Editors From The United States

"Poor baby! She'll be a woman some day! Poor baby! A woman's lot is so hard!"

"The young women of today, free to study, to speak, to write, to choose their occupation, should remember that every inch of this freedom was bought for them at a great price. It is for them to show their gratitude by helping onward the reforms of their own times, by spreading the light of freedom and of truth still wider. The debt that each generation owes to the past it must pay to the future."

"The Internet has been accused of making us shallow. We’re skimming, not reading. We lack the ability to engage deeply with a subject anymore. That’s both true and not true: we skim and browse certain types of content, and read others carefully. Oftentimes, we’ll save a long form journalism article and read it later offline, perhaps on the train home from work."

"Edward Snowden said that if we want to protect ourselves against government agencies scraping our data, we should get off Dropbox, Facebook, and Google and that we should “search for encrypted communication services” because they “enforce your rights.” Few have taken his advice. Zombies can’t be deprogrammed. The social media apparatus beckons us and we become addicted, joining the billion-plus strong for whom a life without social media is an impossibility. Social contacts, dating prospects, job opportunities, communications with loved ones—just about every interaction we have—flows through social media. For most of us it isn’t a choice; it’s a necessity. Even Snowden couldn’t resist: on October 6, 2015, he joined Twitter."

"Many decry the loss of “real time” to capturing moments on-screen, claiming that the recording of memories as they happen threatens to replace the actual memories you have of that moment. I’ve read many articles in which parents bemoan the fact their kids were seeing family vacations through GoPro cameras, rather than actually living them. After a day on the ski slopes, they edit their raw footage into action-packed greatest moments and post it to social media, where it’s shared and commented on by their friends, hyperextending their time on the mountain. For a generation raised on reality TV to be able to replay those moments over and over through a mediated interface is a way of reliving an eternal present, loved for a moment then replaced by the next day’s upload. In this way, we’re simultaneously archiving and forgetting: archiving because we continuously upload media, and forgetting because we rarely go back to visit what we have uploaded. Today’s upload is the best upload and keeps us very much present and mindful in the here and now."

"I've been poor and I've been rich. Rich is better!"

"The cheapness and quickness of modern methods of communication has been like a growth of wings, so that a thousand things which were thought to belong like trees in one place may travel about like birds."

"The librarian must be the librarian militant before he can be the librarian triumphant."

"The predecessors of Newton and Leibnitz knew perfectly well how to determine tangents and areas, but they had to approach each problem from first principles. The great contribution of Newton and Leibnitz was precisely to make the procedures for finding tangents, areas, etc. into a calculus, that is, a systematic way of calculating—a collection of algorithms, to use the currently fashionable word."

"Suppose you want to teach the "cat" concept to a very young child. Do you explain that a cat is a relatively small, primarily carnivorous mammal with retractible claws, a distinctive sonic output, etc.? I'll bet not. You probably show the kid a lot of different cats, saying "kitty" each time, until it gets the idea. To put it more generally, generalizations are best made by abstraction from experience. They should come one at a time; too many at once overload the circuits."

"The fact that N Bourbaki was not a real person and represented a group of mathematicians was known to very few, for example, Ralph Boas, but the world of mathematics had come to believe in his existence. In an article for the Encyclopaedia Britannica, Boas revealed the truth; he was severely reprimanded in a letter to him "From my ashram in the Himalayas", beginning with "You miserable worm, how dare you say that I do not exist?" and signed 'Nicolas Bourbaki'!"

"Book-to-screen adaptations must always strive for two things: First, you must find a way to tell the broad story of the original plot; second, you must somehow reflect the spirit and texture of the novel—that is, you must transform a lot of words into a few pictures. All those digressions, inner monologues, thought processes, turns of phrase, all those word pictures, and especially all that un-photographable stuff that made the novel so delicious, must somehow be represented onscreen by use of the filmmaker's tools: moving pictures, dialogue and performance, sets, costumes, music and all the other tricks of the trade. That's the process a writer must go through to create a successful blueprint for a film."

"As a director, you must keep your sense of humor, your patience and, most of all, your ability to funnel the collective energies of a large group of creative people. For that, you must stay well-hydrated, well-fed, and well-rested. It's also crucial that you have a top-notch ensemble."

"I hate this waaaah-I'm-a-poor-sensitive-weak-woman-protect-me shit. This kind of stuff generates more contempt for women. So fuck niceness!"

"Give us bandwidth or kill us!"

"Girls need modems!"

"I'm a future-hacker; I'm trying to get root access to the future. I want to raid its system of thought."

"Hacking is the clever circumvention of imposed limits, whether imposed by your government, your IP server, your own personality, or the laws of physics."

"I teach his work in my creative writing classes now, to give students a sense of voice and language and just fierce honesty in your writing."

"Writing fearlessly because, as my friend Junot Díaz has said, "a writer is a writer because even when there is no hope, even when nothing you do shows any sign of promise, you keep writing anyway.""

"Junot Díaz, who is a big science fiction fan."

"When I first read Junot Díaz’s short story collection Drown I felt seen for the first time."

"Motherfuckers will read a book that’s one third elvish, but put two sentences in Spanish and they [white people] think we’re taking over."

"This life takes a lot more courage than I ever gave it credit for. When I was growing up around here I was always fantasizing heroic shit without realizing that what was shaping up was going to be the greatest heroic adventure of them all: trying to live and be a decent human being. That shit takes more courage than I ever had."

"I grew up in a world, [a] very New Jersey, American, Dominican, immigrant, African-American, Latino world. And, you know, I went to school and it was basically the same. I went to college; it was basically the same, where largely I wasn't really encouraged to imagine women as fully human. I was in fact pretty much — by the larger culture, by the local culture, by people around me, by people on TV — encouraged to imagine women as something slightly inferior to men. And so I think that a lot of guys, part of our journey is wrestling with, coming to face, our limited imagina[tion] and growing in a way that allows us not only to imagine women as fully human, but to imagine the things that we do to women — that we often do blithely, without thinking, we just sort of shrug off — as actually deeply troubling and as hurting another human being. And this seems like the simplest thing. A lot of people are like, 'Really, that's like a huge leap of knowledge, of the imagination?' But for a lot of guys, that is."

"Our visions of an immigrant community and an immigrant experience are highly moralistic. I feel like our reality is William Gibson meets Toni Morrison, yet the way we’re interpreting the morality of immigrants is Chaucer.”"

"We live in a patriarchal imaginary where men cannot conceptualise women as fully human. What’s really important is how this shit resides in us, how this just lives in us, man, even if we’re the good guy – it should give a motherfucker pause."

"If you think learning salsa is your future, you’re going to be pretty insufferable in salsa classes."

"As to Colonel Chivington, your committee can hardly find fitting terms to describe his conduct. Wearing the uniform of the United States, which should be the emblem of justice and humanity; holding the important position of commander of a military district, and therefore having the honor of the government to that extent in his keeping, he deliberately planned and executed a foul and dastardly massacre which would have disgraced the verist [sic] savage among those who were the victims of his cruelty. Having full knowledge of their friendly character, having himself been instrumental to some extent in placing them in their position of fancied security, he took advantage of their in-apprehension and defenceless [sic] condition to gratify the worst passions that ever cursed the heart of man. Whatever influence this may have had upon Colonel Chivington, the truth is that he surprised and murdered, in cold blood, the unsuspecting men, women, and children on Sand creek, who had every reason to believe they were under the protection of the United States authorities."

"Damn any man who sympathizes with Indians! ... I have come to kill Indians, and believe it is right and honorable to use any means under God's heaven to kill Indians. ... Kill and scalp all, big and little; nits [referring to infants] make lice!"

"Kill all the Indians you come across."

"The problem of the biquadratic equation was laid prominently before Italian mathematicians by Zuanne de Tonini da Coi, who in 1540 proposed the problem, "Divide 10 parts into three parts such that they shall be continued in proportion and that the product of the first two shall be 6." He gave this to Cardan with the statement that it could not be solved, but Cardan denied the assertion, although himself unable to solve it. He gave it to Ferrari, his pupil, and the latter, although then a mere youth, succeeded where the master had failed. ...This method soon became known to algebraists through Cardan's Ars Magna, and in 1567 we find it used by Nicolas Petri [of Deventer]."

"Although Cardan reduced his particular equations to forms lacking a term in x^2, it was Vieta who began with the general formx^3 + px^2 + qx + r = 0and made the substitution x = y -\frac{1}{3}p, thus reducing the equation to the formy^3 + 3by = 2c.He then made the substitutionz^3 + yz = b, or y = \frac{b - z^2}{z},which led to the formz^6 + 2cz^2 = b^2,a sextic which he solved as a quadratic."

"Cardan's originality in the matter seems to have been shown chiefly in four respects. First, he reduced the general equation to the type x^3 + bx = c; second, in a letter written August 4, 1539, he discussed the question of the irreducible case; third, he had the idea of the number of roots to be expected in the cubic; and, fourth, he made a beginning in the theory of symmetric functions. ...With respect to the irreducible case... we have the cube root of a complex number, thus reaching an expression that is irreducible even though all three values of x turn out to be real. With respect to the number of roots to be expected in the cubic... before this time only two roots were ever found, negative roots being rejected. As to the question of symmetric functions, he stated that the sum of the roots is minus the coefficient of x2"

"He used capital vowels for the unknown quantities and capital consonants for the known, thus being able to express several unknowns and several knowns."

"He states that the root of x^3 + 6x = 20 isx = \sqrt[3]{\sqrt{108} + 10} - \sqrt[3]{\sqrt{108} - 10}."

"In the work of Vieta the analytic methods replaced the geometric, and his solutions of the quadratic equation were therefore a distinct advance upon those of his predecessors. For example, to solve the equation x^2 + ax + b = 0 he placed u + z for x. He then hadu^2 + (2z + a)u +(z^2 + az + b) = 0.He now let 2z + a = 0, whence z = -\frac{1}{2}a,and this gaveu^2 - \frac{1}{4}(a^2 - 4b) = 0. u = \pm \frac{1}{2} \sqrt{a^2 - 4b}.andx = u + z = -\frac{1}{2}a \pm \sqrt{a^2 - 4b}."

"He... gave thirteen forms of the cubic which have positive roots, these having already been given by Omar Kayyam."

"[Zuanne de Tonini] da Coi... impuned Tartaglia to publish his method, but the latter declined to do so. In 1539 Cardan wrote to Tartaglia, and a meeting was arranged at which, Tartaglia says, having pledged Cardan to secrecy, he revealed the method in cryptic verse and later with a full explanation. Cardan admits that he received the solution from Tartaglia, but... without any explanation. At any rate, the two cubics x^3 + ax^2 = c and x^3 + bx = c could now be solved. The reduction of the general cubic x^3 + ax^2 + bx = c to the second of these forms does not seem to have been considered by Tartaglia at the time of the controversy. When Cardan published his Ars Magna however, he transformed the types x^3 = ax^2 + c and x^3 + ax^2 = c by substituting x = y + \frac{1}{3}a and x = y - \frac{1}{3}a respectively, and transformed the type x^3 + c = ax^2 by the substitution x = \sqrt[3]{c^2/y}, thus freeing the equations of the term x^2. This completed the general solution, and he applied the method to the complete cubic in his later problems."

"The law which asserts that the equation X = 0, complete or incomplete, can have no more real positive roots than it has changes of sign, and no more real negative roots than it has permanences of sign, was apparently known to Cardan; but a satisfactory statement is possibly due to Harriot (died 1621) and certainly to Descartes."

"Algebra in the Renaissance period received its first serious consideration in Pacioli's Sūma (1494)... which characterized in a careless way the knowledge... thus far accumulated. By the aid of the crude symbolism then in use it gave a considerable amount of work in equations. The noteworthy work... and the first to be devoted entirely to the subject, was Rudolff's Coss (1525). This work made no decided advance in the theory, but it improved the symbolism for radicals and made the science better known in Germany. Stiffel's edition of this work (1553-1554) gave the subject still more prominence. The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). The next great work... to appear in print was the General Trattato of Tartaglia..."

"The first epoch-making algebra to appear in print was the Ars Magna of Cardan (1545). This was devoted primarily to the solution of algebraic equations. It contained the solution of the cubic and biquadratic equations, made use of complex numbers, and in general may be said to have been the first step toward modern algebra."

"The first noteworthy attempt to write an algebra in England was made by , whose Whetstone of witte (1557) was an excellent textbook for its time. The next important contribution was Masterson's incomplete treatise of 1592-1595, but the work was not up to the standard set by Recorde. The first Italian textbook to bear the title of algebra was Bombelli's work of 1572. By this time elementary algebra was fairly well perfected, and it only remained to develop a good symbolism. ...this was worked out largely by Vieta (c. 1590), Harriot (c. 1610), Oughtred (c. 1628), Descartes (1637), and the British school of Newton's time (c. 1675). So far as the great body of elementary algebra is concerned, therefore, it was completed in the 17th century."

"There are only four Hindu writers on algebra whose names are particularly noteworthy. These are Āryabhata, whose Āryabhatiyam (c. 510) included problems in series, permutations, and linear and quadratic equations; , whose Brahmasiddhānta (c. 628) contains a satisfactory rule for solving the quadratic... Mahāvīra, whose Ganita-Sāra Sangraha (c. 850) contains a large number of problems involving series, radicals, and equations; and Bhāskara, whose Bija Ganita (c. 1150)... extends the work through quadratic equations."

"Vieta (c. 1590) rejected the name "algebra" as having no significance in the European languages, and proposed to use the word "analysis," and it is probably to his influence that the popularity of this term in connection with higher algebra is due."

"The first writer on algebra whose works have come down to us is . He has certain problems in linear equations and in series, and these form the essentially new feature in his work. His treatment of the subject is largely rhetorical."

"When we speak of the early history of algebra it is necessary to consider... the meaning of the term. If... we mean the science that allows us to solve the equation ax^2 + bx + c = 0, expressed in these symbols, then the history begins in the 17th century; if we remove the restriction as to these particular signs, and allow for other and less convenient symbols, we might properly begin the history in the 3rd century; if we allow for the solution of the above equation by geometric methods, without algebraic symbols of any kind, we might say that algebra begins with the or a little earlier; and if we say that we should class as algebra any problem that we should now solve with algebra (even though it was as first solved by mere guessing or by some cumbersome arithmetic process), the science was known about 1800 B.C., and probably still earlier.<"

"Vieta was the first algebraist after Ferrari to make any noteworthy advance in the solution of the biquadratic. He began with the type x^4 + 2gx^2 + bx = c, wrote it as x^4 + 2gx^2 = c - bx, added gx^2 + \frac{1}{4}y^2 + yx^2 + gy to both sides, and then made the right side a square after the manner of Ferrari. This method... requires the solution of a cubic resolvent. Descartes (1637) next took up the question and succeeded in effecting a simple solution... a method considerably improved (1649) by his commentator Van Schooten. The method was brought to its final form by Simpson (1745)."

"It is difficult to say when algebra as a science began in China. Problems which we should solve by equations appear in works as early as the Nine Sections (K'iu-ch'ang Suan-shu) and so may have been known by the year 1000 B.C. In 's commentary on this work (c. 250) there are problems of pursuit, the Rule of False Position... and an arrangement of terms in a kind of notation. The rules given by Liu Hui form a kind of rhetorical algebra. The work of Sun-tzï contains various problems which would today be considered algebraic. These include questions involving s. ...Sun-tzï solved such problems by analysis and was content with a single result... The Chinese certainly knew how to solve quadratics as early as the 1st century B.C., and rules given even as early as the K'iu-ch'ang Suan-shu... involve the solution of such equations. Liu Hui (c. 250) gave various rules which would now be stated as algebraic formulas and seems to have deduced these from other rules in much the same way as we should... By the 7th century the cubic equation had begun to attract attention, as is evident from the Ch'i-ku Suan-king of Wang Hs'iao-t'ung (c. 625). The culmination of Chinese is found in the 13th century. ...numerical higher equations attracted the special attention of scholars like Ch'in Kiu-shao (c.1250), Li Yeh (c. 1250), and Chu-Shï-kié (c. 1300), the result being the perfecting of an ancient method which resembles the one later developed by W. G. Horner (1819)."

"Among his [John Wallis'] interesting discoveries was the relation \frac{4}{\pi} = \frac32\cdot\frac34\cdot\frac54\cdot\frac56\cdot\frac76\cdot\frac78\cdots one of the early values of &pi; involving infinite products."