New possibilities opened up by the concept offour-dimensional space (and difficulties involved in trying to visualize it) helped inspire many modern artists in the first half of the twentieth century. EarlyCubists,Surrealists,Futurists, andabstract artists took ideas fromhigher-dimensional mathematics and used them to radically advance their work.^[1]

FrenchmathematicianMaurice Princet was known as "le mathématicien du cubisme" ("the mathematician of cubism").^[2] An associate of theSchool of Paris—a group ofavant-gardists includingPablo Picasso,Guillaume Apollinaire,Max Jacob,Jean Metzinger, andMarcel Duchamp—Princet is credited with introducing the work ofHenri Poincaré and the concept of the "fourth dimension" to the cubists at theBateau-Lavoir during the first decade of the 20th century.^[3]

Princet introduced Picasso toEsprit Jouffret'sTraité élémentaire de géométrie à quatre dimensions (Elementary Treatise on the Geometry of Four Dimensions, 1903),^[4] a popularization of Poincaré'sScience and Hypothesis in which Jouffret describedhypercubes and other complexpolyhedra in fourdimensions and projected them onto the two-dimensional page. Picasso'sPortrait of Daniel-Henry Kahnweiler in 1910 was an important work for the artist, who spent many months shaping it.^[5] The portrait bears similarities to Jouffret's work and shows a distinct movement away from theProto-Cubistfauvism displayed inLes Demoiselles d'Avignon, to a more considered analysis of space and form.^[6]

Early cubistMax Weber wrote an article entitled "In The Fourth Dimension from a Plastic Point of View", forAlfred Stieglitz's July 1910 issue ofCamera Work. In the piece, Weber states,^[7] "In plastic art, I believe, there is a fourth dimension which may be described as the consciousness of a great and overwhelming sense of space-magnitude in all directions at one time, and is brought into existence through the three known measurements."

Another influence on the School of Paris was that ofJean Metzinger andAlbert Gleizes, both painters and theoreticians. The first major treatise written on the subject of Cubism was their 1912 collaborationDu "Cubisme", which says that:^[8]

"If we wished to relate the space of the [Cubist] painters to geometry, we should have to refer it to the non-Euclidian mathematicians; we should have to study, at some length, certain ofRiemann's theorems."

The American modernist painter and photographerMorton Livingston Schamberg wrote in 1910 two letters toWalter Pach,^[9][10] parts of which were published in a review of the1913 Armory Show forThe Philadelphia Inquirer,^[11] about the influence of the fourth dimension on avant-garde painting; describing how the artists' employed "harmonic use of forms" distinguishing between the "representation or rendering of space and the designing in space":^[12][13]

If we still further add to design in the third dimension, a consideration of weight, pressure, resistance, movement, as distinguished from motion, we arrive at what may legitimately be called design in the fourth dimension, or the harmonic use of what may arbitrarily be called volume. It is only at this point that we can appreciate the masterly productions of such a man as Cézanne.

Cézanne's explorations of geometric simplification and optical phenomena inspired the Cubists to experiment withsimultaneity, complex multiple views of the same subject, as observed from differing viewpoints at the same time.^[14]

In 1936 in Paris,Charles Tamkó Sirató published hisManifeste Dimensioniste,^[15] which described how the Dimensionist tendency has led to:

1. Literature leaving the line and entering the plane.
2. Painting leaving the plane and entering space.
3. Sculpture stepping out of closed, immobile forms.
4. The artistic conquest of four-dimensional space, which to date has been completely art-free.

The manifesto was signed by many prominent modern artists worldwide.Hans Arp,Francis Picabia,Kandinsky,Robert Delaunay and Marcel Duchamp amongst others added their names in Paris, then a short while later it was endorsed by artists abroad includingLászló Moholy-Nagy,Joan Miró,David Kakabadze,Alexander Calder, andBen Nicholson.^[15]

In 1953, thesurrealistSalvador Dalí proclaimed his intention to paint "an explosive, nuclear and hypercubic" crucifixion scene.^[16][17] He said that, "This picture will be the great metaphysical work of my summer".^[18] Completed the next year,Crucifixion (Corpus Hypercubus) depicts Jesus Christ upon the net of a hypercube, also known as atesseract. The unfolding of a tesseract into eight cubes is analogous to unfolding the sides of a cube into six squares. TheMetropolitan Museum of Art describes the painting as a "new interpretation of an oft-depicted subject. ..[showing] Christ's spiritual triumph over corporeal harm."^[19]

The concept of the fourth-dimension, and other geometries, influenced artists of the early twentieth century. The definition of the fourth-dimension differed from artist to artist: beforeEinstein, artists would associate the term with an extra spatial dimension; after Einstein's theory of relativity wasvindicated in 1919, the fourth-dimension became associated withtime rather than space.^[1]

Between 1913 to 1915,Piet Mondrian produced paintings employing thespatial interpretation of this principle in hisPier and Ocean series. By 1917 he had developed his theory ofNeo-plasticism which excluded this principle in favour of colour planes and orthogonal lines on a flat surface.^[20] His close collaborator,Theo van Doesburg showed an early interest in the spatial fourth-dimension, later developing his interest to include the temporal dimension in his works. Mondrian rejected both interpretations in favour of stasis ,^[21] and this difference of views played a major role in his departure fromDe Stijl in 1924.^[22] Van Doesburg went on to developElementarism, incorporating the dynamic concept of movement and expansion.^[23][24]

The fourth dimension has been the subject of numerous fictional stories.^[25]

• De Stijl
• Duration (philosophy)
• Elementarism
• Five-dimensional space
• Four-dimensional space
• List of four-dimensional games
• Mathematics and art
• Octacube
• Philosophy of space and time

• Clair, Bryan (16 September 2002)."Spirits, Art, and the Fourth Dimension".Strange Horizons. Archived fromthe original on 7 January 2012. Retrieved25 March 2012.
• Dalí, Salvador; Gómez de la Serna, Ramón (2001) [1988].Dali (Print). Secaucus, NJ: Wellfleet Press.ISBN 1-55521-342-1.
• Décimo, Marc (2007).Maurice Princet, Le Mathématicien du Cubisme (in French). Paris: Éditions L'Echoppe.ISBN 978-2-84068-191-5.
• Gleizes, Albert;Metzinger, Jean (1912).Du "Cubisme" (Edition Figuière). Paris.{{cite book}}: CS1 maint: location missing publisher (link)
• Henderson, Linda Dalrymple (2013).The Fourth Dimension And Non-Euclidean Geometry In Modern Art (Revised ed.). Cambridge, Massachusetts: The MIT Press.ISBN 978-0-262-58244-5.
• Jouffret, Esprit (1903).Traité élémentaire de géométrie à quatre dimensions et introduction à la géométrie à n dimensions (in French). Paris: Gauthier-Villars.OCLC 1445172. Retrieved2008-02-06.
• Kruger, Runette (2007)."Art in the Fourth Dimension: Giving Form to Form – The Abstract Paintings of Piet Mondrian"(PDF).Spaces of Utopia (5). Spaces of Utopia: An Electronic Journal:23–35.ISSN 1646-4729. Retrieved25 March 2012.
• Miller, Arthur I. (2001).Einstein, Picasso: space, time, and beauty that causes havoc (Print). New York: Basic Books.ISBN 0-465-01859-9.
• Oja, Carol J. (2000).Making Music Modern: New York in the 1920s.Oxford University Press, USA. p. 84.ISBN 9780195162578
• Robbin, Tony (2006).Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought (Print). New Haven:Yale University Press. pp. 28–30.ISBN 978-0-300-11039-5.
• Sirató, Charles Tamkó (1936)."Dimensionist Manifesto"(PDF). Paris. Retrieved24 March 2013.
• Weber, Max (1910)."In The Fourth Dimension from a Plastic Point of View".Camera Work.31 (July 1910).
• Blotkamp, Carel (1994).Mondrian: the art of destruction. Reaktion Books.ISBN 1 86189 100 8.
• Blotkamp, Carel (1982).De Stijl: The Formative Years. The MIT Press.ISBN 0262022478.
• Ubink, J. B. (1918)."De vierde afmeting [The Fourth Dimension]".De Nieuwe Gids.33:791–802. Retrieved24 December 2024.
• Baljeu, Joost (1968).De Vierde Dimensie [The Fourth Dimension]. Stejelijk van Abbemuseum.

• Henderson, Linda Dalrymple (1998).Duchamp in Context: Science and Technology in the Large Glass and Related Works. Princeton, N.J:Princeton University Press.ISBN 978-0-691-12386-8.
• Volkert K. (2018)Wanderings of Knowledge – the fourth dimension in art, literature and philosophy. In: In higher rooms. Mathematics in context. Springer Spectrum, Berlin, Heidelberg,ISBN 978-3-662-54794-6
• Hinton, Charles H.,What Is the Fourth Dimension?, 1884. From Scientific Romances, Vol. 1 (1884), pp. 1–22, Speculations on the Fourth Dimension, Selected Writings of Charles H. Hinton, Copyright 1980 by Dover Publications, Inc.,ISBN 0-486-23916-0, LC 79-54399
• Hinton, Charles H.,The fourth dimension, London, S. Sonnenschein & Co., 1906, archive.org

• Talk at the Dali museum on his 4th dimension art

• Modern art
• Dimension
• Mathematics and art
• 4 (number)
• Four-dimensional geometry

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