“If a shadow is a two-dimensional projection of the three-dimensional world, then the three-dimensional world as we know it is the projection of the four-dimensional Universe.”

— Marcel Duchamp

Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "If a shadow is a two-dimensional projection of the three-dimensional world, then the three-dimensional world as we know…" by Marcel Duchamp?

Marcel Duchamp 66

French painter and sculptor 1887–1968

Ronald DeWolf (1934–1991) American critic of Scientology

Interview in Penthouse (June 1983)
Context: I don't think that anyone should think for you. And that's exactly what cults do. All cults, including Scientology, say, "I am your mind, I am your brain. I've done all the work for you, I've laid the path open for you. All you have to do is turn your mind off and walk down the path I have created." Well, I have learned that there's great strength in diversity, that a clamorous discussion or debate is very healthy and should be encouraged. That's why I like our political setup in the United States: simply because you can fight and argue and jump up and down and shout and scream and have all kinds of viewpoints, regardless of how wrongheaded or ridiculous they might be. People here don't have to give up their right to perceive things the way they believe. Scientology and all the other cults are one-dimensional, and we live in a three-dimensional world. Cults are as dangerous as drugs. They commit the highest crime: the rape of the soul.

“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

“The triangles that we can measure are not large enough… to detect the curvature. Fortunately, however, we are, in a way, able to communicate with the fourth dimension. The theory of relativity has given us an insight into the structure of the real universe: …a four-dimensional structure. The study of the way in which the three space-dimensions are interwoven with the time-dimension affords a kind of outside point of view of the three-dimensional space… from this outside point of view we might be able to perceive the curvature of the three-dimensional world.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932)

“The quest of the absolute leads into the four-dimensional world.”

Arthur Stanley Eddington (1882–1944) British astrophysicist

Source: The Nature of the Physical World (1928), Ch. 2 Relativity

“We live in a three-dimensional world, and our brains are organized in three dimensions, so we might as well compute in three dimensions. …Right now, chips, even though they're very dense, are flat.”

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

"The Singularity," The New Humanists: Science at the Edge (2003)

“The ontological concept of truth is in the centre of a logic which may serve as a model of pre- technological rationality. It is the rationality of a two-dimensional universe of discourse which, contrasts with the of thought and behavior that develop in the execution of the technological project.”

Herbert Marcuse book One-Dimensional Man

Source: One-Dimensional Man (1964), p. 130

“It is well known that in three-dimensional elliptic or spherical geometry the so-called Clifford's parallelism or parataxy has many interesting properties. A group-theoretical reason for the most important of these properties is the fact that the universal covering group of the proper orthogonal group in four variables is the direct product of the universal covering groups of two proper orthogonal groups in three variables. This last-mentioned property has no analogue for orthogonal groups in n (>4) variables. On the other hand, a knowledge of three-dimensional elliptic or spherical geometry is useful for the study of orientable Riemannian manifols of four dimensions, because their tangent spaces possess a geometry of this kind.”

Shiing-Shen Chern (1911–2004) mathematician (1911–2004), born in China and later acquiring U.S. citizenship; made fundamental contributio…

[On Riemannian manifolds of four dimensions, Bulletin of the American Mathematical Society, 51, 12, 1945, 964–971, http://www.ams.org/journals/bull/1945-51-12/S0002-9904-1945-08483-3/S0002-9904-1945-08483-3.pdf]

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

Roger Shepard (1929) American psychologist

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

“Since we only consider the universe on a very large scale, and make abstraction of all details and local irregularities, our universe must be homogeneous and isotropic. It follows… that the three-dimensional space of it must be what mathematicians call a space of constant curvature.”

Willem de Sitter (1872–1934) Dutch cosmologist

Kosmos (1932), Above is Beginning Quote of the Last Chapter: Relativity and Modern Theories of the Universe -->

“A glimpse heavenward at a constellation or even at a single star only suggests infinity; actually our vision is limited. We cannot perceive unlimited space; it is immeasurable. The universe, as we know it through our visual experience, is limited. It first came into existence with the formation of matter, and will end with the complete dissolution of matter.<!-- I TRIMMED this portion to simply cut down a little on quotes from this one essay. ~ 2009·03·21 02:36 Kalki} Where there is matter and action, there is space. Pictorial space exists two dimensionally. When the two dimensionality of a picture is destroyed, it falls into parts — it creates the effect of a naturalistic space. When a picture conveys only naturalistic space, it represents a special case, a portion of what is felt about three-dimensional experience. This expression of the artist’s experience is thus incomplete.”

Hans Hofmann (1880–1966) American artist

'Search for the Real in the Visual Arts', p. 40-48
'Search for the Real in the Visual Arts', p. 43
Search for the Real and Other Essays (1948)

“If a shadow is a two-dimensional projection of the three-dimensional world, then the three-dimensional world as we know it is the projection of the four-dimensional Universe.”

Help us to complete the source, original and additional information

Marcel Duchamp 66

Related quotes

Related topics