Is not everything full of significance, symmetry, allusion and strange relations? Might God not manifest Himself in mathematics as well as in every other science?
Max Ernst immigrated to America in 1941 as a refugee from the war in Europe. Having had his life and art disrupted by imprisonment in concentration camps in Vichy France, he wasted little time getting back to work once he landed in New York. His paintings from the late 1930s up to the time of his internment were among his most daring and imaginative experiments. Works from this period in decalcomania such as Swamp Angel and The Robing of the Bride remain some of his most intriguing and enigmatic. Although Ernst continued to work with decalcomania for some time after arriving in New York, he added another very curious element to the mix.
Works from 1942 suddenly featured applications of very fluid paint in ellipses. This “drip” technique represented a strong departure from any of his previous methods. It evoked rapid motion and suggested a flirtation with chaos itself. Ernst frequently had worked in “controlled accidents” that allowed chance elements into his compositions. Along with collage, Ernst added frottage, grattage, and decalcomania to his repertoire and, in each subsequent technical experiment, he allowed chance an ever-greater role. Over the years, his intentional control and force of hand loosened, blurring the line between activity and passivity, eventually arriving at the astonishing level of delicacy shown in such works as Europe After the Rain.
So Ernst, following several years of invention in decalcomania, further extended his sense of adventure, painting with a method that actually employed a fully-automatic function — the law of gravity — to control the paint, leaving the artist’s hand momentarily out of the act altogether. Late in life Ernst wrote in his biographical notes, entitled Tissue of Truth, Tissue of Lies, afew playfully misleading commentsregarding his “drip” technique. Offered here in response are some observations about the process, including a bit of speculation about Ernst’s method and his motives.
Regarding his activities in 1942, Ernst says: “As part of a group exhibition at the Wakefield Bookshop in New York, Betty Parsons showed a painting by M.E. that excited the interest of some young painters. They were especially fascinated by its technique. Max told them it was child’s play. ‘Tie a piece of string, one or two metres long, to an empty tin can, punch a small hole in the bottom and fill the tin with thin paint. Then lay the canvas flat on the floor and swing the tin backwards and forwards over it, guiding it with movements of your hands, arms, shoulders and your whole body. In this way surprising lines will drip onto the canvas. Then you can start playing with free associations.’ The picture, then entitled Abstract Art, Concrete Art, was later renamed Young Man Intrigued by the Flight of a Non-Euclidean Fly.”(1)
Young Man Intrigued by the Flight of a Non-Euclidean Fly, 1942 and 1947 Oil and enamel on canvas, 82x66cm. Private Collection, Zürich
Ernst goes on to say, “It’s true that many New York painters adopted this technique, which they called ‘dripping’, and made abundant use of it. Especially Jackson Pollock, whom his friends nicknamed ‘Jack the Dripper’.”(2)
Ernst’s rather audacious claim regarding his influence upon Pollock will be addressed later in this article. But, for now, I return in more detail to the mechanics of Ernst’s original “drip technique”. Two distinct approaches to dripping are seen in La Planète Affolée, (The Bewildered Planet).
La Planète Affolée, 1942 Oil on canvas, 110x140cm. Tel-Aviv Art Museum
The auspicious title of this painting reflects both the scientific and poetic sensibilities of Max Ernst. It also contains a wry hint about the way in which this and successive works were created. In dripping paint from a can and a piece of string, Ernst employed a mechanical device that he did not mention to Pollock — a compound pendulum, one suspended from two points.
Carefully observing the character of the lines present in each side of this painting, one might surmise that they were produced in two ways. The right side features no regular pattern, no rhythm or cyclical quality in the peregrinations: It appears to have been poured pretty much as Ernst described in his memoirs — by holding a can on a string and simply swinging it with his hand over the canvas on the floor. On the left side, there is an order, an evident periodicity that suggests a Lissajous figure, also known as a Bowditch curve. Lissajous figures can be graphically reproduced with a compound pendulum. Compare the structure of the linear figure on the left in La Planète Affolée with the figure in this photograph:
From Science Magic, by Kenneth M. Swezey.McGraw-Hill, 1952
This illustration shows a compound pendulum, comprised of a wooden dowel, string and a sand-filled paper cone with a small hole in the bottom. Ernst built a similar device and swung a can full of paint instead. He first masked the area around the paint drips, and then he let the can fly. At some point soon after launching, Ernst stopped the can and removed it: had he not, the can eventually would have stopped in a plumb position, leaving a less structured and less intriguing dribble in the center of its arc.
There may be at least two possible explanations for Ernst’s sudden use of the compound pendulum after coming to New York. The first is that he became aware of other artists using the device at that time. Anecdotes suggest that Stanley William Hayter occasionally demonstrated it to students in his studio, but I found no evidence of these ellipses in Hayter’s catalogue raisonné. (3) There were other reports of artists’ experiments with the device, but I know no work that supports them.
The second explanation is that Ernst already had seen the compound pendulum demonstrated at the University of Bonn years before. Compound pendulums have long been used in elementary physics classes to demonstrate the behavior of waveforms approaching one another at perpendicular angles. The pattern demonstrated by the young man in the above photograph represents a ratio of waveforms that can be duplicated electronically today. However, when Ernst was a student at Bonn, these forms were created by mechanical models and illustrated and explained in textbooks. One, in particular, is Spezielle Algebraische und Transzendente Ebene Kurven: Theorie und Geschichte, by Loria and Schütte. It originally was published in Leipzig in 1902, and it seems quite possible that Ernst knew this book.
From Spezielle Algebraische und Transzendente Ebene Kurven. Plate XIV
(Note the four figures on the lower right.)
In a contemporary classroom, these same waveforms might be demonstrated with an oscilloscope or illustrated in a chart such as the one below:
From Vibrations and Waves, by A. P. French. Norton, 1971
The study of these waveforms goes back to the nineteenth century, beginning with the American astronomer and mathematician, Nathaniel Bowditch (1773-1838). Among his many achievements was his English translation of Laplace’s Traité de Mécanique Céleste. In 1815, Bowditch published a paper in the Memoirs of the American Academy of Arts and Sciences called “On the Motion of a Pendulum Suspended from Two Points”.
Ernst’s own lifelong interest in astronomy suggests that he knew Bowditch’s work. Thus, the execution of La Planète Affolée may have constituted a great intuitive leap that playfully links the physics of the compound pendulum with the physics of gravitation between two planets such as that of the earth and the moon. Such a precise analog may be debatable, but in his paper, Nathaniel Bowditch demonstrated his “…equations…are exactly similar to those for finding the apparent motion of the earth viewed from the moon…”. (4) So, the real analogy is visual and more immediate, describing the apparent path of a planet in the heavens to an observer standing on another planet, over the course of time.
The French physicist Jules Antoine Lissajous (1822-1880) studied acoustical vibrations via clever devices that translated sound into visual media (using light beams and mirrors or trays full of dry sand). These graphic methods of “capturing” sound waves could be considered forms of “automatic writing” that pre-date any such notion within the context of art. Again, it is entirely possible that Ernst was familiar with his ideas as well.
Interestingly, the identical mathematics describes the behavior of Bowditch’s compound pendulum and Lissajous’ experiments with sound and light beams and mirrors: thus the interchangeable names for the figures described by the phenomena. I think Ernst was aware of this common thread and stitched it into his own work in 1942. In doing so, he expressed his life-long spirit of reaching “beyond painting” or any previous notion of art to enlarge the scope of his oeuvre.
Ernst and other surrealists — particularly Duchamp, Man Ray, and Magritte — also were interested in areas of mathematics that refuted conventional concepts of form and space. They all knew the ideas of the French mathematician, Henri Poincaré (1854-1912). Perhaps most engaging were Poincaré’s ideas regarding what is generally called non-Euclidean geometry.
Prior to the turn of the nineteenth century, the standard of the geometry of the cosmos was Euclid’s Elements. The so-called “fifth axiom of Euclid” relates to both the idea of three-dimensional space itself as well as its pictorial description. The axiom more or less states that “…through a point next to a straight line only one line can be drawn that is parallel to it, both of them intersecting only at infinity”. (5)
Three people previous to Poincaré produced geometries that disobeyed Euclid’s fifth axiom — Bernard Riemann, János Bolyai, and Nicolai Lobachevsky — but the surrealists were most interested in Poincaré’s work. Certain aspects of Poincaré’s thought processes, including the juxtaposition of rational thought with intuitive leaps, must have appealed to Ernst. Poincaré claimed to be baffled about how he received his inspiration, as though he were simply a conduit for a system that was already in existence. Compare this to Ernst’s own sense of detachment, in which he describes his working method as “the exploitation of the chance meeting of two distant realities on an unfamiliar plane or, to use a shorter term, the culture of systematic displacement and its effects”. (6) Fascination with the unconscious, integral to the theoretical underpinnings of surrealism, by definition negates the central role of the artist as creator ex nihilo.
Returning to Ernst’s meeting with Jackson Pollock and the seminal work, Young Man Intrigued by the Flight of a Non-Euclidean Fly, requires acknowledgement that Ernst already had visited the Poincaré Institute in Paris several times. Before 1942 he had surely acquired a taste for unconventional mathematics and probably knew of the synchronous theories of Bowditch and Lissajous.
Young Man Intrigued…was first shown in 1942 as a non-objective work entitled Abstract Art, Concrete Art and was initially comprised only of ellipses, with no references to a figure. In 1947, Ernst reworked the painting, adding the head and changing the title. (Coincidentally, Jackson Pollock was by then beginning his meteoric rise as a painter and was pretty well on track toward his mature style.) However, one painting of note by Ernst in the interim period is Euclid, done in 1945.
Euclid 1945 Oil on Canvas, 65.4×57.5 cm. Menil Collection, Houston
The irony present in these works is the beginning of what Werner Spies called, in reference to later works by Ernst, as “humorous allegories on the sudden senility of Euclidean space”. (7)
From 1942 until 1948, Max Ernst made about a dozen paintings utilizing paint poured from a suspended can. It appears that he used a compound pendulum in The Bewildered Planet (1942), Young Man Intrigued by the Flight of a Non-Euclidean Fly (1942), Surrealism (1942), Euclid (1945),and Sleeping Eskimo (1948) (8). But the less-regular ellipses in the rest of them were probably produced with the simple hand-held pendulum that Ernst described to Pollock.
Also interesting is that, in La Planète Affolée, not only is the left-hand side an example of a Lissajous figure, but the right-hand side is an example of the “deterministic chaos” of Poincaré. So, Poincaré’s ideas are present in all Ernst’s works in which a simple pendulum is used. (9) It is ironic that the arcs of both the simple and the compound pendulum have nothing to do with non-Euclidean geometry. But Ernst was referring to the fly itself as non-Euclidean and non-Euclidean geometry does deal with objects changing their form while in motion.
The debate around Ernst’s claim of teaching Pollock about “dripping” has been around for decades. Ernst’s supporters have based their cases on Ernst’s own word. Ernst’s detractors have noted that New York painters had already tried various pouring methods before Ernst showed up. The best argument for this was made by William Rubin in part IV of a series of articles called “Jackson Pollock and the Modern Tradition” in Artforum, May, 1967. Most pertinently, Rubin distinguished the difference in intention between Ernst’s consistent figuration and Pollock’s abstraction. He also described several different dripping methods of Pollock’s that had nothing to do with pendulums or mathematical principles.
Ernst’s continued interest in physics was evident in both drawings and collages from 1948, the year he painted Sleeping Eskimo, last in his group of “drip” paintings.
Ausstellungssignet 1948 Pen and Ink on Paper, 5.6×10.5 cm. (10)
This drawing was published both in conjunction with exhibitions by Ernst at both M. Knoedler & Co. and the Museum of Modern Art.
Once Upon a Time there Was a Mouse in Milo
From Paramyths, p.29 (11)
The graphs created by Ernst in both these works show Bessel functions which are prescribed solutions to differential equations found to govern a variety of wave motions, particularly those that are confined to the surface of spheres and cylinders.
Six years later, Ernst was still referring to planetary gravitational fields. (Note the diagram on the head of Venus.) It’s worth noting here that Einstein’s Theory of General Relativity suggests that space/time is not only curved, but it is curved by the force of gravity itself. This further refutes the Elements and contributes to Ernst’s recognition of “the sudden senility of Euclidean space”. Finally, it is altogether appropriate that Ernst had a strong interest in the work of Werner Heisenberg, whose “uncertainty principle” parallels his own disdain of positivist or absolute analysis of anything in the physical world. It is in that spirit that this article is offered — not as a definitive explanation of this aspect of the work of Max Ernst, but as a subjective insight into a larger unknown.
References and Notes
1. Werner Spies, ed., Max Ernst: A Retrospective (Munich, Germany: Prestel-Verlag, 1991) p. 322.
2. Spies  p. 322.
3. Peter Black, The Prints of Stanley William Hayter: a Complete Catalogue (Mount Kisco, New York: Moyer-Bell, 1992)
4. Nathaniel Bowditch, “On the Motion of a Pendulum Suspended from Two Points,” Memoirs of the American Academy of Arts and Sciences, Volume 3, part 2 (1815) p. 434.
5. Gerald Holton, “Henri Poincaré, Marcel Duchamp and Innovation in Science and Art,” Leonardo, Volume 34, no.2 (2001) p.128.
6. Max Ernst, Beyond Painting, and Other Writings by the Artist and His Friends (New York: Wittenborn, Schultz, 1948) pp.16-17.
7. Spies  p. 51.
8. Werner Spies and Sigrid Metken and Günter Metken, eds., Max Ernst Oeuvre-Katalog (Houston, Texas: Menil Foundation; Cologne: Verlag M. DuMont Schauberg, 1987) Volume 5, Werke 1938-53.
9. For a discussion of a simple pendulum as a model see: “Poincaré, or Deterministic Chaos (Sensitivity to Initial Conditions)” pp.131-133 in: Charles Ruhla, The Physics of Chance: From Blaise Pascal to Niels Bohr. (trans. by G. Barton) New York: Oxford University Press, 1993.
10. Spies and Metken  p. 65..
11. Spies and Metken  p. 94.
Essay Copyright 2001 Andy Feehan. Images here appear under the doctrine of fair use, since no commercial intent exists.