Quotes about symmetry

A collection of quotes on the topic of symmetry, use, nature, time.

Quotes about symmetry

“Maxwell's equations… originally consisted of eight equations. These equations are not "beautiful." They do not possess much symmetry. In their original form, they are ugly…. However, when rewritten using time as the fourth dimension, this rather awkward set of eight equations collapses into a single tensor equation. This is what a physicist calls "beauty," because both criteria are now satisfied.”

Michio Kaku book Hyperspace

Source: Hyperspace (1995), Ch.5 Quantum Heresy

Beauty, Time

“Break a vase, and the love that reassembles the fragments is stronger than that love which took its symmetry for granted when it was whole.”

Derek Walcott (1930–2017) Saint Lucian–Trinidadian poet and playwright

Love

“Tyger! Tyger! burning bright
in the forests of the night,
What immortal hand or eye
Could frame thy fearful symmetry?”

William Blake (1757–1827) English Romantic poet and artist

St. 1
1790s, The Tyger (1794)

Fear, Night

“Don't confuse symmetry with balance.”

Tom Robbins Even Cowgirls Get the Blues

Source: Even Cowgirls Get the Blues

“Symmetry is what we see at a glance; based on the fact that there is no reason for any difference…”

Blaise Pascal Pensées

Source: Pensées

“The musical scale is a convention which circumscribes the area of potentiality and permits construction within those limits in its own particular symmetry.”

Iannis Xenakis (1922–2001) Greek composer

Formalized Music

Music

“Now, my countrymen if you have been taught doctrines conflicting with the great landmarks of the Declaration of Independence; if you have listened to suggestions which would take away from its grandeur, and mutilate the fair symmetry of its proportions; if you have been inclined to believe that all men are not created equal in those inalienable rights enumerated by our chart of liberty, let me entreat you to come back. Return to the fountain whose waters spring close by the blood of the Revolution. Think nothing of me, take no thought for the political fate of any man whomsoever; but come back to the truths that are in the Declaration of Independence. You may do anything with me you choose, if you will but heed these sacred principles. You may not only defeat me for the Senate, but you may take me and put me to death. While pretending no indifference to earthly honors, I do claim to be actuated in this contest by something higher than an anxiety for office. I charge you to drop every paltry and insignificant thought for any man's success. It is nothing; I am nothing; Judge Douglas is nothing. But do not destroy that immortal emblem of Humanity; the Declaration of American Independence.”

Abraham Lincoln (1809–1865) 16th President of the United States

1850s, Speech at Lewistown, Illinois (1858)

Death, Men, Fate, Truth

“Nobody performs her or his duties. Governments do not, because they do not know, they are not able or they do not wish, or because they are not permitted by those who effectively govern the world: The multinational and pluricontinental companies whose power — absolutely non-democratic — reduce to next to nothing what is left of the ideal of democracy. We citizens are not fulfilling our duties either. Let us think that no human rights will exist without symmetry of the duties that correspond to them. It is not to be expected that governments in the next 50 years will do it. Let us common citizens therefore speak up. With the same vehemence as when we demanded our rights, let us demand responsibility over our duties. Perhaps the world could turn a little better.”

José Saramago (1922–2010) Portuguese writer and recipient of the 1998 Nobel Prize in Literature

Nobel Banquet Speech

World, Democracy, Thinking

“You & James Ferdinand simply can't learn to distinguish betwixt intellectual opinion & irrelevant instinctive emotion... For instance, he has the idea that I place an exaggerated intellectual valuation on the 18th century merely because my chance emotions have given me a strong but irrational subjective sense of belonging to it. I've told that bird dozens of times that I have no especial intellectual brief for Georgian days... He can't understand my ability to class as merely one period among others an age to which random early impressions have so closely bound my emotions & sense of identity... the point is that my own personal mess of subjective emotions has nothing whatever to do with my intellectual opinions. I have freely declared myself at all times (like everybody else in his respective way) a mere product of my background, & do not consider the values of that background as applicable to outsiders. The only way for the individual to achieve any contentment or harmonic relationship to a pattern is to adhere to the background naturally his; & that is what I am doing. Others I urge to adhere to their own respective backgrounds & traditions, however remote from mine these may be. When I venture now & then to suggest values of a more general kind, I approach the problem in an entirely different way—speaking not as Old Theobald of His Majesty's Rhode-Island Colony, but as the cosmic & impersonal Ec'h-Pi-El, denizen of the invisible world 'Ui-ulh in the second zone of curved space outside angled space... If there is any approach to an absolute value in the cosmos—or at least on this planet—then this is it. Sincerity—is-or-isn't-ness—technical perfection—harmony—coherence—consistency—symmetry—all these things are obviously aspects of one single property of space, energy, & general mathematical harmonics whose universality gives it the deepest possible significance. I have thought this all my life, & that is why to me one Newton or Einstein, one M. Atilius Regulus, M. Porcius Cato, or P. Cornelius Scipio, seems to me in certain ways worth a full dozen of your prattling little Keatses & Baudelaires.”

H.P. Lovecraft (1890–1937) American author

Letter to Frank Belknap Long (27 February 1931), in Selected Letters III, 1929-1931 edited by August Derleth and Donald Wandrei, p. 312
Non-Fiction, Letters, to Frank Belknap Long

Life, Age, World, Way

“But what, Phaedrus, is the contrary of a dream if not some other dream?… A dream of vigilance and tension dreamt by Reason herself!—And what would such a Reason dream?—If a Reason were to dream—a Reason hard, erect, eyes armed, mouth closed, as though mistress of her lips—would not the dream she dreamt be what we see now—this world of exact forces and studied illusions?—A dream, a dream, but a dream interpenetrated with symmetries, all order, acts and sequences!”

Paul Valéry (1871–1945) French poet, essayist, and philosopher

Socrates, p. 35
L'Âme et la danse (1921)

World, Dreams, Study

“Was it an intellectual consequence of this ‘rebirth,’ of this new dignity and rigor, that, at about the same time, his sense of beauty was observed to undergo an almost excessive resurgence, that his style took on the noble purity, simplicity and symmetry that were to set upon all his subsequent works that so evident and evidently intentional stamp of the classical master.”

Thomas Mann book Death in Venice

Source: Death in Venice (1912), Ch. 2, as translated by David Luke

Beauty, Sense, Time

“Symmetry is the aesthetics of the stupid.”

Ludwig Mies van der Rohe (1886–1969) German architect

An early appearance is "Symmetry is the aesthetics of the little man," which appears in the 1965 book Bauen auf dem Lande (Building in the Countryside), volumes 16-17. However, the quote has also variously been attributed to Picasso, Salvatore Dali and Friedensreich Hundertwasser. <br class="br">Disputed <br class="br">Source: "Symmetry is the aesthetics of the stupid." Mies van der Rohe (allegedly), 2018-01-21, 2017-11-12 http://falschzitate.blogspot.com/2017/11/symmetrie-ist-die-asthetik-der-dummen.html,

Stupidity

“Symmetry is not enough by itself. In electromagnetism, for example, if you write down all the symmetries we know, such as Lorentz invariance and gauge invariance, you don’t get a unique theory that predicts the magnetic moment of the electron. The only way to do that is to add the principle of renormalisability – which dictates a high degree of simplicity in the theory and excludes these additional terms that would have changed the magnetic moment of the electron from the value Schwinger calculated in 1948.”

Steven Weinberg (1933) American theoretical physicist

as quoted in an interview by Matthew Chalmers: [Model physicist, CERN Courier, 13 October 2017, http://cerncourier.com/cws/article/cern/70138]

Way, Gauge, Change

“One of the things that excited me so much about quantum chromodynamics after the work of Gross and Wilczek and Politzer was that it seemed to provide a rational explanation for what had always been mysterious to me — the fact that there were symmetries, like parity conservation, charge conjugation invariance, and strangeness conservation, that were very good symmetries of the strong and electromagnetic interactions — as far as we knew exact — and yet were not respected by the weak interactions. Why should nature have … symmetries that are symmetries of part of nature but not other parts of nature?”

Steven Weinberg (1933) American theoretical physicist

"Reminiscences of the Standard Model" - Special Colloquium by Steven Weinberg https://www.youtube.com/watch?v=mX2R8-nJhLQ, 17 October 2017, YouTube video at 1:02:17 of 1:39:24

Nature, Strong, Parting

“Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts.”

Nicolaus Copernicus book De revolutionibus orbium coelestium

Preface Letter to Pope Paul III, Tr. E. Rosen, De Revolutionibus Orbium Coelestium (1978) pp. 4-7.
De revolutionibus orbium coelestium (1543)
Context: Those who devised the eccentrics seen thereby in large measure to have solved the problem of apparent motions with approximate calculations. But meanwhile they introduced a good many ideas which apparently contradict the first principles of uniform motion. Nor could they elicit or deduce from the eccentrics the principal consideration, that is, the structure of the universe and the true symmetry of its parts. On the contrary, their experience was just like someone taking from various places hands, feet, a head, and other pieces, very well depicted it may be, but for the representation of a single person; since these fragments would not belong to one another at all, a monster rather than a man would be put together from them.

Universe, Parting

“… we take comfort in the symmetries we find in life because they suggest a design where there is none.”

Nicole Krauss book Great House

Source: Great House

Life

“Life is sometimes novel-shaped, mocking the efforts of those authors who, in an effort to make their novels life-shaped, spurn the easy symmetry and cheap resonance of reality.”

Stephen Fry book Moab Is My Washpot

Source: Moab Is My Washpot

Life, Reality, Effort

“Human behavior is messy and unpredictable and unconcerned with convenient symmetries.”

Khaled Hosseini book And the Mountains Echoed

Source: And the Mountains Echoed

Behavior

“The heavenly bodies move with such regularity, orderliness, and symmetry that it is truly a marvel; and they continue always to act in this manner ceaselessly, following the established system, without increasing or reducing speed and continuing without respite, as the Scripture says: Summer and winter, night and day they never rest.”

Nicole Oresme (1323–1382) French philosopher

Book II, Ch. 2, p. 283.
Le livre du ciel et du monde (1377)

Winter, Summer, Speed, Night

“I could see that now — how the universe swirled around this one point. I'd never seen the symmetry of the universe before, but now it was plain.
The gravity of the earth no longer tied me to the place where I stood.
It was the baby girl in the blonde vampire's arms that held me here now.
Renesmee.”

Stephenie Meyer (1973) American author

Jacob Black, p. 360
Twilight series, Breaking Dawn (2008)

Girl, Universe, Baby

“Which are the arguments and how many are there? I must have an inbred urge toward symmetry. In canvassing for the principal ways of criticizing, assaulting, and ridiculing the three successive "progressive" thrusts of Marshall's story, I have come up with another triad: that is, with three principal reactive-reactionary theses, which I call the perversity thesis or thesis of the perverse effect, the futility thesis, and the jeopardy thesis. According to the perversity thesis, any purposive action to improve some feature of the political, social, or economic order only serves to exacerbate the condition one wishes to remedy. The futility thesis holds that attempts at social transformation will be unavailing, that they will simply fail to “make a dent.””

Albert O. Hirschman book The Rhetoric of Reaction

Finally, the jeopardy thesis argues that the code of the proposed chafe or reform is too high as it endangers some previous, precious accomplishment.
The Rhetoric of Reaction: Perversity, Futility, Jeopardy (1991), Ch. 1 : Two Hundred Years of Reactionary Rhetoric.

Way, Success

“Perhaps the most profound synthesis of physical sciences came from the realization that everything could be understood from "conservation laws" and symmetry principals.”

Didier Sornette (1957) French scientist

Source: Why Stock Markets Crash - Critical Events in Complex Systems (2003), Chapter 5, Modeling Financial Bubbles And Market Crashes, p. 136

Law, Science

“These are, of course, some things which, for utility's sake, must be made of the same size in a small theatre, and a large one: such as the steps, curved cross-aisles, their parapets, the passages, stairways, stages, tribunals, and any other things which occur that make it necessary to give up symmetry so as not to interfere with utility.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book V, Chapter VI, Sec. 7

“Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way"…. This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics.”

John C. Baez (1961) American mathematician and mathematical physicist

Way, Nature, Problem, Light

“Is not the training of an artist a training in the due relation of one thing with another, and in the faculty of expressing that relation clearly; and, even more, a training in the faculty of disengaging from self the very essence of self — and passing that essence into other selves by so delicate means that none shall see how it is done, yet be insensibly unified? Is not the artist, of all men, foe and nullifier of partisanship and parochialism, of distortions and extravagance, the discoverer of that jack-o'-lantern — Truth; for, if Truth be not Spiritual Proportion I know not what it is. Truth it seems to me — is no absolute thing, but always relative, the essential symmetry in the varying relationships of life; and the most perfect truth is but the concrete expression of the most penetrating vision. Life seen throughout as a countless show of the finest works of Art; Life shaped, and purged of the irrelevant, the gross, and the extravagant; Life, as it were, spiritually selected — that is Truth; a thing as multiple, and changing, as subtle, and strange, as Life itself, and as little to be bound by dogma. Truth admits but the one rule: No deficiency, and no excess! Disobedient to that rule — nothing attains full vitality. And secretly fettered by that rule is Art, whose business is the creation of vital things.”

John Galsworthy (1867–1933) English novelist and playwright

Vague Thoughts On Art (1911)

Life, Men, Truth, Art

“The new architecture has suppressed monotonous repetition and destroyed the equality of two symmetrical halves. It does not allow for continuous repetition. A block of houses is as much a whole as an independent house. Balance and symmetry are two entirely different things. In place of symmetry the new architecture proposes a balanced relationship of unequal parts or parts which differ [in position, proportion, size and materials] in functional character.”

Theo van Doesburg (1883–1931) Dutch architect, painter, draughtsman and writer

Quote from his unpublished writing, 'Fundamental principles', 1930; as cited in Theo van Doesburg, Joost Baljeu, Studio Vista, London 1974, p. 203
1926 – 1931

Parting, Housing

“… the state of a really big system does not at all have to have the symmetry of the laws which govern it; in fact, it usually has less symmetry.”

Philip Warren Anderson (1923) American physicist

Source: More Is Different (1972), p. 395

Law

“Taking courage and looking forward from the standpoint of higher ideas born of the multiplication of the arts, they gave up huts and began to build houses with foundations, having brick or stone walls, and roofs of timber and tiles; next, observation and application led them from fluctuating and indefinite conceptions to definite rules of symmetry. Perceiving that nature had been lavish in the bestowal of timber and bountiful in stores of building material, they… embellished them with luxuries.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book II, Chapter I, Sec. 7

Art, Idea, Courage, Nature

“There were two problems which had to be faced. One was spatial and the other methodological. In the first case I had to do something about relational painting, i. e. the balancing of the various parts of the painting with and against each other. The obvious answer was symmetry – make it the same all over. The question still remained, though, of how to do this in depth. A symmetrical image or configuration symmetrically placed on a open ground is not balanced out in the illusionistic space. The solution I arrived at, and there are probably quite a few, although I only know of one other, color density, forces illusionistic space out of the painting at constant intervals by using a regulated pattern. The remaining problem was simply to find a method of paint application which followed and complemented the design solution. This was done by using the house painters technique and tools.”

Frank Stella (1936) American artist

Source: Quotes, 1960 - 1970, The Pratt lecture (1960), p. 114

Color, Question, Problem, Parting

“Supergravity theories generically contain non-compact global symmetry groups. The general rule is that the scalar fields of the theory in question parametrize a symmetric space. Thus, if the non-compact symmetry group is G, and its maximal compact subgroup is H, the scalar fields map the space-time into the symmetric space G/H, and the number of scalar fields is dim G – dim H. The first supergravity example of this type to be found, N = 4 supergravity is one of the most interesting. In this case there are two scalar fields and the symmetric space is SL(2,R)/SO(2).”

John Henry Schwarz (1941) American theoretical physicist

p. 1

Question, Time

“The good taste we speak of, which is that of literature, is not limited to what we call the sciences, but extends itself imperceptibly to other arts, such as architecture, painting, sculpture, and music. 'Tis the same discerning faculty which introduces universally the same elegance, the same symmetry, and the same order in the disposition of the parts; which inclines us to a noble simplicity, to natural beauties, and a judicious choice of ornaments. On the other hand, the depravation of taste in arts has been always a mark and consequence of the depravation of taste in literature. … The good taste of literature reaches also to public customs, and the manner of living. An habit of consulting the best rules upon one subject, naturally leads to the doing it also upon others.”

Charles Rollin (1661–1741) French historian

The Method of Teaching and Studying the Belles Lettres, Vol. I, The Third Edition (1742), Part II, Ch. 2: 'General Reflections upon what is called good Taste', pp. 45–46

Beauty, Art, Music, Literature

“I see in painters prose writers and poets. Rhyme, measure, and the turning of verses, which is indispensable and which gives them so much vigor, are analogous to the hidden symmetry, to the equilibrium at once wise and inspired, which governs the meeting or separation of lines and spaces, the echoes of color, etc….. but the beauty of verse does not consist of exactitude in obeying rules... It resides in a thousand secret harmonies and conventions which make up the power of poetry and which go straight to the imagination; in just the same way the happy choice of forms and the right understanding of their relationship act on the imagination in the art of painting.”

Eugène Delacroix (1798–1863) French painter

Quote in Delacroix's Journal of 19 September 1847; as cited in Artists on Art – from the 14th – 20th centuries, ed. by Robert Goldwater and Marco Treves; Pantheon Books, 1972, London, p. 229
1831 - 1863

Happiness, Secret, Beauty, Art

“By symmetry we mean the existence of different viewpoints from which the system appears the same. It is only slightly overstating the case to say that physics is the study of symmetry. The first demonstration of the power of this idea may have been by Newton, who may have asked himself the question: What if the matter here in my hand obeys the same laws as that up in the sky—that is, what if space and matter are homogeneous and isotropic?”

Philip Warren Anderson (1923) American physicist

Source: More Is Different (1972), p. 394

Law, Idea, Question, Study

“One reason nature pleases us is its endless use of a few simple principles: the cube-square law; fractals; spirals; the way that waves, wheels, trig functions, and harmonic oscillators are alike; the importance of ratios between small primes; bilateral symmetry; Fibonacci series, golden sections, quantization, strange attractors, path-dependency, all the things that show up in places where you don’t expect them…these rules work with and against each other ceaselessly at all levels, so that out of their intrinsic simplicity comes the rich complexity of the world around us. That tension—between the simple rules that describe the world and the complex world we see—is itself both simple in execution and immensely complex in effect. Thus exactly the levels, mixtures, and relations of complexity that seem to be hardwired into the pleasure centers of the human brain—or are they, perhaps, intrinsic to intelligence and perception, pleasant to anything that can see, think, create?—are the ones found in the world around us.”

John Barnes book Mother of Storms

Source: Mother of Storms (1994), pp. 470-471

Pleasure, World, Law, Way

“It's been on my mind – what would something be like if it were unbalanced? It's been a vexing question for a long time. But it took the experience of working with radical kinds of symmetry, not just a rectangle, but a diamond shape, as well as extreme extensions of shapes, before I finally came to the idea of everything being unbalanced, nothing vertical, nothing horizontal, nothing parallel. I came to the fact that unbalancing has its own order. In a peculiar way, it can still end up feeling symmetrical. I don't know but what the very nature of our response to art is experienced symmetrically.”

Kenneth Noland (1924–2010) American artist

Source: Color, Format and Abstract Art' (1977), pp. 99 – 105

Art, Way, Feeling, Idea

“Darwinian social theory gives us a glimpse of an underlying symmetry and logic in social relationships which, when more fully comprehended by ourselves, should revitalize our political understanding and provide the intellectual support for a science and medicine of psychology. In the process it should also give us a deeper understanding of the many roots of our suffering.”

Robert Trivers (1943) American evolutionary biologist and sociobiologist

Foreword to The Selfish Gene by Richard Dawkins (1976)

Understanding, Support, Suffering, Science

“The name philosopher, which meant originally 'lover of wisdom,' has come in some strange way to mean a man who thinks it is his business to explain everything in a certain number of large books. It will be found, I think, that in proportion to his colossal ignorance is the perfection and symmetry of the system which he sets up; because it is so much easier to put an empty room tidy than a full one.”

William Kingdon Clifford (1845–1879) English mathematician and philosopher

As quoted by A. D'Abro, The Evolution of Scientific Thought from Newton to Einstein https://archive.org/details/TheEvolutionOfScientificThought (1927)

Wisdom, Books, Way, Lovers

“Consistency is the enemy of enterprise, just as symmetry is the enemy of art.”

George Bernard Shaw (1856–1950) Irish playwright

As quoted in Bernard Shaw : The Lure of Fantasy (1991) by Michael Holroyd
1940s and later

Art

“I consider that Curie's Principle has two major consequences:
First: It shows that the class of processes which can be isolated for causal representation, not requiring the inference of external causes, is wider than the class of energetically closed systems. One-way processes in which the system loses energy can be isolable, in the sense that they can be given complete representation without taking their environment into account.
Second: It suggests the possibility of a geometrical physics treating 3D spatial relations, i. e., angles or lengths, as primary. Just as statistical mechanics, the theory of crystal symmetry, and Group theory in quantum mechanics, are useful without assumptions about forces, so Curie's principle, with an appropriate model, can determine the path of a one-way process without such assumptions…”

Lancelot Law Whyte (1896–1972) Scottish industrial engineer

Pierre Curie's Principle of One Way-Process (1970)

Way, Sense

“To let the reader complete the symmetry between words and do no more than suggest it.”

Joseph Joubert (1754–1824) French moralist and essayist

“Only the bad artists of the nineteenth century were frightened by the invention of photography; the good ones all welcomed it and used it. Degas liked it not only because it provided an accurate record, but because the snapshot showed him a means of escape from the classical rules of design. Through it he learnt to make a composition without the use of formal symmetry.”

Kenneth Clark (1903–1983) Art historian, broadcaster and museum director

Source: The Romantic Rebellion (1973), Ch. 13: Degas

“Recently I was visited by a very good friend who had just returned from a long walk in the woods, and I asked her what she had observed. “Nothing in particular,” she replied. I might have been incredulous had I not been accustomed to such responses, for long ago I became convinced that the seeing see little.
How was it possible, I asked myself, to walk for an hour through the woods and see nothing worthy of note? I who cannot see find hundreds of things to interest me through mere touch. I feel the delicate symmetry of a leaf. I pass my hands lovingly about the smooth skin of a silver birch, or the rough, shaggy bark of a pine. In spring I touch the branches of trees hopefully in search of a bud, the first sign of awakening Nature after her winter’s sleep. I feel the delightful, velvety texture of a flower, and discover its remarkable convolutions; and something of the miracle of Nature is revealed to me.”

Helen Keller (1880–1968) American author and political activist

Three Days to See (1933)

Feeling, Search, Spring, Flowers

“The human brain has left and right brain symmetry with its own nature and can process information which initially appears to have no pattern or order. However, the brain has the ability to process visual information much more efficiently.”

Tony Buzan (1942–2019) British psychologist

The Mind Map Book, Buzan and Buzan (1991)

Nature, Appearance

“There is true religion in that man who, instead of endeavoring to perfect but one department of his nature, makes his physical, mental, social, and moral life, equal. Cultivate your physical nature, perfect your life, and in that proportion your soul will be perfect. Cultivate strength, vigor, power, manliness, and symmetry, and in that proportion the soul can think greater thoughts.”

Cora L. V. Scott (1840–1923) American spiritualist, writer

“The Religion of Life” (1858)

Life, Religion, Soul, Nature

“A Right Mind, and Generous Affection, [has] more Beauty and Charm, than all other Symmetrys in the World besides.”

Anthony Ashley-Cooper, 3rd Earl of Shaftesbury (1671–1713) English politician and Earl

Vol. 2, p. 209; "Miscellany III".
Characteristicks of Men, Manners, Opinions, Times (1711)

World, Beauty

“Luther's Qualifications. Luther had a rare combination of gifts for a Bible translator: familiarity with the original languages, perfect mastery over the vernacular, faith in the revealed word of God, enthusiasm for the gospel, unction of the Holy Spirit. A good translation must be both true and free, faithful and idiomatic, so as to read like an original work. This is the case with Luther's version. Besides, he had already acquired such fame and authority that his version at once commanded universal attention.
His knowledge of Greek and Hebrew was only moderate, but sufficient to enable him to form an independent judgment. What he lacked in scholarship was supplied by his intuitive genius and the help of Melanchthon. In the German tongue he had no rival. He created, as it were, or gave shape and form to the modern High German. He combined the official language of the government with that of the common people. He listened, as he says, to the speech of the mother at home, the children in the street, the men and women in the market, the butcher and various tradesmen in their shops, and, "looked them on the mouth," in pursuit of the most intelligible terms. His genius for poetry and music enabled him to reproduce the rhythm and melody, the parallelism and symmetry, of Hebrew poetry and prose. His crowning qualification was his intuitive insight and spiritual sympathy with the contents of the Bible.
A good translation, he says, requires "a truly devout, faithful, diligent, Christian, learned, experienced, and practiced heart."”

Philip Schaff (1819–1893) American Calvinist theologian

Luther's competence as a Bible translator

Women, Men, God, Children

“Men achieve tranquillity through moderation in pleasure and through the symmetry of life. Want and superfluity are apt to upset them and to cause great perturbations in the soul. The souls that are rent by violent conflicts are neither stable nor tranquil. One should therefore set his mind upon the things that are within his power, and be content with his opportunities, nor let his memory dwell very long on the envied and admired of men, nor idly sit and dream of them. Rather, he should contemplate the lives of those who suffer hardship, and vividly bring to mind their sufferings, so that your own present situation may appear to you important and to be envied, and so that it may no longer be your portion to suffer torture in your soul by your longing for more. For he who admires those who have, and whom other men deem blest of fortune, and who spends all his time idly dreaming of them, will be forced to be always contriving some new device because of his [insatiable] desire, until he ends by doing some desperate deed forbidden by the laws. And therefore one ought not to desire other men's blessings, and one ought not to envy those who have more, but rather, comparing his life with that of those who fare worse, and laying to heart their sufferings, deem himself blest of fortune in that he lives and fares so much better than they. Holding fast to this saying you will pass your life in greater tranquillity and will avert not a few of the plagues of life—envy and jealousy and bitterness of mind.”

Democritus Ancient Greek philosopher, pupil of Leucippus, founder of the atomic theory

Source Book in Ancient Philosophy (1907), The Golden Sayings of Democritus

Life, Men, Pleasure, Jealousy

“When one is involved in the discovery and discernment of the marvelous law and symmetries that shape the phenomenal world, one cannot but be struck by the silent and unfathomable intelligence that seems to pervade the Cosmos.”

Varadaraja V. Raman (1932) American physicist

page 142
Truth and Tension in Science and Religion

World, Law, Intelligence

“We all know what the negro has been as a slave. In this relation we have his experience of two hundred and fifty years before us, and can easily know the character and qualities he has developed and exhibited during this long and severe ordeal. In his new relation to his environments, we see him only in the twilight of twenty years of semi-freedom; for he has scarcely been free long enough to outgrow the marks of the lash on his back and the fetters on his limbs. He stands before us, today, physically, a maimed and mutilated man. His mother was lashed to agony before the birth of her babe, and the bitter anguish of the mother is seen in the countenance of her offspring. Slavery has twisted his limbs, shattered his feet, deformed his body and distorted his features. He remains black, but no longer comely. Sleeping on the dirt floor of the slave cabin in infancy, cold on one side and warm on the other, a forced circulation of blood on the one side and chilled and retarded circulation on the other, it has come to pass that he has not the vertical bearing of a perfect man. His lack of symmetry, caused by no fault of his own, creates a resistance to his progress which cannot well be overestimated, and should be taken into account, when measuring his speed in the new race of life upon which he has now entered.”

Frederick Douglass (1818–1895) American social reformer, orator, writer and statesman

1880s, The Future of the Colored Race (1886)

Life, Birth, Sleep, Freedom

“To find out where the origin of symmetry is would be to find out if God exists.”

Matthew Bellamy (1978) English singer-songwriter

Rock Sound Spain magazine, 2001-07-31

God

“The point of departure is the measurement problem, as it appears in physics; the manner in which measurements allow us to characterize subsystems; the role of such subsystems as tools in system analysis; and the relationships existing between different ways of perceiving or interacting with the same system. Our conclusions are: (1) there exists no universal family of of analytic units appropriate for the treatment of all interactions; (2) there are on the contrary many such families of analytic units, all of which are equally “real” and entitled to be treated on the same footing; (3) the appropriate use of natural interactions can enormously extend the class of physical observables accessible to us; (4) the concept of a model must be formulated, in its most general terms, as the sharing of a subsystem by two otherwise distinct systems, capable of imposing the same dynamic on an appropriate system with which they can both interact. We establish these results through a variety of terminologies which turn out to be equivalent: stability, invariance, symmetry, homeostasis.”

Robert Rosen (1934–1998) American theoretical biologist

Introduction; Quoted in: " Fundamentals of Measurement and Representation of Natural Systems by Robert Rosen http://www.panmere.com/?page_id=15" at panmere.com. <br class="br">Fundamentals of measurement and representation of natural systems. (1978)

Family, Way, Departure, Nature

“The reason is not to glorify "bit chasing"; a more fundamental issue is at stake here: Numerical subroutines should deliver results that satisfy simple, useful mathematical laws whenever possible. […] Without any underlying symmetry properties, the job of proving interesting results becomes extremely unpleasant. The enjoyment of one's tools is an essential ingredient of successful work.”

Donald Ervin Knuth book The Art of Computer Programming

Vol. II, Seminumerical Algorithms, Section 4.2.2 part A, final paragraph [Italics in source]
The Art of Computer Programming (1968–2011)

Law, Mathematics, Success

“In making the four-channel video work Dachau, my experience as a weaver directly influenced the basic structuring of the work. The content itself was taped in 1974 at the former concentration camp Dachau. The symmetry of the architecture and the present ambience of the space were the focus of the recordings. The past was recorded only insofar as the sounds of the voices of the present commingled with the feeling absorbed in the wood and revealed in the structure of forms which has no amount of time can erase.”

Beryl Korot (1945) American artist

Source: Dachau 1974, by Beryl Korot, p. 75

Feeling, Time, Past

“Strong, weak and electromagnetic interaction are evidently part of a grand unified theory. These temperatures are today quite inaccessible. They were achieved only in the earliest moments of the Big Bang. Since then, the universe has congealed, losing its symmetry.”

Sheldon L. Glashow (1932) American theoretical physicist

Source: The Charm of Physics (1991), p. 244

Strong, Universe, Parting

“Architecture depends on Order, Arrangement, Eurythmy, Symmetry, Propriety, and Economy.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter II "The Fundamental Principles of Architecture" Sec. 1

Dependency

“One of the chief chores in the next economy is to restore the symmetry of knowledge.”

Kevin Kelly (1952) American author and editor

Out of Control: The New Biology of Machines, Social Systems and the Economic World (1995), New Rules for the New Economy: 10 Radical Strategies for a Connected World (1999)

Knowledge

“Symmetry is overrated. Overrated is symmetry.”

Larry Wall (1954) American computer programmer and author, creator of Perl

[6vhq4r%24a6i@kiev.wall.org, 1998]
Usenet postings, 1998

“Civilization is measured in no small part by these standards. The famous beauty and symmetry of the Greek race in its prime was due in no small part to their general participation in athletic games. This meant development.”

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

1920s, The Democracy of Sports (1924)

Beauty, Game, Parting

“When Physicists speak of "beauty" in their theories, they really mean that their theory possesses at least two essential features: 1. A unifying symmetry 2. The ability to explain vast amounts of experimental data with the most economical mathematical expressions.”

Michio Kaku book Hyperspace

Source: Hyperspace (1995), Ch.5 Quantum Heresy

Beauty, Mathematics

“Much of the skill of the true mathematical physicist and of the mathematical astronomer consists in the power of adapting methods and results carried out on an exact mathematical basis to obtain approximations sufficient for the purposes of physical measurements. It might perhaps be thought that a scheme of Mathematics on a frankly approximative basis would be sufficient for all the practical purposes of application in Physics, Engineering Science, and Astronomy, and no doubt it would be possible to develop, to some extent at least, a species of Mathematics on these lines. Such a system would, however, involve an intolerable awkwardness and prolixity in the statements of results, especially in view of the fact that the degree of approximation necessary for various purposes is very different, and thus that unassigned grades of approximation would have to be provided for. Moreover, the mathematician working on these lines would be cut off from the chief sources of inspiration, the ideals of exactitude and logical rigour, as well as from one of his most indispensable guides to discovery, symmetry, and permanence of mathematical form. The history of the actual movements of mathematical thought through the centuries shows that these ideals are the very life-blood of the science, and warrants the conclusion that a constant striving toward their attainment is an absolutely essential condition of vigorous growth. These ideals have their roots in irresistible impulses and deep-seated needs of the human mind, manifested in its efforts to introduce intelligibility in certain great domains of the world of thought.”

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

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), pp. 285-286; Cited in: Moritz (1914, 229): Mathematics and Science.

Life, World, History, Intelligence

“The design of a temple depends on symmetry, the principles of which must be most carefully observed by the architect.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book III, Chapter I, Sec. 1

Dependency

“Now, what about this negro equality of which we hear so much, in and out of Congress? It is claimed by the Democrats of today, that Jefferson has uttered an untruth in the declaration of principles which underlie our government. I still abide by the democracy of Jefferson, and avow my belief that all men are created equal. Equal how? Not in physical strength, not in symmetry of form and proportion, not in graceful of motion, or loveliness of feature, not in mental endowment, moral susceptibility, and emotional power. Not socially equal, not of necessity politically equal. Not this, but every human being equally entitled to his life, his liberty, and the fruit of his toil. The Democratic Party deny this fundamental doctrine of our government, and say that there is a certain class of human beings which have no rights. If you maliciously kill them, it is no murder. If you take away their liberty, it is no crime. If you deprive them of their earnings, it is no theft. No rights which another is bound to regard. Was there ever so much diabolism compressed into one sentence? Why do |the Democrats come to us with their complaints about the negroes? I for one feel no responsibility in the matter. I did not create them; was not consulted.”

Owen Lovejoy (1811–1864) American politician

As quoted in His Brother's Blood: Speeches and Writings, 1838&ndash;64 https://books.google.com/books?id=qMEv8DNXVbIC&pg=PA177 (2004), edited by William Frederick Moore and Jane Ann Moore, p. 177 <br class="br">1850s, The Fanaticism of the Democratic Party (February 1859)

Life, Men, Feeling, Democracy

“Symmetry is a vast subject, significant in art and nature. Mathematics lies at its root, and it would be hard to find a better one on which to demonstrate the working of the mathematical intellect.”

Hermann Weyl (1885–1955) German mathematician

Symmetry (1952)

Art, Mathematics, Nature

“If there is no connection between quarks and leptons, since quarks make up the proton, then the balance of the proton and electron charge is just a remarkable coincidence. It seems impossible for any thinking person to be satisfied with coincidence as an explanation. Some principle must relate the charges of the quarks and the leptons. What is it? A fancier way of saying it, and more or less equivalent, is that for the electroweak theory to make sense up to arbitrarily high energies, the symmetries on which it is based must survive quantum corrections.”

Chris Quigg (1944) American physicist

Nature's greatest puzzles. http://arxiv.org/PS_cache/hep-ph/pdf/0502/0502070v1.pdf SLAC Summer Institute 2004, p. 9.

Way, Thinking, Sense, Personality

“By ‘successful socialization’ we mean the establishment of a high degree of symmetry between objective and subjective reality.”

Peter L. Berger book The Social Construction of Reality

Source: The Social Construction of Reality, 1966, p. 163

Reality, Success

“God, say some philosophers, manifests himself in the sublunary world in particular beauties, truths and acts of benevolence; properly, the values should be conjoined to shadow their identity in the godhead, but this happens so infrequently that one must suppose divinity condones a kind of diabolic fracture or else, and perhaps my book is already giving some hint of this, he demonstrates his ineffable freedom through contriving at times a wanton inconsistency. If this is so, we need not wonder at Messalina’s failure to match her beauty with a love of truth and goodness. She was a chronic liar and she was thoroughly bad. But her beauty, we are told, was a miracle. The symmetry of her body obeyed all the golden rules of the mystical architects, her skin was without even the most minuscule flaw and it glowed as though gold had been inlaid behind translucent ivory, her breasts were full and yet pertly disdained earth’s pull, the nipples nearly always erect, and visibly so beneath her byssinos, as in a state of perpetual sexual excitation, the areolas delicately pigmented to a kind of russet. The sight of her weaving bare white arms was enough, it is said, to make a man grit his teeth with desire to be encircled by them; the smooth plain of her back, tapering to slenderness only to expand lusciously to the opulence of her perfect buttocks, demanded unending caresses.”

Anthony Burgess (1917–1993) English writer

Fiction, The Kingdom of the Wicked (1985)

Love, God, Truth, Books

“By the time of his Fourth String Quartet, inversional symmetry had become as fundamental a premise of Bartók's harmonic language as it is of the twelve-tone music of Schoenberg, Berg, and Webern. Neither he nor they ever realized that this connection establishes a profound affinity between them in spite of the stylistic features that so obviously distinguish his music from theirs…Nowhere does he [Bartók] recognize the communality of his harmonic language with that of the twelve-tone composers that is implied in their shared premise of the harmonic equivalence of inversionally symmetrical pitch-class relations.”

George Perle (1915–2009) American composer

Pages 46-47
The Listening Composer

Music, Communication, Time

“Under the roof of one controversial assumption about physics, we discuss five big questions that can be addressed using concepts from a modern understanding of digital informational processes. The assumption is called finite nature. The digital mechanics model is obtained by applying the assumption to physics. The questions are as follows: 1. What is the origin of spin? 2. Why are there symmetries and CPT (charge conjugation, parity, and time reversal)? 3. What is the origin of length? 4. What does a process model of motion tell us? 5. Can the finite nature assumption account for the efficacy of quantum mechanics?”

Edward Fredkin (1934) American physicist and computer scientist, a pioneer of digital physics

Five big questions with pretty simple answers, IBM Journal of Research and Development, 48, 1, January 2004, 31–45 https://ieeexplore.ieee.org/abstract/document/5388918/,

Understanding, Question, Nature, Time

“The universality, invariance, and elegance of principles governing the universe may be reflected in principles of the minds that have evolved in that universe - provided that the mental principles are formulated with respect to the abstract spaces appropriate for the representation of biologically significant objects and their properties. (1) Positions and motions of objects conserve their shapes in the geometrically fullest and simplest way when represented as points and connecting geodesic paths in the six-dimensional manifold jointly determined by the Euclidean group of three· dimensional space and the symmetry group of each object. (2) Colors of objects attain constancy when represented as points in a three-dimensional vector space in which each variation in natural illumination is cancelled by application of its inverse from the three-dimensional linear group of terrestrial transformations of the invariant solar source. (3) Kinds of objects support optimal generalization and categorization when represented, in an evolutionarily shaped space of possible objects, as connected regions with associated weights determined by Bayesian revision of maximum entropy priors”

Roger Shepard (1929) American psychologist

R. N. Shepard, (1994). "Perceptual-cognitive universals as reflections of the world." Psychonomic Bulletin and Review, 1, 2–28.

Color, Way, Optimism, Support

“Physicists describe the two properties of physical laws—that they do not depend on when or where you use them—as symmetries of nature. By this usage physicists mean that nature treats every moment in time and every location in space identically—symmetrically—by ensuring that the same fundamental laws are in operation. Much in the same manner that they affect art and music, such symmetries are deeply satisfying; they highlight an order and coherence in the workings of nature. The elegance of rich, complex, and diverse phenomena emerging from a simple set of universal laws is at least part of what physicists mean when they invoke the term "beautiful."”

Brian Greene book The Elegant Universe

The Elegant Universe (1999) Ch. 7 The "Super" in Superstrings.

Law, Beauty, Art, Music

“Geometry… is of much assistance in architecture, and in particular it teaches us the use of the rule and compasses, by which especially we acquire readiness in making plans for buildings in their grounds, and rightly apply the square, the level, and the plummet. By means of optics… the light in buildings can be drawn from fixed quarters of the sky. …Difficult questions involving symmetry are solved by means of geometrical theories and methods.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book I, Chapter I, Sec. 4

Question, Light

“These rules for symmetry were established by Hermogenes, who was also the first to devise the principal of the pseudodipteral octastyle.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book III, Chapter III, Sec. 8

“Your borrowers of books—those mutilators of collections, spoilers of the symmetry of shelves, and creators of odd volumes.”

Charles Lamb book Essays of Elia

The Two Races of Men.
Essays of Elia (1823)

Books

“Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness.”

Eric Temple Bell (1883–1960) mathematician and science fiction author born in Scotland who lived in the United States for most of his li…

As quoted in 777 Mathematical Conversation Starters http://books.google.co.in/books?id=JNbKURWmODkC&pg=PA172 (2002) by John de Pillis, p. 172

Art, Feeling, Mathematics, Sense

“When it appears that a work has been carried out sumptuously, the owner will be the person to be praised for the great outlay which ha has authorized; when delicately, the master workmen will be approved for his execution; but when proportions and symmetry lend it an imposing effect, then the glory of it will belong to the architect.”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book VI, Chapter VIII, Sec. 9

Appearance, Personality

“Ken Noland has put things in the center [of the painting] and I'll use a symmetric pattern, but we use symmetry in a different way. It's non-relational. In the newer American painting [in contrast to European geometric art] we strive to get the thing in the middle, and symmetrical, but just to get a kind of force, just to get the thing on the canvas. The balance factor isn't important.”

Frank Stella (1936) American artist

Source: Quotes, 1960 - 1970, Questions to Stella and Judd' - September 1966, p. 118

Art, Way, Painting

“Ken Noland would use concentric circles; he'd want to get them in the middle [of the painting] because it's the easiest way to get them there, and he want them there in the front, on the surface of the canvas. If you're that much involved with the surface of anything, you're bound to find symmetry the most natural means.”

Frank Stella (1936) American artist

Source: Quotes, 1960 - 1970, Questions to Stella and Judd' - September 1966, p. 118

Way, Nature, Painting

“The room was not a room to elevate the soul. Louis XIV, to pick a name at random, would not have liked it, would have found it not sunny enough, and insufficiently full of mirrors. He would have desired someone to pick up the socks, put the records away, and maybe burn the place down. Michelangelo would have been distressed by its proportions, which were neither lofty nor shaped by any noticeable inner harmony or symmetry, other than that all parts of the room were pretty much equally full of old coffee mugs, shoes and brimming ashtrays, most of which were now sharing their tasks with each other. The walls were painted in almost precisely that shade of green which Raffaello Sanzio would have bitten off his own right hand at the wrist rather than use, and Hercules, on seeing the room, would probably have returned half an hour later armed with a navigable river. It was, in short, a dump, and was likely to remain so for as long as it remained in the custody of Mr Svlad, or 'Dirk', Gently, né Cjelli.”

Douglas Adams The Long Dark Tea-Time of the Soul

Source: The Long Dark Tea-Time of the Soul (1988), Ch. 3

Shoe, Soul, Coffee, Parting

“In the table—and in nature—we find (leaving aside the antineutrino) fifteen fundamental fermions, with diverse strong, weak, and electromagnetic charges. …They are so closely related by symmetry transformations that they are, so to speak, no more than different faces of the same cube.”

Frank Wilczek (1951) physicist

Longing for the Harmonies: Themes and Variations from Modern Physics (1987)

Nature, Strong

“He thought about spiders, twisting thread into beautiful symmetry, taming chaos with ordered nets that greeted the dawn, hung with globes of dew that caught and held cores of sunlight, and tiny images of the world.”

Nina Kiriki Hoffman (1955) American writer

Source: The Thread That Binds the Bones (1993), Chapter 21 (p. 297)

World, Beauty

“In the early 1990s, I came to suspect that the quest for a unified theory is religious rather than scientific. Physicists want to show that all things came from one thing: a force, or essence, or membrane wriggling in eleven dimensions, or something that manifests perfect mathematical symmetry. In their search for this primordial symmetry, however, physicists have gone off the deep end, postulating particles and energies and dimensions whose existence can never be experimentally verified.”

John Horgan (journalist) (1953) American science journalist

(2002 wager, 18 year duration) [Bet 12 (John Horgan vs. Michio Kaku), longbets.org, http://longbets.org/12/]

Search, Mathematics, Perfection

“The Higgs boson is an essential part of the analogy to the Meissner effect in superconductivity that leads us to an excellent understanding of the masses of the electroweak gauge bosons W± and Z0 as consequences of electroweak symmetry breaking.”

Chris Quigg (1944) American physicist

Visions- the coming revolutions of particle physics. http://xxx.uni-augsburg.de/pdf/hep-ph/0204075v1 2002, p. 5.

Understanding, Gauge, Parting

“The church and the world alike demand that those who profess to love the Lord should be careful to love their brethren also. It is for them to have in essentials unity, in non-essentials diversity, in all things charity. Only so can the church realize the ideal of its Divine Founder, and foreshadow its future excellence and beauty. Only so can this spiritual structure be celestial and glorious, revealing in all its fair proportions from dome and turret, from glittering spires and airy traceries, its marvelous symmetry and oneness, while at the same time it swells from every organ pipe, and chants in every choral anthem the praises of Him whose essence is love, and whose being is characterized by unity.”

John McClellan Holmes (1834–1911) US Christian minister and author

Source: Dictionary of Burning Words of Brilliant Writers (1895), P. 112.

Love, World, Beauty, Time

“The phase transition paradigm: The standard model of fundamental physics incorporates, as one of its foundational principles, the idea that “empty space” or “vacuum” can exist in different phases, typically associated with different amounts of symmetry. Moreover, the laws of the standard model itself suggest that phase transitions will occur, as functions of temperature. Extensions of the standard model to build in higher symmetry (gauge unification or especially supersymmetry) can support effective vacua with radically different properties, separated by great distance or by domain walls. That would be a form of failure of universality, in our sense, whose existence is suggested by the standard model.”

Frank Wilczek (1951) physicist

"Multiversality" (2013)

Law, Idea, Failure, Support

“Each of the most basic physical laws that we know corresponds to some invariance, which in turn is equivalent to a collection of changes which form a symmetry group. …whilst leaving some underlying theme unchanged. …for example, the conservation of energy is equivalent to the invariance of the laws of motion with respect to translations backwards or forwards in time… the conservation of linear momentum is equivalent to the invariance of the laws of motion with respect to the position of your laboratory in space, and the conservation of angular momentum to an invariance with respect to directional orientation… discovery of conservation laws indicated that Nature possessed built-in sustaining principles which prevented the world from just ceasing to be. There were fewer roles for the Deity to play…”

John D. Barrow (1952–2020) British scientist

New Theories of Everything (2007)

World, Law, Nature, Change

“The symmetry of form attainable in pure fiction can not so readily be achieved in a narration essentially having less to do with fable than with fact.”

Herman Melville book Billy Budd, Sailor

Source: Billy Budd, the Sailor (1891), Ch. 28
Context: The symmetry of form attainable in pure fiction can not so readily be achieved in a narration essentially having less to do with fable than with fact. Truth uncompromisingly told will always have its ragged edges...

“Hundreds of years ago, natural theologians tried to impress their readers with stories of the wondrous symmetries of Nature; now we see that, ironically, it is the departures from those symmetries that makes life possible. It is upon the flaws of Nature, not the laws of Nature, that the possibility of our existence hinges. …The laws and constants of Nature are features that enforce uniformity and simplicity, while initial conditions and symmetry breakings permit complexity and diversity.”

John D. Barrow (1952–2020) British scientist

The Artful Universe (1995)

Life, Law, Departure, Nature

John D. Barrow (1952–2020) British scientist

The Book of Universes: Exploring the Limits of the Cosmos (2011)
Context: Aristotle believed that the world did not come into being at some time in the past; it had always existed and it would always exist, unchanged in essence for ever. He placed a high premium on symmetry and believed that the sphere was the most perfect of all shapes. Hence the universe must be spherical.... An important feature of the spherical shape... was the fact that when a sphere rotates it does not cut into empty space where there is no matter and it leaves no empty space behind.... A vacuum was impossible. It could no more exist than an infinite physical quantity.... Circular motion was the most perfect and natural movement of all.<!--ch. 1, pp. 12-13

World, Time, Past

“The progress of the sciences toward theories of fundamental unity, cosmic symmetry (as in the unified field theory) — how do such theories differ, in the end, from that unity which Plato called “unspeakable” and “indiscribable,” the holistic knowledge shared by so many peoples of the earth, Christians included, before the advent of the industrial revolution made new barbarians of the peoples of the West?”

Peter Matthiessen book The Snow Leopard

The Snow Leopard (1978)
Context: The progress of the sciences toward theories of fundamental unity, cosmic symmetry (as in the unified field theory) — how do such theories differ, in the end, from that unity which Plato called “unspeakable” and “indiscribable,” the holistic knowledge shared by so many peoples of the earth, Christians included, before the advent of the industrial revolution made new barbarians of the peoples of the West? In the United States, before spiritualist foolishness at the end of the last century confused mysticism with “the occult” and tarnished both, William James wrote a master work of metaphysics; Emerson spoke of “the wise silence, the universal beauty, to which every part and particle is equally related, the eternal One . . .”; Melville referred to “that profound silence, that only voice of God”; Walt Whitman celebrated the most ancient secret, that no God could be found “more divine than yourself.” And then, almost everywhere, a clear and subtle illumination that lent magnificence to life and peace to death was overwhelmed in the hard glare of technology. Yet that light is always present, like the stars of noon. Man must perceive it if he is to transcend his fear of meaningless, for no amount of “progress” can take its place. We have outsmarted ourselves, like greedy monkeys, and now we are full of dread.

People, Knowledge, Science

“Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.”

Aristotle book Metaphysics

Book XIII, 1078a.33
Metaphysics

Beauty, Error, Mathematics, Science

“I wrote Fearful Symmetry during the Second World War, and hideous as the time was, it provided some parallels with Blake's time which were useful for understanding Blake's attitude to the world.”

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

Preface of the 1969 edition of Fearful Symmetry : A Study of William Blake (1947)
"Quotes", Fearful Symmetry : A Study of William Blake (1947)
Context: I wrote Fearful Symmetry during the Second World War, and hideous as the time was, it provided some parallels with Blake's time which were useful for understanding Blake's attitude to the world. Today, now that reactionary and radical forces alike are once more in the grip of the nihilistic psychosis that Blake described so powerful in Jerusalem, one of the most hopeful signs is the immensely increased sense of the urgency and immediacy of what Blake had to say.

War, World, Fear, Understanding

“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]

“Scarcely any specialist of to-day is really master of all the work which has been done in his own comparatively small field. Facts and their classification have been accumulating at such a rate that nobody seems to have leisure to recognise the relations of sub-groups to the whole. It is as if individual workers... were bringing their stones to one great building and piling them on and cementing them... without regard to any general plan... only where some one has placed a great corner stone... the building... rises... more rapidly... till it... is stopped for want of side support. Yet this great structure... possesses a symmetry and unity... in scientific method. The smallest group of facts, if properly classified and logically dealt with, ...has its proper place... wholly independent of the individual workman who... shaped it. Even when two men work unwittingly at the same stone they will but modify and correct each other... In the face of all this enormous progress... when in all civilised lands men are applying the scientific method... the goal of science is and must be infinitely distant.”

Karl Pearson book The Grammar of Science

Introductory
The Grammar of Science (1900)

Men, Support, Distant, Relation ships

“The Key! it is of wonderful construction, with its infinity of combination, and its unlimited capacity to fit every lock. … it is the great master-key which unlocks every door of knowledge and without which no discovery which deserves the name — which is law, and not isolated fact — has been or ever can be made. Fascinated by its symmetry the geometer may at times have been too exclusively engrossed with his science, forgetful of its applications; he may have exalted it into his idol and worshipped it; he may have degraded it into his toy... when he should have been hard at work with it, using it for the benefit of mankind and the glory of his Creator.”

Benjamin Peirce (1809–1880) American mathematician

Ben Yamen's Song of Geometry (1853)

Law, Knowledge, Science, Time

“Aristotle believed that the world did not come into being at some time in the past; it had always existed and it would always exist, unchanged in essence for ever. He placed a high premium on symmetry and believed that the sphere was the most perfect of all shapes. Hence the universe must be spherical. …An important feature of the spherical shape… was the fact that when a sphere rotates it does not cut into empty space where there is no matter and it leaves no empty space behind. …A vacuum was impossible. It could no more exist than an infinite physical quantity. …Circular motion was the most perfect and natural movement of all.”

John D. Barrow (1952–2020) British scientist

The Book of Universes: Exploring the Limits of the Cosmos (2011)

World, Nature, Universe, Time

“To me the most important thing in composition is disparity. Thus black and white are the strong colors, with a spot of red to mark the other corner of a triangle which is by no means equilateral, isosceles, or right. To vary this still further use yellow, then, later, blue. Anything suggestive of symmetry is decidedly undesirable, except possibly where an approximate symmetry is used in a detail to enhance the inequality with the general scheme.”

Alexander Calder (1898–1976) American artist

1940s, Excerpt, A Propos of Measuring a Mobile (1943)

Color, Strong

“When most people think of nature, they want to look for perfection and for symmetry and balance, ... But if you really pay attention you are going to see that what actually makes nature tick are the imbalances, the imperfections, the asymmetries.”

Marcelo Gleiser (1959) Brazilian physicist

" Physicist Marcelo Gleiser Asks the Big Questions" https://news.dartmouth.edu/news/2011/08/physicist-marcelo-gleiser-asks-big-questions, dartmouth.edu (August 26, 2011)

People, Nature, Thinking, Perfection