New possibilities opened up by the concept of four-dimensional space (and difficulties involved in trying to visualize it) helped inspire many modern artists in the first half of the twentieth century. Early Cubists, Surrealists, Futurists, and abstract artists took ideas from higher-dimensional mathematics and used them to radically advance their work.
French mathematician Maurice Princet was known as "le mathÃ©maticien du cubisme" ("the mathematician of cubism"). An associate of the School of Paris, a group of avant-gardists including Pablo Picasso, Guillaume Apollinaire, Max Jacob, Jean Metzinger, and Marcel Duchamp, Princet is credited with introducing the work of Henri PoincarÃ© and the concept of the "fourth dimension" to the cubists at the Bateau-Lavoir in the late 1900s.
Princet introduced Picasso to Esprit Jouffret's TraitÃ© Ã©lÃ©mentaire de gÃ©omÃ©trie Ã quatre dimensions (Elementary Treatise on the Geometry of Four Dimensions, 1903), a popularization of PoincarÃ©'s Science and Hypothesis in which Jouffret described hypercubes and other complex polyhedra in four dimensions and projected them onto the two-dimensional page. Picasso's Portrait of Daniel-Henry Kahnweiler in 1910 was an important work for the artist, who spent many months shaping it. The portrait bears similarities to Jouffret's work and shows a distinct movement away from the Proto-Cubist fauvism displayed in Les Demoiselles d'Avignon, to a more considered analysis of space and form.
Early cubist Max Weber wrote an article entitled "In The Fourth Dimension from a Plastic Point of View", for Alfred Stieglitz's July 1910 issue of Camera Work. In the piece, Weber states, "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 of Jean Metzinger and Albert Gleizes, both painters and theoreticians. The first major treatise written on the subject of Cubism was their 1912 collaboration Du "Cubisme", which says that:
"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 of Riemann's theorems."
In a review of the 1913 Armory Show for the Philadelphia Enquirer, the influence of the fourth dimension on avante-garde painting was discussed; the paper's art-critic describing how the artists' employed "..harmonic use of what may arbitrarily be called volume".
In 1936 in Paris, Charles TamkÃ³ SiratÃ³ published his Manifeste Dimensioniste, which described how
the Dimensionist tendency has led to:
- Literature leaving the line and entering the plane.
- Painting leaving the plane and entering space.
- Sculpture stepping out of closed, immobile forms.
- â¦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 including LÃ¡szlÃ³ Moholy-Nagy, Joan MirÃ³, David Kakabadze, Alexander Calder, and Ben Nicholson.
Crucifixion (Corpus Hypercubus)
In 1953, surrealist Salvador DalÃ proclaimed his intention to paint "an explosive, nuclear and hypercubic" crucifixion scene. He said that, "This picture will be the great metaphysical work of my summer". Completed the next year, Crucifixion (Corpus Hypercubus) depicts Jesus Christ upon the net of a hypercube, also known as a tesseract. The unfolding of a tesseract into eight cubes is analogous to unfolding the sides of a cube into six squares. The Metropolitan Museum of Art describes the painting as a "new interpretation of an oft-depicted subject. ..[showing] Christ's spiritual triumph over corporeal harm."
Some of Piet Mondrian's (1872â"1944) abstractions and his practice of Neoplasticism are said to be rooted in his view of a utopian universe, with perpendiculars visually extending into another dimension.
Other forms of art
The Fourth dimension has been the subject of numerous fictional stories.
- De Stijl
- Five-dimensional space
- Four-dimensional space
- Marcel Duchamp
- Mathematics and art
- Clair, Bryan (16 September 2002). "Spirits, Art, and the Fourth Dimension". Strange Horizons. Retrieved 25 March 2012.Â
- DalÃ, Salvador; GÃ³mez de la Serna, RamÃ³n (2001) . Dali (Print). Secaucus, NJ: Wellfleet Press. ISBNÂ 1555213421.Â
- DÃ©cimo, Marc (2007). Maurice Princet, Le MathÃ©maticien du Cubisme (in French). Paris: Ãditions L'Echoppe. ISBNÂ 2-84068-191-9.Â
- Gleizes, Albert; Metzinger, Jean (1912). Du "Cubisme" (Edition FiguiÃ¨re). Paris.Â
- Henderson, Linda Dalrymple. "Overview of The Fourth Dimension And Non-Euclidean Geometry In Modern Art, Revised Edition". MIT Press. Retrieved 24 March 2013.Â
- Jouffret, Esprit (1903). TraitÃ© Ã©lÃ©mentaire de gÃ©omÃ©trie Ã quatre dimensions et introduction Ã la gÃ©omÃ©trie Ã n dimensions (in French). Paris: Gauthier-Villars. OCLCÂ 1445172. Retrieved 2008-02-06.Â
- Kruger, Runette (Summer 2007). "Art in the Fourth Dimension: Giving Form to Form â" The Abstract Paintings of Piet Mondrian" (PDF) (5). Spaces of Utopia: An Electronic Journal. pp.Â 23â"35. ISSNÂ 1646-4729. Retrieved 25 March 2012.Â
- Miller, Arthur I. (2001). Einstein, Picasso: space, time, and beauty that causes havoc (Print). New York: Basic Books. ISBNÂ 0-465-01859-9.Â
- Oja, Carol J. (2000, February 2003). Making Music Modern: New York in the 1920s. Oxford University Press, USA. p.Â 84.Â ISBN 9780195162578
- Robbin, Tony (2006). Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought (Print). New Haven: Yale University Press. pp.Â 28â"30. ISBNÂ 9780300110395.Â
- SiratÃ³, Charles TamkÃ³ (1936). "Dimensionist Manifesto" (PDF). Paris. Retrieved 24 March 2013.Â
- Weber, Max (1910). "In The Fourth Dimension from a Plastic Point of View". Camera Work 31 (July 1910).Â
- Henderson, Linda Dalrymple (2013). The Fourth Dimension And Non-Euclidean Geometry In Modern Art (Revised ed.). Cambridge, Massachusetts: The MIT Press. ISBNÂ 0262582449.Â
- Henderson, Linda Dalrymple (1998). Duchamp in Context: Science and Technology in the Large Glass and Related Works. Princeton, N.J: Princeton University Press. ISBNÂ 9780691123868.Â
- Talk at the Dali museum on his 4th dimension art