Attempt to demonstrate the 4th dimension in visual arts
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.[1]
Princet introduced Picasso to
Esprit Jouffret's Traité élémentaire de géométrie à quatre dimensions (Elementary Treatise on the Geometry of Four Dimensions, 1903),[4] a popularization of Poincaré'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.[5] The portrait bears similarities to Jouffret's work and shows a distinct movement away from the
Proto-Cubistfauvism displayed in Les Demoiselles d'Avignon, to a more considered analysis of space and form.[6]
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,[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 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:[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 of
Riemann's theorems."
The American modernist painter and photographer
Morton Livingston Schamberg wrote in 1910 two letters to
Walter Pach,[9][10] parts of which were published in a review of the
1913 Armory Show for The 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 with
simultaneity, complex multiple views of the same subject, as observed from differing viewpoints at the same time.[14]
Dimensionist manifesto
In 1936 in Paris,
Charles Tamkó Sirató published his Manifeste Dimensioniste,[15] 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.
The artistic conquest of four-dimensional space, which to date has been completely art-free.
In 1953, the
surrealistSalvador Dalí proclaimed his 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 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."[19]
Abstract art
Some of
Piet Mondrian's 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.[20]
^Robbin, Tony (2006). Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought (Print). New Haven:
Yale University Press. p. 28.
ISBN978-0-300-11039-5.
^Robbin, Tony (2006). Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought (Print). New Haven:
Yale University Press. pp. 28–30.
ISBN978-0-300-11039-5.
^Weber, Max (1910). "In The Fourth Dimension from a Plastic Point of View". Camera Work. 31 (July 1910).
^Gleizes, Albert; Metzinger, Jean (1913). Du Cubisme [translated from French]. London: T.F. Unwin.
^Letter from Schamberg in Philadelphia to Walter Pach in Paris, 29 December 1910, Pach Papers, Reel: 4216, fr. 856
^Letter from Schamberg in Philadelphia to Pach in Paris, 29
December 1910, fr. 857
^Morton Livingston Schamberg, "Post-Impression Exhibit Awaited", The Philadelphia Inquirer, 19 January 1913, col. 2, p. 3
Robbin, Tony (2006). Shadows of Reality: The Fourth Dimension in Relativity, Cubism, and Modern Thought (Print). New Haven:
Yale University Press. pp. 28–30.
ISBN978-0-300-11039-5.
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,
ISBN978-3-662-54794-6
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.,
ISBN0-486-23916-0, LC 79-54399