Ink will run, be dissolved by the tree sap, be washed away by rain, dew, fog, and snow. Nothing as artificial as ink will do for recording eternity and immortality. Graphite is carbon that has been subjected to enormous pressure for millions of years and that might have become coal or diamonds. Instead, however, it has been transformed into something more precious than a diamond; it has become a pencil that can record all that it has seen… A pencil is a greater miracle than a diamond, although the chemical make-up of graphite and diamond is identical.
”
”
Varlam Shalamov (Kolyma Tales)
“
prior probability that the sun will rise, since it’s prior to seeing any evidence. It’s not based on counting the number of times the sun has risen on this planet in the past, because you weren’t there to see it; rather, it reflects your a priori beliefs about what will happen, based on your general knowledge of the universe. But now the stars start to fade, so your confidence that the sun does rise on this planet goes up, based on your experience on Earth. Your confidence is now a posterior probability, since it’s after seeing some evidence. The sky begins to lighten, and the posterior probability takes another leap. Finally, a sliver of the sun’s bright disk appears above the horizon and perhaps catches “the Sultan’s turret in a noose of light,” as in the opening verse of the Rubaiyat. Unless you’re hallucinating, it is now certain that the sun will rise. The crucial question is exactly how the posterior probability should evolve as you see more evidence. The answer is Bayes’ theorem. We can think of it in terms of cause and effect. Sunrise causes the stars to fade and the sky to lighten, but the latter is stronger evidence of daybreak, since the stars could fade in the middle of the night due to, say, fog rolling in. So the probability of sunrise should increase more after seeing the sky lighten than after seeing the stars fade. In mathematical notation, we say that P(sunrise | lightening-sky), the conditional probability of sunrise given that the sky is lightening, is greater than P(sunrise | fading-stars), its conditional probability given that the stars are fading. According to Bayes’ theorem, the more likely the effect is given the cause, the more likely the cause is given the effect: if P(lightening-sky | sunrise) is higher than P(fading-stars | sunrise), perhaps because some planets are far enough from their sun that the stars still shine after sunrise, then P(sunrise | lightening sky) is also higher than P(sunrise | fading-stars).
”
”
Pedro Domingos (The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World)
“
Before leaving the earth altogether, let us as: How does Music stand with respect to its instruments, their pitches, the scales, modes and rows, repeating themselves from octave to octave, the chords, harmonies, and tonalities, the beats, meters, and rhythms, the degrees of amplitude (pianissimo, piano, mezzo-piano, mezzo-forte, forte, fortissimo)? Though the majority go each day to the schools where these matters are taught, they read when time permits of Cape Canaveral, Ghana, and Seoul. And they’ve heard tell of the music synthesizer, magnetic tape. They take for granted the dials on radios and television sets. A tardy art, the art of Music. And why so slow? Is it because, once having learned a notation of pitches and durations, musicians will not give up their Greek? Children have been modern artists for years now. What is it about Music that sends not only the young but adults too as far into the past as they can conveniently go? The module? But our choices never reached around the globe, and in our laziness, when we changed over to the twelve-tone system, we just took the pitches of the previous music as though we were moving into a furnished apartment and had no time to even take the pictures off the walls. What excuse? That nowadays things are happening so quickly that we become thoughtless? Or were we clairvoyant and knew ahead of time that the need for furniture of any kind would disappear? (Whatever you place there in front of you sits established in the air.) The thing that was irrelevant to the structures we formerly made, and this was what kept us breathing, was what took place within them. Their emptiness we took for what it was – a place where anything could happen. That was one of the reasons we were able when circumstances became inviting (chances in consciousness, etc.) to go outside, where breathing is child’s play: no walls, not even the glass ones which, though we could see through them, killed the birds while they were flying.
”
”
John Cage (A Year from Monday: New Lectures and Writings)
“
Entering the office, Evie found Sebastian and Cam on opposite sides of the desk. They both mulled over account ledgers, scratching out some entries with freshly inked pens, and making notations beside the long columns. Both men looked up as she crossed the threshold. Evie met Sebastian’s gaze only briefly; she found it hard to maintain her composure around him after the intimacy of the previous night. He paused in mid-sentence as he stared at her, seeming to forget what he had been saying to Cam. It seemed that neither of them was yet comfortable with feelings that were still too new and powerful. Murmuring good morning to them both, she bid them to remain seated, and she went to stand beside Sebastian’s chair.
“Have you breakfasted yet, my lord?” she asked.
Sebastian shook his head, a smile glinting in his eyes. “Not yet.”
“I’ll go to the kitchen and see what is to be had.”
“Stay a moment,” he urged. “We’re almost finished.”
As the two men discussed a few last points of business, which pertained to a potential investment in a proposed shopping bazaar to be constructed on St. James Street, Sebastian picked up Evie’s hand, which was resting on the desk. Absently he drew the backs of her fingers against the edge of his jaw and his ear while contemplating the written proposal on the desk before him. Although Sebastian was not aware of what the casual familiarity of the gesture revealed, Evie felt her color rise as she met Cam’s gaze over her husband’s downbent head. The boy sent her a glance of mock reproof, like that of a nursemaid who had caught two children playing a kissing game, and he grinned as her blush heightened further.
Oblivious to the byplay, Sebastian handed the proposal to Cam, who sobered instantly. “I don’t like the looks of this,” Sebastian commented. “It’s doubtful there will be enough business in the area to sustain an entire bazaar, especially at those rents. I suspect within a year it will turn into a white elephant.”
“White elephant?” Evie asked.
A new voice came from the doorway, belonging to Lord Westcliff. “A white elephant is a rare animal,” the earl replied, smiling, “that is not only expensive but difficult to maintain. Historically, when an ancient king wished to ruin someone he would gift him with a white elephant.” Stepping into the office, Westcliff bowed over Evie’s hand and spoke to Sebastian. “Your assessment of the proposed bazaar is correct, in my opinion. I was approached with the same investment opportunity not long ago, and I rejected it on the same grounds.”
“No doubt we’ll both be proven wrong,” Sebastian said wryly. “One should never try to predict anything regarding women and their shopping.
”
”
Lisa Kleypas (Devil in Winter (Wallflowers, #3))
“
You have asked too many questions. If you want more, you will have to win them.”
He showed no sign of distraction now. As they played, he ignored her attempts to provoke him or make him laugh. “I’ve seen your tricks on others,” he said. “They won’t work with me.”
He won. Kestrel waited, nervous, and wondered if the way she felt was how he felt when he lost.
His voice came haltingly. “Will you play for me?”
“Play for you?”
Arin winced. In a more determined tone, he said, “Yes. Something I choose.”
“I don’t mind. It’s only…people rarely ask.”
He stood from the table, searched the shelves along the wall, and returned with a sheaf of sheet music. She took it. “It’s for the flute,” he said. “It will probably take you time to transpose it for the piano. I can wait. Maybe after our next game--”
She fanned the paper impatiently to silence him. “It’s not that hard.”
He nodded, then sat in the chair farthest away from the piano, by the glass garden doors. Kestrel was glad for his distance. She settled on the piano’s bench, flipping through the sheet music. The title and notations were in Herrani, the page yellow with age. She propped the paper on the piano’s rack, taking more time than necessary to neaten the sheets. Excitement coursed through her fingers as if she had already plunged her hands into the music, but that feeling was edged with a metallic lace of fear.
”
”
Marie Rutkoski (The Winner's Curse (The Winner's Trilogy, #1))
“
It takes a lot of time, focus and energy to realize the enormity of being the ocean with your very own tide every month. However, by honoring the demands of bleeding, our blood gives something in return. The crazed bitch from irritation hell recedes. In her place arises a side of ourselves with whom we may not—at first—be comfortable. She is a vulnerable, highly perceptive genius who can ponder a given issue and take her world by storm. When we’re quiet and bleeding, we stumble upon the solutions to dilemmas that’ve been bugging us all month. Inspiration hits and moments of epiphany rumba ‘across de tundra of our senses. In this mode of existence one does not feel antipathy towards a bodily ritual so profoundly and routinely reinforces our cuntpower.
”
”
Inga Muscio (Cunt: A Declaration of Independence)
“
They had a nice,if not private, reunion before Rupert joined them. He didn't exactly ruin it, but if he insisted on enacting their pretense tonight, even for her mother,it surely would. Unfortunately, he entered the room wearing a horribly bright lime-green dinner jacket that had his mother immediately scowling at him. So even after that kiss upstairs, he'd decided on an evening of humorously baiting his mother again. Bad timing, with her own mother there, or maybe not.At least it kept Rebecca's own mood light for the moment, since she knew why he did it.
Nor did Julie hold her tongue, remarking in disgust, "I see your taste is still beyond flamboyant. You're a bloody peacock, Rue."
He actually looked behind him as he replied, "I thought I had my feathers tucked away nicely.
”
”
Johanna Lindsey (A Rogue of My Own (Reid Family, #3))
“
Butterhorn?” Ben asked, holding out a bag full of pastries.
“Well, you did condemn yourself to bad luck just to get them for me,” I said, “So absolutely!”
“Yeah,” Ben agreed, “they’d better be worth it.”
“Mmmm, completely worth it,” I said with my mouth full. “The rest of you have to have some of these.”
“Hmmm,” Sage mused, examining his, “no garlic. I’m not entirely sure my taste buds will know how to handle this.”
“Um, you guys,” Rayna asked, “where am I driving?”
“Excellent question-let’s find out!” I pulled the cribbage board out of duffel bag and handed it to Sage, pointing out the longitude and latitude notations on the back. “Where is that?”
Sage took out his phone, then entered the coordinates. “Interesting.”
“What?” I asked. “It’s not Antarctica, is it? I didn’t pack a parka.
”
”
Hilary Duff (Elixir (Elixir, #1))
“
In a 16 June 1919 telegram to Lenin from the Petrograd front, he wrote with slightly comical bravado and arrogance: “Naval experts assert that the capture of Krasnaya Gorka [a Petrograd fort] from the sea runs counter to naval science. I can only deplore such so-called science. The swift capture of Gorka was due to the grossest interference in the operations by me and civilians generally, even to the point of countermanding orders on land and sea and imposing our own. I consider it my duty to declare that I shall continue to act in this way in future, despite all my reverence for science.”30 Lenin, who knew that the fort had not, despite Stalin’s claim, fallen from a naval attack, seems to have been amused by Stalin’s swagger. He left a notation on the telegram: “??? Krasnaya Gorka was taken by land.”31
”
”
Oleg V. Khlevniuk (Stalin: New Biography of a Dictator)
“
People should not make a virtue out of their sensitivity. They may experience it and preserve it as it was experienced. But they should not adorn themselves with it. Sensitivity will make an addict out of anyone who displays its medals on his chest. He will require more and more objects to enable him to demonstrate his sensitivity, and if he runs out of them, he will simply make things up - and his sensitivity will then reveal itself for what it is: precious, brittle, and rotted through and through.
”
”
Elias Canetti (The Agony of Flies: Notes and Notations)
“
Maybe it was because of his ignorance of music that he had been capable of receiving so confused an impression, the kind of impression that is, however, perhaps the only one which is purely musical, immaterial, entirely original, irreducible to any other order of impression. An impression of this kind is, for an instant, so to speak, sine materia. No doubt the notes we hear then tend already, depending on their loudness and their quantity, to spread out before our eyes over surfaces of varying dimensions, to trace arabesques, to give us sensations of breadth, tenuousness, stability, whimsy. But the notes vanish before these sensations are sufficiently formed in us not to be submerged by those already excited by the succeeding or even simultaneous notes. And this impression would continue to envelop with its liquidity and its “mellowness” the motifs that at times emerge from it, barely discernible, immediately to dive under and disappear, known only by the particular pleasure they give, impossible to describe, to recall, to name, ineffable—if memory, like a laborer working to put down lasting foundations in the midst of the waves, by fabricating for us facsimiles of these fleeting phrases, did not allow us to compare them to those that follow them and to differentiate them. And so, scarcely had the delicious sensation which Swann had felt died away than his memory at once furnished him with a transcription that was summary and temporary but at which he could glance while the piece continued, so that already, when the same impression suddenly returned, it was no longer impossible to grasp. He could picture to himself its extent, its symmetrical groupings, its notation, its expressive value; he had before him this thing which is no longer pure music, which is drawing, architecture, thought, and which allows us to recall the music. This time he had clearly distinguished one phrase rising for a few moments above the waves of sound. It had immediately proposed to him particular sensual pleasures which he had never imagined before hearing it, which he felt could be introduced to him by nothing else, and he had experienced for it something like an unfamiliar love.
”
”
Marcel Proust (Swann's Way (In Search of Lost Time, #1))
“
The three main mediaeval points of view regarding universals are designated by historians as realism, conceptualism, and nominalism. Essentially these same three doctrines reappear in twentieth-century surveys of the philosophy of mathematics under the new names logicism, intuitionism, and formalism.
Realism, as the word is used in connection with the mediaeval controversy over universals, is the Platonic doctrine that universals or abstract entities have being independently of the mind; the mind may discover them but cannot create them. Logicism, represented by Frege, Russell, Whitehead, Church, and Carnap, condones the use of bound variables to refer to abstract entities known and unknown, specifiable and unspecifiable, indiscriminately.
Conceptualism holds that there are universals but they are mind-made. Intuitionism, espoused in modern times in one form or another by Poincaré, Brouwer, Weyl, and others, countenances the use of bound variables to refer to abstract entities only when those entities are capable of being cooked up individually from ingredients specified in advance. As Fraenkel has put it, logicism holds that classes are discovered while intuitionism holds that they are invented—a fair statement indeed of the old opposition between realism and conceptualism. This opposition is no mere quibble; it makes an essential difference in the amount of classical mathematics to which one is willing to subscribe. Logicists, or realists, are able on their assumptions to get Cantor’s ascending orders of infinity; intuitionists are compelled to stop with the lowest order of infinity, and, as an indirect consequence, to abandon even some of the classical laws of real numbers. The modern controversy between logicism and intuitionism arose, in fact, from disagreements over infinity.
Formalism, associated with the name of Hilbert, echoes intuitionism in deploring the logicist’s unbridled recourse to universals. But formalism also finds intuitionism unsatisfactory. This could happen for either of two opposite reasons. The formalist might, like the logicist, object to the crippling of classical mathematics; or he might, like the nominalists of old, object to admitting abstract entities at all, even in the restrained sense of mind-made entities. The upshot is the same: the formalist keeps classical mathematics as a play of insignificant notations. This play of notations can still be of utility—whatever utility it has already shown itself to have as a crutch for physicists and technologists. But utility need not imply significance, in any literal linguistic sense. Nor need the marked success of mathematicians in spinning out theorems, and in finding objective bases for agreement with one another’s results, imply significance. For an adequate basis for agreement among mathematicians can be found simply in the rules which govern the manipulation of the notations—these syntactical rules being, unlike the notations themselves, quite significant and intelligible.
”
”
Willard Van Orman Quine
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You Play the Game How You Act How You Think How You Brand & Market Yourself How You Sound How You Look How You Respond 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 47. 48. 49. Category Total Category Total Category Total Category Total Category Total Category Total Category Total Overall Total INTERPRETATION OF YOUR SCORES Overall Score of 159–196 or A Category Score of 22–28 You go, girl! Your score indicates you must already have the corner office or are well on your way to getting it. To stay on track, focus on those questions where you rated yourself “1” or “2.” Also, remember to pay it forward by mentoring other women. Overall Score of 110–158 or A Category Score of 14–21 Fine-tuning is the name of your game! Although you often engage in behaviors worthy of a winning woman, there are times when you don’t get your due because you get caught up in nice girl syndrome. First read the chapters that correspond with your lowest category scores, then go back and read the rest as a refresher course. Overall Score of 49–109 or A Category Score of 7–13 Danger! You are falling into the trap of acting like the nice little girl you were taught to be in childhood. You frequently wonder why you’re not achieving the success you’ve worked so hard for. This book was written for you, so take out your pen and start making notations for what you commit to doing differently.
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Lois P. Frankel (Nice Girls Don't Get the Corner Office (Nice Girls))
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My sister and I grew older. My mother educated us herself, always reminding us that though the Daglan had been vanquished, evil lived on. Evil lurked beneath our very feet, always waiting to devour us. I believe she told us this in order to keep us honest and true, certainly more than she had ever been. Yet as we aged and grew into our power, it became clear that only one throne could be inherited. I loved Helena more than anything. Should she have wanted the throne, it was hers. But she had as little interest in it as I did. It was not enough for my mother. Possessing all she had ever wanted was not enough. “Classic stage mom,” Bryce muttered. My mother remembered the talk of the Daglan—their mention of other worlds. Places they had conquered. And with two daughters and one throne … only entire worlds would do for us. For her legacy. Bryce shook her head again. She knew where this was going. Remembering the teachings of her former mistress, my mother knew she might wield the Horn and Harp to open a door. To bring the Fae to new heights, new wealth and prestige. Bryce rolled her eyes. Same corrupt, delusional Fae rulers, different millennium. Yet when she announced her vision to her court, many of them refused. They had just overthrown their conquerors—now they would turn conqueror, too? They demanded that she shut the door and leave this madness behind her. But she would not be deterred. There were enough Fae throughout her lands, along with some of the fire-wielders from the south, who supported the idea, merchants who salivated at the thought of untapped riches in other worlds. And so she gathered a force. It was Pelias who told her where to cast her intention. Using old, notated star maps from their former masters, he’d selected a world for them.
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Sarah J. Maas (House of Flame and Shadow (Crescent City, #3))
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Such was the ugly face of the Middle Ages. It is not surprising that mathematics made little progress; toward the Renaissance, European mathematics reached a level that, roughly, the Babylonians had attained some 2,000 years earlier and much of the progress made was due to the knowledge that filtered in from the Arabs, the Moors and other Muslim peoples, who themselves were in contact with the Hindus, and they, in turn, with the Far East.
The history of Pi in the Middle Ages bears this out. No significant progress in the method of determining Pi was made until Viete discovered an infinite product of square roots in 1593, and what little progress there was in the calculation of its numerical value, by various modifications of the Archimedean method, was due to the decimal notation which began to infiltrate from the East through the Muslims in the 12th century.
Arab mathematicians came to Europe through the trade in the Mediterranean, mainly via Italy; ironically, the other stream of mathematics was the Church itself. Not only because the mediaeval priests had a near monopoly of learning, but also because they needed mathematics and astronomy as custodians of the calendar. Like the Soviet High Priests who publish Pravda for other but read summaries of the New York Times themselves, sot he mediaeval Church condemned mathematics as devilish for others, but dabbled quite a lot in it itself. Gerbert d'Aurillac, who ruled as Pope Sylvester II from 999 to 1003, was quite a mathematician; so was Cardinal Nicolaus Cusanus (1401-1464); and much of the work done on Pi was done behind thick cloister walls. And just like the Soviets did not hesitate to spy on the atomic secrets of bourgeois pseudo-science, so the mediaeval Church did not hesitate to spy on the mathematics of the Muslim infidels.
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Petr Beckman (A History of Pi)
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You didn’t tell me you were a horse whisperer.” “I’m not—at least I don’t think I am.” “Well, you nearly gave me a heart attack. If you were one of my men, I’d fire you on the spot for being reckless.” “I’m not one of your men.” “Thank God for that.” Still, he needed to make his point. “You could have been killed. I’ve seen stallions go crazy and injure experienced horsemen, men who raised them. You took a real chance stepping in here.” “I’m sorry I frightened you. I saw how afraid Chinook was, and I just had to do something.” He handed her the curry comb. “Most people who saw a stallion in that state would see only aggression and feel afraid. But you saw that the stallion was afraid, and so you had no fear. You amaze me.” She looked up at him and smiled. “That goes both ways.” He was glad to hear that. In the course of the evening, he’d come to realize that he loved her. For the second time in his life, he’d fallen head over heels in love with a woman.
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Pamela Clare (Soul Deep (I-Team, #6.5))