Algebraic Expression Quotes

Why not spend that time on art: painting, sculpting, charcoal, pastel, oils? Are words or numbers more important than images? Who decides this? Does algebra move you to tears? Can plural possessives express the feelings in your heart? If you don't learn art now, you will never learn to breathe!

I deliberately and consciously give preference to a dramatic, mythological way of thinking and speaking, because this is not only more expressive but also more exact than an abstract scientific terminology, which is wont to toy with the notion that its theoretic formulations may one fine day be resolved into algebraic equations.

I'm glad this happened," he said softly. I hoped it was for real,and I didn't want to talk about it too much and ruin the lovely illusion that we were a couple. So I said noncommittally, "Me too." "Because I've been trying to get you back since the seventh grade." I must have given him a very skeptical look. He laughed at my expression. "Yeah, I have a funny way of showing it. I know. But you're always on my mind. You're in the front of my mind,on the tip of my tongue. So if someone breaks a beaker in chemistry class, I raise my hand and tell Ms. Abernathy you did it. If somebody brings a copy of Playboy to class, I stuff it in your locker." "Oh!" I thought back to the January issue. "I wondered where that came from." "And if Everett Walsh tells the lunch table what a wicked kisser you are and how far he would have gotten with you if his mother hadn't come in-" I stamped my foot on the floorboard of the SUV."That is so not true! He'd already gotten as far as he was going. He's not that cute, and I had to go home and study for algebra. "-It drives me insane to the point that I tell him to shut up or I'll make him shut up right there in front of everybody. Because I am supposed to be your boyfriend, and my mother is supposed to hate you,and you're supposed to be making out with me." Twisted as this declaration was,it was the sweetest thing a boy had ever said to me.I dwelled on the soft lips that had formed the statement,and on the meaning of his words. "Okay." I scooted across the seat and nibbled the very edge of his superhero chin. "Ah," he gasped, moving both hands from the steering wheel to the seat to brace himself. "I didn't mean now.I meant in general.Your dad will come out of the house and kill me.

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!

The Babylonians had achieved great competence in arithmetic, using a number system based on 60 rather than 10. They had also developed some simple techniques of algebra, such as rules (though these were not expressed in symbols) for solving various quadratic equations.

Take a ton of pictures, text your friends stupid things, check in with old friends as often as possible, express admiration to coworkers, and every day, tell as many people as you can that you love them. A couple of minutes every day—the payoff is small at first, and then it’s immense.

Chemistry has the same quickening and suggestive influence upon the algebraist as a visit to the Royal Academy, or the old masters may be supposed to have on a Browning or a Tennyson. Indeed it seems to me that an exact homology exists between painting and poetry on the one hand and modem chemistry and modem algebra on the other. In poetry and algebra we have the pure idea elaborated and expressed through the vehicle of language, in painting and chemistry the idea enveloped in matter, depending in part on manual processes and the resources of art for its due manifestation.

Someties it is hard to criticize, one wants only to chronicle. The good and mediocre books come in from week to week, and I put them aside and read them and think of what to say; but the "worthless" books come in day after day, like the cries and truck sounds from the street, and there is nothing that anyone could think of that is good enough for them. In the bad type of thin pamphlets, in hand-set lines on imported paper, people's hard lives and hopeless ambitions have expressed themselves more directly and heartbreakingly than they have ever expressed in any work of art:. it is as if the writers had sent you their ripped-out arms and legs, with "This is a poem" scrawled on them in lipstick. After a while one is embarrassed not so much for them as for poetry, which is for these poor poets one more of the openings against which everyone in the end beats his brains out; and one finds it unbearable that poetry should be so hard to write - a game of Pin the Tail on the Donkey in which there is for most of the players no tail, no donkey, not even a booby prize. If there were only some mechanism (like Seurat's proposed system of painting, or the projected Universal Algebra that Gödel believes Leibnitz to have perfected and mislaid) for reasonably and systematically converting into poetry what we see and feel and are! When one reads the verse of people who cannot write poems - people who sometimes have more intelligence, sensibility, and moral discrimination than most of the poets - it is hard not to regard the Muse as a sort of fairy godmother who says to the poet, after her colleagues have showered on him the most disconcerting and ambiguous gifts, "Well, never mind. You're still the only one that can write poetry.

He says we will graduate knowing how to read and write because we'll spend a million hours learning how to read and write. "Why not spend that time on art: painting, sculpting, charcoal, pastel, oils? Are words or numbers more important than images? Who decided this? Does algebra move you to tears?" (Hands raise, thinking he wants answers.) "Can the plural possessive express the feelings in your heart? If you don't learn art now, you will never learn to breathe!!!

Great teaching is the ability to distinguish between what can and needs to be explained and what cannot be explained. The working of a computer needs to be explained as it is made by the human mind. But a butterfly need not always be explained. A butterfly has to be seen with gleaming eyes of wonder as it is a natural expression of life and not of the mind. Great teaching is more like a craft than a technique. To evoke the curiosity in the learner, to care for the learner and to take the learner on a journey of discovery are some of the most critical elements of this craft.

When Benjamin Bloom studied his 120 world-class concert pianists, sculptors, swimmers, tennis players, mathematicians, and research neurologists, he found something fascinating. For most of them, their first teachers were incredibly warm and accepting. Not that they set low standards. Not at all, but they created an atmosphere of trust, not judgment. It was, “I’m going to teach you,” not “I’m going to judge your talent.” As you look at what Collins and Esquith demanded of their students—all their students—it’s almost shocking. When Collins expanded her school to include young children, she required that every four-year-old who started in September be reading by Christmas. And they all were. The three- and four-year-olds used a vocabulary book titled Vocabulary for the High School Student. The seven-year-olds were reading The Wall Street Journal. For older children, a discussion of Plato’s Republic led to discussions of de Tocqueville’s Democracy in America, Orwell’s Animal Farm, Machiavelli, and the Chicago city council. Her reading list for the late-grade-school children included The Complete Plays of Anton Chekhov, Physics Through Experiment, and The Canterbury Tales. Oh, and always Shakespeare. Even the boys who picked their teeth with switchblades, she says, loved Shakespeare and always begged for more. Yet Collins maintained an extremely nurturing atmosphere. A very strict and disciplined one, but a loving one. Realizing that her students were coming from teachers who made a career of telling them what was wrong with them, she quickly made known her complete commitment to them as her students and as people. Esquith bemoans the lowering of standards. Recently, he tells us, his school celebrated reading scores that were twenty points below the national average. Why? Because they were a point or two higher than the year before. “Maybe it’s important to look for the good and be optimistic,” he says, “but delusion is not the answer. Those who celebrate failure will not be around to help today’s students celebrate their jobs flipping burgers.… Someone has to tell children if they are behind, and lay out a plan of attack to help them catch up.” All of his fifth graders master a reading list that includes Of Mice and Men, Native Son, Bury My Heart at Wounded Knee, The Joy Luck Club, The Diary of Anne Frank, To Kill a Mockingbird, and A Separate Peace. Every one of his sixth graders passes an algebra final that would reduce most eighth and ninth graders to tears. But again, all is achieved in an atmosphere of affection and deep personal commitment to every student. “Challenge and nurture” describes DeLay’s approach, too. One of her former students expresses it this way: “That is part of Miss DeLay’s genius—to put people in the frame of mind where they can do their best.… Very few teachers can actually get you to your ultimate potential. Miss DeLay has that gift. She challenges you at the same time that you feel you are being nurtured.

However, as I reread her words I was none the less a little disappointed to realize how little of our person remains in our correspondence. Of course the characters we trace express our thoughts, as do our features; it is always a process of thinking that confronts us. But even so, in a person, thought appears to us only after being filtered through the bloom of the face, flowering like a water-lily only on the surface. And this, it has to be said, does modify it considerably. And perhaps one of the causes of our perpetual disappointment in love is this perpetual slippage, which causes every anticipation of the ideal being whom we love to be confronted at each meeting by a flesh-and-blood person who already has little in common with our dream. And then, when we expect something from this person, what we receive from her is a letter where very little of the person herself remains, as in those letters used in algebraic formulae, where there remains none of the qualities characterized by the arithmetical numbers, which themselves already no longer encapsulated the properties of the fruit or the flowers that were being assessed.

we have much to learn from the struggles in Alabama and Mississippi in the early 1960s. In the spring of 1963 the Southern Christian Leadership Conference led by Dr. King launched a “fill the jails” campaign to desegregate downtown department stores and schools in Birmingham. But few local blacks were coming forward. Black adults were afraid of losing their jobs, local black preachers were reluctant to accept the leadership of an “Outsider,” and city police commissioner Bull Connor had everyone intimidated. Facing a major defeat, King was persuaded by his aide, James Bevel, to allow any child old enough to belong to a church to march. So on D-day, May 2, before the eyes of the whole nation, thousands of schoolchildren, many of them first graders, joined the movement and were beaten, fire-hosed, attacked by police dogs, and herded off to jail in paddy wagons and school buses. The result was what has been called the “Children’s Miracle.” Inspired and shamed into action, thousands of adults rushed to join the movement. All over the country rallies were called to express outrage against Bull Connor’s brutality. Locally, the power structure was forced to desegregate lunch counters and dressing rooms in downtown stores, hire blacks to work downtown, and begin desegregating the schools. Nationally, the Kennedy administration, which had been trying not to alienate white Dixiecrat voters, was forced to begin drafting civil rights legislation as the only way to forestall more Birminghams. The next year as part of Mississippi Freedom Summer, activists created Freedom Schools because the existing school system (like ours today) had been organized to produce subjects, not citizens. People in the community, both children and adults, needed to be empowered to exercise their civil and voting rights. A mental revolution was needed. To bring it about, reading, writing, and speaking skills were taught through discussions of black history, the power structure, and building a movement. Everyone took this revolutionary civics course, then chose from more academic subjects such as algebra and chemistry. All over Mississippi, in church basements and parish halls, on shady lawns and in abandoned buildings, volunteer teachers empowered thousands of children and adults through this community curriculum. The Freedom Schools of 1964 demonstrated that when Education involves young people in making community changes that matter to them, when it gives meaning to their lives in the present instead of preparing them only to make a living in the future, young people begin to believe in themselves and to dream of the future.

an algebraic expression. [GEOLOGY] denoting the uppermost soil horizon, especially the topsoil. the human blood type (in the ABO system) containing the A antigen and lacking the B. (with numeral) denoting a series of international standard paper sizes each twice the area of the next, as A0, A1, A2, A3, A4, etc., A4 being 210 × 297 mm. 2 a shape like that of a capital A: [in combination] an A-shape. 3 [MUSIC] the sixth note of the diatonic scale of C major. The A above middle C is usually used as the basis for tuning and in modern music has a standard frequency of 440 Hz. a key based on a scale with A as its keynote.

Stalin formulated the economic aims of socialism as: “The securing of the maximum satisfaction of the constantly rising material and cultural requirements of the whole society.” [Economic Problems of Socialism in U.S.S.R., English edition, p. 45.] Taken positively, this has no more content than any metaphysical slogan; like the slogan “All men are equal,” it expresses its point of view through negations. “Constantly rising” requirements means that there is no foreseeable limit to the possible rise in productivity (for, of course, it is not so much the needs as the means to satisfy them that will continually increase). “Cultural” requirements means that growing wealth is not to be confined to physical goods (though these alone enter into the Marxist definition of output). “The whole society” implies a condemnation of the arbitrary distribution of wealth. There is nothing in this that the orthodox economists can object to. Indeed, it takes the very words out of their mouth. But they were wont to excuse the inequality generated by private property in the means of production because it was necessary to make total income greater. If income grows faster without it, they are in an awkward situation. Perhaps this is why they have crept off to hide in thickets of algebra and left the torch of ideology to be carried by the political argument that capitalist institutions are the bulwark of liberty. [pp. 109-110]

Seventh, to reach the widest range of minds, ideas in every discipline should be presented in many forms. There is no one single imaginative skill or creative technique that is adequate for all thinking needs. The intuitive approach is as valuable as the logical one; the analytical, algebraic mind is no better than the geometric, visual mind or the kinesthetic, empathic one. Every idea can and should be transformed into several equivalent forms, each of which has a different formal expression and emphasizes a different set of thinking tools. The more ways students can imagine an idea, the better their chances of insight. The more ways they can express that insight, the better their chances that others will understand and appreciate it.

The second basic function of algebra is to convert expressions into more useful ones. Gauss’s

In the natural sciences we understand a phenomenon when we have reduced it one level into concepts that seem more elementary. For example, from the high level of continuum mechanics we descend one level to atomistic structures, from atomism one level down to electrons, protons, then to the quark level? We shall reduce mind activities to elementary ideas and mental operations on them. Connecting the ideas according to certain rules we will be led to an algebraic structure, one for each cultural sphere. Within such a sphere individuals are characterized by the usage they make of the mental concepts as expressed by a probability measure resulting in a calculus of ideas.

Arithmetic numbers are merely algebraic general expression wherein x stands for 10 (Example- 351 = 3* x^2 + 5x +1 where x=10) is simple intuition (?) which is used by 'Father of Vedic math' to simplify basic operation. Those who want to advance 'Vedic math', should use it fully

The refusal to examine Islamic culture and traditions, the sordid dehumanization of Muslims, and the utter disregard for the intellectual traditions and culture of one of the world’s great civilizations are characteristic of those who disdain self-reflection and intellectual inquiry. Confronting this complexity requires work and study rather than a retreat into slogans and cliches. And enlightened, tolerant civilizations have flourished outside the orbit of the United Sates and Europe. The ruins of the ancient Mughal capital, Fatehpur Sikri, lie about 100 miles south of Delhi. The capital was constructed by the emperor Akbar the Great at the end of the sixteenth century. The emperor’s court was filled with philosophers, mystics and religious scholars, including Sunni, Sufi, and Shiite Muslims, Hindu followers of Shiva and Vishnu, as well as atheists, Christians, Jains, Jews , Buddhists and Zoroastrians. They debated ethics and beliefs. He forbade any person to be discriminated against on the basis of belief and declared that everyone was free to follow any religion. This took place as the Inquisition was at its height in Spain and Portugal, and as Giordano Bruno was being burnt at the stake in Rome’s Campo de Fiori. Tolerance, as well as religious and political plurality, is not exclusive to Western culture. The Judeo-Christian tradition was born and came to life in the Middle East. Its intellectual and religious beliefs were cultivated and formed in cities such as Jerusalem, Antioch, Alexandria and Constantinople. Many of the greatest tenets of Western civilization, as is true with Islam and Buddhism, are Eastern in origin. Our respect for the rule of law and freedom of expression, as well as printing, paper, the book, the translation and dissemination of the classical Greek philosophers, algebra, geometry and universities were given to us by the Islamic world. One of the first law codes was invented by the ancient Babylonian ruler Hammurabi, in what is now Iraq. One of the first known legal protections of basic freedoms and equality was promulgated in the third century B.C. by the Buddhist Indian emperor Ashoka. And, unlike, Aristotle, he insisted on equal rights for women and slaves. The division set up by the new atheists between superior Western, rational values and the irrational beliefs of those outside our tradition is not only unhistorical but untrue. The East and the West do not have separate, competing value systems. We do not treat life with greater sanctity than those we belittle and dismiss. Eastern and Western traditions have within them varied ethical systems, some of which are repugnant and some of which are worth emulating. To hold up the highest ideals of our own culture and to deny that these great ideals exist in other cultures, especially Eastern cultures, is made possible only by a staggering historical and cultural illiteracy. The civilization we champion and promote as superior is, in fact, a product of the fusion of traditions and beliefs of the Orient and the Occident. We advance morally and intellectually only when we cross these cultural lines, when we use the lens of other cultures to examine our own. It is then that we see our limitations, that we uncover the folly of or own assumptions and our prejudices. It is then that we achieve empathy, we learn and make wisdom possible.

The letter is susceptible of operations which enables one to transform literal expressions and thus to paraphrase any statement into a number of equivalent forms. It is this power of transformation that lifts algebra above the level of a convenient shorthand.

Most of us were required to take three or four years of coursework in high school, starting with algebra and working up the chain: geometry, algebra 2, trigonometry, precalculus, calculus. Lockhart writes, “If I had to design a mechanism for the express purpose of destroying a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done—I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.

Mathiness: British economic journalist John Kay defines mathiness as a “use of algebraic symbols and quantitative data to give an appearance of scientific content to ideological preconceptions.” Expressing an idea in mathematical symbols instead of straightforward literary terms helps legitimize it in the minds of many people, thanks to a seeming similarity with natural science. In this respect math is basically a form of numerical rhetoric. “The American economist Paul Romer has recently written of ‘mathiness,’ by analogy with ‘truthiness,’ a term coined by American talk show host Stephen Colbert. Truthiness presents narratives which are not actually true, but consistent with the world view of the person who spins the story. It is exemplified in rightwing fabrications about European health systems – their death panels and forced euthanasia.” Paul Samuelson, for instance, trivialized economics in terms that give the outward appearance of science by being expressed mathematically, even when its assumptions are purely hypothetical (and not all realistic)and there are no quantitative statistics to illustrate its categories.

Having a good person express how wonderful you are hundreds of times changes everything. College, professional success, an impressive mate—these were aspirations, not givens for a remarkably unremarkable kid in an upper-lower-middle-class household. My mom was forty-three, single, and making $15,000 a year as a secretary. She was also a good person who made me feel connected and, while waiting for our Opel, gave me the confidence that I had value, that I was capable and deserving of all these things. Holding hands and laughing, I was tethered.

The Babylonians did not write equations. All their calculations were expressed as word problems. For instance, one tablet contained the spellbinder, “four is the length and five is the diagonal. What is the breadth? Its size is not known. Four times four is sixteen. Five times five is twenty-five. You take sixteen from twenty-five and there remains nine. What times what shall I take in order to get nine? Three times three is nine. Three is the breadth.” Today, we would write “x2 = 52 – 42.” The disadvantage of the rhetorical statement of problems isn’t as much the obvious one—its lack of compactness—but that the prose cannot be manipulated as an equation can, and rules of algebra, for instance, are not easily applied. It took thousands of years before this particular shortcoming was remedied: the oldest known use of the plus sign for addition occurs in a German manuscript written in 1481.

Shannon was interested in building a machine that could play chess—and more generally in building mechanisms that imitated thought. In 1940, he published his master’s thesis, which was titled “A Symbolic Analysis of Relay Switching Circuits.” In it, he showed that it was possible to build electrical circuits equivalent to expressions in Boolean algebra. In Shannon’s circuits, switches that were open or closed corresponded to logical variables of Boolean algebra that were true or false. Shannon demonstrated a way of converting any expression in Boolean algebra into an arrangement of switches.

People who are different are dangerous, they belong to another tribe; they want our lands and our women. We must marry, have children, reproduce the species. Love is only a small thing,, enough for one person, and any suggestion that the heart might be larger than this is considered perverse. When we marry we are authorized to take possession of the other person, body and soul. We must do jobs we detest because we are part of an organized society and if everyone did what they wanted to do, the world would come to a standstill We must buy jewellery, it identifies us with our tribe, just as body piercing identifies those of a different tribe. We must be amusing at all times and sheer at those who express their real feelings, it is dangerous to a tribe to allow its members to show their feelings. We must at all costs avoid saying "No" because people prefer those who always say "Yes", and this allows us to survive in hostile territory. What other people think is more important than what we feel. Never make a fuss, it might attract the attention of an enemy tribe because you could infect others and destroy something that was extremely difficult to organize in the first place. We must always consider the look of our new cave, and if we don't have a clear idea of our own, then we must call in a decorator who will do his best to show others what good taste we have. We must eat three meals a day, even if we're not hungry, and when we fail to fit in the current ideal of beauty we must fast, even if we're starving. We must dress according to the dictates of fashion, make love whether we feel like it or not, kill in the name of our country's frontiers, wish time away so that retirements comes more quickly, elect politicians, complain about the cost of living, change our hairstyle, criticize anyone who is different, go to a religious service on Sunday, Saturday or Friday , depending on our religion, and there beg for forgiveness for our sins and puff ourselves up with the other tribe who worship another god. Our children must follow in our steps, after all we are older and know about the world. We must have a university degree even if we never get a job in the area of knowledge we were forced to study. We must study things we will never use but which someone told us was important to know: algebra, trigonometry, the code of Hammurabi. We must never make our parents sad, even if this means giving up everything that makes us happy. We must play music quietly, talk quietly, weep in private

studies of science that began in the 1970s revealed that even the paradigm of explicit knowledge-scientific data or the algebraic expressions of theory-can be understood only against a background of tacit knowledge. This has revealed that the idea of the explicit is much more complicated than was once believed.

expressions

A 1 (also a)   n. (pl.As or A's) 1 the first letter of the alphabet.    denoting the first in a set of items, categories, sizes, etc.  denoting the first of two or more hypothetical people or things: suppose A had killed B.  the highest class of academic mark.  (a) [CHESS] denoting the first file from the left, as viewed from white's side of the board.  (usu. a) the first fixed quantity in an algebraic expression.  (A) the human blood type (in the ABO system) containing the A agglutinogen and lacking the B.

For the most part, women instinctively have within them what men try to achieve with religion and spirituality. A man trying to express his spiritual discoveries to his wife, is like, a high school teacher trying to teach Algebra to Albert Einstein. She's completely uninterested, because she is far more spiritually advanced than you can ever hope to be. Poetry may exist to woo women, but spirituality and religion exists to have and to hold, honor and obey women.

In his first class of the day, correlated language arts, a class for students at least two years below their grade level in English, Boobie Miles spent the period working on a short research paper that he called “The Wonderful Life of Zebras.” He thumbed through various basic encyclopedia entries on the zebra. He ogled at how fast they ran (“Damn, they travel thirty miles”) and was so captivated by a picture of a zebra giving birth that he showed it to a classmate (“Want to see it have a baby, man?”). By the end of the class, Boobie produced the following thesis paragraph: Zebras are one of the most unusual animals in the world today. The zebra has many different kind in it nature. The habitat of the zebra is in wide open plain. Many zebras have viris types of relatives. He then went on to algebra I, a course that the average college-bound student took in ninth grade and some took in eighth. Because of his status as a special needs student, Boobie hadn’t taken the course until his senior year. He was having difficulty with it and his average midway through the fall was 71. After lunch it was on to creative writing, where Boobie spent a few minutes playing with a purple plastic gargoyle-looking monster. He lifted the fingers of the monster so it could pick its nose, then stuck his own fingers into its mouth. There were five minutes of instruction that day; students spent the remaining fifty-odd minutes working on various stories they were writing. They pretty much could do what they wanted. Boobie wrote a little and also explained to two blond-haired girls what some rap terms meant, that “chillin’ to the strength,” for example, meant “like cool to the max.” Boobie enjoyed this class. It gave him an unfettered opportunity to express himself, and the teacher didn’t expect much from him. His whole purpose in life, she felt, was to be a football player. “That’s the only thing kids like that have going for them, is that physical strength,” she said.