Quotes about curve (252 quotes, page 3)

“A thrown-stone trajectory is a good metaphor for so many phenomena: the curve of an event, any event; the curve of a life, any life; the curve of a hypothesis; the curve experienced in the manufacture of a work of art; the curve of interest experienced in the manufacture of a catalogue.”

Peter Greenaway (1942) British film director

Flying Out of This World

Life , Art

“Yes it was 1949. How I came to that. That's like how one gets to know a human being. It so happens that I've always had a preference – as everyone has prejudices and preferences – for the square as a shape in preference to the circle as a shape. And I have known for a long time that a circle always fools me by not telling me whether it's standing still or not. And if a circle circulates you don't see it. The outer curve looks the same whether it moves or does not move. So the square is much more honest and tells me that it is sitting on one line of the four, usually a horizontal one, as a basis. And I have also come to the conclusion that the square is a human invention, which makes it sympathetic to me. Because you don't see it in nature. As we do not see squares in nature, I thought that it is man-made. But I have corrected myself. Because squares exist in salt crystals, our daily salt. We know this because we can see it in the microscope. On the other hand, we believe we see circles in nature. But rarely precise ones. Mature, it seems, is not a mathematician. Probably there are no straight lines either. Particularly not since Einstein says in his theory of relativity that there is no straight line, rod knows whether there are or not, I don't. I still like to believe that the square is a human invention. And that tickles me. So when I have a preference for it then I can only say excuse me.”

Josef Albers (1888–1976) German-American artist and educator

Homage to the square' (1964), Oral history interview with Josef Albers' (1968)

Fools , Nature , Time

“I could give here several other ways of tracing and conceiving a series of curved lines, each curve more complex than any preceding one, but I think the best way to group together all such curves and them classify them in order, is by recognizing the fact that all points of those curves which we may call "geometric," that is, those which admit of precise and exact measurement, must bear a definite relation to all points of a straight line, and that this relation must be expressed by a single equation. If this equation contains no term of higher degree than the rectangle of two unknown quantities, or the square of one, the curve belongs to the first and simplest class, which contains only the circle, the parabola, the hyperbola, and the ellipse; but when the equation contains one or more terms of the third or fourth degree in one or both of the two unknown quantities (for it requires two unknown quantities to express the relation between two points) the curve belongs to the second class; and if the equation contains a term of the fifth or sixth degree in either or both of the unknown quantities the curve belongs to the third class, and so on indefinitely.”

René Descartes book La Géométrie

Second Book
La Géométrie (1637)

Way , Thinking

“Finally anger took possession of him. It was his turn to ask the question already raised by so many others: We, down there, the ones who join up, we're giving everything we have to give, maybe our arms and our two legs. He looked up at the high grills, the curving driveways, the sumptuous facades, and completed his thought: Are these people giving all they have to give?”

Gabrielle Roy book The Tin Flute

Source: The Tin Flute (1945), P. 319-320

People , Question , Anger

“While then for a long time everyone was at a loss, Hippocrates of Chios was the first to observe that, if between two straight lines of which the greater is double of the less it were discovered how to find two mean proportionals in continued proportion, the cube would be doubled; and thus he turned the difficulty in the original problem into another difficulty no less than the former. Afterwards, they say, some Delians attempting, in accordance with an oracle, to double one of the altars fell into the same difficulty. And they sent and begged the geometers who were with Plato in the Academy to find for them the required solution. And while they set themselves energetically to work and sought to find two means between two given straight lines, Archytas of Tarentum is said to have discovered them by means of half-cylinders, and Eudoxus by means of the so-called curved lines. It is, however, characteristic of them all that they indeed gave demonstrations, but were unable to make the actual construction or to reach the point of practical application, except to a small extent Menaechmus and that with difficulty.”

Thomas Little Heath (1861–1940) British civil servant and academic

Apollonius of Perga (1896)

Problem , Loss , Time

“There was no way, without full understanding, that one could have confidence that conditions the next time might not produce erosion three times more severe than the time before. Nevertheless, officials fooled themselves into thinking they had such understanding and confidence, in spite of the peculiar variations from case to case. A mathematical model was made to calculate erosion. This was a model based not on physical understanding but on empirical curve fitting.”

Richard Feynman (1918–1988) American theoretical physicist

Rogers Commission Report (1986)

Fools , Way , Confidence , Mathematics

“The vertical is in my spirit. It helps me to define precisely the direction of lines, and in quick sketches I never indicate a curve, that of a branch in landscape for example, without being aware of its relationship to the vertical.
My curves are not mad.”

Henri Matisse (1869–1954) French artist

La verticale est dans mon esprit. Elle m'aide à préciser la direction des lignes, et dans mes dessins rapides je n'indique pas une courbe, par exemple, celle d'une branche dans un paysage, sans avoir conscience de son rapport avec la verticale.
Mes courbes ne sont pas folles.
1940s, Jazz (1947)

Help , Madness

“In Professor Pigou's study the argument that free enterprise lead to excessive investments in industry having relatively upward-sloping cost curves is developed with the aid of concrete example, the case of two roads; Suppose that between two points there are two highways, one of which is broad enough to accommodate without crowding all the traffic which may care to use it, but is poorly graded and surfaced; while the other is a much better road, but narrow and quite limited in capacity. If a large number of trucks operate between the two termini and are free to choose either of the two routes, they will tend to distribute themselves between the roads in such proportions that the cost per unit of transportation, or effective returns per unit of investment, will be the same for every truck on both routes. As more trucks use the narrower and better road, congestion develops, until at a certain point it becomes equally profitable to use the broader but poorer highway.”

Frank Knight (1885–1972) American economist

Source: The Ethics of Competition, 1935, p. 211

Study

“The first notion of constructing a free goal-seeking mechanism goes back a wartime talk with the psychologist, Kenneth Craik, whose untimely death was one of the greatest losses Cambridge has suffered in years. When he was engaged on a warjob for the Government, he came to get the help of an automatic analyzer with some very complicated curves he had obtained, curves relating to the aiming errors of air gunners. Goal-seeking missiles were literally much in the air in those days; so, in our minds, were scanning mechanisms. Long before the home study was turned into a workshop, the two ideas, goal-seeking and scanning, had combined as the essential mechanical conception of a working model that would behave like a very simple animal.”

William Grey Walter (1910–1977) American-born British neuroscientist and roboticist

Source: The Living Brain (1953), p. 82.

Death , Error , Home , Idea

“Whenever like mates with like (genetically), the statistical distribution curve, which describes the frequency of the purely fortuitous combinations of genes, is flattened out, its mode is depressed, and its extremes are increased. The reduces the number of the mediocre produced and increases the numbers both of the sub-normal and the talented groups. It is possible that, without this increase in the number of extreme variants, no nation, race or group could produce enough superior individuals to maintain a complex culture. Certainly not enough to operate or advance a civilization. …Any number of social customs have stood, and still stand, in the way of an optimum amount of selective matings. In a feudal society, opportunities are denied to many able men who, consequently, never develop to the high level of their biological potential and thus they remain among the undistinguished. Such able men (and women) might also be diffused throughout an "ideal" classless society and, lacking the means to separate themselves from the generality, or to develop their peculiar talents, would be effectively swamped. In such a society they could hardly segregate in groups. In fact, only a few of the able males might ever meet an able female who appealed to them erotically. Obviously an open society—one in which the able may rise and the dim-wits sick, and where like intelligences have a greater chance of meeting and mating—has advantages that other societies do not have. Our own society today—incidentally and without design—is providing more and more opportunities for intelligent matrimonial discrimination. It is possible that our co-educational colleges, where highly-selected males and females meet when young, are as important in their function of bringing together the parents of our future superior individuals as they are in educating the present crop.”

Conway Zirkle (1895–1972)

"Some Biological Aspects of Individualism," Essays on Individuality (Philadelphia: 1958), pp. 59-61

Women , Men , Education , Way

“It was only within comparatively recent times that several refinements in Greek architecture… such as the slight entasis of the columns, the greater size of the corner columns, and the convex curve of the stylobate were discovered.”

Ernest Flagg (1857–1947) American architect

Source: Small Houses: Their Economic Design and Construction (1922), Ch. II

Time

“I like to have curves and feel like a woman. I hope that people see that in my photos and know that healthy is better than skinny.”

Marisa Miller (1978) American model

[Marisa Miller Profile, New York Magazine, http://nymag.com/fashion/models/mmiller/marisamiller/, 2009-10-14]

People , Hope , Feeling , Photo

“Alfie was an organizer. He would telephone the other kids a week before that first practice session (which he euphemistically called spring training), and he would knock on their doors the morning of, and they would look out the windows and say, "Hey, it's snowing," and he would say, "It's not snowing all that hard. See you in a half-hour." So we would gather our tired, cold bodies together, throw on our baseball clothes—old shirts, old pants, sneakers, old baseball gloves—and grab a couple of bats and scuffed-up balls, and we would pile onto the subway and ride to Van Cortland Park. We would run to make sure we'd be first to claim a ball field. Of course we were first. Nobody else was that crazy. My brother would direct practice for a couple of hours, batting practice, catching fungoes, fielding, practicing our curves and drops on the sidelines, fingers aching from contact with batted or thrown baseballs. We threw ourselves across that hard bone of a field so we would be ready when the spring suns finally thawed the ground at our feet. If the still-awake dreams of hunting lions in Africa were the peak moments of my night life, those frozen ball fields of February were the highlights of my days.”

Arnold Hano (1922) American writer

Recalling his late brother, from "Life with Alfie," https://books.google.com/books?id=PWEEAAAAMBAJ&pg=PA233&dq=%22Alfie+was+an+organizer%22&hl=en&sa=X&ved=0CBQQ6AEwAGoVChMIiqWJ2oHaxwIVipANCh2Utw2g#v=onepage&q=%22Alfie%20was%20an%20organizer%22&f=false in Orange Coast Magazine (November 1990), pp. 233–234
Other Topics

Life , Dreams , Spring , Sun

“Some maintain that such a tendency distorts the curve of tradition. Do they derive their arguments from the future or the past? The future does not belong to them, as far as we are aware, and one be singularly ingenuous to seek to measure that which exists by that which exists no longer.”

Jean Metzinger (1883–1956) French painter

Du Cubisme (1912)

Past , Future

“Of the contemporaries of Newton one of the most prominent was John Wallis. …Wallis was a voluminous writer, and not only are his writings erudite, but they show a genius in mathematics… He was one of the first to recognize the significance of the generalization of exponents to include negative and fractional as well as positive and integral numbers. He recognized also the importance of Cavalieri's method of indivisibles, and employed it in the quadrature of such curves as y=xn, y=x1/n, and y=x0 + x1 + x2 +… He failed in his attempts at the approximate quadrature of the circle by means of series because he was not in possession of the general form of the binomial theorem. He reached the result, however, by another method. He also obtained the equivalent of ds = \! dx \sqrt{1+(\frac{dy}{dx})^2} for the length of an element of a curve, thus connecting the problem of rectification with that of quadrature.”

David Eugene Smith (1860–1944) American mathematician

History of Mathematics (1923) Vol.1

Mathematics , Problem

“I remained there [in The Netherlands, 1914-18] for the duration of the war, continuing my work of abstraction in a series of church. facades, trees, houses, etc. But I felt that I still worked as an Impressionist and was continuing to express particular feelings, not pure reality. Although I was thoroughly conscious that we can never be absolutely 'objective', I felt that one can become less and less subjective, until the subjective no longer predominates in one's work. More and more I excluded from my painting all curved lines, until finally my compositions consisted only of vertical and horizontal lines which formed crosses, each separate and detached from the other. Observing sea, sky and stars, I sought to indicate their plastic function through a multiplicity crossing verticals and horizontals.”

Piet Mondrian (1872–1944) Peintre Néerlandais

Source: Quote of Mondrian about 1914-1918; in 'Mondrian, Essays' ('Plastic art and pure plastic art', 1937 and his other essays, (1941-1943) by Piet Mondrian; Wittenborn-Schultz Inc., New York, 1945, p. 10; as cited in De Stijl 1917-1931 - The Dutch Contribution to Modern Art, by H.L.C. Jaffé http://www.dbnl.org/tekst/jaff001stij01_01/jaff001stij01_01.pdf; J.M. Meulenhoff, Amsterdam 1956, p. 43

War , Feeling , Star , Reality

“So I had carved one face with hollows curving in-out, in-out, very simple really. I set the timber upright and Frank Stella came in and came over and looked at the chiseling and said it looked good. He turned around to the back of the piece which was uncut – the backside of the timber – and he said, you know that's sculpture too. I supposed what he meant to say was, that cutting was a good idea and the idea of not cutting was good too. But you know, I thought to myself, yes the uncut side is really much better than the cut side. The form of the timber was by no way improved by my cutting into it. From that time, I began to think that the next timbers I get I'm not going to cut. I'm going to combine the timbers; I'm going to use them as cuts in space. I began to look for what I call 'particles”

Carl Andre (1935) American artist

that is, units which are identical in shape – and finding ways to combine these particles by properties of the individual particles. That is, no gluing and no nailing and no joining.
Source: Artists talks 1969 – 1977, p. 29

Way , Idea , Thinking , Time

“The range of H 1255 is only four tenths of a magnitude, and on account of its brightness it is difficult to observe on all plates except those taken with the 1-inch Cooke lens. It seemed necessary, therefore, to take unusual precautions in order to secure accurate observations, and to give each one its full weight. Accordingly, one hundred and thirty six photographs were selected, including nearly all of those taken with the Cooke lens, and also those taken with the 8 inch Bache Telescope on which the variable was certainly faint. Four independent estimates of brightness were made on each plate, and means were taken, thus reducing the probable error one half. The phase was computed for each observation, thus covering all parts of the light curve. …H 1255 and H 1303 differ from the other variables in a marked degree as in each case the duration of the phase of minimum is very long in proportion to the length of the period. This fact led to considerable difficulty in determining their periods as they were apparently at their minimum brightness for some time before and after the actual minima occurred. In H 1255, the change in brightness is obviously continuous throughout the period, although it is much more rapid near minimum than near maximum. This is clearly seen in Plate IV, Figs. 5 and 6.”

Henrietta Swan Leavitt (1868–1921) astronomer

"Ten Variable Stars of the Algol Type" http://books.google.com/books?id=UkdWAAAAYAAJ&pg=PA87 (1908) Annals of the Astronomical Observatory of Harvard College Vol.60. No.5

Error , Light , Change , Time

“The great Cartesian invention had its roots in those famous problems of antiquity which originated in the days of Plato. In endeavoring to solve the problems of the trisection of an angle, of the duplication of the cube and of the squaring of the circle, the ruler and compass having failed them, the Greek geometers sought new curves. They stumbled on the conic sections…There we find the nucleus of the method which Descartes later erected into a principle. Thus Apollonius referred the parabola to its axis and principal tangent, and showed that the semichord was the mean propotional between the latus rectum and the height of the segment. Today we express this relation by x2 = Ly, calling the height the ordinate (y) and the semichord the abscissa (x); the latus rectum being… L. …the Greeks named these curves and many others… loci… Thus the ellipse was the locus of a point the sum of the distances of which from two fixed points was constant. Such a description was a rhetorical equation of the curve…”

Tobias Dantzig (1884–1956) American mathematician

Number: The Language of Science (1930)

Lying , Problem

“The really deep divergence between the humanistic and scientific sensibilities is one of temporality. Very nearly by definition, the scientist knows that tomorrow will be in advance of today. A twentieth-century schoolboy can manipulate mathematical and experimental concepts inaccessible to a Galileo or a Gauss. For a scientist the curve of the future is positive. Inevitably, the humanist looks back.”

George Steiner (1929–2020) American writer

"Tomorrow".
In Bluebeard's Castle (1971)

Mathematics , Future

“Behold, the atheists' nightmare. Now if you study a well-made banana, you'll find, on the far side, there are three ridges. On the close side, two ridges. If you get your hand ready to grip a banana, you'll find on the far side there are three grooves, on the close side, two grooves. The banana and the hand are perfectly made, one for the other. You'll find the maker of the banana, Almighty God, has made it with a non-slip surface. It has outward indicators of inward contents — green: too early; yellow: just right; black: too late. Now if you go to the top of the banana, you'll find, as with the soda can makers have placed a tab at the top, so God has placed a tab at the top. When you pull the tab, the contents don't squirt in your face. You'll find a wrapper which is biodegradable, has perforations. Notice how gracefully it sits over the human hand. Notice it has a point at the top for ease of entry. It's just the right shape for the human mouth. It's chewy, easy to digest and its even curved toward the face to make the whole process so much easier. Seriously, Kirk, the whole of creation testifies to the genius of God's creation.”

Ray Comfort (1949) New Zealand-born Christian minister and evangelist

God , Study

“It was so flat, you know, you could see the curves of the earth. And when a train came into vision at nine o'clock in the morning, it was still leaving at noon.... it took that long to get across the prairie.”

Agnes Martin (1912–2004) American artist

In Mary Lance's intimate documentary 'With My Back to the World' (2002)
Martin's quote about the landscape of her youth in Macklin, Saskatchewan, where her parents Malcolm and Margaret Martin farmed the vast, sometimes hard land
after 2000

Training

“It is in the nature of exponential growth that events develop extremely slowly for extremely long periods of time, but as one glides through the knee of the curve, events erupt at an increasingly furious pace. And that is what we will experience as we enter the twenty-first century.”

Ray Kurzweil (1948) Author, scientist, inventor, and futurist

The Age of Spiritual Machines: When Computers Exceed Human Intelligence (1999)

Nature , Time

“The melodic curves of speech are an expression of the complete organism and of all phases of its spiritual activities. They demonstrate whether a man is stupid or intelligent, sleepy or awake, tired or alert. They tell us whether he is a child or an old man, whether it is morning or evening, light or darkness, heat or frost, and disclose whether a person is alone or in company. The art of dramatic writing is to compose a melodic curve that will, as if by magic, reveal immediately a human being in one definite phase of his existence.”

Leoš Janáček (1854–1928) Czech composer

Leoš Janáček: Letters and Reminiscences (Stedron, Bohumir, ed. Translated by Geraldine Thomsen. Prague: Artia, 1995).

Stupidity , Art , Intelligence , Light

“Often you shall think your road impassable, sombre and companionless. Have will and plod along; and round each curve you shall find a new companion.”

Mikha'il Na'ima book The Book of Mirdad

The Book of Mirdad (1948)

Thinking

“Suppose then I want to give myself a little training in the art of reasoning; suppose I want to get out of the region of conjecture and probability, free myself from the difficult task of weighing evidence, and putting instances together to arrive at general propositions, and simply desire to know how to deal with my general propositions when I get them, and how to deduce right inferences from them; it is clear that I shall obtain this sort of discipline best in those departments of thought in which the first principles are unquestionably true. For in all 59 our thinking, if we come to erroneous conclusions, we come to them either by accepting false premises to start with—in which case our reasoning, however good, will not save us from error; or by reasoning badly, in which case the data we start from may be perfectly sound, and yet our conclusions may be false. But in the mathematical or pure sciences,—geometry, arithmetic, algebra, trigonometry, the calculus of variations or of curves,—we know at least that there is not, and cannot be, error in our first principles, and we may therefore fasten our whole attention upon the processes. As mere exercises in logic, therefore, these sciences, based as they all are on primary truths relating to space and number, have always been supposed to furnish the most exact discipline. When Plato wrote over the portal of his school. “Let no one ignorant of geometry enter here,” he did not mean that questions relating to lines and surfaces would be discussed by his disciples. On the contrary, the topics to which he directed their attention were some of the deepest problems,—social, political, moral,—on which the mind could exercise itself. Plato and his followers tried to think out together conclusions respecting the being, the duty, and the destiny of man, and the relation in which he stood to the gods and to the unseen world. What had geometry to do with these things? Simply this: That a man whose mind has not undergone a rigorous training in systematic thinking, and in the art of drawing legitimate inferences from premises, was unfitted to enter on the discussion of these high topics; and that the sort of logical discipline which he needed was most likely to be obtained from geometry—the only mathematical science which in Plato’s time had been formulated and reduced to a system. And we in this country [England] have long acted on the same principle. Our future lawyers, clergy, and statesmen are expected at the University to learn a good deal about curves, and angles, and numbers and proportions; not because these subjects have the smallest relation to the needs of their lives, but because in the very act of learning them they are likely to acquire that habit of steadfast and accurate thinking, which is indispensable to success in all the pursuits of life.”

Joshua Girling Fitch (1824–1903) British educationalist

Source: Lectures on Teaching, (1906), pp. 291-292

Life , God , Truth , World

“In the third period, which lasted from the middle of the eighteenth century until late in the nineteenth century, attention was turned to critical investigations of the true nature of the number π itself, considered independently of mere analytical representations. The number was first studied in respect of its rationality or irrationality, and it was shown to be really irrational. When the discovery was made of the fundamental distinction between algebraic and transcendental numbers, i. e. between those numbers which can be, and those numbers which cannot be, roots of an algebraical equation with rational coefficients, the question arose to which of these categories the number π belongs. It was finally established by a method which involved the use of some of the most modern of analytical investigation that the number π was transcendental. When this result was combined with the results of a critical investigation of the possibilities of a Euclidean determination, the inferences could be made that the number π, being transcendental, does not admit of a construction either by a Euclidean determination, or even by a determination in which the use of other algebraic curves besides the straight line and the circle are permitted. The answer to the original question thus obtained is of a conclusive negative character; but it is one in which a clear account is given of the fundamental reasons upon which that negative answer rests.”

E. W. Hobson (1856–1933) British mathematician

Source: Squaring the Circle (1913), p. 12

Question , Nature , Study

“The discovery of Hippocrates amounted to the discovery of the fact that from the relation
(1)\frac{a}{x} = \frac{x}{y} = \frac{y}{b}it follows that(\frac{a}{x})^3 = [\frac{a}{x} \cdot \frac{x}{y} \cdot \frac{y}{b} =] \frac{a}{b}and if a = 2b, [then (\frac{a}{x})^3 = 2, and]a^3 = 2x^3.The equations (1) are equivalent [by reducing to common denominators or cross multiplication] to the three equations
(2)x^2 = ay, y^2 = bx, xy = ab[or equivalently…y = \frac{x^2}{a}, x = \frac{y^2}{b}, y = \frac{ab}{x} ]Doubling the Cube
the 2 solutions of Menaechmusand the solutions of Menaechmus described by Eutocius amount to the determination of a point as the intersection of the curves represented in a rectangular system of Cartesian coordinates by any two of the equations (2).
Let AO, BO be straight lines placed so as to form a right angle at O, and of length a, b respectively. Produce BO to x and AO to y.
The first solution now consists in drawing a parabola, with vertex O and axis Ox, such that its parameter is equal to BO or b, and a hyperbola with Ox, Oy as asymptotes such that the rectangle under the distances of any point on the curve from Ox, Oy respectively is equal to the rectangle under AO, BO i. e. to ab. If P be the point of intersection of the parabola and hyperbola, and PN, PM be drawn perpendicular to Ox, Oy, i. e. if PN, PM be denoted by y, x, the coordinates of the point P, we shall have

\begin{cases}y^2 = b. ON = b. PM = bx\\ and\\ xy = PM. PN = ab\end{cases}whence\frac{a}{x} = \frac{x}{y} = \frac{y}{b}.
In the second solution of Menaechmus we are to draw the parabola described in the first solution and also the parabola whose vertex is O, axis Oy and parameter equal to a.”

Thomas Little Heath (1861–1940) British civil servant and academic

The point P where the two parabolas intersect is given by<center><math>\begin{cases}y^2 = bx\\x^2 = ay\end{cases}</math></center>whence, as before,<center><math>\frac{a}{x} = \frac{x}{y} = \frac{y}{b}.</math></center>
Apollonius of Perga (1896)

Drawing

“Unfortunately, the Laffer curve did not work as advertised. Lower tax rates did not produce more tax revenues. They produced deficits.”

Robert Kuttner (1943) American journalist

Source: The Economic Illusion (1984), Chapter 5, Taxes, p. 208
Context: The total impact of the Reagan tax cuts on capital lowered the effective cost of capital to American industry by an estimated 1.2 percent. Unfortunately, the Laffer curve did not work as advertised. Lower tax rates did not produce more tax revenues. They produced deficits.

“The Initiate who is aware Who he is can always check is conduct by reference to the determinants of his curve, and calculate his past, his future, his bearings, and his proper course at any assigned moment; he can even comprehend himself as a simple idea.”

Aleister Crowley (1875–1947) poet, mountaineer, occultist

Appendix VI : A few principal rituals – Liber Reguli.
Magick Book IV : Liber ABA, Part III : Magick in Theory and Practice (1929)
Context: A parabola is bound by one law which fixes its relations with two straight lines at every point; yet it has no end short of infinity, and it continually changes its direction. The Initiate who is aware Who he is can always check is conduct by reference to the determinants of his curve, and calculate his past, his future, his bearings, and his proper course at any assigned moment; he can even comprehend himself as a simple idea.

Idea , Past , Future

“Who shall call me ungentle, unfair,
I long'd so heartily then and there
To give him the grasp of fellowship;
But while I past he was humming an air,
Stopt, and then with a riding whip,
Leisurely tapping a glossy boot,
And curving a contumelious lip,
Gorgonised me from head to foot
With a stony British stare.”

Alfred, Lord Tennyson (1809–1892) British poet laureate

Part I, section xiii, stanza 2
Maud; A Monodrama (1855)

Past

“Oh pale and brittle pencils ever to try
One grass-blade's curve, or the throat of one bird
That clings to twig, ruffled against white sky.”

Robinson Jeffers (1887–1962) American poet

"Love the Wild Swan" (1935)
Context: I hate my verses, every line, every word.
Oh pale and brittle pencils ever to try
One grass-blade's curve, or the throat of one bird
That clings to twig, ruffled against white sky.
Oh cracked and twilight mirrors ever to catch
One color, one glinting flash, of the splendor of things.

Bird , Grass

“Taken to its logical extreme, the Laffer curve makes no sense because, if you lower your taxes to zero, how are you going to get higher revenues?”

Jean Chrétien (1934) 20th Prime Minister of Canada

Source: My Years As Prime Minister (2007), Chapter Two, The Virtuous Circle, p. 75
Context: I never bought into the Laffer curve, a theory, named after an American supply-side economist who had been an adviser to the Reagan administration, that essentially argues that a government will increase its revenue by reducing its taxes. If it were that easy, everybody would do it. What politician doesn't want to reduce taxes in order to win votes? Taken to its logical extreme, the Laffer curve makes no sense because, if you lower your taxes to zero, how are you going to get higher revenues? In practice, every government that toyed with this theory ended up with larger deficits, higher interest rates and greater social inequality.

Sense

“No revolution, no heresy is comfortable or easy. For it is a leap, it is a break in the smooth evolutionary curve, and a break is a wound, a pain.”

Yevgeny Zamyatin (1884–1937) Russian author

On Literature, Revolution, Entropy and Other Matters (1923)
Context: A new form is not intelligible to everyone; many find it difficult. Perhaps. The ordinary, the banal is, of course, simpler, more pleasant, more comfortable. Euclid's world is very simple, and Einstein's world is very difficult — but it is no longer possible to return to Euclid. No revolution, no heresy is comfortable or easy. For it is a leap, it is a break in the smooth evolutionary curve, and a break is a wound, a pain. But the wound is necessary: most of mankind suffers from hereditary sleeping sickness, and victims of this sickness (entropy) must not be allowed to sleep, or it will be their final sleep, death.
The same disease often afflicts artists and writers: they sink into satiated slumber in forms once invented and twice perfected. And they lack the strength to wound themselves, to cease loving what they once loved, to leave their old, familiar apartments filled with the scent of laurel leaves and walk away into the open field, to start anew.
Of course, to wound oneself is difficult, even dangerous. But for those who are alive, living today as yesterday and yesterday as today is still more difficult.

Pain

“Our course of advance … is neither a straight line nor a curve. It is a series of dots and dashes.”

Benjamin N. Cardozo (1870–1938) United States federal judge

Other writings, The Paradoxes of Legal Science (1928)
Context: Our course of advance... is neither a straight line nor a curve. It is a series of dots and dashes. Progress comes per saltum, by successive compromises between extremes, compromises often … between "positivism and idealism". The notion that a jurist can dispense with any consideration as to what the law ought to be arises from the fiction that the law is a complete and closed system, and that judges and jurists are mere automata to record its will or phonographs to pronounce its provisions.

“The abstractions of Einstein's curved space and time gave rise to analogies and pictures that played a new explanatory role.”

John D. Barrow (1952–2020) British scientist

Cosmic Imagery: Key Images in the History of Science (2008)
Context: The abstractions of Einstein's curved space and time gave rise to analogies and pictures that played a new explanatory role. Space and time gave way to space-time, visible light was augmented by images across the rest of the electromagnetic spectrum, and we realised that we could see back towards the apparent beginnings of time.<!--part. 1, p. 8

Time

“Our argument is not flatly circular, but something like it. It has the form, figuratively speaking, of a closed curve in space.”

Willard van Orman Quine Two Dogmas of Empiricism

"Two Dogmas of Empiricism", p. 26
From a Logical Point of View: Nine Logico-Philosophical Essays (1953)

“A smile is a curve that sets everything straight. ”

Phyllis Diller (1917–2012) American actress and stand-up comedianne

Cute , Smile

“Mirror symmetry is concerned with counting the number of holomorphic curves on Calabi-Yau manifolds, i.e. compact Kähler manifolds X with trivial canonical bundle KX.”

Robbert Dijkgraaf (1960) Dutch mathematical physicist and string theorist

[Mirror symmetry and elliptic curves by Robert Dijkgraaf, The moduli space of curves, 149–163, Progress in Mathematics, vol. 129, Birkhäuser Boston, 1995, 10.1007/978-1-4612-4264-2_5]

“You must either make a tool of the creature, or a man of him. You cannot make both. Men were not intended to work with the accuracy of tools, to be precise and perfect in all their actions. If you will have that precision out of them, and make their fingers measure degrees like cog-wheels, and their arms strike curves like compasses, you must unhumanize them. All the energy of their spirits must be given to make cogs and compasses of themselves….On the other hand, if you will make a man of the working creature, you cannot make him a tool. Let him but begin to imagine, to think, to try to do anything worth doing; and the engine-turned precision is lost at once. Out come all his roughness, all his dulness, all his incapability; shame upon shame, failure upon failure, pause after pause: but out comes the whole majesty of him also; and we know the height of it only when we see the clouds settling upon him.”

John Ruskin book The Stones of Venice

Volume II, chapter VI, section 12
The Stones of Venice (1853)

Imagination , Perfection , Thinking , Making love

“It was a long way down. Before she had gone very far the curious dizziness she had known before came over her again, a dizziness not entirely induced by the spirals she whirled around, but a deeper, atomic unsteadiness as if not only she but also the substances around her were shifting. There was something queer about the angles of those curves. She was no scholar in geometry or aught else, but she felt intuitively that the bend and slant of the way she went were somehow outside any other angles or bends she had ever known. They led into the unknown and the dark, but it seemed to her obscurely that they led into deeper darkness and mystery than the merely physical, as if, though she could not put it clearly even into thoughts, the peculiar and exact lines of the tunnel had been carefully angled to lead through poly-dimensional space as well as through the underground—perhaps through time, too.”

C. L. Moore (1911–1987) American author

Black God's Kiss (1934); pp. 10-11
Short fiction, Jirel of Joiry (1969)

Way , Time

“Luis Valdez said it long ago: The beauty and the frustration of theater is it is one permanent long shot…You never get up close in someone’s eyes. And that kind of blew me away (while shooting) a close-up. That was all new storytelling for me, and I had to figure it out on a very fast learning curve.”

Richard Montoya (1959) actor

On how he transitioned into filmmaking in “Culture Clash’s Richard Montoya becomes a movie multitasker” https://www.sacbee.com/entertainment/movies-news-reviews/article18414926.html in The Sacramento Bee (2015 Apr 13)

Beauty , Learning

“Since we all breathe, all the time, it is amazing what happens when someone else directs you how and when to breathe. And how vividly someone with no imagination whatsoever can see what he’s told is right there, complete with banister and rubber runners, curving down and rightward into a darkness that recedes before you.”

David Foster Wallace book The Pale King

The Pale King (2011)

Imagination , Time

“You know, yourself—Walter Johnson. The only way you could hit him was to poke the ball. I used to wait for his curve. Used to kid him by standing up straight with the bat leaning against my hip.”

Joe Jackson (1887–1951) American baseball player

When asked to name the best pitcher he ever faced; as quoted in "Twelve Years After White Sox Scandal..."

Way , Waiting

“Let the letters a b c denote the three angular points of a rectilineal triangle. If the point did move continuously over the lines ab, bc, ca, that is, over the perimeter of the figure, it would be necessary for it to move at the point b in the direction ab, and also at the same point b in the direction bc. These motions being diverse, they cannot be simultaneous. There-fore, the moment of presence of the movable point at vertex b, considered as moving in the direction ab, is different from the moment of presence of the movable point at the same vertex b, considered as moving in the same direction bc. But between two moments there is time; therefore, the movable point is present at point b for some time, that is, it rests. Therefore it does not move continuously, which is contrary to the assumption. The same demonstration is valid for motion over any right lines including an assignable angle. Hence a body does not change its direction in continuous motion except by following a line no part of which is straight, that is, a curve, as Leibnitz maintained.”

Immanuel Kant (1724–1804) German philosopher

Kant's Inaugural Dissertation (1770), Section III On The Principles Of The Form Of The Sensible World

Time , Parting , Change

“These people are buying Brazil in installments. This purchase in the past was also done by demarcating land. Brazil would only make deals overseas in exchange for forgoing its sovereignty, demarcating indigenous territories, expanding parks. It can’t go on like this. You can’t do anything in 61 percent of Brazil. In some places, if you want to produce, you can’t, because you can’t go on a straight line to export, or sell, you have to go on a huge curve to go around a quilombola community, an indigenous territory, an environmental reserve. They’re ruining the country. As long as I am president, no indigenous land will be demarcated. They own 14 percent of the national territory. Imagine the Southeast—an area larger than that is indigenous. Isn’t that enough? Yesterday, I was once again with a group of indigenous people, and they want freedom to work in their area; they don’t want to live in confinement, like prehistoric beings.”

Jair Bolsonaro (1955) Brazilian president elect

On 16 August 2019. Bolsonaro says he will do no indigenous land demarcation http://agenciabrasil.ebc.com.br/en/politica/noticia/2019-08/bolsonaro-says-he-will-do-no-indigenous-land-demarcation. Agência Brasil (16 August 2019).

Imagination , Freedom , Country , Past

“Besides these improvements,… there are others,… which may… be interesting to those… engaged in those departments… Among these may be ranked, in the division of mechanics, properly so called, a simple demonstration of the law of the force by which a body revolves in an ellipsis; another of the properties of cycloidal pendulums; an examination of the mechanism of animal motions; a comparison of the measures and weights of different countries; and a convenient estimate of the effect of human labour: with respect to architecture, a simple method of drawing the outline of a column: an investigation of the best forms for arches; a determination of the curve which affords the greatest space for turning; considerations on the structure of the joints employed in carpentry, and on the firmness of wedges; and an easy mode of forming a kirb roof: for the purposes of machinery of different kinds, an arrangement of bars for obtaining rectilinear motion; an inquiry into the most eligible proportions of wheels and pinions; remarks on the friction of wheel work, and of balances; a mode of finding the form of a tooth for impelling a pallet without friction; a chronometer for measuring minute portions of time; a clock escapement; a calculation of the effect of temperature on steel springs; an easy determination of the best line of draught for a carriage; an investigation of the resistance to be overcome by a wheel or roller; and an estimation of the ultimate pressure produced by a blow.”

Thomas Young (scientist) (1773–1829) English polymath

Preface
A Course of Lectures on Natural Philosophy and the Mechanical Arts (1807)

Drawing , Time , Law , Country

“One can and should debate whether the tests in question are appropriate for the purposes at hand, but one shouldn’t be surprised when normal curves behave normally.”

John Allen Paulos book A Mathematician Reads the Newspaper

Section 2, “Local, Social, and Business Issues” Chapter 11, “Company Charged with Ethnic Bias in Hiring” (p. 61)
A Mathematician Reads the Newspaper (1995)

Question

“Distribution of reaction to change What Mr. Koenigsaecker’s diagram suggests is that only a small percentage of people in the organization (the right tail of the curve) will welcome a change effort and actively participate.”

Mike Rother (1958) American business academic

Change , People , Effort

“The exact description of any physical process must include the effects of quantum gravity. But our experience suggests that there is a separation of scales, so that under suitable conditions we get 'lab physics'; i.e., physics described to good accuracy by quantum fields on gently curved spacetime.”

Samir D. Mathur Indian physicist

[What the information paradox is not., arXiv preprint arXiv:1108.0302, 2011, https://arxiv.org/abs/1108.0302]

“The dramaturgy of audiences and communities is crucial: how they think, how they hear stories, how they relate to the theatre…That was an interesting curve. Not having lived in the Midwest, I found that it’s segregated, it’s tribal.”

Chay Yew (1975) Singaoprean playwriter

On connecting with audiences in “Artistic director Chay Yew: ‘Audiences come here wanting a dialogue about America’” https://www.thestage.co.uk/features/interviews/2019/artistic-director-chay-yew-audiences-come-here-wanting-to-have-a-dialogue-about-america/ in The Stage (2019 Aug 5)

Communication , Thinking

“We have to take care of the cure. That will make the problem worse, no matter what. No matter what. We know what has to be done. We know you have to — you're tired of hearing the phrase, you got to flatten that curve where it's going up like this, people getting it, and then it comes down.”

Joe Biden (1942) 47th Vice President of the United States (in office from 2009 to 2017)

2020, March 2020

People , Problem

Quotes about curve page 3

Quotes about curve
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