Quotes about dimension
page 4

Germaine Greer photo
Elia M. Ramollah photo
Klaus Kinski photo
Barbara Hepworth photo
Hans Reichenbach photo

“Whereas the conception of space and time as a four-dimensional manifold has been very fruitful for mathematical physicists, its effect in the field of epistemology has been only to confuse the issue. Calling time the fourth dimension gives it an air of mystery. One might think that time can now be conceived as a kind of space and try in vain to add visually a fourth dimension to the three dimensions of space. It is essential to guard against such a misunderstanding of mathematical concepts. If we add time to space as a fourth dimension it does not lose any of its peculiar character as time. …Musical tones can be ordered according to volume and pitch and are thus brought into a two dimensional manifold. Similarly colors can be determined by the three basic colors red, green and blue… Such an ordering does not change either tones or colors; it is merely a mathematical expression of something that we have known and visualized for a long time. Our schematization of time as a fourth dimension therefore does not imply any changes in the conception of time. …the space of visualization is only one of many possible forms that add content to the conceptual frame. We would therefore not call the representation of the tone manifold by a plane the visual representation of the two dimensional tone manifold.”

Hans Reichenbach (1891–1953) American philosopher

The Philosophy of Space and Time (1928, tr. 1957)

Ralph Bunche photo
Henry Van Dyke photo

“As long as habit and routine dictate the pattern of living, new dimensions of the soul will not emerge.”

Henry Van Dyke (1852–1933) American diplomat

This may be misattributed. It appears to be a direct and original quote from "Individuality and encounter: a brief journey into loneliness and sensitivity groups" by Dr Clark E Moustakas (1971 p15, prev 1968)
Attributed

Jane Roberts photo
Albert Einstein photo

“Nature shows us only the tail of the lion. But there is no doubt in my mind that the lion belongs with it even if he cannot reveal himself to the eye all at once because of his huge dimension. We see him only the way a louse sitting upon him would.”

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

Variant: Nature shows us only the tail of the lion. But I do not doubt that the lion belongs to it even though he cannot at once reveal himself because of his enormous size.

As quoted by Abraham Pais in Subtle is the Lord:The Science and Life of Albert Einstein (1982), p. 235 ISBN 0-192-80672-6
Source: Letter to Heinrich Zangger (10 March 1914), quoted in The Curious History of Relativity by Jean Eisenstaedt (2006), p. 126 http://books.google.com/books?id=d2bnXTOtCD8C&lpg=PP1&pg=PA126#v=onepage&q&f=false.

Hans Reichenbach photo

“It is remarkable that this generalization of plane geometry to surface geometry is identical with that generalization of geometry which originated from the analysis of the axiom of parallels. …the construction of non-Euclidean geometries could have been equally well based upon the elimination of other axioms. It was perhaps due to an intuitive feeling for theoretical fruitfulness that the criticism always centered around the axiom of parallels. For in this way the axiomatic basis was created for that extension of geometry in which the metric appears as an independent variable. Once the significance of the metric as the characteristic feature of the plane has been recognized from the viewpoint of Gauss' plane theory, it is easy to point out, conversely, its connection with the axiom of parallels. The property of the straight line as being the shortest connection between two points can be transferred to curved surfaces, and leads to the concept of straightest line; on the surface of the sphere the great circles play the role of the shortest line of connection… analogous to that of the straight line on the plane. Yet while the great circles as "straight lines" share the most important property with those of the plane, they are distinct from the latter with respect to the axiom of the parallels: all great circles of the sphere intersect and therefore there are no parallels among these "straight lines". …If this idea is carried through, and all axioms are formulated on the understanding that by "straight lines" are meant the great circles of the sphere and by "plane" is meant the surface of the sphere, it turns out that this system of elements satisfies the system of axioms within two dimensions which is nearly identical in all of it statements with the axiomatic system of Euclidean geometry; the only exception is the formulation of the axiom of the parallels.”

Hans Reichenbach (1891–1953) American philosopher

The geometry of the spherical surface can be viewed as the realization of a two-dimensional non-Euclidean geometry: the denial of the axiom of the parallels singles out that generalization of geometry which occurs in the transition from the plane to the curve surface.
The Philosophy of Space and Time (1928, tr. 1957)

Jane Roberts photo

“Those portions of the brain, seemingly unused, deal with these other dimensions, and physically, you begin to use these portions, though minutely, for the first time, under psychedelic situations.”

Jane Roberts (1929–1984) American Writer

Session 308, Page 217
The Early Sessions: Sessions 1-42, 1997, The Early Sessions: Book 7

Ilana Mercer photo
Aldous Huxley photo

““What about spatial relationships?” the investigator inquired, as I was looking at the books. It was difficult to answer. True, the perspective looked rather odd, and the walls of the room no longer seemed to meet in right angles. But these were not the really important facts. The really important facts were that spatial relationships had ceased to matter very much and that my mind was perceiving the world in terms of other than spatial categories. At ordinary times the eye concerns itself with such problems as Where?—How far?—How situated in relation to what? In the mescalin experience the implied questions to which the eye responds are of another order. Place and distance cease to be of much interest. The mind does its Perceiving in terms of intensity of existence, profundity of significance, relationships within a pattern. I saw the books, but was not at all concerned with their positions in space. What I noticed, what impressed itself upon my mind was the fact that all of them glowed with living light and that in some the glory was more manifest than in others. In this context position and the three dimensions were beside the point. Not, of course, that the category of space had been abolished. When I got up and walked about, I could do so quite normally, without misjudging the whereabouts of objects. Space was still there; but it had lost its predominance. The mind was primarily concerned, not with measures and locations, but with being and meaning.”

describing his experiment with mescaline, pp. 19-20
Source: The Doors of Perception (1954)

John Desmond Bernal photo
Ralph Waldo Emerson photo

“I think no virtue goes with size;
The reason of all cowardice
Is, that men are overgrown,
And, to be valiant, must come down
To the titmouse dimension.”

Ralph Waldo Emerson (1803–1882) American philosopher, essayist, and poet

The Titmouse http://www.readbookonline.net/readOnLine/1176/, st. 5
1860s, May-Day and Other Pieces (1867)

Roger Penrose photo
Martin Amis photo
David Wood photo

“What I would like to show is that there is a vital dimension of their writing, which I call performative reflexivity, which if ignored or misunderstood will impede an adequate response to it.”

David Wood (1946) British philosopher, born 1946

Source: Philosophy At The Limit (1990), Chapter 8, Performative Reflexivity, p. 134

Marshall McLuhan photo

“Omnipresence has become an ordinary human dimension.”

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

1970s, Forces interview (1973)

Ward Cunningham photo
François Englert photo

“Three distinct geometries on S7 arise as solutions of the classical equations of motion in eleven dimensions. In addition to the conventional riemannian geometry, one can also obtain the two exceptional Cartan-Schouten compact flat geometries with torsion.”

François Englert (1932) Belgian theoretical physicist

[10.1016/0370-2693(82)90684-0, 1982, Spontaneous compactification of eleven-dimensional supergravity, Physics Letters B, 119, 4–6, 339–342]

Herbert Marcuse photo
Herbert Marcuse photo

“The supremacy of thought (consciousness) also pronounces the impotence of thought in an empirical world which philosophy transcends and corrects — in thought. The rationality in the name of which philosophy passed its judgments obtained that abstract and general purity” which made it immune against the world in which one had to live. With the exception of the materialistic “heretics,” philosophic thought was rarely afflicted by the afflictions of human existence. Paradoxically, it is precisely the critical intent in philosophic thought which leads to the idealistic purifications critical intent which aims at the empirical world as a whole, and not merely at certain modes of thinking or behaving within it. Defining its concepts in terms of potentialities which are of an essentially different order of thought and existence, the philosophic critique finds itself blocked by the reality from which it dissociates itself, and proceeds to construct a realm of Reason purged from empirical contingency. The two dimensions of thought — that of the essential and that of — the apparent truths — no longer interfere with each other, and their concrete dialectical relation becomes an abstract epistemological or ontological relation. The judgments passed on the given reality are replaced by propositions defining the general forms of thought, objects of thought, and relations between thought and its objects. The subject of thought becomes the pure and universal form of subjectivity, from which all particulars are removed.”

Source: One-Dimensional Man (1964), pp. 135-136

Ilana Mercer photo

“The paleolibertarian grasps that liberty has a civilizational dimension, stripped of which the libertarian non-aggression axiom, by which we all must live, cannot endure.”

Ilana Mercer South African writer

" Cathy Reisenwitz Redux: Steigerwald, Oy Vey Gevalt! https://thelibertarianalliance.com/2015/01/14/ilana-mercer-cathy-reisenwitz-redux-steigerwald-oy-gevalt/" Libertarian Alliance, January 14, 2015
2010s, 2015

William Grey Walter photo
Ursula Goodenough photo
Paul Fussell photo
Javad Alizadeh photo
Li Hongzhi photo

“Until the artist is dead, we are not able to determine his work in all its dimensions.”

Anselm Kiefer (1945) German painter and sculptor

(1986) n.p.
Structures are no longer valid', in "Ein Gespräch..."

“Most work for their belly, for cloth of cubit dimension
Some worship Lakshmi’s spouse for salvation
Lifting palanquins Is for their belly
Fighting powerful wrestlers is for the belly
Telling lies is for the belly
Thinking of Lord is for salvation
Concocting politics is for the belly
Riding elephant or horse is for the belly
Hurting other people is for belly
To pray Lord is for emancipation
Lifting heavy rocks is for the belly
Yelling loud is for the belly
Pray Purandara Vittala is for salvation
With pre-planned contemplation.”

Purandara Dasa (1484–1564) Music composer

In this composition Dasa describes the plight of the working class to work for their survival as the rich exploit them, as quoted here[Narayan, M.K.V., Lyrical Musings on Indic Culture: A Sociology Study of Songs of Sant Purandara Dasa, http://books.google.com/books?id=-r7AxJp6NOYC&pg=PA79, 1 January 2010, Readworthy, 978-93-80009-31-5, 85]

Bill McKibben photo
Varadaraja V. Raman photo

“The aesthetic dimensions of science, like that of great classical music, are evident to the aficionado.”

Varadaraja V. Raman (1932) American physicist

page 299
Truth and Tension in Science and Religion

Theo van Doesburg photo
Alberto Giacometti photo
Theodore Wilbur Anderson photo
Herbert Marcuse photo
Edwin Abbott Abbott photo
Humberto Maturana photo
Jan Oort photo
Ken Wilber photo
Henry Moore photo
Pauline Kael photo
Slavoj Žižek photo
Benoît Mandelbrot photo
Rudy Rucker photo

“I had formed a vague idea that the sex sphere was a hypersphere extending into the fourth dimension. Which meant that if the sphere's giant cunt swallowed me I could end up somewhere very... different.”

Rudy Rucker (1946) American mathematician, computer scientist, science fiction author and philosopher

Source: The Sex Sphere (1983), p. 84

Zhuangzi photo
John Horgan (journalist) photo
Ossip Zadkine photo
Ernest Flagg photo
Lisa Randall photo
Solomon Asch photo
Marshall McLuhan photo

“The anguish of the third dimension is given its first verbal manifestation in poetic history in King Lear.”

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

Source: 1960s, The Gutenberg Galaxy (1962), p. 18

Herbert Marcuse photo

“In the most advanced areas of this civilization, the social controls have been introjected to the point where even individual protest is affected at its roots. The intellectual and emotional refusal “to go along” appears neurotic and impotent. This is the socio-psychological aspect of the political event that marks the contemporary period: the passing of the historical forces which, at the preceding stage of industrial society, seemed to represent the possibility of new forms of existence. But the term “introjection” perhaps no longer describes the way in which the individual by himself reproduces and perpetuates the external controls exercised by his society. Introjection suggests a variety of relatively spontaneous processes by which a Self (Ego) transposes the “outer” into the “inner.” Thus introjection implies the existence of an inner dimension distinguished from and even antagonistic to the external exigencies—an individual consciousness and an individual unconscious apart from public opinion and behavior. The idea of “inner freedom” here has its reality: it designates the private space in which man may become and remain “himself.” Today this private space has been invaded and whittled down by technological reality. Mass production and mass distribution claim the entire individual, and industrial psychology has long since ceased to be confined to the factory. The manifold processes of introjection seem to be ossified in almost mechanical reactions. The result is, not adjustment but mimesis: an immediate identification of the individual with his society and, through it, with the society as a whole. This immediate, automatic identification (which may have been characteristic of primitive forms of association) reappears in high industrial civilization; its new “immediacy,” however, is the product of a sophisticated, scientific management and organization. In this process, the “inner” dimension of the mind in which opposition to the status quo can take root is whittled down. The loss of this dimension, in which the power of negative thinking—the critical power of Reason—is at home, is the ideological counterpart to the very material process in which advanced industrial society silences and reconciles the opposition. The impact of progress turns Reason into submission to the facts of life, and to the dynamic capability of producing more and bigger facts of the same sort of life. The efficiency of the system blunts the individuals' recognition that it contains no facts which do not communicate the repressive power of the whole. If the individuals find themselves in the things which shape their life, they do so, not by giving, but by accepting the law of things—not the law of physics but the law of their society.”

Source: One-Dimensional Man (1964), pp. 9-11

Abraham Joshua Heschel photo
Joyce Carol Oates photo
John Perkins photo
Vitruvius photo
Edwin Abbott Abbott photo
Willem de Sitter photo

“To help us to understand three-dimensional spaces, two-dimensional analogies may be very useful… A two-dimensional space of zero curvature is a plane, say a sheet of paper. The two-dimensional space of positive curvature is a convex surface, such as the shell of an egg. It is bent away from the plane towards the same side in all directions. The curvature of the egg, however, is not constant: it is strongest at the small end. The surface of constant positive curvature is the sphere… The two-dimensional space of negative curvature is a surface that is convex in some directions and concave in others, such as the surface of a saddle or the middle part of an hour glass. Of these two-dimensional surfaces we can form a mental picture because we can view them from outside… But… a being… unable to leave the surface… could only decide of which kind his surface was by studying the properties of geometrical figures drawn on it. …On the sheet of paper the sum of the three angles of a triangle is equal to two right angles, on the egg, or the sphere, it is larger, on the saddle it is smaller. …The spaces of zero and negative curvature are infinite, that of positive curvature is finite. …the inhabitant of the two-dimensional surface could determine its curvature if he were able to study very large triangles or very long straight lines. If the curvature were so minute that the sum of the angles of the largest triangle that he could measure would… differ… by an amount too small to be appreciable… then he would be unable to determine the curvature, unless he had some means of communicating with somebody living in the third dimension…. our case with reference to three-dimensional space is exactly similar. …we must study very large triangles and rays of light coming from very great distances. Thus the decision must necessarily depend on astronomical observations.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

“He had come there dissatisfied with his work, even though his multi-kinetic work was admired and winning him professional recognition. However, at that moment, other ideas were gestating and he wanted to add what he called a "fifth dimension" to his art - that of artificial intelligence. […] : [At the colony, ] he was able to turn his thoughts inward, hoping to discover the new methods and direction that would more deeply satisfy his creative needs. It was at this point, while watching the motions and patterns of sun on leaves in the New Hampshire woods one morning, that Tsai finally achieved the revelatory breakthrough that changed his art and liberated his creative energies. As he put it, he wanted to create "natural movements in dynamic equilibrium, with intelligence," and he found his solution in an unlikely combination of natural phenomenon, the precedent of Gabo's singular (and unrepeated) kinetic sculpture, and the new resource of contemporary analog and digital technology. Speaking of this moment of revelation, Tsai said that he had quite deliberately turned himself into "a sort of plant": facing his chair into the sunshine in the morning, he turned his body in stages throughout the day, mulling over ways of make an "art that presented the observer with natural movements in dynamic equilibrium, and art that could convey the awe I felt while watching sunbeams shimmer through forest leaves." But a work that would "shimmer" simply did not do enough either for the artist or viewer, Tsai concluded. It must also respond in some way to the observer; it would have to work on a new feedback principle and actually engage the observer directly. In short, a cybernetic sculpture was required. To create such radically participatory works, he understood, would require that he draw on his engineering skills rather than suppress them, as he had been trying to do in his period of oil painting.”

Sam Hunter (1923–2014) American art historian

Source: The Cybernetic Sculpture of Tsai Wen-Ying, 1989, p. 67

Jane Roberts photo
Charles Bukowski photo

“Business process reengineering encompasses the envisioning of new work strategies, the actual process design activity, and the implementation of the change in all its complex technological, human, and organizational dimensions”

Thomas H. Davenport (1954) American academic

Thomas H. Davenport, "Need radical innovation and continuous improvement? Integrate process reengineering and TQM." Planning Review 21.3 (1993): 6-12.

“Hui Shih was a man of many devices and his writings would fill five carriages. But his doctrines were jumbled and perverse and his words wide of the mark. His way of dealing with things may be seen from these sayings:
"The largest thing has nothing beyond it; it is called the One of largeness. The smallest thing has nothing within it; it is called the One of smallness."
"That which has no thickness cannot be piled up; yet it is a thousand li in dimension."
"Heaven is as low as earth; mountains and marshes are on the same level."
"The sun at noon is the sun setting. The thing born is the thing dying."
"Great similarities are different from little similarities; these are called the little similarities and differences. The ten thousand things are all similar and are all different; these are called the great similarities and differences."
"The southern region has no limit and yet has a limit."
"I set off for Yueh today and came there yesterday."
"Linked rings can be separated."
"I know the center of the world: it is north of Yen and south of Yueh."”

"Let love embrace the ten thousand things; Heaven and earth are a single body."
'With sayings such as these, Hui Shih tried to introduce a more magnanimous view of the world and to enlighten the rhetoricians.'
Zhuangzi, Ch. 33, as translated by Burton Watson (1968), p. 374; this contains the core of what has survived of Hui Shi's philosophy, most of the records of it having been eradicated in the vast "burning of books and burying of scholars" during the Legalism of the Qin dynasty.

Gilbert Wakefield photo
Paul Klee photo
Rollo May photo
Andrea Dworkin photo
Byron Katie photo

“We are entering the dimension where we have control - the inside.”

Byron Katie (1942) American spiritual writer

Loving What Is: Four Questions That Can Change Your Life (2002)

Václav Havel photo

“There are no exact guidelines. There are probably no guidelines at all. The only thing I can recommend at this stage is a sense of humor, an ability to see things in their ridiculous and absurd dimensions, to laugh at others and at ourselves, a sense of irony regarding everything that calls out for parody in this world.”

Václav Havel (1936–2011) playwright, essayist, poet, dissident and 1st President of the Czech Republic

Address upon receiving the Open Society Prize awarded by Central European University (24 June 1999) http://old.hrad.cz/president/Havel/speeches/1999/2406_uk.html
Variant translation: There are no exact directions. There are probably no directions at all. The only things that I am able to recommend at this moment are: a sense of humour; an ability to see the ridiculous and the absurd dimensions of things; an ability to laugh about others as well as about ourselves; a sense of irony; and, of everything that invites parody in this world. In other words: rising above things, or looking at them from a distance; sensibility to the hidden presence of all the more dangerous types of conceit in others, as well as in ourselves; good cheer; an unostentatious certainty of the meaning of things; gratitude for the gift of life and courage to assume responsibility for it; and, a vigilant mind.
Those who have not lost the ability to recognize that which is laughable in themselves, or their own nothingness, are not arrogant, nor are they enemies of an Open Society. Its enemy is a person with a fiercely serious countenance and burning eyes.
Context: There are no exact guidelines. There are probably no guidelines at all. The only thing I can recommend at this stage is a sense of humor, an ability to see things in their ridiculous and absurd dimensions, to laugh at others and at ourselves, a sense of irony regarding everything that calls out for parody in this world. In other words, I can only recommend perspective and distance. Awareness of all the most dangerous kinds of vanity, both in others and in ourselves. A good mind. A modest certainty about the meaning of things. Gratitude for the gift of life and the courage to take responsibility for it. Vigilance of spirit.

Roger Ebert photo

“I find it a way to elevate the whole story into a larger realm of inexplicable but real behavior. We need something beyond the human to add another dimension.”

Roger Ebert (1942–2013) American film critic, author, journalist, and TV presenter

Review of Magnolia (1999), in review for Great Movies (27 November 2008) http://www.rogerebert.com/reviews/great-movie-magnolia-1999
Reviews, Four star reviews
Context: Magnolia is a film of sadness and loss, of lifelong bitterness, of children harmed and adults destroying themselves. As the narrator tells us near the end, "We may be through with the past, but the past is never through with us." In this wreckage of lifetimes, there are two figures, a policeman and a nurse, who do what they can to offer help, hope and love. … The central theme is cruelty to children, and its lasting effect. This is closely linked to a loathing or fear of behaving as we are told, or think, that we should. … As an act of filmmaking, it draws us in and doesn't let go. It begins deceptively, with a little documentary about amazing coincidences (including the scuba diver scooped by a fire-fighting plane and dumped on a forest fire) … coincidences and strange events do happen, and they are as real as everything else. If you could stand back far enough, in fact, everything would be revealed as a coincidence. What we call "coincidences" are limited to the ones we happen to notice. … In one beautiful sequence, Anderson cuts between most of the major characters all simultaneously singing https://www.youtube.com/watch?v=aNmKghTvj0E Aimee Mann's "It's Not Going to Stop." A directorial flourish? You know what? I think it's a coincidence. Unlike many other "hypertext movies" with interlinking plots, Magnolia seems to be using the device in a deeper, more philosophical way. Anderson sees these people joined at a level below any possible knowledge, down where fate and destiny lie. They have been joined by their actions and their choices.
And all leads to the remarkable, famous, sequence near the film's end when it rains frogs. Yes. Countless frogs, still alive, all over Los Angeles, falling from the sky. That this device has sometimes been joked about puzzles me. I find it a way to elevate the whole story into a larger realm of inexplicable but real behavior. We need something beyond the human to add another dimension. Frogs have rained from the sky eight times this century, but never mind the facts. Attend instead to Exodus 8:2, which is cited on a placard in the film: "And if thou refuse to let them go, behold, I will smite your whole territory with frogs." Let who go? In this case, I believe, it refers not to people, but to fears, shames, sins.
Magnolia is one of those rare films that works in two entirely different ways. In one sense, it tells absorbing stories, filled with detail, told with precision and not a little humor. On another sense, it is a parable. The message of the parable, as with all good parables, is expressed not in words but in emotions. After we have felt the pain of these people, and felt the love of the policeman and the nurse, we have been taught something intangible, but necessary to know.

“Great drama, drama that may reach the alchemical level, must have dimension and its relevance will take care of itself.”

Robertson Davies (1913–1995) Canadian journalist, playwright, professor, critic, and novelist

Alchemy in the Theatre (1994).
Context: Great drama, drama that may reach the alchemical level, must have dimension and its relevance will take care of itself. Writing about AIDS rather than the cocktail set, or possibly the fairy kingdom, will not guarantee importance.... The old comment that all periods of time are at an equal distance from eternity says much, and pondering on it will lead to alchemical theatre while relevance becomes old hat.

John F. Kennedy photo

“I want to talk about our common responsibilities in the face of a common danger. The events of recent weeks may have helped to illuminate that challenge for some; but the dimensions of its threat have loomed large on the horizon for many years.”

John F. Kennedy (1917–1963) 35th president of the United States of America

1961, Address to ANPA
Context: I want to talk about our common responsibilities in the face of a common danger. The events of recent weeks may have helped to illuminate that challenge for some; but the dimensions of its threat have loomed large on the horizon for many years. Whatever our hopes may be for the future — for reducing this threat or living with it — there is no escaping either the gravity or the totality of its challenge to our survival and to our security — a challenge that confronts us in unaccustomed ways in every sphere of human activity.
This deadly challenge imposes upon our society two requirements of direct concern both to the press and to the President — two requirements that may seem almost contradictory in tone, but which must be reconciled and fulfilled if we are to meet this national peril. I refer, first, to the need for a far greater public information; and, second, to the need for far greater official secrecy.

Edwin Abbott Abbott photo

“Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial Revelation has been made to me for nothing. Prometheus up in Spaceland was bound for bringing down fire for mortals, but I — poor Flatland Prometheus — lie here in prison for bringing down nothing to my countrymen. Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.”

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 22. How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result
Context: My brother is one of the best of Squares, just, sensible, cheerful, and not without fraternal affection; yet I confess that my weekly interviews, at least in one respect, cause me the bitterest pain. He was present when the Sphere manifested himself in the Council Chamber; he saw the Sphere's changing sections; he heard the explanation of the phenomena then given to the Circles. Since that time, scarcely a week has passed during seven whole years, without his hearing from me a repetition of the part I played in that manifestation, together with ample descriptions of all the phenomena in Spaceland, and the arguments for the existence of Solid things derivable from Analogy. Yet — I take shame to be forced to confess it — my brother has not yet grasped the nature of the Third Dimension, and frankly avows his disbelief in the existence of a Sphere.Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial Revelation has been made to me for nothing. Prometheus up in Spaceland was bound for bringing down fire for mortals, but I — poor Flatland Prometheus — lie here in prison for bringing down nothing to my countrymen. Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.That is the hope of my brighter moments. Alas, it is not always so. Heavily weighs on me at times the burdensome reflection that I cannot honestly say I am confident as to the exact shape of the once-seen, oft-regretted Cube; and in my nightly visions the mysterious precept, "Upward, not Northward", haunts me like a soul-devouring Sphinx. It is part of the martyrdom which I endure for the cause of the Truth that there are seasons of mental weakness, when Cubes and Spheres flit away into the background of scarce-possible existences; when the Land of Three Dimensions seems almost as visionary as the Land of One or None; nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the substantial realities of Flatland itself, appear no better than the offspring of a diseased imagination, or the baseless fabric of a dream.

Bill Bailey photo
Edwin Abbott Abbott photo

“I awoke rejoicing, and began to reflect on the glorious career before me. I would go forth, methought, at once, and evangelize the whole of Flatland. Even to Women and Soldiers should the Gospel of Three Dimensions be proclaimed. I would begin with my Wife.”

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 21. How I Tried to Teach the Theory of Three Dimensions to My Grandson, and With What Success
Context: I awoke rejoicing, and began to reflect on the glorious career before me. I would go forth, methought, at once, and evangelize the whole of Flatland. Even to Women and Soldiers should the Gospel of Three Dimensions be proclaimed. I would begin with my Wife.
Just as I had decided on the plan of my operations, I heard the sound of many voices in the street commanding silence. Then followed a louder voice. It was a herald's proclamation. Listening attentively, I recognized the words of the Resolution of the Council, enjoining the arrest, imprisonment, or execution of any one who should pervert the minds of the people by delusions, and by professing to have received revelations from another World.

Edwin Abbott Abbott photo

“I take shame to be forced to confess it — my brother has not yet grasped the nature of the Third Dimension, and frankly avows his disbelief in the existence of a Sphere.”

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 22. How I Then Tried to Diffuse the Theory of Three Dimensions by Other Means, and of the Result
Context: My brother is one of the best of Squares, just, sensible, cheerful, and not without fraternal affection; yet I confess that my weekly interviews, at least in one respect, cause me the bitterest pain. He was present when the Sphere manifested himself in the Council Chamber; he saw the Sphere's changing sections; he heard the explanation of the phenomena then given to the Circles. Since that time, scarcely a week has passed during seven whole years, without his hearing from me a repetition of the part I played in that manifestation, together with ample descriptions of all the phenomena in Spaceland, and the arguments for the existence of Solid things derivable from Analogy. Yet — I take shame to be forced to confess it — my brother has not yet grasped the nature of the Third Dimension, and frankly avows his disbelief in the existence of a Sphere.Hence I am absolutely destitute of converts, and, for aught that I can see, the millennial Revelation has been made to me for nothing. Prometheus up in Spaceland was bound for bringing down fire for mortals, but I — poor Flatland Prometheus — lie here in prison for bringing down nothing to my countrymen. Yet I exist in the hope that these memoirs, in some manner, I know not how, may find their way to the minds of humanity in Some Dimension, and may stir up a race of rebels who shall refuse to be confined to limited Dimensionality.That is the hope of my brighter moments. Alas, it is not always so. Heavily weighs on me at times the burdensome reflection that I cannot honestly say I am confident as to the exact shape of the once-seen, oft-regretted Cube; and in my nightly visions the mysterious precept, "Upward, not Northward", haunts me like a soul-devouring Sphinx. It is part of the martyrdom which I endure for the cause of the Truth that there are seasons of mental weakness, when Cubes and Spheres flit away into the background of scarce-possible existences; when the Land of Three Dimensions seems almost as visionary as the Land of One or None; nay, when even this hard wall that bars me from my freedom, these very tablets on which I am writing, and all the substantial realities of Flatland itself, appear no better than the offspring of a diseased imagination, or the baseless fabric of a dream.

Gerald James Whitrow photo

“Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century.”

Gerald James Whitrow (1912–2000) British mathematician

"Why Physical Space has Three Dimensions," British Journal for the Philosophy of Science, 6 #21 (May 1955)
Context: Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century. In a manuscript treatise, he sought a graphic representation of the Aristotelian forms, such as heat, velocity, sweetness, by laying down a line as a basis designated longitudo, and taking one of the forms to be represented by lines (straight or circular) perpendicular to this either as a latitudo or an altitudo. The form was thus represented graphically by a surface. Oresme extended this process by taking a surface as the basis which, together with the latitudo, formed a solid. Proceeding still further, he took a solid as a basis and upon each point of this solid he entered the increment. He saw that this process demanded a fourth dimension which he rejected; he overcame the difficulty by dividing the solid into numberless planes and treating each plane in the same manner as the plane above, thereby obtaining an infinite number of solids which reached over each other. He uses the phrase "fourth dimension" (4am dimensionem).

Gerald James Whitrow photo

“He uses the phrase "fourth dimension" (4am dimensionem).”

Gerald James Whitrow (1912–2000) British mathematician

"Why Physical Space has Three Dimensions," British Journal for the Philosophy of Science, 6 #21 (May 1955)
Context: Perhaps the first to approach the fourth dimension from the side of physics, was the Frenchman, Nicole Oresme, of the fourteenth century. In a manuscript treatise, he sought a graphic representation of the Aristotelian forms, such as heat, velocity, sweetness, by laying down a line as a basis designated longitudo, and taking one of the forms to be represented by lines (straight or circular) perpendicular to this either as a latitudo or an altitudo. The form was thus represented graphically by a surface. Oresme extended this process by taking a surface as the basis which, together with the latitudo, formed a solid. Proceeding still further, he took a solid as a basis and upon each point of this solid he entered the increment. He saw that this process demanded a fourth dimension which he rejected; he overcame the difficulty by dividing the solid into numberless planes and treating each plane in the same manner as the plane above, thereby obtaining an infinite number of solids which reached over each other. He uses the phrase "fourth dimension" (4am dimensionem).

Edwin Abbott Abbott photo

“An unspeakable horror seized me. There was a darkness; then a dizzy, sickening sensation of sight that was not like seeing; I saw a Line that was no Line; Space that was not Space: I was myself, and not myself. When I could find voice, I shrieked aloud in agony, "Either this is madness or it is Hell." "It is neither," calmly replied the voice of the Sphere, "it is Knowledge; it is Three Dimensions: open your eye once again and try to look steadily."”

Source: Flatland: A Romance of Many Dimensions (1884), PART II: OTHER WORLDS, Chapter 18. How I came to Spaceland, and What I Saw There
Context: An unspeakable horror seized me. There was a darkness; then a dizzy, sickening sensation of sight that was not like seeing; I saw a Line that was no Line; Space that was not Space: I was myself, and not myself. When I could find voice, I shrieked aloud in agony, "Either this is madness or it is Hell." "It is neither," calmly replied the voice of the Sphere, "it is Knowledge; it is Three Dimensions: open your eye once again and try to look steadily."I looked, and, behold, a new world! There stood before me, visibly incorporate, all that I had before inferred, conjectured, dreamed, of perfect Circular beauty. What seemed the centre of the Stranger's form lay open to my view: yet I could see no heart, nor lungs, nor arteries, only a beautiful harmonious Something — for which I had no words; but you, my Readers in Spaceland, would call it the surface of the Sphere.