Quotes about interval
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“The yearning for an afterlife is the opposite of selfish: it is love and praise for the world that we are privileged, in this complex interval of light, to witness and experience.”

John Updike (1932–2009) American novelist, poet, short story writer, art critic, and literary critic

Source: Self-Consciousness : Memoirs (1989), Ch. 6

Love, World, Light, Selfishness

“The most likely reason for the adoption of a relatively small number of discrete intervals as the tonal material for music is that discretization or categorization is a typical, if not universal, strategy used by animals in order to reduce information overload and facilitate processing when subjected to the high-information-conetent signals and/or high information rates from a highly developed sensory system (e. g., Estes, 1972; Terhardt, 1991). An obvious example is the processing of speech information by humans, wherein each language selects a relatively small portion of the available timbral-differences that can be produced by the vocal tract as information-carrying units (phonemes) in the language. A related reason for discrete scales, and another obvious analogy with speech perception, lies in the social aspect of music. Music first developed as, and still largely remains, a social phenomenon associated with religious or other rituals that, like language, necessitated an easily remembered common framework.”

Edward Burns (1968) American actor and director

Burns, Edward M. (1999). "Intervals, Scales, and Tuning", 'The Psychology of Music second edition, p. 218. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0122135644

Music, Universe, Animals

“Reginald sat in a corner of the Princess's salon and tried to forgive the furniture, which started out with an obvious intention of being Louis Quinze, but relapsed at frequent intervals into Wilhelm II.”

Saki (1870–1916) British writer

"Reginald in Russia"
Reginald in Russia (1910)

Forgiveness, Princess

“The Law of Accelerating Returns: As order exponentially increases, time exponentially speeds up (that is, the time interval between salient events grows shorter as time passes). The Law… applies specifically to evolutionary processes.”

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

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

Law, Time, Speed

“The method applied by Newton to the grounding of the Infinitesimal Calculus, and which since the beginning of this century has been recognised by the best mathematicians as the only one that furnishes sure results, is the method of limits. The method consists in this, viz., instead of considering a continuous transition from one value of a quantity to another, from one position to another, or, speaking generally, from one determination of a concept to another, one considers in the first place a transition through a finite number of intervals and then allows the number of these intervals to increase so that the distances of two successive points of division all decrease infinitely.”

Bernhard Riemann (1826–1866) German mathematician

General Relation of the Concept System of Thesis and Antithesis
Gesammelte Mathematische Werke (1876)

Success

“The interval between the decay of the old and the formation and establishment of the new constitutes a period of transition which must always necessarily be one of uncertainty, confusion, error, and wild and fierce fanaticism.”

John C. Calhoun (1782–1850) 7th Vice President of the United States

A Disquisition on Government (1851), p. 90
1850s

Error

“In fact, this infinitesimally spread-out consciousness is a direct feeling of its contents as spread out. In an infinitesimal interval we directly perceive the temporal sequence of its beginning, middle, and end… Now upon this interval follows another, whose beginning is the middle of the former, and whose middle is the end of the former. Here we have an immediate perception of the temporal sequence of its beginning, middle and end, or say, of the second, third, and fourth instants.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The Law of Mind (1892)

Feeling

“The Chinese used the intervals between things as the primary means of getting 'in touch' with situations.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

Source: 1980s, Laws of Media: The New Science (with Eric McLuhan) (1988), p. 77

“During the long interval which elapsed before the revival and reconstitution of the Secretary-ship in 1885, `the Lord Advocate of the day was really Minister for Scotland. The technical right to control Scottish affairs in their various departments no doubt belonged to the various Ministers of the Crown; but so little was known in London about Scotland and the country was in so distrubed and backward a condition that responsibility was easily devolved upon the only man who knew or cared much about the subject.”

Hugh Macmillan, Baron Macmillan (1873–1952) British judge

Source: A Man of Law's Tale (1952), At the Scottish bar, p. 86

Country

“This conversation taught me that some of us can meet reality on this side of the grave. I do not envy them. Such adventures may profit the disembodied soul, but as long as I have flesh and blood I pray that my grossness preserve me. Our lower nature has its dreams. Mine is of a certain farm, windy but fruitful, half-way between the deserted moorland and the uninhabitable sea. Hither, at rare intervals, she should descend and he ascend, to shatter their spiritual communion by one caress.”

E.M. Forster (1879–1970) English novelist

The Rock
The Life to Come and other stories (1972)

Dreams, Way, Soul, Nature

“This book was dictated to Benoni B. Gattell at intervals between the years 1912 and 1932. Since then it has been worked over again and again. Now, in 1946, there are few pages that have not been at least slightly changed.”

Harold W. Percival book Thinking and Destiny

Author's Forward, p. xxi
Thinking and Destiny (1946)

Books, Change

“Contour refers to the pattern of musical pitch in a melody—the sequence of ups or downs that the melody takes—regardless of the size of the interval.”

Daniel Levitin (1957) American psychologist

This is Your Brain on Music (2006)

Music

“I had to decide [he said later] whether I would be a lawyer by profession and a revolutionary at intervals, or a revolutionary by profession and a lawyer at intervals.”

Eleftherios Venizelos (1864–1936) Greek politician

[Bagger, E. S., Eminent Europeans; studies in continental reality, G.P. Putnam's Sons, 1922, http://www.archive.org/download/eminenteuropeans00bagg/eminenteuropeans00bagg.pdf], p. 61

“I believe that robotic thinking helps precision of psychological thought, and will continue to help it until psychophysiology is so far advanced that an image is nothing other than a neural event, and object constancy is obviously just something that happens in the brain. That time is still a long way off, and in the interval I choose to sit cozily with my robot, squeezing his hand and feeling a thrill -- a scientist's thrill -- when he squeezes mine back again.”

Edwin Boring (1886–1968) American psychologist

Edwin Boring (1946). Mind and mechanism; Cited in: Melford E. Spiro (1992) Anthropological Other Or Burmese Brother?: Studies in Cultural Analysis.. p. 68

Way, Feeling, Thinking, Time

“It was unbelievable! My family and close friends were sitting together till quite late in the night. People outside the gate just kept standing, hordes and hordes of them. It was overwhelming. I kept going out to meet them at half-hour intervals. But it just wasn't enough.”

Amitabh Bachchan (1942) Indian actor

Quotable quotes by Amitabh Bachchan.

People, Family, Night

“The term fuzzy logic is used in this paper to describe an imprecise logical system, FL, in which the truth-values are fuzzy subsets of the unit interval with linguistic labels such as true, false, not true, very true, quite true, not very true and not very fake, etc…. As a consequence, the truth tables and the rules of inference in fuzzy logic are (i) inexact and (ii) dependent on the meaning associated with the primary truth-value true as well as the modifiers very quite.”

George Klir (1932–2016) American computer scientist

Lotfi Asker Zadeh, George Klir, Bo Yuan (1996) Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers. p. 238.

Truth, Dependency, Falseness

“Here, in the company of the mindless trees, the free-flying birds, the bugs and frogs that passed from stimulus directly to response without the interval of consciousness between, did I hope to lose myself in the living mandala of evolution’s less self-tortured forms.”

Norman Spinrad book The Void Captain's Tale

Source: The Void Captain's Tale (1983), Chapter 10 (pp. 117-118)

Hope, Bird, Tree, Flying

“Tactility is space of the interval.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

1970s, Culture Is Our Business (1970)

“Leisure moments: each life well regulated has some such intervals, and he who cannot make way for them does not know how to live.”

Marguerite Yourcenar book Memoirs of Hadrian

Des moments libres. Toute vie bien réglée a les siens, et qui ne sait pas les provoquer ne sait pas vivre.
Source: Memoirs of Hadrian (1951), p. 43

Life, Way

“We do not mechanically connect the sensation of white with the idea of light, any more than we connect the sensation of black with the idea of darkness. We admit that a black jewel, even if of a dead black, may be more luminous than the white or pink satin of its case. Loving light, we refuse to measure it, and we avoid the geometrical ideas of the focus and the ray, which imply the repetition-contrary to the principle of variety which guides us-of bright planes and sombre intervals in a given direction. Loving colour, we refuse to limit it, and subdued or dazzling, fresh or muddy, we accept all the possibilities contained between the two extreme points of the spectrum, between the cold and the warm tone.”

Albert Gleizes (1881–1953) French painter

1910s, Du Cubisme (1912)

Love, Idea, Light, Dead

“We must appraise civilization in relation to its territory and in relation to its duration. The character of the medium of communication tends to create a bias in civilization favourable to an over-emphasis on the time concept or on the space concept and only at rare intervals are the biases offset by the influence of another medium and stability achieved.”

Harold Innis (1894–1952) Canadian professor of political economy

A Plea for Time (1950), a paper presented at the University of New Brunswick, published in The Bias of Communication (1951) p. 64.
The Bias of Communication (1951)

Communication, Time

“The interval during which a painting is mistaken for the real thing, or a real thing for a painting, is the triumphant moment of trompe l'oeil art. The artist appears to be potent as nature, if not superior to it. Almost immediately, though, the spectator's uncertainty is eliminated by his recognition that the counterfeit is counterfeit. Once the illusion is dissolved, what is left is an object that is interesting not as a work of art but as a successful simulation of something that is not art. The major response to it is curiosity: "How did he do it?"”

Harold Rosenberg (1906–1978) American writer and art critic

Source: Art on the Edge, (1975), p. 237-9, "Reality Again: The New Photorealism"

Art, Nature, Appearance, Success

“The planet has seen many changes. It has appeared and disappeared many times. It flickers off and on -- but because of the intervals of your attention each on period seems to last for millions of years, of course, while at other levels the earth is like a firefly, flickering off and on.”

Jane Roberts (1929–1984) American Writer

Session 918, Page 368
Dreams, Evolution and Value Fulfillment, Volume Two (1986)

Appearance, Change, Time

“The Pre-Lutheran German Bible. The precise origin of the mediaeval German Bible is still unknown. Dr. Ludwig Keller of Münster first suggested in his Die Reformation und die älteren Reformparteien, Leipzig, 1885, pp. 257-260, the hypothesis that it was made by Waldenses (who had also a Romanic version); and he tried to prove it in his Die Waldenser und die deutschen Bibelübersetzungen, Leipzig, 1886 (189 pages). Dr. Hermann Haupt, of Würzburg, took the same ground in his Die deutsche Bibelübersetzung der mittelalterlichen Waldenser in dem Codex Teplensis und der ersten gedruckten Bibel nachgewiesen, Würzburg, 1885 (64 pages); and again, in self-defense against Jostes, in Der waldensische Ursprung des Codex Teplensis und der vor-lutherischen deutschen Bibeldrucke, Würzburg, 1886. On the other hand, Dr. Franz Jostes, a Roman Catholic scholar, denied the Waldensian and defended the Catholic origin of that translation, in two pamphlets: Die Waldenser und die vorlutherische Bibelübersetzung, Münster, 1885 (44 pages), and Die Tepler Bibelübersetzung. Eine zweite Kritik, Münster, 1886 (43 pages). The same author promises a complete history of German Catholic Bible versions.
The hostility of several Popes and Councils to the circulation of vernacular translations of the Bible implies the existence of such translations, and could not prevent their publication, as the numerous German editions prove. Dutch, French, and Italian versions also appeared among the earliest prints. See Stevens, Nos. 687 and 688 (p. 59 sq.). The Italian edition exhibited in 1877 at London is entitled: La Biblia en lingua Volgare (per Nicolo di Mallermi). Venetia: per Joan. Rosso Vercellese, 1487, fol. A Spanish Bible by Bonif. Ferrer was printed at Valencia, 1478 (see Reuss, Gesch. der heil. Schr. N. T., II. 207, 5th Ed.).
The Bible is the common property and most sacred treasure of all Christian churches. The art of printing was invented in Catholic times, and its history goes hand in hand with the history of the Bible. Henry Stevens says (The Bibles in the Caxton Exhibition, p. 25): ""The secular history of the Holy Scriptures is the sacred history of Printing. The Bible was the first book printed, and the Bible is the last book printed. Between 1450 and 1877, an interval of four centuries and a quarter, the Bible shows the progress and comparative development of the art of printing in a manner that no other single book can; and Biblical bibliography proves that during the first forty years, at least, the Bible exceeded in amount of printing all other books put together; nor were its quality, style, and variety a whit behind its quantity.""”

Philip Schaff (1819–1893) American Calvinist theologian

Roman Catholic rival German versions of the Bible

Hostility, Books, Art, History

“Rousseau … asked himself how he might make as much as possible of the interval that remained; and he was not biassed by anything in his previous life when he decided that it must be by intellectual excitement.”

Walter Pater (1839–1894) essayist, art and literature critic, fiction writer

Conclusion The Renaissance http://www.authorama.com/renaissance-1.html (1873)

Life

“To the great Greek teachers, even to Socrates, as it still is practically to us all, this one and only truth of living religion was more or less but a distant thought, summoned into direct consciousness at intervals by a reflective effort, and brought to bear upon conduct amid the clamours of our animal being. To Jesus, on the contrary, it is an ever-present perception, like light to vision, like space to our movements, like time to our projects in life.”

George Holmes Howison (1834–1916) American philosopher

Source: The Limits of Evolution, and Other Essays, Illustrating the Metaphysical Theory of Personal Ideaalism (1905), The Right Relation of Reason to Religion, p.244

Life, Truth, Religion, Effort

“America is the only nation in history which miraculously has gone directly from barbarism to degeneration without the usual interval of civilization.”

Georges Clemenceau (1841–1929) French politician

Attributed to Clemenceau by Hans Bendix, in "Merry Christmas, America!" The Saturday Review of Literature (1 December 1945), p. 9; this appears to be the earliest reference to such a remark as one by Clemenceau, though earlier, in Frank Lloyd Wright : An Autobiography (1943) there is mention that "A witty Frenchman has said of us: 'The United States of America is the only nation to plunge from barbarism to degeneracy with no culture in between.'" Similar remarks are sometimes attributed without a source to Oscar Wilde and George Bernard Shaw.
Variants:
America is the only nation in history which miraculously has gone directly from barbarism to decadence without the usual interval of civilization.
America is the only country that went from barbarism to decadence without civilisation in between.
Post-Prime Ministerial

History

“Steno conceded, as Fabio Colonna had done before him, that all marine fossils might have been transported into their present situation at the time of the Noachian deluge. He maintained that fossil vegetables had been once living plants, and he hinted that they might, in some instances, indicate the distinction between fluvial and marine deposits. He also inferred that the present mountains had not existed ever since the origin of things, suggesting that many strata of submarine origin had been accumulated in the interval between the creation and deluge. Here he displayed his great anxiety to reconcile his theory with the Scriptures; for he at the same time advanced an opinion, which does not seem very consistent with such a doctrine, viz., that there was a wide distinction between the shelly, and nearly horizontal beds at the foot of the Apennines, and the older mountains of highly inclined stratification. Both, he observed, were of sedimentary origin; and a considerable interval of time must have separated their formation. Tuscany, according to him, had successively passed through six different states; and to explain these mighty changes, he called in the agency of inundations, earthquakes, and subterranean fires.”

Charles Lyell book Principles of Geology

Chpt.3, p. 32
Principles of Geology (1832), Vol. 1

Mountain, Change, Time, Success

“A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this 'variance equation' completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or non-stationary statistics.
The variance equation is closely related to the Hamiltonian (canonical) differential equations of the calculus of variations. Analytic solutions are available in some cases. The significance of the variance equation is illustrated by examples which duplicate, simplify, or extend earlier results in this field.
The duality principle relating stochastic estimation and deterministic control problems plays an important role in the proof of theoretical results. In several examples, the estimation problem and its dual are discussed side-by-side.
Properties of the variance equation are of great interest in the theory of adaptive systems. Some aspects of this are considered briefly.”

Rudolf E. Kálmán (1930–2016) Hungarian-born American electrical engineer

Source: New results in linear filtering and prediction theory (1961), p. 95 Article summary; cited in: " Rudolf E. Kálmán http://www-history.mcs.st-andrews.ac.uk/Biographies/Kalman.html", MacTutor History of Mathematics archive, 2010

Error, Optimism, Problem

“To suppose that chemistry and poetry are incompatible (as I am sure Prof Donnan would not do!), or that biology is inconsistent with a religious outlook on the world (I don not say with theology!) is to misunderstand entirely what the human mind, by contemplation and experiment, has achieved. By extreme specialization at intervals, by overloading the machine to its limit, discoveries and progress are made: but their bearing is best seen by letting the engine idle and giving oneself time to look around. The chemist and the poet are both right, the biologist and the saint: and each must pull up now and then to find whither he is going and to adjust his spectacles.”

Archibald Hill (1886–1977) English physiologist and biophysicist

The Ethical Dilemma of Science and Other Writings https://books.google.com.mx/books?id=zaE1AAAAIAAJ&printsec=frontcover#v=onepage&q&f=false (1960, Cap 1. Scepticism and Faith, p. 41)

World, Time

“A number of social problems arose. I had been told that neither smoking nor alcoholic beverages were allowed in the [Saudi] Royal Presence. As I was the host at luncheon I raised the matter at once, and said to the interpreter that if it was the religion of His Majesty [Ibn Saud] to deprive himself of smoking and alcohol I must point out that my rule of life prescribed as an absolutely sacred rite smoking cigars and also the drinking of alcohol before, after, and if need be during all meals and in the intervals between them. The King graciously accepted the position. His own cup-bearer from Mecca offered me a glass of water from its sacred well, the most delicious I had ever tasted.”

Winston S. Churchill (1874–1965) Prime Minister of the United Kingdom

Discussion of an audience with Saudi King Ibn Saud at the Fayoum oasis, Egypt, on February 17, 1945; in The Second World War, Volume VI : Triumph and Tragedy (1953), Chapter 23 (Yalta: Finale), pp. 348-349.
Post-war years (1945–1955)

Life, Alcohol, Religion, Drink

“Consonant intervals and dissonant intervals are processed via separate mechanisms in the auditory cortex.”

Daniel Levitin (1957) American psychologist

This is Your Brain on Music (2006)

“Everywhere, no matter what the sphere of interest (whether religious, political, or personal), the really creative acts are represented as those deriving from some sort of dying to the world; and what happens in the interval of the hero's nonentity, so that he comes back as one reborn, made great and filled with creative power, mankind is also unanimous in declaring. We shall have only to follow, therefore, a multitude of heroic figures through the classic stages of the universal adventure in order to see again what has always been revealed. …the singleness of the human spirit in its aspirations, powers, vicissitudes, and wisdom.”

Joseph Campbell book The Hero with a Thousand Faces

Source: The Hero with a Thousand Faces (1949), Chapter 3

Wisdom, World, Universe, Personality

“There was nothing for it but to pace through just behind or ahead of the spooling present that was never there, caught in the nonexistent interval between the nonexistent past and the nonexistent future.”

Kim Stanley Robinson book Galileo's Dream

Source: Galileo's Dream (2009), Ch. 13, p. 282

Past, Future

“Peter the Hermit, Calvin, and Robespierre, each at an interval of three hundred years and all three from the same region, were, politically speaking, the Archimedean screws of their age, — at each epoch a Thought which found its fulcrum in the self-interest of mankind.”

Honoré de Balzac (1799–1850) French writer

Pierre l'Ermite, Calvin et Robespierre, chacun à trois cents ans de distance, ces trois Picards ont été, politiquement parlant, des leviers d'Archimède.C'était à chaque époque une pensée qui recontrait un point d'appel dans les intérêts et chez les hommes.
Source: About Catherine de' Medici (1842), Part I: The Calvinist Martyr, Ch. XIII: Calvin.

Age

“The folksong collectors Bartok (Hungary) and Plicka (Czechoslovakia) notated the perceived interval deviations with a plus or minus sign (+,-). Older folksong collectors had notated all the intervals in the system of semitones, not observing the finer modifications of intervals. This first gained currency from the phongraph and tape recordings of folk music from various lands…. From folksong I learned to perceive melodic intervals a little smaller or greater than those of the semitone-system…. In my youth it often happened that the folk singers, who during the intermissions of dance festivals sang songs of "their kind," deviating from the semitone system, demanded that the first violinist of the Wisowitzer Kapelle play "their" melody just as they sang it. Once a tempermental singer threatened to strike the double-bass player with a beer mug if he didn't "play along" with the song, exactly as he sang it.”

Alois Hába (1893–1973) Czech music educator and composer

Mein Weg zur Viertel- und Sechsteltonmusik (1971) Düsseldorf: Verlag der Gesellschaft zur Förderung der systematische Musikwissenschaft, 12, 14; translated by and printed in Modernism and Music: An Anthology of Sources(2004) by Daniel Albright ISBN 0226012670 .

Youth, Music, Beer, Learning

“Mr Mayor and gentlemen - I have great pleasure in associating myself in how ever humble and transitory manner with this great and splendid undertaking. I am glad to be associated with an enterprise which I hope will carry still further the prosperity and power of Liverpool, and which will carry down the name of Liverpool to posterity as the place where a great mechanical undertaking first found its home. Sir William Forwood has alluded to the share which this city took in the original establishment of railways. My memory does not quite carry me back to the melancholy event by which that opening was signalised, but I can remember that which presents to my mind a strange contrast with the present state of things. Almost the earliest thing I can recollect is being brought down here to my mother's house which is close in the neighbourhood, and we took two days on the road, and had to sleep half way. Comparing that with my journey yesterday I feel what an enormous distance has been traversed in the interval, and perhaps a still larger distance and a still more magnificent rate of progress will be achieved before a similar distance of time has elapsed from the present day. I will not detain you in a room where it is perhaps difficult to hear. Of all my oratorical efforts, the one which I find most difficult to achieve is that of competing with a steam engine. Occasionally you are invited to do it at railway stations, and I know distinguished statesmen who do it with effect, but I think I have never ventured to compete in that line. I will therefore, though with some fear and trembling, fulfil the injunctions of Sir William Forwood, and proceed to handle the electric machinery which is to set this line in motion. I only hope the result will be no different from what he anticipates.”

Robert Gascoyne-Cecil, 3rd Marquess of Salisbury (1830–1903) British politician

At the opening of the Liverpool Overhead Railway, 4 February 1893. Quoted in the Liverpool Echo of the same day, p. 3
1890s

Pleasure, Fear, Hope, Way

“It is estimated that the value of the crops for this harvest year may reach $13,000,000,000, which is an increase of over $3,000,000,000 in three years. It compares with $7,100,000,000 in 1913, arid if we make deduction from the figures of 1924 for the comparatively decreased value of the dollar, the yield this year still exceeds 1913 in purchasing power by over $1,000,000,000, and in this interval there has been no increase in the number of farmers. Mostly by his own effort the farmer has decreased the cost of production. A marked increase in the price of his products and some decrease in the price of his supplies has brought him about to a parity with the rest of the Nation. The crop area of this season is estimated at 370,000,000 acres, which is a decline of 3,000,000 acres from last year, and 6,000,000 acres from 1919. This has been a normal and natural application of economic laws, which has placed agriculture on a foundation which is undeniably sound and beginning to be satisfactory.”

Calvin Coolidge (1872–1933) American politician, 30th president of the United States (in office from 1923 to 1929)

1920s, Second State of the Union Address (1924)

Law, Nature, Effort, Season

“In the presence of our addictions, we are not free to ask what we really desire. Eros is silent. The addiction floods us with the noise of its demands, the plans for its satisfaction. There is no interval for deliberation.”

Sam Keen (1931) author, professor, and philosopher

Source: The Passionate Life (1983), p. 139

“Reader, — This Enchiridion, I present thee with, is the Fruit of Solitude: A School few care to learn in, tho' None Instructs us better. Some Parts of it are the Result of serious Reflection: Others the Flashings of Lucid Intervals: Writ for private Satisfaction, and now publish'd for an Help to Human Conduct.”

William Penn (1644–1718) English real estate entrepreneur, philosopher, early Quaker and founder of the Province of Pennsylvania

The Preface
Fruits of Solitude (1682)

School, Solitude, Learning, Help

“I am insane, with small intervals of horrible sanity.”

Arin Paul (1980) Indian film director

Facebook http://www.facebook.com/aarinzz/posts/190116454331893 (2010)

“Ever since [ Copernicus], writers eager to drive the lesson home have urged us […] to abandon all sentimental egoism, and to see ourselves objectively in the true perspective of time and space. What precisely does this mean? In a full 'main feature' film, recapitulating faithfully the complete history of the universe, the rise of human beings from the first beginnings of man to the achievements of the twentieth century would flash by in a single second. Alternatively, if we decided to examine the universe objectively in the sense of paying equal attention to portions of equal mass, this would result in a lifelong preoccupation with interstellar dust, relieved only at brief intervals by a survey of incandescent masses of hydrogen — not in a thousand million lifetimes would the turn come to give man even a second's notice. It goes without saying that no one — scientists included — looks at the universe in this way, whatever lip-service is given to 'objectivity.”

Michael Polanyi (1891–1976) Hungarian-British polymath

Source: Personal Knowledge (1958), p. 3

Way, Home, History, Sense

“Why do entrepreneurs appear, not continuously, that is singly in every appropriately chosen interval, but in clusters? Exclusively because the appearance of one or a few entrepreneurs facilitates the appearance of others, and these the appearance of more, in ever-increasing numbers.”

Joseph Alois Schumpeter The Theory of Economic Development

The Theory of Economic Development (1934), Ch. 6 : The Business Cycle

Appearance

“Interface, of the resonant interval as 'where the action is', whether chemical, psychic or social, involves touch.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

Source: 1980s, Laws of Media: The New Science (with Eric McLuhan) (1988), p. 102

“Folds of scarlet drapery shut in my view to the right hand; to the left were the clear panes of glass, protecting, but not separating me from the drear November day. At intervals, while turning over the leaves in my book, I studied the aspect of that winter afternoon. Afar, it offered a pale blank of mist and cloud; near, a scene of wet lawn and storm-beat shrub, with ceaseless rain sweeping away wildly before a long and lamentable blast.”

Charlotte Brontë book Jane Eyre

Jane (Ch. 1)
Jane Eyre (1847)

Books, Study, Winter

““If you can see a thing whole,” he said, “it seems that it’s always beautiful. Planets, lives…. But close up, a world’s all dirt and rocks. And day to day, life’s a hard job, you get tired, you lose the pattern. You need distance, interval. The way to see how beautiful the earth is, is to see it as the moon. The way to see how beautiful life is, is from the vantage point of death.”
“That’s all right for Urras. Let it stay off there and be the moon—I don’t want it! But I’m not going to stand up on a gravestone and look down on life and say, ‘O lovely!’ I want to see it whole right in the middle of it, here, now. I don’t give a hoot for eternity.””

Ursula K. Le Guin Hainish Cycle

Source: Hainish Cycle, (1974), Chapter 6 (p. 190)

Love, Life, Death, World

“The pre-atomist multisensory void was an animate, pulsating, and moving vibrant interval, neither container nor contained, acoustic space penetrated by tactility.”

Marshall McLuhan (1911–1980) Canadian educator, philosopher, and scholar-- a professor of English literature, a literary critic, and a …

Source: 1980s, Laws of Media: The New Science (with Eric McLuhan) (1988), p. 34

Animals

“The question therefore now comes forward, To what other objects shall these surpluses be appropriated, and the whole surplus of impost, after the entire discharge of the public debt, and during those intervals when the purposes of war shall not call for them? Shall we suppress the impost and give that advantage to foreign over domestic manufactures? On a few articles of more general and necessary use the suppression in due season will doubtless be right, but the great mass of the articles on which impost is paid are foreign luxuries, purchased by those only who are rich enough to afford themselves the use of them.
Their patriotism would certainly prefer its continuance and application to the great purposes of the public education, roads, rivers, canals, and such other objects of public improvement as it may be thought proper to add to the constitutional enumeration of Federal powers. By these operations new channels of communications will be opened between the States, the lines of separation will disappear, their interests will be identified, and their union cemented by new and indissoluble ties. Education is here placed among the articles of public care, not that it would be proposed to take its ordinary branches out of the hands of private enterprise, which manages so much better all the concerns to which it is equal, but a public institution can alone supply those sciences which though rarely called for are yet necessary to complete the circle, all the parts of which contribute to the improvement of the country and some of them to its preservation.”

Thomas Jefferson (1743–1826) 3rd President of the United States of America

Thomas Jefferson's Sixth State of the Union Address (2 December 1806). Advising the origination of an annual fund to be spent through new constitutional powers (by new amendments) from projected surplus revenue.
1800s, Second Presidential Administration (1805-1809)

War, Education, Communication, Question

“An energetic crudity, even a riotous absurdity, has more promise in it than a clever and elegant mediocrity, because it shows that the young man is speaking out of his own heart, and struggling to express himself in his own way rather than in the way he finds in other men's books. The early works of original writers are usually very bad; then succeeds a short interval of imitation in which the influence of some favourite author is distinctly traceable; but this does not last long, the native independence of the mind reasserts itself, and although perhaps academic and critical demands are somewhat disregarded, so that the original writer on account of his very originality receives but slight recognition from the authorities, nevertheless if there is any real power in the voice it soon makes itself felt in the world.”

George Henry Lewes (1817–1878) British philosopher

The Principles of Success in Literature (1865)

Men, Books, World, Way

“… in truth Publius Scipio was one, who was himself enthusiastic, and who inspired enthusiasm. He was not one of the few who by their energy and iron will constrain the world to adopt, and to move in, new paths for centuries, or who grasp the reins of destiny for years till its wheels roll over them…. a wide interval separates such a man from an Alexander or a Caesar. As an officer, he rendered at least no greater service to his country than Marcus Marcellus; and as a politician, although not perhaps himself fully conscious of the unpatriotic and personal character of his policy, he injured hi country at least as much, as he benefited it by his military skill.”

Theodor Mommsen (1817–1903) German classical scholar, historian, jurist, journalist, politician, archaeologist and writer

The History Of Rome, Volume 2. Chapter 6. Translated by W.P.Dickson
The History of Rome - Volume 2

Truth, World, Personality, Country

“The Posthumous Works of Robert Hooke M. D.,'… appeared in 1705, containing 'A Discourse of Earthquakes'… His treatise… is the most philosophical production of that age, in regard to the causes of former changes in the organic and inorganic kingdoms of nature. 'However trivial a thing,' he says, 'a rotten shell may appear to some, yet these monuments of nature are more certain tokens of antiquity than coins or medals, since the best of those may be counterfeited or made by art and design, as may also books, manuscripts, and inscriptions, as all the learned are now sufficiently satisfied has often been actually practised,' &c.; 'and though it must be granted that it is very difficult to read them and to raise a chronology out of them, and to state the intervals of the time wherein such or such catastrophes and mutations have happened, yet it is not impossible.”

Charles Lyell book Principles of Geology

Chpt.3, p. 36
Principles of Geology (1832), Vol. 1

Books, Age, Art, Nature

“I don’t know if you have had the same experience, but a thing I have found in life is that from time to time, as you jog along, there occur moments which you are able to recognize immediately with the naked eye as high spots. Something tells you that they are going to remain etched, if etched is the word I want, for ever on the memory and will come back to you at intervals down the years, as you are dropping off to sleep, banishing that drowsy feeling and causing you to leap on the pillow like a gaffed salmon.”

P.G. Wodehouse book The Code of the Woosters

The Code of the Woosters (1938)

Life, Feeling, Sleep, Memory

“The earliest doctrines of the Indian and Egyptian schools of philosophy agreed in ascribing the first creation of the world to an omnipotent and infinite Being. They concurred also in representing this Being, who had existed from all eternity, as having repeatedly destroyed and reproduced the world and all its inhabitants. …We have no right to refer to mere chance the prevailing notion that the earth and its inhabitants had formerly undergone a succession of revolutions and catastrophes, interrupted by long intervals of tranquility.”

Charles Lyell book Principles of Geology

Chpt.2, p. 6
Principles of Geology (1832), Vol. 1

World, School, Chance, Success

“Lucid intervals and happy pauses.”

Francis Bacon (1561–1626) English philosopher, statesman, scientist, jurist, and author

History of King Henry VII, III (1622)

Happiness

“I have never had the sort of experience the mystics talk about, never felt a revelation of reality through or beyond nature, never felt like Adam in Paradise, never felt, in direct experience, that the world is wholly other than it seems…The nearest I have come to such experiences are glimpses of my own creative powers…and these are moments or intervals of inspiration rather than vision. I’m not sure that I want it unless I can have clarity about other things with it.”

Northrop Frye (1912–1991) Canadian literary critic and literary theorist

Source: "Quotes", The "Third Book" Notebooks of Northrop Frye, 1964–1972 (2002), p. 60–1

World, Nature, Reality

“Z-relation, or rather, "that certain pitch-class collections share the same 'interval vector' even though they are neither transpositionally nor inversionally equivalent was first pointed out by Howard Hanson in Harmonic Materials of Modern Music (New York: Appleton-Century-Crofts, 1960), p. 22, and by David Lewin in "Re: The Intervallic Content of a Collection of Notes," Journal of Music Theory 4:1 (1960). For a general criticism of Forte's concepts of pitch-class set equivalence see Perle, "Pitch-Class Set Analysis: An Evaluation," Journal of Musicology 8:2”

George Perle (1915–2009) American composer

1990
Page 67, note 8
See: Musical set theory
The Listening Composer

Music

“It was a day of gloom, and strange suspense,
And feverish, and inexplicable dread,
In Herculaneum's walls. The heavy, thick,
And torrid atmosphere; the solid, vast,
And strong--edg'd clouds, that through the firmament
In various and opposing courses moved:
The wild scream of the solitary bird
That, at long intervals, flew terror-driven
On high:--the howling of the red-ey'd dog
As he gaz'd trembling on the angry heavens:
The hollow moans that swept along the air,
Though every wind was lock'd,-portended all
That nature with some dire event was big,
And labour'd in its birth.”

Edwin Atherstone (1788–1872) British writer

The Last Days of Herculaneum (1821)

Dogs, Birth, Nature, Bird

“This mechanical element, which one is sorry to see disappear from the screen, and which one is impatient to see again, is discreet; it appears only at intervals, and far off, like a spotlight that flashes on in a long, intermittent, harrowing drama of totally uncompromising realism. The plastic event is non-the less there and seems to me be laden with consequences both in itself and for the future.”

Fernand Léger (1881–1955) French painter

on the filming of Abel Gance's La Roue, 1922
Quote in: Fernand Léger - The Later Years -, catalogue edited by Nicolas Serota, published by the Trustees of the Whitechapel Art gallery, London, Prestel Verlag, 1988, p. 21
Quotes of Fernand Leger, 1920's

Appearance, Future

“Consciousness must essentially cover an interval of time; for if it did not, we could gain no knowledge of time, and not merely no veracious cognition of it, but no conception whatever.”

Charles Sanders Peirce (1839–1914) American philosopher, logician, mathematician, and scientist

The Law of Mind (1892)
Context: Consciousness must essentially cover an interval of time; for if it did not, we could gain no knowledge of time, and not merely no veracious cognition of it, but no conception whatever. We are therefore, forced to say that we are immediately conscious through an infinitesimal interval of time.

Knowledge, Time

“Further, at intervals they lay single stones which run through the entire thickness of the wall.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book II, Chapter VIII, Sec. 7
Context: Our workmen, in their hurry to finish, devote themselves only to the facings of the walls, setting them upright but filling the space between with a lot of broken stones and mortar thrown in anyhow. This makes three different sections in the same structure; two consisting of facing and one of filling between them. The Greeks, however, do not build so; but laying their stones level and building every other stone lengthwise into the thickness, they do not fill the space between, but construct the thickness of their walls in one solid and unbroken mass from the facings to the interior. Further, at intervals they lay single stones which run through the entire thickness of the wall. These stones... by their bonding powers... add very greatly to the solidity of the walls.

“Things essentially incorporeal, because they are more excellent than all body and place, are every where, not with interval, but impartibly.”

Porphyry (philosopher) (233–301) Neoplatonist philosopher

2 - 4
Auxiliaries to the Perception of Intelligible Natures
Context: Things essentially incorporeal, because they are more excellent than all body and place, are every where, not with interval, but impartibly.
Things essentially incorporeal are not locally present with bodies but are present with them when they please; by verging towards them so far as they are naturally adapted so to verge. They are not, however, present with them locally, but through habitude, proximity, and alliance.
Things essentially incorporeal, are not present with bodies, by hypostasis and essence; for they are not mingled with bodies. But they impart a certain power which is proximate to bodies, through verging towards them. For tendency constitutes a certain secondary power proximate to bodies.

“[I]t is impossible that each of the elements should be infinite. For that is body which has interval on all sides; and that is infinite which has extension without bound.”

Aristotle book Physics

Book III, Ch. VII, p. 159.
Physics

“He knows he’s aged a lot: he sees it, feels it.
Yet it seems he was young just yesterday.
So brief an interval, so very brief.”

Constantine P. Cavafy (1863–1933) Greek poet

An Old Man http://www.cavafy.com/poems/content.asp?id=39&cat=1 Collected Poems (1992) Context: He knows he’s aged a lot: he sees it, feels it. Yet it seems he was young just yesterday. So brief an interval, so very brief. And he thinks of Prudence, how it fooled him, how he always believed — what madness — that cheat who said: “Tomorrow. You have plenty of time.”

Age, Feeling

“We ourselves become the bridges out over the interval that is the world and time.”

R. A. Lafferty (1914–2002) American writer

Source: The Flame is Green (1971), Ch. 9 : Oh, The Steep Roofs of Paris
Context: We ourselves become the bridges out over the interval that is the world and time. It is a daring thing to fling ourselves out over that void that is black and scarlet below and green and gold above. A bridge does not abandon its first shore when it grows out in spans towards the further one.

World, Time

“If we suppose that similar intervals exist between all the stars,”

Robert Chambers (publisher, born 1802) book Vestiges of the Natural History of Creation

Footnote: By Mr. Henderson Professor of Astronomy in the Edinburgh University and Lieutenant Meadows.
p. 3
Vestiges of the Natural History of Creation (1844)
Context: A sensible parallax of about one second has been ascertained in the case of the double star [ Alpha Centauri ] of the constellation of the Centaur, and one of the third of that amount for the double star, 61 Cygni; which gave reason to presume that the distance of the former might be about twenty thousand millions of miles, and the latter of much greater amount. If we suppose that similar intervals exist between all the stars, we shall readily see that the space occupied by even the comparatively small number visible to the naked eye, must be vast beyond all powers of conception.

Star

“Fortunate circumstances must concur, even to the greatest, to render them eminently successful. It is not permitted to all to be born, like Archimedes, when a science was to be created; nor, like Newton, to find the system of the world "without form and void;" and, by disclosing gravitation, to shed throughout that system the same irresistible radiance as that with which the Almighty Creator had illumined its material substance. It can happen to but few philosophers, and but at distant intervals, to snatch a science, like Dalton, from the chaos of indefinite combination, and binding it in the chains of number, to exalt it to rank amongst the exact.”

Charles Babbage (1791–1871) mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable c…

p. 21 http://www.gutenberg.org/files/1216/1216-h/1216-h.htm Reflections on the Decline of Science in England, and on Some of its Causes (1830) Context: If we look at the fact, we shall find that the great inventions of the age are not, with us at least, always produced in universities. The doctrines of "definite proportions," and of the "chemical agency of electricity,"—principles of a high order, which have immortalized the names of their discoverers,—were not produced by the meditations of the cloister: nor is it in the least a reproach to those valuable institutions to mention truths like these. Fortunate circumstances must concur, even to the greatest, to render them eminently successful. It is not permitted to all to be born, like Archimedes, when a science was to be created; nor, like Newton, to find the system of the world "without form and void;" and, by disclosing gravitation, to shed throughout that system the same irresistible radiance as that with which the Almighty Creator had illumined its material substance. It can happen to but few philosophers, and but at distant intervals, to snatch a science, like Dalton, from the chaos of indefinite combination, and binding it in the chains of number, to exalt it to rank amongst the exact. Triumphs like these are necessarily "few and far between;", nor can it be expected that that portion of encouragement, which a country may think fir to bestow on science, should be adapted to meet such instances. Too extraordinary to be frequent, they must be left, if they are to be encouraged at all, to some direct interference of the governemeɳt. The dangers to be apprehended from such a specific interference, would arise from one, or several of the following circumstance:—That class of society, from whom the government is selected, might not possess sufficient knowledge either to judge themselves, or know upon whose judgment to rely. Or the number of persons devoting themselves to science, might not be sufficiently large to have due weight in the expression of public opinion. Or, supposing this class to be large, it might not enjoy, in the estimation of the world, a sufficiently high character for independence. Should these causes concur in any country, it might become highly injurious to commit the encouragement of science to any department of the government. This reasoning does not appear to have escaped the penetration of those who advised the abolition of the late Board of Longitude. The question whether it is good policy in the government of a country to encourage science, is one of which those who cultivate it are not perhaps the most unbiased judges. In England, those who have hitherto pursued science, have in general no very reasonable grounds of complaint; they knew, or should have known, that there was no demand for it, that it led to little honour, and to less profit. That blame has been attributed to the government for not fostering the science of the country is certain; and, as far as regards past administrations, is, to a great extent, just; with respect to the present ministers, whose strength essentially depends on public opinion, it is not necessary that they should precede, and they cannot remain long insensible to any expression of the general feeling. But supposing science were thought of some importance by any administration, it would be difficult in the present state of things to do much in its favour; because, on the one hand, the higher classes in general have not a profound knowledge of science, and, on the other, those persons whom they have usually consulted, seem not to have given such advice as to deserve the confidence of government. It seems to be forgotten, that the money allotted by government to purposes of science ought to be expended with the same regard to prudence and economy as in the disposal of money in the affairs of private life.

World, Distant, Science, Success

“There exist moments in life, separated by long intervals of time, but linked together by their inner content and by a certain singular sensation peculiar to them.”

P. D. Ouspensky (1878–1947) Russian esotericist

A New Model of the Universe (1932)
Context: There exist moments in life, separated by long intervals of time, but linked together by their inner content and by a certain singular sensation peculiar to them. Several such moments always recur to my mind together, and I feel then that it is these that have determined the chief trend of my life.

Life, Time

“If the result is inconclusive, the conflict will be renewed after an uneasy interval.”

Winston S. Churchill (1874–1965) Prime Minister of the United Kingdom

On the Great War, The Sinister Hypothesis, The Sunday Pictorial, 9 July 1916.
Reproduced in The Collected Essays of Sir Winston Churchill, Vol I, Churchill at War, Centenary Edition (1976), Library of Imperial History, p. 91.
Early career years (1898–1929)
Context: Only the final results can prove whether military autocracies or Parliamentary Governments are more likely — take them for all in all — to preserve the welfare and safety of great nations. If the result is inconclusive, the conflict will be renewed after an uneasy interval. But when an absolute decision is obtained the system of the victors — whoever they are — will probably be adopted to a very great extent by the vanquished.

“The devils stroll the earth again and infect with the red sickness. They must, at all cost to themselves, destroy the growing tendrils before such can touch the other side. For, whenever one least growing creeper touches across the interval, that means the extinction of a devil.”

R. A. Lafferty (1914–2002) American writer

Source: The Flame is Green (1971), Ch. 9 : Oh, The Steep Roofs of Paris
Context: The devils stroll the earth again and infect with the red sickness. They must, at all cost to themselves, destroy the growing tendrils before such can touch the other side. For, whenever one least growing creeper touches across the interval, that means the extinction of a devil. It is a thing to be tested. Notice it that whenever there is the special shrilling, when there is the wild flinging out of catchwords to catch you in, when there are the weird exceptions and inclusions, when there are specious arguments and the murderous defamations, when all the volubility of the voltairians and the cuteness of the queers has been assembled to confound you, then one green growth has almost reached across to the other side, one devil is in danger of extinction. Oh, they will defend against that!

“The perturbations which the motions of planets suffer from the influence other planets, are so small and so slow that they only become sensible after a long interval of time; within a shorter time”

Carl Friedrich Gauss (1777–1855) German mathematician and physical scientist

Theoria motus corporum coelestium... (1809) Tr. Charles Henry Davis as Theory of the Motion of the Heavenly Bodies moving about the Sun in Conic Sections (1857)
Context: The perturbations which the motions of planets suffer from the influence other planets, are so small and so slow that they only become sensible after a long interval of time; within a shorter time, or even within one or several revolutions, according to circumstances, the motion would differ so little from motion exactly described, according to the laws of Kepler, in a perfect ellipse, that observations cannot show the difference. As long as this is true, it not be worth while to undertake prematurely the computation of the perturbations, but it will be sufficient to adapt to the observations what we may call an osculating conic section: but, afterwards, when the planet has been observed for a longer time, the effect of the perturbations will show itself in such a manner, that it will no longer be possible to satisfy exactly all the observations by a purely elliptic motion; then, accordingly, a complete and permanent agreement cannot be obtained, unless the perturbations are properly connected with the elliptic motion.

Suffering, Time

“These great sages or masters have never been discouraged in their work for humanity by the fact that the body of truths which at cyclical intervals they promulgate anew would have to undergo periods of degeneration. Directed by spiritual beings even greater than they, they do this sublime work and without intermission throughout the whirling cycles of time.”

Gottfried de Purucker (1874–1942) Author, Theosophist

Source: The Esoteric Tradition (1935), Chapter 22

Truth, Time

“And when all things were created as has been described by Moses — both heaven and earth, and the things therein — the twelve angels of the Mother were divided into four principles, and each fourth part of them is called a river — Phison, and Gehon, and Tigris, and Euphrates, as, he says, Moses states. These twelve angels being mutually connected, go about into four parts, and manage the world, holding from Edem a sort of viceregal authority over the world. But they do not always continue in the same places, but move around as if in a circular dance, changing place after place, and at set times and intervals retiring to the localities subject to themselves. And when Phison holds sway over places, famine, distress, and affliction prevail in that part of the earth, for the battalion of these angels is niggardly.”

Hippolytus of Rome Refutation of all Heresies

Ante-Nicene Christian Library, Volume 6: Hippolytus, Bishop Of Rome, Volume 1 p. 187
Refutation of All Heresies

World, Angels, Affliction, Change

“The bases of music are rhythm and harmony. Rhythm is ordered recurrence in time… As the planets move around the sun, they repeat their orbits periodically; thus there is already a primitive kind of rhythm in their motion. …Harmony …can be considered a special kind of rhythm. …pure musical tones are produced when the vibrations are… periodic or… repeat themselves regularly in time. Two tones harmonize if their intervals of repetition are in rhythm—or, in mathematical language, if their periods are in proportion.”

Frank Wilczek (1951) physicist

Kepler... in the third book of Harmonice mundi... attempted to make other... related, connections between musical harmony and mathematical proportion.
Longing for the Harmonies: Themes and Variations from Modern Physics (1987)

Music, Mathematics, Time, Sun

“Most intelligent people of the eighties had developed a type of radio deafness which enabled them not to hear a human voice coming from a loud-speaker, although they could hear and enjoy the then infrequent intervals of music between announcements. In an age when advertising competition was so keen that there was scarcely a bare wall or an unbillboarded lot within miles of a population center, discriminating people could retain normal outlooks on life only by carefully cultivated partial blindness and partial deafness which enabled them to ignore the bulk of that concerted assault upon their senses.”

Fredric Brown (1906–1972) American novelist, short story author

Pi in the Sky (p. 242)
Short fiction, From These Ashes (2000)

Life, People, Age, Music