No Places and Other Spaces

A Look at Time Travel, the Fourth Dimension, and Peripatopian Architecture


14.04.09 Study Model 4


One concept in the early 20th Century stood out as a topic of fascination across many disciplines. Math, physics, art, literature, and architecture all fell privy to the wonderment of the fourth dimension. Described as the passing of time across a direction within the third dimension, the fourth dimension represented liberation from tradition for the great thinkers of the time. It also bridged the sphere of science with that of art through the writing of the Manifeste Dimensioniste, which encouraged artists to break free of immobile forms. This interest in Dimensionism continued into the later 20th Century in the form of imagined spaces, as explained by Michel Foucault in Of Other Spaces. Thinking of space as a layering of dimensions, Foucault coined the term ‘heterotopia’ to describe the unreal spaces that exist in real society. Considering both the objectives of Dimensionism and the principles of heterotopias, architecture can also break free from traditional static solidity. Instead, peripatopian design explores how architecture can change dimensions in order to move from place to place. The space-breaking conceptions of these 20th Century thinkers have paved the way for 21st Century notions of placeless, purposeless, and peripatetic architecture.


‘You know of course that a mathematical line, a line of thickness nil, has no real existence. They taught you that? Neither has a mathematical plane. These things are mere abstractions.’

‘That is all right,’ said the Psychologist.

‘Nor having only length, breadth, and thickness, can a cube have a real existence.’

– H.G. Wells The Time Machine[1]

In the same era H.G. Wells published The Time Machine in 1895, Isaac Newton’s view of reality was being questioned. Austrian physicist and mathematician Georg Riemann stumbled upon a completely different understanding of physical reality by suggesting the existence of higher dimensions and non-Euclidean geometries. Essentially, an “unseen fourth dimension” exists as a result of the third-dimension being curved.[2] Riemann postulated that, in the same way Newton had based his understanding of three-dimensional space off of the assumption that it is absolute, Euclid had based his geometry off of the assumption that it was situated in a flat planar surface.[3] These challenges towards historically sanctified norms would bring about new conceptions of space in both science and the arts. One such conception is described in Edwin A. Abbot’s Flatland, a scientific romance describing math, physics, and society all before the work of H.G. Wells.[4] Building off of Riemann’s theories and the popularity of an alleged fourth dimension, the 1916 General Theory of Relativity by a young Albert Einstein surpassed Newton’s understanding even further; which assumed space is absolute and uniform, and that time passes through it as an independent entity.[5] Instead, Einstein proposed spacetime as a unifying force between the terms. This theory became accepted in circles beyond the purely scientific, igniting interest in the art and literature of 20th Century pop culture, just as Flatland had done the century before.[6] It seemed as though no major art movement of the first three decades was spared; Cubists, Futurists, Surrealists, Dadaists, Suprematists, and Constructivists all participated.[7] Some movements found the fourth dimension to be a justifiable means of experimenting in new kinds of art, literature, language, and music.[8] Surrealist Salvador Dali, for example, found both the scientific and mystical sides of the fourth dimension attractive.[9] Constructivist Kazimir Malevich thought it representative of a higher enlightened power.[10] Because interpretations spread across so many disciplines the line between science and mysticism blurred. Trained mathematician, but mystic by vocation, Charles Howard Hinton published The Fourth Dimension as an endeavor “to present the subject of the higher dimensionality of space in a clear manner, devoid of mathematical subtleties and technicalities.”[11] To do so, Hinton utilized the tesseract, or hypercube, to visually represent a four dimensional object in a three dimensional world.[12] Still, through the publication of The Fourth Dimension and his other writings, Hinton was only able to represent his conceptions of space on a two dimensional page. Thus the objective of the artists became even more determined.


‘Can a cube that does not last for any time at all, have a real existence?’

Filby became pensive. ‘Clearly,’ the Time Traveller proceeded, ‘any real body must have extension in four directions: it must have Length, Breadth, Thickness, and – Duration.’

– H.G. Wells The Time Machine[13]

Wells’ character of the Time Traveller states that besides the three planes of space, the fourth is simply another way of looking at time.[14] Though Hinton’s representations of the fourth dimension include time, the terms are not interchangeable; it is the passing of time within the third dimension that reveals the tesseract.[15] An example of the passing of time in the third dimension is an object in motion. Motion studies became the most direct method that abstract artists could use in achieving the fourth dimension. Marcel Duchamp, aware of Hinton’s writings, worked to compress time on canvas in Nudes Descending a Staircase.[16] For Duchamp, the studies became ways to go beyond traditional painting techniques and investigate the interrelationship of dimensions.[17] Though the painter realized that merely representing motion on a canvas is not fourth dimensional itself, Duchamp acknowledged that the concepts of form-through-time lead abstract art into geometry and mathematics.[18] Fellow painters of the era, Kandinsky and Delauney, too, found the fourth dimension as a means of redefining aesthetic space and traditional forms. According to Delauney, “The dynamics of space are created here by a latent movement of masses, not by objects frozen in postures of movement.”[19] To the Constructivists, kinetic sculpture became the method of articulating the fourth dimension in art because it conveyed abstract motion.[20] Similarly, the cubist/surrealist sculptor Oscar Dominguez found the life of objects in time fascinating, coining the term lithochronic surface to describe the path of such objects.[21] What these artists were unaware of was how such experimentation would play a progressive role in the future of avant-garde work.


‘That Space, as our mathematicians have it, is spoken of as having three dimensions, which one may call Length, Breadth, and Thickness, and is always definable by reference to three planes, each at right angles to the others. But some philosophical people have been asking why three dimensions particularly – why not another direction at right angles to the other three? – and have even tried to construct a Four-Dimension geometry.’

– H.G. Wells The Time Machine[22]

With such widespread interest in how to represent the fourth dimension, it is almost surprising that it would take until the late 1930s for this conglomeration of “philosophical people” to discuss as a whole. In 1936, avant-gardes ranging from Duchamp to Kandinsky to Moholy-Nagy met in Paris to sign what painter Charles Tamkó Sirató penned as the Manifeste Dimensioniste. By then, the proclamations of these Dimensionists were simply reiterations of earlier beliefs. None the matter, Sirató credited Einstein’s theory as the driving force of “Dimensionisme.”[23] “It is, on the one hand, the modern spirit’s completely new conception of space and time…and on the other, the technical givens of our age, that have called Dimensionism to life.”[24] Essentially, the Manifeste provided a common law for art of the avant-garde: N + 1, meaning all modern art should strive for the next dimension.[25]  Broken into four succinct but vague statements equipped with examples, the Manifeste Dimensioniste declared that I.) Literature should leave the line and enter the plane, 2.) Painting should leave the plane and occupy space, 3.) Sculpture should abandon closed, immobile form, and 4.) The creation of an absolutely new art: cosmic art, or, “the artistic conquest of four-dimensional space” will develop.[26] The art world was already accomplishing the first three proclamations; novels were becoming films, paintings were becoming sculpture and even architecture, and sculpture was becoming kinetic, as exemplified by Rodchenko’s spatial constructions and Calder’s mobiles. Despite these advancements, the manifesto never gained the sort of public attention it deserved. Success, instead, was found in its ability to bring the great avant-gardes of the century together and discuss the combining of modern art with modern science.[27]


‘In some of these visions of Utopias and coming times which I have read, there is a vast amount of detail about building, and social arrangements, and so forth. But while such details are easy enough to obtain when the whole world is contained in one’s imagination, they are altogether inaccessible to a real traveller amid such realities as I found here.’

– H.G. Wells The Time Machine[28]

At the heart of the relationship between modern art and modern science was a desire to break tradition. Just as Einstein had challenged Newton, and Riemann had challenged Euclid, artists of the avant-garde challenged reality. Learning from the advancements of n-dimensional and non-Euclidean geometries, the fourth dimension became a symbol of liberation for artists, departing from visual reality.[29] Until the 20th Century, artists were hindered by traditions such as the musical scale, solid sculpture material, and three-point perspective painting.[30] Instead, the fourth dimension provided a place for the sort of utopian convictions of a higher reality.[31] The way in which Michel Foucault described utopia in Of Other Spaces seems closely related to the convictions of these artists when he says utopias present “society turned upside down.”[32] However, Foucault’s establishment of heterotopias is perhaps more representative of the fourth dimension. Foucault defined heterotopias as the unreal places located in real society.[33] He uses the mirror as an example, because the mirror is a physical object within space that contains a placeless place, providing a “sort of mixed, joint experience.”[34] Interestingly, early theorists like Hinton also saw the mirror as virtual, but this time as a representation of the fourth dimension, because “the surface of the mirror” is “the plane about which movement takes place.” [35] In other words, it is the only moment in three-dimensional space in which the right changes to the left. Hinton went so far as to believe the mirroring of the two sides of the human body was “proof of a fourth dimension spilling out into the world through a central seam.”[36] This overlapping of dimensions becomes prevalent in Foucault’s breaking down of heterotopian principles, the third stating, “the heterotopia is capable of juxtaposing in a single real place several spaces, several sites that are in themselves incompatible.”[37] For example, the cinema projects a three-dimensional space on a two-dimensional screen. In the fourth principle, Foucault again seems to write in the spirit of dimensionism and lithochronic surfaces, describing heterochronies, or “slices in time” in which “men arrive at a sort of absolute break with their traditional time.”[38] Lastly, the sixth principle states that the role of heterotopias is either to create a space of illusion, or to create a space that is other.[39] Foucault’s example of “terrestrial space” speaks vaguely about heterotopias in the same way Sirató’s interest in cosmic space speaks vaguely about the fourth dimension. Whether they are called utopias, heterotopias, four dimensions, or unreal spaces, all terms serve to provoke a questioning of truth and tradition.


‘I have been at work upon this geometry of Four Dimensions for some time. Some of my results are curious.’

– H.G. Wells The Time Machine[40]

Questioning the norm is a view that should be taken in all forms of art: architecture being no exception. Therefore, why not apply the Manifeste Dimensioniste to architectural design? Revisiting the manifesto asserts that architecture has gone beyond structure to the kinetic; beyond program to the purposeless; beyond beauty to the visually ambiguous; and beyond site to the peripatetic. “It is not possible to disregard the fatal intersection of time with space,” writes Foucault.[41] This notion of architecture moving through time and space then pushes the formerly static beyond the third dimension. Let us go beyond constructing walls to create space, because such spaces are static. Let us go beyond immobile places that sit motionless accumulating time. Given the nature of life, constantly moving through time, architecture should support that by having no defined site. Society has already created such undefined spaces; if a subway passenger begins eating a sandwich on the train, that space is no longer only a train, it is a picnic space. According to Foucault, place is just a beginning point for a thing’s movement, which in a way makes every place a no place, or a utopia.[42] The idea of having no place can also be applied to a project that moves from place to place, or peripatopian architecture. “Peripatopian” derives from peri– meaning “around” +patien meaning “to walk” +topos meaning “place.” Add in the purposeless and visually ambiguous construction and, simply put, peripatopian is having an undefined place for an undefined space. The creation of this new construct of architecture could be identified as a heterotopia; simultaneously represented, constructed, and contested.[43] It serves to instill the same desires of the avant-garde, to liberate society from traditional norms, and provoke curiosity in whichever no place it lands.


 ‘A vast, green structure, different in character than any I had hitherto seen…the face of it having the lustre, as well as the pale green tint, a kind of bluish-green…This difference in aspect suggested a difference in use, and I was minded to push on and explore.’

– H.G. Wells The Time Machine[44]

Representing the fourth dimension will forever be a challenge plagued in obscurity; a challenge, however, that should continue to inspire artists, scientists, and especially architects in the forthcoming centuries. The writing of the Manifeste Dimensioniste by Sirató, the representations of Dimensionism by the avant-gardes, and the principles of ‘other’ spaces by Foucault have set the stage for continued exploration. Current research in physics is already pushing beyond General Relativity Theory to String Theory, with the uncovering of dimensions beyond the fourth. These advancements are results of exploration in both concept and action. The principles of peripatopian architecture have been written, and it is the responsibilities of the 21st Century thinkers to act on them. Like the “vast, green structure” that the oracle Wells describes: materials, scale, and tectonics are starting points for architects to experiment with. Through the act of moving architecture in a direction, over time, and across the third dimension, experiencing the fourth dimension is possible. Human life is in motion, and architecture should be too.


Clemons, Leigh. “Staging New Dimensions: Wassily Kandinsky, Der Blaue Reiter Almanac and the Reconfiguration of Artistic Space.” Journal of Dramatic Theory and Criticism vol. 9, no. 1 (1994): 135-142.

Fisher, Kevin. “A Conceptual Prehistory Tracing the Tesseract of the Morph.” In Meta-morphing: visual transformation and the culture of quick-change. Minneapolis: University of Minnesota Press, 2000. 103-127.

Foucault, Michel, and Jay Miskowiec. “Of Other Spaces.” diacritics vol. 16, no. 1 (1986): 22.

Henderson, Linda Dalrymple. “Italian Futurism and “The Fourth Dimension”.” Art Journal vol. 41, no. 4 (1981): 317-323.

Henderson, Linda Dalrymple. “The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion.” Leonardo vol. 17, no. 3 (1984): 205-210.

Malloy, Vanja, M. Crosta, M. Gramegna, and M.l. Ruggiero. “Non-Euclidean Space, Movement and Astronomy in Modern Art: Alexander Calder’s Mobiles and Ben Nicholson’s Reliefs.” EPJ Web of Conferences vol. 58 (2013): 04004.

Wells, H. G.. The Time Machine. S.l.: Duke Classics, 2012. Print.

[1] Wells, 1.

[2] Fisher, 110.

[3] Clemons, 136.

[4] Ibid.

[5] Fisher, 109.

[6] Malloy, 2.

[7] Henderson, Italian Futurism and “The Fourth Dimension”, 317.

[8] Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 206.

[9] Ibid, 208.

[10] Bannister.

[11] Fisher, 114. Hinton begins his preface of The Fourth Dimension by stating how he wants the reader’s interest to be engaged, with a lack of mathematical knowledge proving no disadvantage to the reader.

[12] Fisher, 106.

[13] Wells, 1-2.

[14] Ibid, 2.

[15] Fisher, 115.

[16] Ibid.

[17] Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 205.

[18] Henderson, Italian Futurism and “The Fourth Dimension”, 319. The expression “form-through-time” is used by Fisher in Tracing the Tesseract, 105.

[19] Clemons, 137. Clemons quotes Delauney from “Robert Delaunay’s Methods of Composition,” an article praising his work by E. von Brusse.

[20] Bannister.

[21] Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 208. Though Dominguez recognized time as the fourth dimension, like Wells, Henderson states that his ideas are closer to those that combine time and space, like Hinton’s.

[22] Wells, 2.

[23] Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 206.

[24]Sirató, Manifeste Dimensioniste.

[25] Malloy, 2.

[26]Sirató, Manifest Dimensioniste.

[27] Malloy, 4.

[28] Wells, 51.

[29] Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 205.

[30] Clemons, 137.

[31] Henderson, The Fourth Dimension and Non-Euclidean Geometry in Modern Art, 205.

[32] Foucault, 24.

[33] Ibid.

[34] Ibid.

[35] Fisher, 121.

[36] Ibid.

[37] Foucault, 25.

[38] Ibid, 26.

[39] Ibid, 27.

[40] Wells, 3.

[41] Foucault, 26.

[42] Ibid, 23.

[43] Ibid, 24.

[44] Wells, 66.


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