Quotes about dimension
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“Man's position in the world is defined by the fact that in every dimension of his being and behavior he finds himself at every moment between two boundaries. This condition appears as the formal structure of our existence, filled always with different contents in life's diverse provinces, activities, and destinies. We feel that the content and value of every hour stands between a higher and a lower; every thought between a wiser and a more foolish; every possession between a more extended and a more limited; every deed between a greater and a lesser measure of meaning, adequacy, and morality.”

Georg Simmel (1858–1918) German sociologist, philosopher, and critic

Source: The View of Life (1918), p. 1. Opening line of first essay "Life as Transcendence"

Life, World, Behavior, Feeling

“Prehistoric images speak to us more evocatively than any other element of the archeological record: colorful, vibrant paintings of horses, of bison, of a panoply of animals and humans that often seem alive and in motion. And yet there is a dimension of unreality about them… The images seem plucked from life… often arranged chaotically to our eye, frequently superimposed… sometimes apparently incomplete. …There is an enigma in these images, a profound challenge to our understanding of the past.”

Richard Leakey (1944) Kenyan paleoanthropologist, conservationist, and politician

Origins Reconsidered: In Search of What Makes Us Human (1992)

Life, Color, Understanding, Past

“[My audiences] discover they are producing a tonal dimension of the music which interacts melodically, rhythmically, and spatially with the tones in the room. Tones ‘dance’ in the immediate space of their body, around them like a sonic wrap, cascade inside ears, and out to space in front of their eyes … Do not be alarmed! Your ears are not behaving strange or being damaged! … these virtual tones are a natural and very real physical aspect of auditory perception, similar to the fusing of two images resulting in a third three dimensional image in binocular perception… I want to release this music which is produced by the listener…”

Maryanne Amacher (1938–2009) Composer and installation artist

Quoted in: " Maryanne Amacher, Synaptic Island http://datagarden.org/5483/maryanne-amacher-synaptic-island/," on datagarden.org, 2015.

Music, Nature, Dance

“A Logarithmic Table is a small table by the use of which we can obtain a knowledge of all geometrical dimensions and motions in space, by a very easy calculation. It is deservedly called very small, because it does not exceed in size a table of sines; very easy, because by it all multiplications, divisions, and the more difficult extractions of roots are avoided; for by only a very few most easy additions, subtractions, and divisions by two, it measures quite generally all figures and motions.”

John Napier (1550–1617) Scottish mathematician

The Construction of the Wonderful Canon of Logarithms (1889)

Knowledge

“I arrived at as an undergraduate with two driving passions: a consuming interest for a politics of justice grounded in a Christian theology and acting, as a ‘revelation of the treasures of the human soul’ not as a form of exhibitionism. My search for justice grew out of the pain I experienced when I saw the ridicule my malformed brother elicited. I became aware of the evil that is prejudice, a form of injustice. My urge to redress this prejudice took a more social dimension during my years as a boarder at St Dominic’s Convent, where the great Barbara Hogan matriculated a year later than me though I only got acquainted with her at Wits.”

Angelique Rockas South African actress and founder of Internationalist Theatre, London

The South African Interview (August 8, 2011)

Pain, Justice, Soul, Search

“(Jokingly) Sex in ten dimensions is impossible… topologically.”

Leonard Susskind (1940) American physicist

Lecture "Cosmic landscape and illusion of intelligent design", DESY Hamburg (28 September, 2006).

Sex

“One thing is sure – we have to transform the three-dimensional world of objects into the two-dimensional world of the canvas... To transform three into two dimensions is for me an experience full of magic in which I glimpse for a moment that fourth dimension which my whole being is seeking.”

Max Beckmann (1884–1950) German painter, draftsman, printmaker, sculptor and writer

Source: 1930s, On my Painting (1938), p. 16

World

“Although the human rights dimension of trade is obvious, investors and corporations think that they can continue working in a human-rights-free zone.”

Alfred de Zayas (1947) American United Nations official

Report of the Independent Expert on the promotion and protection of all human rights, civil, political, economic, social and cultural rights, including the right to development https://documents-dds-ny.un.org/doc/UNDOC/GEN/G16/151/19/PDF/G1615119.pdf?OpenElement. 2016, Report submitted to the UN Human Rights Council

Thinking

“Another great writer who led me on It this stage was Bankim Chandra Chatterjee. I had read all his novels but had never been able to understand why he had been honoured as a rishi. I myself was a novelist and had already written several humane stories. I thought that a novelist dealt with the dimensions of human character and mapped the heights it could scale and the depths to which it could sink. Why should we foist the title of a rishi on this poor fellow? That way rishis will be available a dime a dozen. My doubts about Bankim Chandra being a rishi were removed when I read the second volume of his Collected Works in Bengali. His insights into the innermost core of Hindu culture were a revelation. His Ramayaner Alochona made me see the monstrosities of modern Indology, more than ever before. I immediately translated this masterpiece into Hindi.”

Sita Ram Goel (1921–2003) Indian activist

How I became a Hindu (1982)

Way, Understanding, Reading

“The dimensions of this mercy are above my thoughts. It is for aught I know, a crowning mercy.”

Oliver Cromwell (1599–1658) English military and political leader

Letter to William Lenthall, Speaker of the House of Commons (4 September 1651)

“Ideology is not a dreamlike illusion that we build to escape insupportable; in its basic dimension, it is a fantasy-construction which serves as a support for our reality itself; an illusion which structures our effective, real social relations and thereby masks some insupportable, real, impossible kernel.”

Slavoj Žižek book The Sublime Object of Ideology

45
The Sublime Object of Ideology (1989)

Support, Reality

“Elementarism has been born partly in reaction to an over-dogmatic and often narrow-minded application of NeoPlasticism [a critic on his former artist-companion Piet Mondrian, partly as its consequence but ultimately from what is primarily a radical correction of Neo-plastic ideas. Elementarism rejects the demands of pure statics which led to sterility and to the laming of creative potentialities. Instead of denying Time and Space, Elementarism acknowledge these elements to be the most elementary means for creating a new plastic expression... In contrast to the Neo-plastic [= De Stijl] manner of expression, which is restricted to two dimensions [the plane], Elementarism acknowledges a form of plastic expression in four dimensions, the realm of space-time. In opposition to the orthogonal style of plastic expression, which is 'homogeneous' with natural construction, Elementarism postulates a 'heterogeneous' contrasting, unstable manner of plastic expression based upon planes oblique in relation to the static, perpendicular axis of gravitation”

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

Quote of van Doesburg, in van 'Painting and plastic art': Elementarism – fragment of a manifesto' Paris, December 1926 – April 1927; in De Stijl, Theo van Doesburg – series XIII, 78, 1926–27, pp. 82–87
1926 – 1931

Idea, Nature, Time

“Survival—of the species of the culture of the faith—has a biological dimension. What would have befallen our Hominid ancestors had they implemented gender parity in their hunter-gatherer societies—sometimes the women hunt while the men forage and mind the kids, and vice versa?”

Ilana Mercer South African writer

" Emasculated West Primed For A Muscular, Muslim Takeover http://www.frontpagemag.com/fpm/263677/emasculated-west-primed-muscular-muslim-takeover-ilana-mercer," FrontPage Magazine, July 29, 2016. 2010s, 2016

Women, Men, Faith

“It might help if you imagine an inner living dimension within yourself in which you create, in miniature psychic form, all the exterior conditions that you know. Simply put, you do exactly this. Your thoughts, feelings and mental pictures can be called incipient exterior events, for in one way or another each of these is materialized into physical reality.”

Jane Roberts (1929–1984) American Writer

Source: The Nature of Personal Reality (1974), p. 35

Way, Feeling, Imagination, Reality

“Stress phenomena are… not independent of scale, as was the case pertaining to simple external static equilibrium. …with increasing dimensions of a structural element the volume and therefore the proper weight increases more rapidly than its cross-sectional areas…”

Eduardo Torroja (1899–1961) Spanish architect

Philosophy of Structures (1958)

“I have been strongly influenced by the Mahabharata, discourses of the Buddha, Sri Aurobindo and Plato. My masters have been Vyasa, Buddha and Sri Aurobindo, as elucidated by Ram Swarup. … Paganism was a term of contempt invented by Christianity for people in the countryside who lived close to and in harmony with Nature, and whose ways of worship were spontaneous as opposed to the contrived though-categories constructed by Christianity’s city-based manipulators of human minds. In due course, the term was extended to cover all spiritually spontaneous culture of the world – Greek, Roman, Iranian, Indian, Chinese, native American. It became a respectable term for those who revolted against Christianity in the modern West. But it has yet to recover its spiritual dimension which Christianity had eclipsed. For me, Hinduism preserves ancient Paganism in all its dimensions. In that sense, I am a Pagan. The term "Polytheism' comes from Biblical discourse, which has the term 'theism' as its starting point. I have no use for these terms. They create confusion. I dwell in a different universe of discourse which starts with 'know thyself' and ends with the discovery, 'thou art that'…
I met her [Mother Theresa] briefly in Calcutta in 1954 or 1955 when she was unknown. I had gone to see an American journalist who was a friend and had fallen ill, when she came to his house asking for money for her charity set-up. The friend went inside to get some cash, leaving his five or six year old daughter in the drawing room. Teresa told her, "He is not your real father. Your real father is in heaven." The girl said, "He is very ill." Theresa commented, "If he dies, your father does not die. For your real father who is in heaven never 'dies."”

Sita Ram Goel (1921–2003) Indian activist

The girl was in tears. Interview, The Observer. Date : February 22, 1997. http://sathyavaadi.tripod.com/truthisgod/Articles/goel.htm https://egregores.blogspot.com/2009/10/buddha-sri-aurobindo-and-plato.html https://egregores.wordpress.com/2009/11/16/hindus-and-pagans-a-return-to-the-time-of-the-gods/

Money, People, World, Art

“As we have already glimpsed and will continue to discover, we are able to expand our awareness beyond the perceived limitations of our own person and access the dimensions of a transpersonal consciousness. As we open ourselves to the realization of the in-formed universe, this shift in our collective awareness heralds a resolution of the schisms that have divided us for so long—both among and within us”

Ervin László (1932) Hungarian musician and philosopher

Ervin Laszlo, Jude Currivan (2008) CosMos. p. 101.

Universe, Personality

“There is no general reason to expect evolution to be progressive – even in the weak, value-neutral sense. There will be times when increased size of some organ is favoured and other times when decreased size is favoured. Most of the time, average-sized individuals will be favoured in the population and both extremes will be penalised. During these times the population exhibits evolutionary stasis (i. e., no change) with respect to the factor being measured. If we had a complete fossil record and looked for trends in some particular dimension, such as leg length, we would expect to see periods of no change alternating with fitful continuations or reversals in direction – like a weathervane in changeable, gusty weather.”

Richard Dawkins (1941) English ethologist, evolutionary biologist and author

The Evolutionary Future of Man (1993)

Sense, Change, Time, Weather

“We who scream exist ecstatically. We stand out beyond ourselves, we exist in two dimensions. The scream implies a tension between that which exists and that which might conceivably exist, between the indicative (that which is) and the subjunctive (that which might be).”

John Holloway book Change the World Without Taking Power

Change the World Without Taking Power (2002)

“I have found in my experience in government that I could ignore neither the age-old nor the brand-new dimensions of world politics.”

Joseph Nye (1937) American political scientist

Source: Understanding International Conflicts: An Introduction to Theory and History (6th ed., 2006), Chapter 1, Is There an Enduring Logic of Conflict in World Politics?, p. 2.

Age, World

“Through characters, non-linear plot lines, or the involvement of multiple dimensions, it ultimately witnesses the physical world as inextricable from consciousness or the observer of that world.”

Vanna Bonta (1958–2014) Italian-American writer, poet, inventor, actress, voice artist (1958-2014)

Vanna Bonta Talks About Quantum fiction: Author Interview (2007)

World

“My mantra is “stay perpendicular.” Horizontal is not as good. Half the people that came along and up with with me are either gone to another dimension or don’t remember what they had for lunch. I’m fortunate. I don’t know why. I just want to have a good time.”

Martin Landau (1928–2017) American actor and acting coach

Martin Landau: ‘Doubt Is Important’, Washington Times (December 25, 2016)

People, Time

“ A frustrated or unhappy animal can do relatively little about its tensions. A human being, however, with an extra dimension (the world of symbols) to move around in, not only undergoes experience, but he also symbolizes his experience to himself. Our states of tension--especially the unhappy tensions -- become tolerable as we manage to state what is wrong -- to get it said -- whether to a sympathetic friend, or on paper to a hypothetical sympathetic reader, or even to oneself. If our symbolizations are adequate and sufficiently skillful, our tensions are brought symbolically under control. To achieve this control, one may employ what Kenneth Burke has called "symbolic strategies" -- that is, ways of reclassifying our experiences so that they are "encompassed" and easier to bear. Whether by processes of "pouring out one's heart" or by "symbolic strategies" or by other means, we may employ symbolizations as mechanisms of relief when the pressures of a situation become intolerable. ”

S. I. Hayakawa book Language in Thought and Action

Source: Language in Thought and Action (1949), Bearing the Unbearable, p. 144-145

World, Way, Heart, Animals

“What I affirm is the intuition that where God's presence is no longer a tenable supposition and where His absence is no longer a felt, indeed overwhelming weight, certain dimensions of thought and creativity are no longer attainable. And I would vary Yeats's axiom so as to say: no man can read fully, can answer answeringly to the aesthetic, whose "nerve and blood" are at peace in sceptical rationality, are now at home in immanence and verification. We must read as if.”

George Steiner (1929–2020) American writer

Source: Real Presences (1989), III: Presences, Ch. 7 (p. 229).

God, Peace, Home, Reading

“Starting from a drawing, a pure creation of the mind, I expand it in space by giving it three dimensions, by giving it a material body [in polystyrene] and then enlarge it to the proportions of a site where it can evolve. In this way, instead of having only the drawing before you while remaining anchored in the everyday world, you can finally leave the world and penetrate into drawing, and thus inhabit the creation of the mind instead of merely looking at it prudently in a frame on the wall. The experience consists, therefore, in abstracting yourself totally from the natural everyday world in order to feed your eyes solely on your own mental elaborations.”

Jean Dubuffet (1901–1985) sculptor from France

Note of 7 mai 1968, as quoted in the catalogue of the exhibition La Fiast invita all'incontro con Jean Dubuffet, Turin 1978
posthumous

World, Way, Nature, Drawing

“Composition, the aim of which is expression, alters itself according to the surface to be covered. If I take a sheet of paper of given dimensions I will jot down a drawing which will have a necessary relation to its format – I would not repeat this drawing on another sheet of different dimensions, for instance on a rectangular sheet.... a drawing must have a power of expansion which can bring to life the space which surrounds it.”

Henri Matisse (1869–1954) French artist

Source: 1905 - 1910, Notes d'un Peintre' (Notes of a Painter) (1908), p. 410

Life, Drawing

“Some… agreeing with Philolaus, believe that the proportion is called harmonic because it attends upon all geometric harmony, and they say that 'geometric harmony' is the cube because it is harmonized in all three dimensions, being the product of a number thrice multiplied together. For in every cube this proportion is mirrored; there are in every cube 12 sides, 8 angles and 6 faces; hence 8, the [harmonic] mean between 6 and 12, is according to harmonic proportion…”

Nicomachus (60–120) Ancient Greek mathematician

this harmonic proportion may be expressed as <math>\frac{12}{6}=\frac{12-8}{8-6}</math> or inversely.
Nicomachus of Gerasa: Introduction to Arithmetic (1926)

“The system R forms a well-arranged domain of one dimension extending to infinity on two opposite sides. What is meant by this is sufficiently indicated by my use of expressions borrowed from geometric ideas; but just for this reason it will be necessary to bring out clearly the corresponding purely arithmetic properties in order to avoid even the appearance as if arithmetic were in need of ideas foreign to it.”

Richard Dedekind (1831–1916) German mathematician

p, 125
Stetigkeit und irrationale Zahlen (1872)

Idea, Appearance

“Let me start a different/ analysis by recalling an idea from Max Weber. He characterized cultural modernity as the separation of the substantive reason expressed in religion and metaphysics into three autonomous spheres. They are science, morality and art. These came to be differentiated because the unified world-views of religion and metaphysics fell apart. Since the 18th century, the problems inherited from these older world-views could be arranged so as to fall under specific aspects of validity: truth, normative rightness, authenticity and beauty. They could then be handled as questions of knowledge, or of justice and morality, or of taste. Scientific discourse, theories of morality, Jurisprudence, and the production and criticism of art could in turn be institutionalized. Each domain of culture could be made to correspond to cultural professions in which problems could be dealt with as the concern of special experts. This professionalized treatment of the cultural tradition brings to the fore the intrinsic structures of each of the three dimensions of culture. There appear the structures of cognitive-instrumental, of moral-practical and of aesthetic-expressive rationality, each of these under the control of specialists who seem more adept at being logical in these particular ways than other people are. As a result, the distance grows between the culture of the experts and that of the larger public. What accrues to culture through specialized treatment and reflection does not immediately and necessarily become the property of everyday praxis. With cultural rationalization of this sort, the threat increases that the life-world, whose traditional substance has already been devalued, will become more and more impoverished.”

Manuel Castells (1942) Spanish sociologist (b.1942)

Source: Modernity — An Incomplete Project, 1983, p. 8-9

Life, People, Truth, World

“The first dimension is called "competition," and it refers to that aspect of an economic system in which exchanges of one sort or another play the most important part. In capitalism, of course, competition and exchange occur primarily in markets.”

Samuel Bowles (1939) American economist

Source: Understanding Capitalism: Competition, Command, and Change, 2005, p. 54

Parting

“Back! back! Away from me, or you must go with me — whither you know not — into the Land of Three Dimensions!""Fool! Madman! Irregular!" I exclaimed; "never will I release thee; thou shalt pay the penalty of thine impostures.""Ha! Is it come to this?" thundered the Stranger: "then meet your fate: out of your Plane you go. Once, twice, thrice! 'Tis done!"”

Edwin Abbott Abbott book Flatland

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 17. How the Sphere, Having in Vain Tried Words, Resorted to Deeds

Fate, Penalty, Fools

“Jesus as protagonist in the Gospels is good because, like Superman, he’s been sent from another dimension; like Superman, he’s decided to dedicate himself to saving humanity; and, like Superman, he’s got special powers: heal the sick, walk on water, food multiplication. His vulnerability is that he is part man and as such can be speared, mocked, nailed up, and, at least carnally, sacrificed.”

Russell Brand book Revolution

Revolution (2014)

Food, Water, Parting

“The manufacturing of Fake News by the Deep State, circa 2017, is of a piece with the anatomy of the ramp-up to war in Iraq, in 2003. Except that back then, Republicans, joined by diabolical Democrats like Hillary Clinton, were the ones dreaming up Homer Simpson's Third Dimension.”

Ilana Mercer South African writer

"The War On Trump: A Guide For Conservatives, Libertarians & Liberals," http://www.thelibertyconservative.com/war-trump-guide-conservatives-libertarians-liberals/ The Liberty Conservative, June 17, 2017 2010s, 2017

War, Dreams

“In our search for a lasting solution to the Kashmir problem, both in its external and internal dimensions, we shall not traverse solely on the beaten track of the past. Mindsets will have to be altered and historical baggage jettisoned.”

Atal Bihari Vajpayee (1924–2018) 10th Prime Minister of India

Quoted in [Sumantra Bose, Kashmir: Roots of Conflict, Paths to Peace, http://www.questia.com/read/118148594/kashmir-roots-of-conflict-paths-to-peace, 2003, Harvard University Press, 1]

Search, Problem, Past

“You mention the circle and I agree with your definition.... why does the circle fascinates me? It is (1) the most modern form, but asserts itself unconditionally, (2) a precise but inexhaustible variable, (3) simultaneously stable and unstable, (4) simultaneously loud and soft, (5) a single tension that caries countless tensions within it. The circle is the synthesis of the greatest oppositions. It combines the concentric and the eccentric in a single form, and in balance. Of the three primary forms (triangle, square, circle), it points most clearly to the fourth dimension.”

Wassily Kandinsky (1866–1944) Russian painter

Quote from Kandinsky's letter to Will Grohmann, c. 1926; as cited in Kandinsky, Frank Whitford, Paul Hamlyn Ltd, London 1967, p. 36
1920 - 1930

“It is an assumption that there is always one single dimension for assessing persons and their actions that has canonical priority. This is the dimension of moral evaluation; “good/evil” is supposed always to trump any other form of evaluation, but that is an assumption, probably the result of the long history of the Christianisation and then gradual de-Christianisation of Europe, which one need not make. Evaluation need not mean moral evaluation, but might include assessments of efficiency, … simplicity, perspicuousness, aesthetic appeal, and so on.”

Raymond Geuss book Philosophy and Real Politics

Source: Philosophy and Real Politics (2008), p. 39.

History, Evil, Personality

“The essence of what I have learned about writing and performing music is the authenticity you are faced with in your day-to-day work. No matter what other people or even critics will say, you have to follow your own direction which not necessarily has to be a straight line to success; sometimes it will be a curly, dramatic curve you have to go, but that’s the only way to leave a little landmark of brave respect to others and to the dimensions of your own capability.”

Edgar Froese (1944–2015) German musician and founder of Tangerine Dream

People, Music, Way, Learning

“As to those in the World Trade Center… Well, really. Let's get a grip here, shall we? True enough, they were civilians of a sort. But innocent? Gimme a break. They formed a technocratic corps at the very heart of America's global financial empire – the "mighty engine of profit" to which the military dimension of U. S. policy has always been enslaved – and they did so both willingly and knowingly.”

Ward Churchill (1947) Political activist

Some People Push Back: On the Justice of Roosting Chickens http://www.kersplebedeb.com/mystuff/s11/churchill.html, September 12, 2001

World, Heart

“The third dimension of three-dimensional economics, change, suggests that studying economics also means studying history. The process of change in society cannot be understood without considering the past and how it changed, eventually becoming the present. Change in political economy may be contrasted with the static approach of conventional economics that freezes time at a moment.”

Samuel Bowles (1939) American economist

Source: Understanding Capitalism: Competition, Command, and Change, 2005, p. 57

History, Study, Change, Time

“And this was your Cradle? Why, surely, my Jenny,
Such cozy dimensions go clearly to show
You were an exceedingly small pickaninny,
Some nineteen or twenty short summers ago.”

Frederick Locker-Lampson (1821–1895) British poet

The old Cradle; reported in Bartlett's Familiar Quotations, 10th ed. (1919).

Summer

“I told you once that in those terms I would be considered as Ruburt's number 6 or 7 self. You had better change Ruburt to Jane in that sentence. Ruburt then, would be considered Jane's third self in approximate terms. In the analogy these future selves would dwell in other dimensions, and usually self one, or Jane, would be relatively unaware of their, existence or knowledge. In this case self one is able to make such contacts however.”

Jane Roberts (1929–1984) American Writer

Session 444, Page 124
The Early Sessions: Sessions 1-42, 1997, The Early Sessions: Book 9

Knowledge, Change, Future

“If in the case of a notion whose specialisations form a continuous manifoldness, one passes from a certain specialisation in a definite way to another, the specialisations passed over form a simply extended manifoldness, whose true character is that in it a continuous progress from a point is possible only on two sides, forwards or backwards. If one now supposes that this manifoldness in its turn passes over into another entirely different, and again in a definite way, namely so that each point passes over into a definite point of the other, then all the specialisations so obtained form a doubly extended manifoldness. In a similar manner one obtains a triply extended manifoldness, if one imagines a doubly extended one passing over in a definite way to another entirely different; and it is easy to see how this construction may be continued. If one regards the variable object instead of the determinable notion of it, this construction may be described as a composition of a variability of n + 1 dimensions out of a variability of n dimensions and a variability of one dimension.”

Bernhard Riemann (1826–1866) German mathematician

On the Hypotheses which lie at the Bases of Geometry (1873)

Way, Imagination

“The principal way that cognitive science can contribute to epistemology, I claim, is to identify basic belief-forming, or problem-solving processes. Once identified, these processes would be examined by primary epistemology according to the evaluative dimensions and standards adduced in Part I.”

Alvin Goldman (1938) American philosopher

Alvin Goldman (1986), Epistemology and Cognition. p. 81

Way, Problem, Science, Parting

“The shrinking of church religion, however, is only one – and the sociologically less interesting – dimension of the problem of secularization. For the analysis of contemporary society another question is more important. What are the dominant values overarching contemporary culture? What is the socio-structural basis of these values and what is their function in the live of contemporary man?”

Thomas Luckmann (1927–2016) American-Austrian sociologist

Source: The invisible religion, 1967, p. 40

Religion, Question, Problem

“A psychological space is established for any set of stimuli by determining metric distances between the stimuli such that the probability that a response learned to any stimulus will generalize to any other is an invariant monotonic function of the distance between them. To a good approximation, this probability of generalization (i) decays exponentially with this distance, and (ii) does so in accordance with one of two metrics, depending on the relation between the dimensions along which the stimuli vary. These empirical regularities are mathematically derivable from universal principles of natural kinds and probabilistic geometry that may, through evolutionary internalization, tend to govern the behaviors of all sentient organisms.”

Roger Shepard (1929) American psychologist

Source: "Toward a universal law of generalization for psychological science," 1987, p. 1317

Behavior, Mathematics, Nature, Learning

“Our little Spaceship Earth is only eight thousand miles in diameter, which is almost a negligible dimension in the great vastness of space.... Spaceship Earth was so extraordinarily well invented and designed that to our knowledge humans have been on board it for two million years not even knowing that they were on board a ship.”

Buckminster Fuller (1895–1983) American architect, systems theorist, author, designer, inventor and futurist

1960s, Operating Manual for Spaceship Earth (1963)

Knowledge

“Man is called to a fullness of life which far exceeds the dimensions of his earthly existence, because it consists in sharing the very life of God. The loftiness of this supernatural vocation reveals the greatness and the inestimable value of human life even in its temporal phase.”

Pope John Paul II (1920–2005) 264th Pope of the Catholic Church, saint

Encyclical Evangelium vitae, 25 March 1995 Source: Libreria Editrice Vaticana http://www.vatican.va/holy_father/john_paul_ii/encyclicals/documents/hf_jp-ii_enc_25031995_evangelium-vitae_en.html

Life, God

“The Church does not have technical solutions to offer and does not claim “to interfere in any way in the politics of States.” She does, however, have a mission of truth to accomplish, in every time and circumstance, for a society that is attuned to man, to his dignity, to his vocation. Without truth, it is easy to fall into an empiricist and sceptical view of life, incapable of rising to the level of praxis because of a lack of interest in grasping the values — sometimes even the meanings — with which to judge and direct it. Fidelity to man requires fidelity to the truth, which alone is the guarantee of freedom (cf. Jn 8:32) and of the possibility of integral human development. For this reason the Church searches for truth, proclaims it tirelessly and recognizes it wherever it is manifested. This mission of truth is something that the Church can never renounce. Her social doctrine is a particular dimension of this proclamation: it is a service to the truth which sets us free. Open to the truth, from whichever branch of knowledge it comes, the Church's social doctrine receives it, assembles into a unity the fragments in which it is often found, and mediates it within the constantly changing life-patterns of the society of peoples and nations”

Pope Benedict XVI (1927) 265th Pope of the Catholic Church

2009, Cartias in Vertitate (29 June 2009)

Life, People, Truth, Way

“Interviewer: The critical issue as far as the international community and indeed I think as far as the Tamils are concerned, is the international dimension of the president said last week there will be no international involvement in this investigation.”

Ranil Wickremesinghe (1949) Former Prime Minister of Sri Lanka

Communication, Thinking

“Policies should take account of the emotional dimensions of human behaviour rather than assuming rational action.”

Nayef Al-Rodhan (1959) philosopher, neuroscientist, geostrategist, and author

Source: Emotional amoral egoism (2008), p.203

“This provides us with our first major clue to the solutions of the problem. Even if the left cannot see the world as full of potentiality, it can hold on to the moments of insight and refuse to let go of them. If I know that present difficulties will end in triumph, I am un-discourageable; I merely have to know it intellectually. And if I can 'know' that reality actually has a third dimension, I shall never fall into the mistake of complaining that there is nothing new under the sun and that life is futile.”

Colin Wilson (1931–2013) author

Source: Access to Inner Worlds (1990), p. 13

Life, World, Problem, Reality

“In my pictures I would use speech as an extra dimension supplementing the image … Speech would not come off the screen in coincidence with the sequences, but from without, as if it were a surplus unconnected with the organism - a cravat of drivel hung on an ivory tooth.”

Isidore Isou (1925–2007) Romanian-born French poet, film critic and visual artist

Venom and Eternity (1951), Danielle's Monologue

“Of all the indignities to have been visited upon Dracula during the past century (including being the "inspiration" for a cereal and a Sesame Street character, and being lampooned by Mel Brooks), none is more unsettling than what has happened to the world's most famous vampire in Dracula 2000. Dimension Films, the exploitation division of Miramax, decided that, with their two horror franchises currently on hold (the Scream and Halloween films), they would turn their attention in another direction. So they sunk their greedy fangs into the most venerable monster they could find and sucked him dry.”

James Berardinelli (1967) American film critic

Review http://www.reelviews.net/movies/d/dracula2000.html of Dracula 2000 (2000). One-star reviews

World, Past

“As a rule, each entity is born so that he experiences at least three roles, that of mother, father and child... Beside the three necessary roles there is another quality, different in dimension, which is also necessary for the personality, and this involves the fullest use of potential.”

Jane Roberts (1929–1984) American Writer

Session 163
The Early Sessions: Sessions 1-42, 1997, The Early Sessions: Book 4

Personality

“Since language is linear, whereas the unfolding of the universe takes place in a multitude of dimensions, language is limited in its ability to describe reality.”

Subhash Kak (1947) Indian computer scientist

The Circle of Memory, An Autobiography (2016)

Reality, Universe

“Harry Dresden: Sometimes the most remarkable things seem commonplace. I mean, when you think about it, jet travel is pretty freaking remarkable. You get in a plane, it defies the gravity of a entire planet by exploiting a loophole with air pressure, and it flies across distances that would take months or years to cross by any means of travel that has been significant for more than a century or three. You hurtle above the earth at enough speed to kill you instantly should you bump into something, and you can only breathe because someone built you a really good tin can that seems tight enough to hold in a decent amount of air. Hundreds of millions of man-hours of work and struggle and research, blood, sweat, tears and lives have gone into the history of air travel, and it has totally revolutionized the face of our planet and societies.
But get on any flight in the country, and I absolutely promise you that you will find someone who, in the face of all that incredible achievement, will be willing to complain about the drinks. The drinks, people. That was me on the staircase to Chicago-Over-Chicago. Yes, I was standing on nothing but congealed starlight. Yes, I was walking up through a savage storm, the wind threatening to tear me off and throw me into the freezing waters of lake Michigan far below. Yes, I was using a legendary and enchanted means of travel to transcend the border between one dimension and the next, and on my way to an epic struggle between ancient and elemental forces. But all I could think to say, between panting breaths, was, "Yeah. Sure. They couldn't possibly have made this an escalator."”

Jim Butcher The Dresden Files

The Dresden Files, Summer Knight (2002)

People, Way, Travel, History

“[in response to a question about what was meant by his "cosmic religion"] It is not a religion that teaches that man is made in the image of God—that is anthropomorphic. Man has infinite dimensions and finds God in his conscience. This religion has no dogma other than teaching man that the universe is rational and that his highest destiny is to ponder it and co-create with its laws. There are only two limiting factors: first, that what seems impenetrable to us is as important as what is cut and dried; and, second, that our faculties are dull and can only comprehend wisdom and serene beauty in crude forms, but the heart of man through intuition leads us to greater understanding of ourselves and the universe. My religion is based on Moses: Love God and love your neighbor as yourself. And for me God is the First Cause. David and the prophets knew that there could be no love without justice or justice without love. I don't need any other religious trappings.”

Albert Einstein (1879–1955) German-born physicist and founder of the theory of relativity

Source: Attributed in posthumous publications, Einstein and the Poet (1983), p. 108

Love, Wisdom, God, Religion

“The methods of logical procedure are very different in ancient and modem logic, but behind all difference is the construction of a universally valid order of thought, neutral with respect to material content. Long before technological man and technological nature emerged as the objects of rational control and calculation, the mind was made susceptible to abstract generalization. Terms which could be organized into a coherent logical system, free from contradiction or with manageable contradiction, were separated from those which could not. Distinction was made between the universal, calculable, “objective” and the particular, incalculable, subjective dimension of thought.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), pp. 137-138

Nature, Universe

“The grand design of nature perceived broadly in four dimensions, including the forces that move the universe and created man, with special focus on evolution in our own biosphere, is something intrinsically good that it is right to preserve and enhance, and wrong to destroy and degrade.”

Roger Wolcott Sperry (1913–1994) American neuroscientist

Source: Science and the Problem of Values (1972), p. 127

Nature, Universe

“When I first lived in a monastery, I learned very quickly that monastic life did not afford more escape from the world than any other place. Rather, it presented a deeper encounter with it. The monastic life is not a rejection of the world; it is a decision to engage with this world from a different dimension, from the enlarged perspective of love, as perceived by the Gospel in its utter simplicity and clarity.”

Wayne Teasdale (1945–2004) American writer

Source: A Monk in the World: Cultivating a Spiritual Life (2003), p. 1

Love, Life, World, Decision

“To the cosmic corpuscles we should find it natural to attribute an individual radius of action as limited as their dimensions. We find, on the contrary, that each of them can only be defined by virtue of its influence on all around it. Whatever space we suppose it to be in, each cosmic element radiates in it and entirely fills it. However narrowly the heart of an atom may be circumscribed, its realm is co-extensive, at least potentially, with that of every other atom. This strange property we will come across again, even in the human molecule.”

Pierre Teilhard De Chardin book The Phenomenon of Man

The Phenomenon of Man (1955)

Nature, Heart

“If space in infinite, how about the space inside man? Blake said that eternity opens from the center of an atom. My former terror vanished. Now I saw that I was mistaken in thinking of myself as an object in a dead landscape. I had been assuming that man is limited because his brain is limited, that only so much can be packed into the portmanteau. But the spaces of the mind are a new dimension. The body is a mere wall between two infinities. Space extends to infinity outwards; the mind stretches to infinity inwards.”

Colin Wilson book The Mind Parasites

Source: The Mind Parasites (1967), p. 38

Thinking, Dead

“A painter should never speak because words are not the means at his command. Words cannot express visually dimension at a glance they can only establish their own relationship in time.
However, it is possible for a painter, at certain moments of his development to formulate some of the problems he is facing in the growth of his work. A painting cannot be explained. Words can only stimulate the act of looking.
A visual problem is never put a priori as a mathematical problem but is born in the process of painting and evolves in a state of unawareness of the painter.”

Fritz Glarner (1899–1972) Swiss artist

Source: George L. K. Morris, Willem De Kooning, Alexander Calder, Fritz Glarner, Robert Motherwell, Stuart Davis. " What Abstract Art Means to Me http://www.jstor.org/stable/4058250," in: The Bulletin of the Museum of Modern Art, Vol. 18, No. 3, (Spring, 1951), pp. 2-15

Mathematics, Problem, Time, Painting

“The freedom secured by the Constitution consists, in one of its essential dimensions, of the right of the individual not to be injured by the unlawful exercise of governmental power. The mandate for segregated schools, Brown v. Board of Education, 347 U. S. 483 (1954); a wrongful invasion of the home, Silverman v. United States, 365 U. S. 505 (1961); or punishing a protester whose views offend others, Texas v. Johnson, 491 U. S. 397 (1989); and scores of other examples teach that individual liberty has constitutional protection, and that liberty’s full extent and meaning may remain yet to be discovered and affirmed. Yet freedom does not stop with individual rights. Our constitutional system embraces, too, the right of citizens to debate so they can learn and decide and then, through the political process, act in concert to try to shape the course of their own times and the course of a nation that must strive always to make freedom ever greater and more secure. Here Michigan voters acted in concert and statewide to seek consensus and adopt a policy on a difficult subject against a historical background of race in America that has been a source of tragedy and persisting injustice. That history demands that we continue to learn, to listen, and to remain open to new approaches if we are to aspire always to a constitutional order in which all persons are treated with fairness and equal dignity. Were the Court to rule that the question addressed by Michigan voters is too sensitive or complex to be within the grasp of the electorate; or that the policies at issue remain too delicate to be resolved save by university officials or faculties, acting at some remove from immediate public scru-tiny and control; or that these matters are so arcane that the electorate’s power must be limited because the people cannot prudently exercise that power even after a full debate, that holding would be an unprecedented restriction on the exercise of a fundamental right held not just by one person but by all in common. It is the right to speak and debate and learn and then, as a matter of political will, to act through a lawful electoral process.”

Anthony Kennedy (1936) Associate Justice of the Supreme Court of the United States

Schuette v. Coalition to Defend Affirmative Action, 572 U. S. ____, (2016), plurality opinion.

People, Education, School, Law

“Godzilla 2014 missed the mark primarily because it is not an origins story. Gojira was a monster of our own making. Similarly Gino was supposed to impose nature’s response to our meddling. But G2014 pre-existed genetic modifications and nuclear testing. We have no responsibility for him, nor the mutos either. They come from a time that never was, millions of years ago, “when the world was much more radioactive than it is today”. The story implies that mutos ‘eat radiation’. In the film, they can track it through every kind of protective shielding, and they eat nuclear devices like fruit -metallic peal and all. I guess millions of years ago, nuclear missiles grew on trees, and kaiju were common even though they’re absent from the fossil record -with only one top-secret exception. As an advocate of science education with a deep interest in paleontology, and as someone who would rather see humans held accountable for what they do to their environment, this film was very disappointing. As an atheist, it was even worse. The star of the film not only has impossible dimensions and an inexplicable power, he is also immortal. He’s been alive forever, and spends all his time sleeping. He awakens only he senses submarines or the arrival of other kaiju, because he has a mission to protect humanity. G2014 put the ‘god’ in Godzilla. The director called him a god, and some of the characters in the movie describe him as a god too. So he’s not a lizard, not a dinosaur, but one of the Lovecraftian great old ones like Cthulhu. In a video I made years ago, I too joked about Godzilla being a god. But it was still somewhat disappointing to see him depicted that way.”

Aron Ra (1962) Aron Ra is an atheist activist and the host of the Ra-Men Podcast

Patheos, Weighing in on Godzilla http://www.patheos.com/blogs/reasonadvocates/2014/06/08/weighing-in-on-godzilla/ (June 8, 2014)

God, Secret, World, Education

“Orbs are an extension of consciousness. When we are not in the physical form, we often travel in a light sphere. It’s way beyond the nuts and bolts to understand this kind of science. In the universe we live in, we can measure less than one percent [of existing reality], and physicists believe there’s another 99 percent out there we cannot measure. There are other planes, other dimensions, and the orbs are a byproduct of these planes and dimensions.”

James Gilliland (1952) American academic and author

James describing what Orbs are.
Source: Levin, Ken (February/March 2004). "Orbs Come Out to Play", UFO Magazine 19 (1): 39

Way, Travel, Understanding, Reality

“Since such very powerful kings have not disdained walls built of brick, although… they might often have had them not only of masonry or dimension stone but even of marble, I think that one ought not to reject buildings made of brick-work, provided that they are properly "topped."”

Vitruvius book De architectura

Source: De architectura (The Ten Books On Architecture) (~ 15BC), Book II, Chapter VIII, Sec. 16

Thinking

“Vibrating strings in 10 dimensions is just a weird fact… An explanation of that weird fact would tell you why there are 10 dimensions in the first place.”

Edward Witten (1951) American theoretical physicist

as quoted by K.C. Cole, "A Theory of Everything" New York Times Magazine (1987) Oct.18

“Phenomena unfold on their own appropriate scales of space and time and may be invisible in our myopic world of dimensions assessed by comparison with human height and times metered by human lifespans. So much of accumulating importance at earthly scales […] is invisible by the measuring rod of a human life. So much that matters to particles in the microscopic world of molecules […] either averages out to stability at our scale or simply stands below our limits of perception.”

Stephen Jay Gould book Eight Little Piggies

"The Golden Rule: A Proper Scale for Our Environmental Crisis", pp. 41–42
Eight Little Piggies (1993)

Life, World, Time

“Geometry is that of mathematical science which is devoted to consideration of form and size, and may be said to be the best and surest guide to study of all sciences in which ideas of dimension or space are involved. Almost all the knowledge required by navigators, architects, surveyors, engineers, and opticians, in their respective occupations, is deduced from geometry and branches of mathematics. All works of art constructed according to the rules which geometry involves; and we find the same laws observed in the works of nature. The study of mathematics, generally, is also of great importance in cultivating habits of exact reasoning; and in this respect it forms a useful auxiliary to logic.”

Robert Chambers (publisher, born 1802) (1802–1871) Scottish publisher and writer

Robert Chambers, Chambers's Information for the People (1875) Vol. 2 https://books.google.com/books?id=vNpTAAAAYAAJ

Law, Art, Mathematics, Idea

“Organisations are technical instruments; designed as means to definite goals… they are expendable. Institutions… may be partly engineered, but they have also a “natural” dimension. They are the products of interaction and adaptation; they become the receptacles of group idealism; they are less readily expendable.”

Philip Selznick (1919–2010) American sociologist

Philip Selznick, quoted in Charles Perrow (1960, p.4), as cited in: Owen A. Jones. The Sources of Goal Incongruence in a Public Service Network. 2013. p. 35-36

Nature

“I have always had a fascination with traveling to magical places. Many of my own stories take place in other places, other dimensions. I guess I'm the ultimate escapist.”

Robert D. San Souci (1946–2014) Children's writer

Robert D. San Souci – Penguin Books USA http://www.penguin.com/author/robert-d-san-souci/26813

Travel

“In the realm of physics it is perhaps only the theory of relativity which has made it quite clear that the two essences, space and time, entering into our intuition, have no place in the world constructed by mathematical physics. Colours are thus "really" not even æther-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time.”

Hermann Weyl (1885–1955) German mathematician

Introduction
Space—Time—Matter (1952)

World, Mathematics, Time

“Perhaps it was his return to Paris [In June 1919 Piet Mondrian returned to Paris] that was needed to provide him with fresh new possibilities in his work. Invigoration. His most recent work is without composition. The division of the picture plane is modular. That means ordinary rectangles, all the same size. The only contrast is in the colour. In my view, this runs counter to his theory concerning the abolition of position and dimension. This is in effect equality of position and dimension.”

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

Quote from his letter to the Dutch modern architect Oud, 24 June 1919; as quoted in Mondrian, -The Art of Destruction, Carel Blotkamp, Reaktion Books LTD. London 2001, p. 126
1912 – 1919

“Gandhi remained committed to nonviolence; I followed the Gandhian strategy for as long as I could, but then there came a point in our struggle when the brute force of the oppressor could no longer be countered through passive resistance alone. We founded Umkhonto we Sizwe and added a military dimension to our struggle. Even then, we chose sabotage because it did not involve the loss of life, and it offered the best hope for future race relations. Militant action became part of the African agenda officially supported by the Organization of African Unity (O. A. U.) following my address to the Pan-African Freedom Movement of East and Central Africa (PAFMECA) in 1962, in which I stated, "Force is the only language the imperialists can hear, and no country became free without some sort of violence."”

Nelson Mandela (1918–2013) President of South Africa, anti-apartheid activist

2000s, The Sacred Warrior (2000)

Life, Hope, Support, Freedom

“The conformal invariance of the Yang-Mills equations in four dimensions greatly facilitates the study of the temporal asymptotic behavior of their solutions.”

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

[Scattering for the Yang-Mills equations, Trans. Amer. Math. Soc., 315, 1989, 823–832, 10.1090/S0002-9947-1989-0949897-7] (p. 823)

Behavior, Study

“The five attitudes are: Upper, Middle, Lower, Right Side, and Left Side. These are the five. Although attitude has these five dimensions, the one purpose of all of them is to cut the enemy. There are none but these five attitudes.
Whatever attitude you are in, do not be conscious of making the attitude; think only of cutting.”

Miyamoto Musashi (1584–1645) Japanese martial artist, writer, artist

Go Rin No Sho (1645), The Water Book

Thinking

“Like 'real', 'free' is only used to rule out the suggestion of some or all of its recognized antitheses. As 'truth' is not a name of a characteristic of assertions, so 'freedom' is not a name for a characteristic of actions, but the name of a dimension in which actions are assessed.”

J. L. Austin (1911–1960) English philosopher

Source: Philosophical Papers (1979), p. 180.

Truth, Freedom

“"You hear your fate," said the Sphere to me, while the Council was passing for the third time the formal resolution. "Death or imprisonment awaits the Apostle of the Gospel of Three Dimensions." "Not so," replied I, "the matter is now so clear to me, the nature of real space so palpable, that methinks I could make a child understand it. Permit me but to descend at this moment and enlighten them." "Not yet," said my Guide, "the time will come for that. Meantime I must perform my mission. Stay thou there in thy place." Saying these words, he leaped with great dexterity into the sea (if I may so call it) of Flatland, right in the midst of the ring of Counsellors. "I come," cried he, "to proclaim that there is a land of Three Dimensions."”

Edwin Abbott Abbott book Flatland

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 18. How I came to Spaceland, and What I Saw There

Death, Fate, Understanding, Nature

“Archytas of Tarentum found the two mean proportionals by a very striking construction in three dimensions, which shows that solid geometry, in the hands of Archytas at least, was already well advanced. The construction was usually called mechanical, which it no doubt was in form, though in reality it was in the highest degree theoretical. It consisted in determining a point in space as the intersection of three surfaces: (a) a cylinder, (b) a cone, (c) an "anchor-ring" with internal radius = 0.”

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

Achimedes (1920)

Reality

“From the start, the bourgeois-positivistic fraction of enlightenment was uncomfortable about the unpredictable, subversive dimensions of the new category, the unconscious. With it, the motif of critical self-reflection was introduced into civilization in a way that could not please those who held themselves to be the representatives of civilization. If every ego is underlaid by an unconscious, then that is the end of the self-satisfaction of a consciousness that thinks it knows itself, and thus knows how to value itself. The “unconscious” touched on the cultural narcissism of all social classes.”

Peter Sloterdijk (1947) German philosopher

Source: Kritik der zynischen Vernunft [Critique of Cynical Reason] (1983), p. 50

Way, Thinking

“When war reaches such dimensions as to involve the whole nation, and when the people at its conclusion find they have gained nothing but only observe widespread calamity around them, they are inclined to become more sceptical and desire to investigate the foundations of the arguments which inspired their patriotism, inflamed their passions, and prepared them to offer the supreme sacrifice. They are curious to know why the ostensible objects for which they fought have none of them been attained, more especially if they are the victors.”

Arthur Ponsonby (1871–1946) British Liberal and later Labour politician and pacifist

Falsehood in Wartime (1928), Introduction

War, People, Passion

“You do not understand the dimensions into which your own thoughts drop, for they continue their own existence, and others look up to them and view them like stars. I am telling you that your own thoughts and mental actions appear to inhabitants of other systems like the stars and planets within your own; and those inhabitants do not perceive what lies within and behind the stars in their own heavens.”

Jane Roberts (1929–1984) American Writer

Source: The Seth Material (1970), p. 312

Star, Understanding, Appearance

“[M]ost of our structures in the past consisted of individual members having relatively small transverse dimensions as compared with their length, and in such members stress analysis is much more simple. …[M]any modern structures consist of frameworks of this type, and frequently the word "structure" refers specifically to assemblies consisting of linear elements.”

Eduardo Torroja (1899–1961) Spanish architect

Philosophy of Structures (1958)

Past

“Institutionalized desublimation thus appears to be an aspect of the “conquest of transcendence” achieved by the one-dimensional society. Just as this society tends to reduce, and even absorb opposition (the qualitative difference!) in the realm of politics and higher culture, so it does in the instinctual sphere. The result is the atrophy of the mental organs for grasping the contradictions and the alternatives and, in the one remaining dimension of technological rationality, the Happy Consciousness comes to prevail.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 79

Happiness, Appearance

“Total abstraction was something intellectual to me. I didn't feel it; I could talk about Mondrian but it didn't occur to me to do it. [around 1950]. I saw a Dubuffet show at Pierre Matisse [the son of Henri Matisse, running an art-gallery in New York then] in the late forties and came back with a new vocabulary. Also when Baziotes won the Carnegie (1948) there was a reproduction in 'The Times'. I remember bringing it to class. It was source of bewilderment, delineated configurations that seemed to come out of Cubism. It was something new. Those were the tastes of a whole dimension that was to come, much more abstract and allover and I didn't see much more of it until I came to New York. I would go to the old Guggenheim to look at Kandinsky. I liked the early abstractions but the later ones I didn't like at all..”

Helen Frankenthaler (1928–2011) American artist

Source: 1960s, Interview with Henry Geldzahler', in 'Artforum', 1965, p. 36

Art, Feeling, Time

“In the form of the oeuvre, the actual circumstances are placed in another dimension where the given reality shows itself as that which it is. Thus it tells the truth about itself; its language ceases to be that of deception, ignorance, and submission. Fiction calls the facts by their name and their reign collapses; fiction subverts everyday experience and shows it to be mutilated and false.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 62

Truth, Reality, Falseness

“A fractal is by definition a set for which the Hausdorff-Besicovitch dimension strictly exceeds the topological dimension.”

Benoît Mandelbrot book The Fractal Geometry of Nature

The Fractal Geometry of Nature (1982)

“There are many ways to practice and make art. There are also various ways to express, such as comedy, sculpture, music, painting etc. Dimensions can be immense even in such small spaces as the head of a pin.”

Eugenio Cruz Vargas (1923–2014) Chilean poet and painter

Quote Source: Famous phrase of Eugenio Cruz Vargas http://www.angelred.com/urls/arte.htm| Source: Sky http://viaf.org/viaf/13641853/| Source: From Library of Congress Name Authority File of U.S.A. http://id.loc.gov/authorities/names/n81126660.html|

Art, Music, Way, Painting

“It must be emphasized that in seeing a work of art that has been composed by precise means, the viewer does not perceive dominant details. His impression is one of perfect balance to which all the parts contribute, an impression which not only applies to the parts as such, but is transmitted also to the relation existing between the work of art and the viewer. Although it is very difficult to express in words the effect of a work of art, it may be said that the viewer’s deepest impression can best be defined as the achievement of a balance between objective meaning and subjective meaning, both directly penetrated by awareness. He has a sensation of height and of depth which are no longer in any way bound to natural conditions or to spatial dimensions, a sensation which places the viewer in a state of consciousness harmony.”

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

1922
Quote from 'Grundbegriffe der neuen Gestaltenden Kunst', essay by Van Doesburg (published between 1921-23 in De Stijl) - last Chapter; as quoted in 'Fifty Years of Accomplishment, From Kandinsky to Jackson Pollock', by Michel Seuphor, Dell Publishing Co. 1964, p. 85-86
1920 – 1926

Art, Way, Nature, Parting