Part 5 (1/2)
Figure 66
Figure 67 Interestingly, two other men who played significant roles in the history of the Golden Ratio before Kepler (and whose work was described in previous chapters) also showed interest in tiling-the tenth-century mathematician Abu'l-Wafa and the painter Albrecht Durer. Both of them presented designs containing figures with fivefold symmetry. (An example of Durer's work is shown in Figure 67 Figure 67.) The fifth book of Harmony of the World Harmony of the World contains Kepler's most significant result in astronomy-Kepler's Third Law of planetary motion. This represents the culmination of all of his agonizing over the sizes of the orbits of the planets and their periods of revolution around the Sun. Twenty-five years of work have been condensed into one incredibly simple law: The ratio of the period squared to the semimajor axis cubed is the same for all the planets (the semimajor axis is half the long axis of the ellipse; contains Kepler's most significant result in astronomy-Kepler's Third Law of planetary motion. This represents the culmination of all of his agonizing over the sizes of the orbits of the planets and their periods of revolution around the Sun. Twenty-five years of work have been condensed into one incredibly simple law: The ratio of the period squared to the semimajor axis cubed is the same for all the planets (the semimajor axis is half the long axis of the ellipse; Figure 62 Figure 62). Kepler discovered this seminal law, which served as the basis for Newton's formulation of the law of universal gravitation, only when Harmony of the World Harmony of the World was already in press. Unable to control his exhilaration he announced: ”I have stolen the golden vessels of the Egyptians to build a tabernacle for my G.o.d from them, far away from the borders of Egypt.” The essence of the law follows naturally from the law of gravity: The force is stronger the closer the planet is to the Sun, so inner planets must move faster to avoid falling toward the Sun. was already in press. Unable to control his exhilaration he announced: ”I have stolen the golden vessels of the Egyptians to build a tabernacle for my G.o.d from them, far away from the borders of Egypt.” The essence of the law follows naturally from the law of gravity: The force is stronger the closer the planet is to the Sun, so inner planets must move faster to avoid falling toward the Sun.
In 1626, Kepler moved to Ulm and completed the Rudolphine Tables Rudolphine Tables, the most extensive and accurate astronomical tables produced until that time. While I was visiting the University of Vienna in June 2001, my hosts showed me in the observatory's library a first edition of the tables (147 copies are known to exist today). The frontispiece of the book (Figure 68), a symbolic representation of the history of astronomy, contains at the lower left corner what may be Kepler's only self-portrait (Figure 69). It shows Kepler working by candlelight, under a banner listing his important publications.
Kepler died at noon on November 15, 1630, and was buried in Regensburg. Befitting his turbulent life, wars have totally destroyed his tomb, without a trace. Luckily, a sketch of the gravestone made by a friend survived, and it contains Kepler's epitaph:
Figure 68
Figure 69 I used to measure the heavens, Now the Earth's shadows I measure My mind was in the heavens, Now the shadow of my body rests here.
Today, Kepler's originality and productivity are almost incomprehensible. We should realize that this was a man who endured unimaginable personal hards.h.i.+ps, including the loss of three of his children in less than six months during 1617 and 1618. The English poet John Donne (15721631) perhaps described him best when he said that Kepler ”hath received it into his care, that no new thing should be done in heaven without his knowledge.”
Painting isn't an aesthetic operation; it's a form of magic designed as a mediator between this strange hostile world and us.-PABLO P PICa.s.sO (18811973) (18811973) The Renaissance produced a significant change in direction in the history of the Golden Ratio. No longer was this concept confined to mathematics. Now the Golden Ratio found its way into explanations of natural phenomena and into the arts.
We have already encountered claims that the architectural design of various structures from antiquity, such as the Great Pyramid and the Parthenon, had been based on the Golden Ratio. A closer examination of these claims revealed, however, that in most cases they could not be substantiated. The introduction of the notion of the existence of a ”Divine Proportion” and the general recognition of the importance of mathematics for perspective made it more conceivable that some artists would start using scientifically based methods in general and the Golden Ratio in particular in their works. Contemporary painter and draftsman David Hockney argues in his book Secret Knowledge Secret Knowledge (2001), for example, that starting with around 1430, artists began secretly using cameralike devices, including lenses, concave mirrors, and the camera obscura, to help them create realistic-looking paintings. But did artists really use the Golden Ratio? And if they did, was the Golden Ratio's application restricted to the visual arts or did it penetrate into other areas of artistic endeavor? (2001), for example, that starting with around 1430, artists began secretly using cameralike devices, including lenses, concave mirrors, and the camera obscura, to help them create realistic-looking paintings. But did artists really use the Golden Ratio? And if they did, was the Golden Ratio's application restricted to the visual arts or did it penetrate into other areas of artistic endeavor?
THE ARTIST'S SECRET GEOMETRY?.
Many of the a.s.sertions concerning the employment of the Golden Ratio in painting are directly a.s.sociated with the presumed aesthetic properties of the Golden Rectangle. I shall discuss the reality (or falsehood) of such a canon for aesthetics later in the chapter. For the moment, however, I shall concentrate on the much simpler question: Did any pre-and Renaissance painters actually base their artistic composition on the Golden Rectangle? Our attempt to answer this question takes us back to the thirteenth century.
The ”Ognissanti Madonna” (also known as ”Madonna in Glory,” Figure 70 Figure 70; currently in the Uffizi Gallery in Florence) is one of the greatest panel paintings by the famous Italian painter and architect Giotto di Bondone (12671337). Executed between 1306 and 1310, the painting shows a half-smiling, enthroned Virgin caressing the knee of the Child. The Madonna and Child are surrounded by angels and saints arranged in some sort of perspectival ”hierarchy.” Many books and articles on the Golden Ratio repeat the statement that both the painting as a whole and the central figures can be inscribed precisely in Golden Rectangles (Figure 71).
Figure 70
Figure 71 A similar claim is made about two other paintings with the same general subject: the ”Madonna Rucellai” (painted in 1285) by the great Sienese painter Duccio di Buoninsegna, known as Duccio (ca. 12551319), and the ”Santa Trinita Madonna” by the Florentine painter Cenni di Pepo, known as Cimabue (ca. 12401302). As fate would have it, currently the three paintings happen to be hanging in the same room in the Uffizi Gallery in Florence. The dimensions of the Ognissanti,” ”Rucellai,” and ”Santa Trinita” Madonnas give height to width ratios of 1.59, 1.55, and 1.73, respectively. While all three numbers are not too far from the Golden Ratio, two of them are actually closer to the simple ratio of 1.6 rather than to the irrational number . This fact could indicate (if anything) that the artists followed the Vitruvian suggestion for a simple proportion, one that is the ratio of two whole numbers, rather than the Golden Ratio. The inner rectangle in the ”Ognissanti Madonna” (Figure 71) leaves us with an equally ambiguous impression. Not only are the boundaries of the rectangle drawn usually (e.g., in Trudi Hammel Garland's charming book Fascinating Fibonaccis) Fascinating Fibonaccis) with rather thick lines, making any measurement rather uncertain, but, in fact, the upper horizontal side is placed somewhat arbitrarily. with rather thick lines, making any measurement rather uncertain, but, in fact, the upper horizontal side is placed somewhat arbitrarily.
Remembering the dangers of having to rely on measured dimensions alone, we may wonder if there exist any other reasons to suspect that these three artists might have desired to include the Golden Ratio in their paintings. The answer to this question appears to be negative, unless they were driven toward this ratio by some unconscious aesthetic preference (a possibility that will be discussed later in the chapter). Recall that the three Madonnas were painted more than two centuries before the publication of The Divine Proportion The Divine Proportion brought the ratio to wider attention. brought the ratio to wider attention.
The French painter and author Charles Bouleau expresses a different view in his 1963 book The Painter's Secret Geometry. The Painter's Secret Geometry. Without referring to Giotto, Duccio, or Cimabue specifically, Bouleau argues that Pacioli's book represented an end to an era rather than its beginning. He a.s.serts that Without referring to Giotto, Duccio, or Cimabue specifically, Bouleau argues that Pacioli's book represented an end to an era rather than its beginning. He a.s.serts that The Divine Proportion The Divine Proportion merely ”reveals the thinking of long centuries of oral tradition” during which the Golden Ratio ”was considered as the expression of perfect beauty.” If this were truly the case, then Cimabue, Duccio, and Giotto indeed might have decided to use this accepted standard for perfection. Unfortunately, I find no evidence to support Bouleau s statement. Quite to the contrary; the doc.u.mented history of the Golden Ratio is inconsistent with the idea that this proportion was particularly revered by artists in the centuries preceding the publication date of Pacioli's book. Furthermore, all the serious studies of the works of the three artists by art experts (e.g., merely ”reveals the thinking of long centuries of oral tradition” during which the Golden Ratio ”was considered as the expression of perfect beauty.” If this were truly the case, then Cimabue, Duccio, and Giotto indeed might have decided to use this accepted standard for perfection. Unfortunately, I find no evidence to support Bouleau s statement. Quite to the contrary; the doc.u.mented history of the Golden Ratio is inconsistent with the idea that this proportion was particularly revered by artists in the centuries preceding the publication date of Pacioli's book. Furthermore, all the serious studies of the works of the three artists by art experts (e.g., Giotto Giotto by Francesca Flores D'Arcais; by Francesca Flores D'Arcais; Cimabue Cimabue by Luciano Bellosi) give absolutely no indication whatsoever that these painters might have used the Golden Ratio-the latter claim appears only in the writings of Golden Number enthusiasts and is based solely on the dubious evidence of measured dimensions. by Luciano Bellosi) give absolutely no indication whatsoever that these painters might have used the Golden Ratio-the latter claim appears only in the writings of Golden Number enthusiasts and is based solely on the dubious evidence of measured dimensions.
Another name that invariably turns up in almost every claim of the appearance of the Golden Ratio in art is that of Leonardo da Vinci. Some authors even attribute the invention of the name ”the Divine Proportion” to Leonardo. The discussion usually concentrates on five works by the Italian master: the unfinished canvas of ”St. Jerome,” the two versions of ”Madonna of the Rocks,” the drawing of ”a head of an old man,” and the famous ”Mona Lisa.” I am going to ignore the ”Mona Lisa” here for two reasons: It has been the subject of so many volumes of contradicting scholarly and popular speculations that it would be virtually impossible to reach any unambiguous conclusions; and the Golden Ratio is supposed to be found in the dimensions of a rectangle around Mona Lisa's face. In the absence of any clear (and doc.u.mented) indication of where precisely such a rectangle should be drawn, this idea represents just another opportunity for number juggling. I shall return, however, to the more general topic of proportions in faces in Leonardo's paintings, when I shall discuss the drawing ”a head of an old man.”
Figure 72
Figure 73 The case of the two versions of ”Madonna of the Rocks” (one in the Louvre in Paris, Figure 72 Figure 72, and the other in the National Gallery in London, Figure 73 Figure 73) is not particularly convincing. The ratio of the height to width of the painting thought to have been executed earlier (Figure 72) is about 1.64 and of the later one 1.58, both reasonably close to but also close to the simple ratio of 1.6.
The dating and authenticity of the two ”Madonna of the Rocks” also put an interesting twist on the claims about the presence of the Golden Ratio. Experts who studied the two paintings concluded that, without a doubt, the Louvre version was done entirely by Leonardo's hand, while the execution of the National Gallery version might have been a collaborative effort and is still the source of some debate. The Louvre version is thought to be one of the first works that Leonardo produced in Milan, probably between 1483 and 1486. The National Gallery painting, on the other hand, usually is a.s.sumed to have been completed around 1506. The reason that these dates may be of some significance is that Leonardo met Pacioli for the first time in 1496, in the Court of Milan. The seventy-first chapter of the Divina Divina (the end of the first portion of the book) was, in Pacioli's words: ”Finished this day of December 14, at Milan in our still cloister the year 1497.” The first version (and the one with no doubts about authenticity) of the ”Madonna of the Rocks” was therefore completed about ten years before Leonardo had the opportunity to hear directly from the horse's mouth about the ”divine proportion.” The claim that Leonardo used the Golden Ratio in ”Madonna of the Rocks” therefore amounts to believing that the artist adopted this proportion even before he started his collaboration with Pacioli. While this is not impossible, there is no evidence to support such an interpretation. (the end of the first portion of the book) was, in Pacioli's words: ”Finished this day of December 14, at Milan in our still cloister the year 1497.” The first version (and the one with no doubts about authenticity) of the ”Madonna of the Rocks” was therefore completed about ten years before Leonardo had the opportunity to hear directly from the horse's mouth about the ”divine proportion.” The claim that Leonardo used the Golden Ratio in ”Madonna of the Rocks” therefore amounts to believing that the artist adopted this proportion even before he started his collaboration with Pacioli. While this is not impossible, there is no evidence to support such an interpretation.
Either version of ”Madonna of the Rocks” represents one of Leonardo's most accomplished masterpieces. Perhaps in no other painting did he apply better his poetic formula: ”every opaque body is surrounded and clothed on its surface by shadows and light.” The figures in the paintings literally open themselves to the emotional partic.i.p.ation of the spectator. To claim that these paintings derive any part of their strength from the mere ratio of their dimensions trivializes Leonardo's genius unnecessarily. Let us not fool ourselves; the feeling of awe we experience when facing ”Madonna of the Rocks” has very little to do with whether the dimensions of the paintings are in a Golden Ratio.
A similar uncertainty exists with respect to the unfinished ”St. Jerome” (Figure 74; currently in the Vatican museum). Not only is the painting dated to 1483, long before Pacioli's move to Milan, but the claim made in some books (e.g., in David Bergamini and the editors of Life Magazine's Mathematics) Life Magazine's Mathematics) that ”a Golden Rectangle fits so neatly around St. Jerome” requires quite a bit of wishful thinking. In fact, the sides of the rectangle miss the body (especially on the left side) and head entirely, while the arm extends well beyond the rectangle's side. that ”a Golden Rectangle fits so neatly around St. Jerome” requires quite a bit of wishful thinking. In fact, the sides of the rectangle miss the body (especially on the left side) and head entirely, while the arm extends well beyond the rectangle's side.
The last example for a possible use of the Golden Ratio by Leonardo is the drawing of ”a head of an old man” (Figure 75; the drawing is currently in the Galleria dell'Accademia in Venice). The profile and diagram of proportions were drawn in pen some time around 1490. Two studies of hors.e.m.e.n in red chalk, which are a.s.sociated with Leonardo's ”Battle of Anghiari,” were added to the same page around 15031504.
While the overlying grid leaves very little doubt that Leonardo was indeed interested in various proportions in the face, it is very difficult to draw any definitive conclusions from this study. The rectangle in the middle left, for example, is approximately a Golden Rectangle, but the lines are drawn so roughly that we cannot be sure. Nevertheless, this drawing probably comes the closest to a demonstration that Leonardo used rectangles to determine dimensions in his paintings and that he might have even considered the application of the Golden Ratio to his art.
Leonardo's interest in proportions in the face may have another in-
Figure 74
Figure 75 teresting manifestation. In an article that appeared in 1995 in the Scientific American Scientific American, art historian and computer graphics artist Lillian Schwarz presented an interesting speculation. Schwarz claimed that in the absence of his model for the ”Mona Lisa,” Leonardo used his own facial features to complete the painting. Schwarz's suggestion was based on a computer-aided comparison between various dimensions in Mona Lisa's face and the respective dimensions in a red chalk drawing that is considered by many (but not all) to be Leonardo's only self-portrait.
However, as other art a.n.a.lysts have pointed out, the similarity in the proportions may simply reflect the fact that Leonardo used the same formulae of proportion (which may or may not have included the Golden Ratio) in the two portraits. In fact, Schwarz herself notes that even in his grotesques-a collection of bizarre faces with highly exaggerated chins, noses, mouths, and foreheads-Leonardo used the same proportions in the face as in the ”head of an old man.”
If there exist serious doubts regarding whether Leonardo himself, who was not only a personal friend of Pacioli but also the ill.u.s.trator for the Oivina Oivina, used the Golden Ratio in his paintings, does this mean that no other artist ever used it? Definitely not. With the surge of Golden Ratio academic literature toward the end of the nineteenth century, the artists also started to take notice. Before we discuss artists who did use the Golden Ratio, however, another myth still needs to be dispelled.
In spite of many existing claims to the contrary, the French pointillist Georges Seurat (18591891) probably did not use the Golden Ratio in his paintings. Seurat was interested in color vision and color combination, and he used the pointillist (multidotted) technique to approximate as best as he could the scintillating, vibratory quality of light. He was also concerned late in life with the problem of expressing specific emotions through pictorial means. In a letter he wrote in 1890, Seurat describes succinctly some of his views: Art is harmony. Harmony is the a.n.a.logy of contradictions and of similars, in tone, shade, line, judged by the dominant of those and under the influence of a play of light in arrangements that are gay, light, sad. Contradictions are..., with respect to line, those that form a right angle.... Gay lines are lines above the horizontal;... calm is the horizontal; sadness lines in the downward direction.
Seurat used these ideas explicitly in ”The Parade of a Circus” (sometimes called ”The Side Show;” Figure 76 Figure 76; currently in The Metropolitan Museum of Art, New York). Note in particular the right angle formed by the bal.u.s.trade and the vertical line to the right of the middle of the painting. The entire composition is based on principles that Seurat adopted from art theorist David Sutter's book h ha philosophie des Beaux-Arts appliquee a la peinture Beaux-Arts appliquee a la peinture (The philosophy of the fine arts applied to painting; 1870). Sutter wrote: ”when the dominant is horizontal, a succession of vertical objects can be placed on it because this series will concur with the horizontal line.” (The philosophy of the fine arts applied to painting; 1870). Sutter wrote: ”when the dominant is horizontal, a succession of vertical objects can be placed on it because this series will concur with the horizontal line.”
Figure 76 Golden Ratio aficionados often present a.n.a.lyses of ”The Parade” (as well as other paintings, such as ”The Circus”) to ”prove” the use of . Even in the beautiful book Mathematics Mathematics, by Bergamini and the editors of Life Magazine Life Magazine, we find: ”La Parade ”La Parade, painted in the characteristic multi-dotted style of the French impressionist Georges Seurat, contains numerous examples of Golden proportions.” The book goes even further with a quote (attributed to ”one art expert”) that Seurat ”attacked every canvas by the Golden Section.” Unfortunately, these statements are unfounded. This myth was propagated by the Romanian born prelate and author Matila Ghyka (18811965), who was also the ”art expert” quoted by Bergamini. Ghyka published two influential books, Esthetique des proportions dans la nature et dans les arts Esthetique des proportions dans la nature et dans les arts (Aesthetics of proportions in nature and in the arts; 1927) and (Aesthetics of proportions in nature and in the arts; 1927) and Le Nombre d'Or: Rites et rythmes pytagoriciens dans le developpement de la civilisation occidentale Le Nombre d'Or: Rites et rythmes pytagoriciens dans le developpement de la civilisation occidentale (The golden number, Pythagorean rites and rhythms in the development of Western civilization; 1931). Both books are composed of semimystical interpretations of mathematics. Alongside correct descriptions of the mathematical properties of the Golden Ratio, the books contain a collection of inaccurate anecdotal materials on the occurrence of the Golden Ratio in the arts (e.g., the Parthenon, Egyptian temples, etc.). The books have been almost inexplicably influential. (The golden number, Pythagorean rites and rhythms in the development of Western civilization; 1931). Both books are composed of semimystical interpretations of mathematics. Alongside correct descriptions of the mathematical properties of the Golden Ratio, the books contain a collection of inaccurate anecdotal materials on the occurrence of the Golden Ratio in the arts (e.g., the Parthenon, Egyptian temples, etc.). The books have been almost inexplicably influential.
Concerning ”The Parade” specifically, while it is true that the horizontal is cut in proportions close to the Golden Ratio (in fact, the simple ratio eight-fifths), the vertical is not. An a.n.a.lysis of the entire composition of this and other paintings by Seurat, as well as paintings by the Symbolist painter Pierre Puvis de Chavannes (18241898), led even a Golden Ratio advocate like painter and author Charles Bouleau to conclude that ”I do not think we can, without straining the evidence to regard his [Puvis de Chavannes s] compositions as based on the Golden Ratio. The same applies to Seurat.” A detailed a.n.a.lysis in 1980 by Roger Herz-Fischler of all of Seurat s writings, sketches, and paintings reached the same conclusion. Furthermore, the mathematician, philosopher, and art critic Charles Henry (18591926) stated firmly in 1890 that the Golden Ratio was ”perfectly ignored by contemporary artists.”
Who, then, did use the Golden Ratio either in actual paintings or in the theory of painting? The first prominent artist and art theorist to employ the ratio was probably Paul Serusier (18641927). Serusier was born in Paris, and after studying philosophy he entered the famous art school Academie Julian. A meeting with the painters Paul Gaugin and emile Bernard converted him to their expressive use of color and symbolist views. Together with the post-Impressionist painters Pierre Bon-nard, edouard Vuillard, Maurice Denis, and others he founded the group called the Nabis, from the Hebrew word meaning ”prophets.” The name was inspired by the group's half-serious, half-burlesque pose regarding their new style as a species of religious illumination. The composer Claude Debussy was also a.s.sociated with the group. Serusier probably heard about the Golden Ratio for the first time during one of his visits (between 1896 and 1903) to his friend the Dutch painter Jan Verkade (18681946). Verkade was a novice in the Benedictine monastery of Beuron, in South Germany. There groups of monk-painters were executing rather dull religious compositions based on ”sacred measures,” following a theory of Father Didier Lenz. According to Father Lenz's theory, the great art works of antiquity (e.g., Noah's Ark, Egyptian works, etc.) were all based on simple geometrical ent.i.ties such as the circle, equilateral triangle, and hexagon. Serusier found the charm of this theory captivating, and he wrote to Verkade: ”as you can imagine, [I] have talked a great deal about your measures.” The painter Maurice Denis (18701943) wrote biographical notes on Serusier, from which we learn that those ”measures” employed by Father Lenz included the Golden Ratio. Even though Serusier admits that his initial studies of the mathematics of Beuron were ”not all plain sailing,” the Golden Ratio and the story of its potential a.s.sociation with the Great Pyramid and Greek artworks made it also into Serusier's important art theory book L'ABC de la Peinture L'ABC de la Peinture (The ABC of painting). (The ABC of painting).
While Serusier's interest in the Golden Ratio appears to have been more philosophical than practical, he did make use of this proportion in some of his works, mainly to ”verify, and occasionally to check, his inventions of shapes and his composition.”
Following Serusier, the concept of the Golden Ratio propagated into other artistic circles, especially that of the Cubists. The name ”Cubism” was coined by art critic Louis Vauxcelles (who, by the way, had also been responsible for ”Expressionism” and ”Fauvism”) after viewing an exhibition of Georges Braque's work in 1908. The movement was inaugurated by Pica.s.so's painting ”Les Demoiselles d Avignon” and Braque's ”Nude.” In revolt against the pa.s.sionate use of color and form in Expressionism, Pica.s.so and Braque developed an austere, almost monochrome style that deliberately rejected any subject matter that was likely to evoke emotional a.s.sociations. Objects like musical instruments and even human figures were dissected into faceted geometrical planes, which were then combined in s.h.i.+fting perspectives. This a.n.a.lysis of solid forms for the purpose of revealing structure was quite amenable to the use of geometrical concepts like the Golden Ratio. In fact, some of the early Cubists, such as Jacques Villon and his brothers Marcel and Raymond Duchamp-Villon, together with Albert Gleizes and Francis Picabia, organized in Paris in October 1912 an entire exhibition ent.i.tled ”Section d'Or” (”The Golden Section”). In spite of the highly suggestive name, none of the paintings that was exhibited actually included the Golden Section as a basis for its composition. Rather, the organizers chose the name simply to project their general interest in questions that related art to science and philosophy. Nevertheless, some Cubists, like the Spanish-born painter Juan Gris (18871927) and the Lithuanian-born sculptor Jacques (Chaim Jacob) Lipchitz (18911973) did use the Golden Ratio in some of their later works. Lipchitz wrote: ”At the time, I was very interested in theories of mathematical pro portions, like the other cubists, and I tried to apply them to my sculptures. We all had a great curiosity for that idea of a golden rule or Golden Section, a sys tem which was reputed to lay under the art and architecture of ancient Greece.” Lipchitz helped Juan Gris in the construction of the sculpture ”Arlequin” (currently in the Philadelphia Museum of Art; Figure 77 Figure 77), in which the two artists used Kepler's triangle (which is based on the Golden Ratio; see Figure 61 Figure 61) for the production of the desired proportions.
Figure 77 Another artist who used the Golden Ratio in the early 1920s was the Italian painter Gino Severini (18831966). Severini attempted in his work to reconcile the somewhat conflicting aims of Futurism and Cubism. Futurism represented an effort by a group of Italian intellectuals from literary arts, the visual arts, theater, music, and cinema to bring about a cultural rejuvenation in Italy. In Severini's words: ”We choose to concentrate our attention on things in motion, because our modern sensibility is particularly qualified to grasp the idea of speed.” The first painters' Futurist manifesto was signed in 1910, and it strongly urged the young Italian artists to ”profoundly despise all forms of imitation.” While still a Futurist himself, Severini found in Cubism a ”notion of measure” that fit his ambition of ”making, by means of painting, an object with the same perfection of craftsmans.h.i.+p as a cabinet maker making furniture.” This striving for geometrical perfection led Severini to use the Golden Section in his preparatory drawings for several paintings (e.g., ”Maternity,” currently in a private collection in Rome; Figure 78 Figure 78).
Figure 78 Russian Cubist painter Maria Vorobeva, known as Marevna, provides an interesting instance of the role of the Golden Ratio in Cubist art. Marevna's 1974 book, Life with the Painters of La Ruche Life with the Painters of La Ruche, is a fascinating account of the lives and works of her personal friends-a group that included the painters Pica.s.so, Modigliani, Soutine, Rivera (with whom she had a daughter), and others in Paris of the 1920s. Although Marevna does not give any specific examples and some of her historical comments are inaccurate, the text implies that Pica.s.so, Rivera, and Gris had used the Golden Ratio as ”another way of dividing planes, which is more complex and attracts experienced and inquisitive minds.”