THE 4 th DIMENSION
IN DUCHAMP'S BOXES
An Essay submitted as a requirement for module 220 (BA Hons).
Coventry University School of Design and Visual Arts, 2004
Chosen topic:
What ideas, concepts, philosophies and critical writings in your view have been influential for contemporary artists? Illustrate and defend your views citing particular cases you consider being important in the development of art in the 20 th century.
Acknowledgements:
I would like to thank Ian Hays for all his support.
Contents:
Preface 4
Introduction .. ..6
Chapter 1 The 4 th Dimension - Historical Perspective .7
Chapter 2 - Duchamp's Boxes ..10
Chapter 3 - The Green Box 14
Chapter 4 After the White Box (A l'infinitif) ..19
Chapter 5 - Relativity . .21
Conclusion 24
Bibliography .25
Illustration list ... 26
Preface
For this essay I was planning to write about Mathematics and Art but I just felt that would be more appropriate for next year due to the limitations of word counting. Narrowing the subject more and more I tried to find something that would suit my desires (art and science) and meet the university requirements.
After going through all the questions I could choose for this dissertation's topic I decided to investigate an influent idea in the 20 th century art history (the fourth dimension) within the context of a couple of very influent texts: the Green and the White Boxes.
The fourth dimension is the main subject of my studio practice and it was also through Duchamp (Fig.1 and Fig.10) I first knew about its importance in the art world. This was crucial to make this subject more relevant then any other. I also felt I would regret if I didn't write this thesis about Duchamp because he is one of the most influent artists in my work and it was also with him I learned the difference between context and content.
What I wanted to achieve with this investigation was a deeper understanding on Duchamp's notes and how the fourth dimension influenced the beginning of conceptual art. As a bonus I would inform my studio practice and appreciate the evolution of a scientific myth and concept through time. All the intellectual and artistic adventures I've been living with Mathew Dalgleish and Ian Hays about Duchamp and extra dimensions would be pushed forwards by these two boxes analysis.
It may seem silly but after writing this essay I felt the need to write notes for my own work too. I realized how crucial that can be for people to understand the rules of irrational intuition. As consequence I started writing my own notes using Leonardo Da Vinci's manuscripts typotranslated and downloaded from the internet as a background to write and draw about my studio projects.
Fig. 1 Duchamp's Studio, New York, 1917-1918
Introduction
There are several examples of texts that were vital for the course of events through this last century, many of them were written by critics and artists. To explore the importance of writing I decided to research two textual works I believe are still influent in contemporary art.
In this essay I will embrace a subject specific analysis on Duchamp's Green and White Box. These texts were a great influence in the last century's art and were studied and scrutinized by both researchers and artists.
The subject I chose to write about was the 4 th dimension. This idea is interesting as a popular myth (it used to be) and also as a concept which evolved through literature, geometry, art and physics.
To start developing my ideas I'll start with an art historical perspective on the 4 th Dimension. Then I am going to explore some ideas on the Green and the White Boxes searching for Duchamp's use of non-Euclidian geometries and 4D references. Finally I will try to succinctly question the way most art criticism, and Linda Henderson in particular, rejects the connections between Einstein's Relativity and Duchamp's work.
Chapter 1 - 4th Dimension - Historical Perspective
[The forth dimension] along with non-Euclidean Geometry, played a vital role in the development of modern art and theory. [ ] once the artistic impact of he new geometries is understood, the art and critical literature of the early modern era regain a unity and a level of meaning that has long been lost.
Henderson , 1993, page 230
The fourth dimension during the 19 th century was developed by mathematicians and used in literature such as in Abbott's Flatland when it was just starting to be scientifically relevant:
Sphere. But where is this land of Four Dimensions?
I. I Know not: But doubtless my Teacher Knows.
Abbott, 1884, Chapter 19
In the first three decades of the 20 th century the fourth dimension was present in almost every major modern movement. Cubists, Futurists, Constructivists, Dadaists and other artistic circles through out the world were investigating new geometries and properties of this concept.
In the 1920's Einstein Relativity theory almost banished the spatial fourth dimension from the public imagination, replacing it by the temporal fourth dimension. Even so, one more artistic group was still to come and save this idea and non-Euclidean geometry's presence in the art world, that movement was French Surrealism.
For many artists such as Metzinger, Gleizes, Duchamp, Dada founder Tzara and the surrealists (just to mention a few) non-Euclidean geometry meant new freedom from traditional ways of thinking. The 4 th dimension was also a symbol of the liberation for artists until the 1930's. It was used widely in painting allowing abstract artists to reject the one point perspective system that was used since the Renascence.
Although non-Euclidean geometries have always been strongly connected to the idea of forth dimension, they never achieved the popularity of this pre-Einstein concept which had many other non-geometric features. At first associated with cubist faceted forms and later on with gravity by Duchamp, the fourth dimension was also related to antigravity by Malevich, spirals by the futurists and even the Platonic realm by Synthetic Cubists. Many artists also added motion as an attribute of the fourth dimension (these included Duchamp, Kupka, Boccioni, Malevich and many others).
According to Lynda Henderson during the 1930's the fourth dimension was not just limited by the Relativity Theory but also the increase discouragement of deep space in modern painting by a formalist art theory. Never the less the Manifeste Dimensioniste was published in Paris 1936. This document was signed by artists from all over the world and from different artistic tendencies, such as: Miró, Hans Arp, Moholy-Nagy, Duchamp, Picabia, Kandinsky, Ben Nicholson, Alexander Calder, Robert Delaunay, etc A very impressive and extensive list of names approved this attempt to adapt previous viewpoints on the 4 th dimension to Einstein's Space-time.
In the 1940's the 4 th dimension was discussed by Breton, Dali, Dominguez and many other. In a very surreal way, time and the initial 4D concept were being merged and related to Freud, unconscious, mysticism and attacks on reason.
During the 1950's and 1960's very few were still interested in the fourth dimension of space, even amongst surrealists but in the 1970's some individuals, artists and mathematicians, tried to give visual form to the concept again. A symposium, Hypergraphics: visualizing Complex Relationships in Art, Science and Technology (1978) started the new era of the fourth dimension: computer graphics (Fig.2) and programs were opening new doors to the visual and the mind.
Fig. 2 Stereogram built using online resources (see illustration list)
Chapter 2 - Duchamp's boxes
Duchamp was not satisfied for long with the cubist technique for evoking the fourth dimension and in 1912 he starts a serious study on dimensions and perspective. In that same year took a job as a librarian at the Bibliotèque Sainte-Geneviève (Fig. 3) and he claimed he first glimpsed the fourth dimension in his work. He published three assemblages of his notes: the Box of 1914, the Green Box (1934) and the White Box - À L'infinitif (1967). The last two were reproduced in facsimile first and published in books after being typo-translated many years later.
The aim of Duchamp's notes was a diverse and complex pattern of ideas and concepts that explored with rigour and innovation the very up to date worries on the time on the 4 th dimension. Inspired in Leonardo Da Vinci, Duchamp's notes on the Large Glass are handwritten, coded and diagrammatic. His notes include small drawings and explore perspective to the maximum depth possible. Duchamp also tried to make his notes visually as much alike as possible to the notes of renascence master (Fig. 4) leaving us a legacy of pages without any specific order as Leonardo did.
Fig.4 Duchamp, Wasp or Sex Cylinder , 1913, original lost, facsimile in the Green Box (reproduced in Duchamp in Context fig.105)
Steefel wrote about this traditionalist / modernist duplicity in his book Duchamp's Glass in the Development of His Art :
The individual talent draws from tradition the strength to go ahead and, by being of the present, revivifies and transforms the past.
[ ] his whole approach is intimately involved with problems of perspective and disorder, and with perspective on himself, in the widest sense of the word perspective. Hence Duchamp's irony and his seriousness, his absurdity and his logic, in life and art.
Steefel, 1977, page 8-10
He also says that Duchamp aims at a four dimensional point outside the work. I believe that is only accessible to the observer through the written notes because these texts are not only about the fourth dimension, they also show the vanishing point of this imaginary fourth dimensional perspective system of the Large Glass.
The reason why these boxes are successful and crucial for the recent art history is the randomness associated to their interpretation and the conceptual structure they created for a masterpiece (the Large Glass Fig. 5) that would be probably ignored without them. Duchamp plays a game with ironic, serious, irrational, scientific, humorous and dramatic references. These become a catalyst for a sequence of events in the observer's mind.
All in all the creative act is not performed by the artist alone; the spectator brings the work in contact with the external world by deciphering and interpreting its inner qualifications and thus adds his contribution to the creative act.
Duchamp, as quoted by Steefel, 1977, page390
Fig.5 Duchamp, The Bride Stripped Bare by Her Bachelors, Even (The Large Glass), 1915-23, oil, varnish, lead wire, lead foil, mirror silvering and dust on two glass panels (cracked), Philadelphia Museum of Art
His goal was obviously achieved with the numerous books on his work that have been published through the last century. From all the books on the Large Glass there is one that is as fascinating as it is complex: Duchamp in Context by Lynda Henderson. It isn't just the deep and detailed research she did on science and technology or even the time she put into that project (over 8 years) the biggest surprise is the academic seriousness she showed on her writing, giving the reader very few clues on the playful and ironical attitude Duchamp had towards science. Steefel unlike her gives a lot of emphasis to the tong on the cheek effect Duchamp achieves with his works .
It is a fact Duchamp was aware of future critical and historical analysis on his work. In 1956 Duchamp emphasized many effects would be the result of unconscious factors which he would leave to art historians.
Chapter 3 - The Green Box
Fig. 6- The Green Box
For Duchamp the Green Box (Fig. 6) is the ideal catalogue for The Bride Stripped Bare by Her Bachelors, Even. These two works are unified (complementary of each other) and open to all interpretations. Nevertheless they clearly try to show, more then anything else, the artist's mind domination over his hand. Many would say it is a masterful statement of the conceptual approach to art.
Fig.7- Diagram - components of Duchamp's Large Glass (Philadelphia Museum of Art)
This set of documents (primarily about the iconography of the Large Glass Fig.7) has only a few references to geometry. However dimensionality was present in Duchamp's life and it was a subject explored in this document:
The negative apparition (determined conventionally by the linear perspective but always in an environment of n-1 dimensions. for an object of n dimensions)
Duchamp, Green Box
These direct references to n dimensions are rare but the 4 th dimension is a crucial idea through out the Green Box. Duchamp wanted some of the elements described in this box to relate effectively to the fourth dimension (Fig. 8):
[ ] any three dimensional object, which we see dispassionately, is a projection of any three-dimensional object, something we are not familiar with. It was a bit of sophism, but still it was possible. The Bride in the Large Glass was based on this, as if it were the projection of a four-dimensional object.
Duchamp, as quoted in Cabanne, 1971, page 40
Fig. 8 Stereogram: The Bride's Milky Way , made with 3D Maker 3.2.1 (see illustration list)
The poetical complexity and range of ideas one can read in the Green Box makes it a multi-layer text that apparently changes every time it is read. These documents have no boundaries in format or content. Their complexity could probably make the meanings and ideas achieved when the reader stops to think one of the manuscript's fourth dimensions.
Duchamp shows unmistakably he is what the French call Avant la lettre when he generates this work in the second and third decades of the 20 th century. One must obviously take in consideration its sexual meaning and the prejudice present at the time. A few years after, Duchamp declares the sexual act the pre-eminent fourth dimensional situation
Chapter 4 After the White Box ( À l'infinitif )
Fig. 9 The White Box (À l'infinitif)
Duchamp's intellect is laid bare in the sections of A l'infinitif on Perspective and the Continuum. In these notes Duchamp was attempting to work out the mechanics of portraying the fourth dimension [ ]
Henderson , 1983, page 122
The "typotranslators" of the White Box (Fig. 9), Richard Hamilton and Ecke Bonk, wrote in an introductory text ( An unknown object of four dimensions ) that the White and the Green Box relationship was not understood when the White box first appeared (32 years after). The distinction between them is small because all the notes were written during the same period, but according to them, it took some time to appreciate that.
Both collections of notes concern the same quest: to evade vanity engaging in an art of rigour and ideas. Nevertheless À l'infinitif records the evolution of the theory behind the forms of the Large Glass and that is probably why most of the references to Jouffret and Poincaré are in this set of notes:
[ ] also, for the continuum in 4 dimensions: Poincaré's explication, by n dimensional continuums [ ]
The shadow cast by a figure in 4 dimensions: on our space is a shadow in 3 dimensions (see Jouffret Geom. in 4 dim. Page 186, last 3 lines)
Duchamp, White Box, page 77 and 81
Duchamp is revealed in a quite different way from his traditional image which was much more ironical and humorous.
Although Duchamp said in many occasions that he drawn his conclusions about the fourth dimension from Lobachesky, Reimann, Jouffret and Poincaré he denies it when interviewed in Cabanne's:
Cabanne: On this scientific side, you have considerable knowledge
Duchamp: Very little. I never was the scientific type.
Cabanne: So little? Your mathematical abilities are astonishing, especially since you didn't have a scientific upbringing.
Duchamp: No, not at all. What we were interested in at the time was the fourth dimension. In the Green Box there are heaps of notes on the fourth dimension.
Cabanne, 1967, page 39
In the continuation of his interview he mentions fake mathematician's and irony experts such as Princet from the cubist circle instead of true scientific influences. With the White Box analysis these ironies would become increasingly obvious.
The white box is about the artist's inspirations, aspirations, methods, references, technical and mind developing activities. Instead of exploring the fourth dimension in a strictly poetical and figurative sense (as he did in the Green Box), Duchamp writes down his individual and personal mathematical viewpoints on the 4 th dimension:
3 lines intersecting don't determine a sp. Therefore in a space 4 lines intersecting do not determine a hyperspace.
Duchamp, 1966, White Box (page 67)
Duchamp doesn't explore a mathematical and scientific language because he loves science, on the contrary, he usually tries to discredit it. By using the appearance of rigour and showing his personal interpretation of the fourth dimension he achieves an irony only accessible to people that question scientific language, goals and emotional limitations:
A finite 4 dim continuum is thus generated by a finite 3 dim. Continuum rotating (here the word loses its physical meaning)
Duchamp, 1966, White Box (page72) 8
Chapter 5 Relativity
Fig. 10 Duchamp at the chessboard, 1967
(Photo Ugo Mulas)
Einstein, like Duchamp (Fig. 10), lived the first decades of 20 th century and those were his most productive years. Although they revolutionized science and art respectively there is no historical evidence that could relate them to each other. Linda Henderson states in both Duchamp in Context and The Fourth Dimension and Non-Euclidean Geometry in Modern Art that connecting Duchamp's or any other modernist work with Einstein is a commonplace art critics like her have been fighting for decades.
Non-Euclidean Geometry and identifying time with the fourth dimension where central ideas in Einstein theories and the Equivalence Principle was a essential step for him to achieve the General Relativity Theory.
Fig. 11 Duchamp, Readymade malheureux , 1919
Duchamp studied non-Euclidean Geometries (Fig.11) far more extensively than any other artist and his scientific inspiration resides clearly on 19 th century. However in some of his notes on the 4 th dimension one feels Relativity Theory is present:
Gravity generate in horizontal and vertical in space 3 [ ] We always reduce the experience of gravity to a self perceived sensation, imagined or real, felt internally near the stomach.
Duchamp, 1966, White Box (page 99)
Even if Duchamp never read any of Einstein's ideas, nor shared enough scientific methods to get to the same conclusions, after reading this note one can't think of anything else but Einstein Equivalence Principle. I must emphasize these quotes about gravity are contextualized within fourth dimension in both the White and the Green Box:
-Regime of Gravity-
Ministry of coincidences
Department (or better):
Regime of Coincidence
Ministry of gravity
Duchamp, Green Box
There are a few other concepts Duchamp outlines in his notes that can be easily connected to Einstein's Relativity such as the idea of movement related to the fourth dimension and the change of a moving object's shape:
Playfulness of Duchamp's new physics is a demonstration of the basic principle of a non-Euclidean geometry that rejects Euclid 's assumption of the indeformability of figures in movement
Henderson , 1983, page 132
Linda Henderson explains that the scientific influence that made Duchamp write these ideas were Reimann (and other 19 th century mathematicians). These were also Einstein references when he assumed Space -Time was curved and that an object goes thinner and thinner the faster it moves.
Conclusion
One could finally say the fourth dimension is an evolving concept contemporary artists can explore using new media (such as computer based art). Its metaphorical power also provides a fertile context for all the scientific myths that grow in the western society. Duchamp is a crucial contextual reference in this subject because of the depth of his geometry studies and at the same time the distance he managed to keep from science by using irony and contradiction skilfully.
From his manuscripts we can conclude the balance between past and present, poetry and coded message, rational and irrational show how influent and creative an artist's written work can be. His technical and scientific knowledge combined with the playfulness of his wit gives these boxes an eternal feel of intuition and mystery.
The chapter about Relativity in this essay was inconclusive but deeper research will either show Einstein shared many mathematical references or that Duchamp in fact could have read something about the emerging Physics.
The papers and books written on Duchamp's notes are not over. Neither is the topic of the fourth dimension as artists will always need to pursuit the unachievable.
Bibliography
- Duchamp, M., (1967) À l'infinitif - White Box , typotranslated by R. Hamilton and E. Bonk, Typosophic Society
- Duchamp, M., (1934) Green Box , typotranslated by R. Hamilton (1960) under the title: The Bride Stripped Bare by Her Bachelors, Even , Percy Lund, Humphries & Co. Ltd
- Henderson, L., (1998), Duchamp in Context , Princeton , New Jersey : Princeton University Press
- Henderson, L., (1993), The Fourth Dimension and non-Euclidean Geometry in Modern Art: Conclusion , article in Leonardo and The Visual Mind Leonardo Book (page 229)
- Abbott, E., (1884), Flatland A romance of many dimensions , online text: http://www.geom.uiuc.edu/~banchoff/Flatland/
- Henderson, L., (1983), The Fourth Dimension and non-Euclidean Geometry in Modern Art , New Jersey : Princeton University Press
- Steefel, L., (1977) The Position of Duchamp's Glass in the Development f His Art , New York and London : Garland Publishing, Inc.
- Mink, J., (1996), Duchamp , Bonn : Taschen
- Cabanne, P., (1971), Dialogues with Marcel Duchamp , London : Thames and Hudson
Illustration list
- Duchamp's Studio, 1917-1918, photography, in Henderson L., (1998), Duchamp in Context , Princeton , New Jersey : Princeton University Press, Fig.140
- Stereogram made by myself, the words non-Euclid and Geometry rearranged, February 2005. 3D image behind the pattern:
• Saint Geneviève Library, 1913, photography, in Mink, J., (1996), Duchamp , Bonn : Taschen
• Duchamp, Wasp, or Sex Cylinder , 1913, facsimile in the Green Box in Henderson L., (1998), Duchamp in Context , Princeton , New Jersey : Princeton University Press, Fig. 105
- Duchamp, The Bride Stripped Bare by Her Bachelors, Even (The Large Glass), 1915-23, oil, varnish, lead wire, lead foil, mirror silvering and dust on two glass panels (cracked), 277X175,8 cm, Philadelphia Museum of Art, Bequest of Katherine S. Dreier, in Mink, J., (1996), Duchamp , Bonn: Taschen
• The Green Box, photography, in R. Hamilton, 1960, The Bride Stripped Bare by Her Bachelors, Even , Percy Lund, Humphries & Co. Ltd
- Diagram - components of Duchamp's Large Glass (Philadelphia Museum of Art), in Henderson L., (1998), Duchamp in Context , Princeton, New Jersey: Princeton University Press, Fig. 77
• Stereogram made by myself to illustrate the Bride's extra dimensions, February 2005. 3D image behind the pattern:
- The White Box (À l'infinitif), photography, in Duchamp, M., (1967) À l'infinitif - White Box , typotranslated by R. Hamilton and E. Bonk, Typosophic Society
- Ugo Mulas, Duchamp at the chessboard, 1967, photography, in Cabanne, P., (1971), Dialogues with Marcel Duchamp , London : Thames and Hudson
- Duchamp, Readymade malheureux , 1919, retouched photography, in Mink, J., (1996), Duchamp , Bonn : Taschen
