[…] While giving someone a definition of the fourth dimension is relatively easy, giving someone an intuitive understanding of **the fourth dimension** can be quite difficult. A definition of the fourth dimension could go like this: **The fourth dimension** is all space that one can get to by travelling in a direction perpendicular to three-dimensional space. Whenever an uninitiated person hears this, they start pointing their finger around in the air, trying to figure out how it’s possible for such a direction to exist. Such a short explanation gives them no intuitive feeling of **the fourth dimension**. […]

[…] **The Fourth Dimension**, space-time continuum, is reality. In **the fourth dimension** the infinite number of solids in the Universe are in relationship with each other through time and energy. In the Time domain, **the Fourth Dimension** continues the movement of the Third Dimension (Past) to form a wave, constituting fractally the space-time continuum. […]

[…] **The fourth dimension** is, simply, something beyond our comprehension.Or maybe, everything. As a mathematical possibility, **the fourth dimension** begins with Euclid’s Fifth Postulate, which outlines the following proof: […]

“The ideas in The Large Glass are more important than the actual realization. The Large Glass constitutes a rehabilitation of perspective. For me, it’s a mathematical, scientific perspective, based on calculations and on dimensions. Everything was becoming conceptual, that is, it depended on things other than the retina. What we were interested in at the time was **the fourth dimension**. Simply, I thought of the idea of a projection, of an invisible **fourth dimension**, something you couldn’t see with your eyes. The Bride in The Large Glass was based on this, as if it were the projection of a **four-dimensional** object. I called The Bride a “delay in glass”. A tactile sensation which envelops every side of an object approaches a tactile sensation of **four dimensions**. Consequently the act of love as tactile sublimation could be felt as a physical interpretation of **the 4th dimension**.” Marcel Duchamp

[…] According to Marcel Duchamp, “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” (University of Vienna). **The fourth dimension****,** time, was an elusive element to capture using traditional methods of art, but with the advent of Net art, characterizing time is no longer an obstacle. […]

[…] In striking contrast to Marcel Duchamp’s Nude Descending a Staircase (1912) where the figures represent successive points in time, seen as coexisting in t**he fourth dimension**, Picasso’s painting culminates with a superimposed set of three-dimensional projections of an object in **four** spatial **dimensions**. […]

[…] Compare then the relationships in the Large Glass. The whole of the Glass is female and represents the world or nature, which is prior to the formation of the human female (in the top half of the work), and the formation of the male from the female, who do not consummate their relationship. Because his primary concern is the logic of myth, Duchamp leaves the sexual outside the Large Glass, in what he calls
**the fourth dimension** and, as an aesthete, he refrains from expressing an understanding of good and evil. […]

[…] Transexual Geometry (Deconstructing Duchamp) A three-dimensional object casts a shadow in only two dimensions. From that observation Duchamp concluded that a three-dimensional object must, in turn, be the shadow of another object in **four dimensions**. […]

[…] To summarize, Duchamp described his Large Glass as **four-dimensional**; the fourth dimension cannot be physically seen, yet we see the Glass in three-dimensions. The Poincaré cut itself can translate a **fourth-dimensional** system that we can’t see into a lower third-dimensional slice that becomes visible. Look at Illustration 2B. […]

[…] This idea of **the fourth dimension**, (while somewhat difficult to grasp since we can only perceive the world in 3 dimensions) has parallels to the notion of “cyberspace” that annoying term for the nebulous universe of computer interaction. “The glass as ‘ground’ has a function and status anticipating that of the computer monitor as a screen of operations – of transformations – and the site of interaction and negotiation of meaning”. […]

[…] I think that the avant-garde with its radical change of viewpoint contributed to adding to this fascination with the past. Man Ray looked at tribal cultures, Gauguin exotic cultures, Duchamp with the esoteric. It is they who opened the doors for a different perception of time and space. Then Einstein’s **fourth dimension**, which the avant-garde was witness to, changed man’s relationship with time-space. […]

[…] Whichever of the formulations one picks the consequence is the destruction of the time continuum. By having space/time,
**the fourth dimension**, invade the materiality of the world all is turned into light and time into a ‘tele-presence’. […]

[…] The skeleton was then mathematically extruded into **the fourth dimension** by adding a fourth coordinate to every three-dimensional point. Thus, points became lines, lines became polygons, polygons became cubes and cubes became hypercubes. The resulting four-dimensional object was rotated about a plane in **four-dimensional space** according to the appropriate matrix transformations. The transformed object, projected back into three-dimension space, became a space-frame of variant dimensions. The skin was not extruded into **the fourth dimension** but instead remapped to create a rippling, non-homogeneous surface. […]

[…] They make up an “information” or “orbital front,” as Virilio has called it, which operates in **a fourth dimension**, an “exo-spheric” and strictly temporal dimension, “that of the real time of ubiquity and instantaneity, ... less physical than microphysical”. 20,000 kilometers and 6/100ths of a second overhead, they are transmitting – now. […]

[…] In so doing, Constant perpetuated the precepts of “moving urban situations” championed by Debord and the Situationists. He was also subject both to the influence of the mega-structures and “streets in space” proposed by Team X and Aldo van Eyck, who themselves develop maze-like, suspended urban forms, and to the influence of Alison and Peter Smithson, in England, who support the concept of “ceaseless changes” within urban grids and the complexity of the “human association”. “New Babylon” time is one involving a slow flow of human movements. “It is actually more a question of a continually changing micro-structure, in which the time factor – **the fourth dimension** – plays a considerable role” (2). In the 1980s, Deleuze and Guattari developed the concept of “deterritorialization”, a decentralized, hierarchy-less space ; and they defended the idea of intensities and their nomadic organization of movement and flux. Nowadays, an architect like Michael Sorkin is updating this notion of trajectory in his urban projects. He talks to us about a “culture of encapsulation” (vehicles, trains etc) which co-exists with a phenomenon of neo-nomadism with an electronic heart. […]

[…] The mass transportation revolution of the nineteenth century changed the ways cities were occupied and conceived. The broadband revolution of the twentieth century alters the modernist conception of space-time. Virilio describes being “telepresent” (10) as being in two places at the same time; events take place in no place. Thus **the fourth dimension** of time (or the dimension of the present) is called into question. Urbanization of the city is replaced by the urbanization of man’s corporeal body in which he becomes, “the ultimate vehicle: the static audio-visual vehicle…” […]

[…] “10. TIME AND SPACE – The new architecture takes account not only of space but also of time as an architectural value. The unity of space and time gives architectural vision a more complete aspect. 11. THE PLASTIC ASPECT is obtained by **the fourth dimension** of space time… 15. COLOR… with the birth of modern architecture the painter-constructor found his true field of creative action. He organizes color aesthetically in space-time and makes a new dimension visible plastically...” […]

[…] **The fourth dimension** resurfaced in popular culture earlier than a casual observer might think. “It had been there all along in science fiction”, Chernosky notes, “in that sub-genre known as space opera”. The real rebirth, however, came with the rise of computer networks in the early 1980s. “A technology gets invented that needs a word”, Chernosky says. “It’s hard to trace exactly where a usage begins, but very quickly the word becomes popularized.” […]

[…] So this kind of **fourth dimension** or new continent is to be understood under the term Cyberia. “We are mutating into another species – from Aquaria to the Terrarium, and now we’re moving into Cyberia. We are creatures crawling to the center of the cybernetic world.” (Leary 1994: VII) And America is so heading to replace our cosmology and creation stories: “A worldpower like the United States has the possibilities and the technical means to create an own mythology of the 20th century. [..] The old european, chtonic creation-stories become this way replaced through galactic myths.” (Bilwet 1994: 188 – transl. S.J:) This new mythology says that everything is digital. So let’s get wired, let’s enter **the fourth dimension**. […]

[…] Science has therefore introduced a **fourth dimension**, namely time. One has however to realise, that that, what we perceive as time is only the indirect perception, of what is represented in a **fourth dimension**. [..] In astronomy however there are concrete models of the world, in which time becomes included into many reflections as **the fourth dimension** and as concrete fact. […]

[…] The apotheosis of humor in contemporary sculpture-defined broadly as three-dimensional work, often with **a fourth dimension** introduced by motors, lights, or video-owes everything to the most humorless revolution in art history: Minimalism. […]

[…] This is Stelarc’s “Fractal Body”. In the cyborg **fourth dimension**, the serial probings, sensitizations, expressions, transductions, relays, and transmissions of the body are coaxed into co-presence with each other. All of the operations are held in ready reserve, as randomly accessible openings. The body as RAO (random-access opening) can connect in any number of ways to itself, its objects, and other bodies. It can open, split and reconnect at any point, inside or out. It is no longer an objective volume, but an extendability. Its dimensionality has increased beyond the three of spatial presence: from the three-dimensions of the voluminous, to **the fourth dimension** of the extensile. Except that this **“fourth” dimension** is actually fractal, between dimensions. Split and extend: the basic operation used to generate fractal figures. The “fractalization” of the body is no metaphor. It is an operation: the ur-operation of the posthuman. […]

[…] Any adaptation, indeed, every realization of a **fourth dimension** can be a world constituent only if it is not considered as a merely incremental, but as an integrating dimension. If it is considered, in other words, merely as an incremental dimension and utilized as such, the result is merely a further expansion of ‘space’ which can and would have a world-destructive effect. There are already initial and extremely tangible examples of the effects of an incompletely realized **fourth dimension**, as in the negative manifestation of atomic fission. For this reason we emphasize that **the fourth dimension** of the aperspectival world must serve consciousness as an integral function, as systasis; only then will it be a world-constituent. If it serves on the other hand as a merely incremental and expansive quantity it will destroy not just the mental-rational structure but also the genuine form of the incipient integral structure. […]

Hyperspace Structures – Exploring the **fourth dimension**

Spirits, Art, and **the Fourth Dimension**

Signs of **the Fourth Dimension** in Modern Art

Manning, Henry P., ed. **The Fourth Dimension** Simply Explained

Some Notes on **the Fourth Dimension**

Astronomy Bizarre: **The Fourth Dimension**