The Science of Art
The future of education is in interdisciplinary study. Most professors and scholars are hard-pressed to find much research on the relationship of science to art. Thus, very few universities offer combined study in science and art. The University of Iceland should be an exception. While adding a new course to our already extensive catalogue does have its drawbacks, for instance time and funding, many benefits also exist. A course in the science of art taught in English has the potential to bring new international students to the university. We will be among the handful of universities to have a program with such a crossover area in the study of both art and science. Our students who are involved in the interdisciplinary program, the arts, or the sciences will gain a deeper understanding of the relationship between two seemingly very different topics.
I expect a range of students, mostly those in the interdisciplinary studies, visual arts, and humanities departments. Ideally, the class will be a requirement for interdisciplinary studies majors, and a core elective for those seeking at least a minor in visual arts, physics, or mathematics. Students of physics and mathematics tend not to elect visual arts classes, beyond what is required for graduation. The converse often occurs among visual arts students as well. These two clusters of students in particular should have an opportunity to explore the way in which their disciplines relate to each other.
The Science of Art is an interdisciplinary course that covers some of the scientific principles behind the visual arts. The bulk of the course focuses on electromagnetism as it relates to light and color, the mathematics behind perspective and design, and the relationship between modern physics and modern art. The first part of the course covers color and light. We will discuss the dual nature of light, electromagnetic radiation, and the visible spectrum. Also in this section, students learn about the nature of color – what it is and how it is used to create optical illusions.
Part two of the course is comprised of the study of perspective. The main topics of this section are the history of perspective, the geometry of perspective, and what happens when perspective is warped. In the latter, we will perform some analysis of warped perspective using works such as those of M.C. Escher. Part three goes deeper into the involvement of mathematics in art. Students will begin learning about phi, the golden ratio, and how it relates to nature and art. There will be some detailed discussion of Leonardo da Vinci, architecture, and aesthetics. The course closes with a glimpse into modern physics and its relation to modern art. The majority of this section encompasses space, time, and surrealism. Important topics include modern sculpture, the concept of spacetime, and surrealism through the study of artists like Alexander Calder, Salvador Dali and René Magritte…
Visual art would not exist without light. Light is defined as “something that makes things visible.” In order to grasp the scientific principles behind visual art, we need a basic understanding of light and color. Modern physics has developed a description of light as being simultaneously waves and particles, known as photons. This concept, called the dual nature of light, is difficult to visualize, therefore light is often termed particle waves or “wavicles.” For theoretical purposes, light is described by either the wave model or particle model. I recommend Dr. Rod Nave’s “Wave-Particle Duality” (http://hyperphysics.phyastr.gsu.edu/hbase/mod1.html) for more detailed information on the dual nature of light.
Electromagnetism describes the inextricable relationship between electricity and magnetism. Changing a magnetic field necessarily produces an electric field and vice-versa. What we are concerned with here is electromagnetic radiation, self-propagating electromagnetic waves, which are categorized by frequency or wavelength.2 Researchers in the fields of astrophysics and cosmology most commonly use the particle model of light. The electromagnetic spectrum, shown in Figure 1, represents the range of electromagnetic radiation that we can currently detect. The partitions indicate the characteristic frequencies of the different classes of radiation.
The visible spectrum appears between the ultraviolet and infrared spectra, ranging in wavelength from approximately 400 nm to 750 nm, as illustrated in Figure 1. The anatomy of the human eye is the limiting factor in our inability to see beyond red and violet… One of my areas of research involves an explanation of the physics behind our visible color range. The basis for my current theory is a possible correlation between our sun as a type G yellow star (see Appendix for a chart of spectral types) and the color yellow as our median visible wavelength.
The brain perceives the juxtaposition of certain colors as an optical illusion. The use of color in Op Art, or Optical Art, often creates the illusion of depth or movement in a two-dimensional plane. In Figure 2, Julian Stanczak uses “numerous shifts in color that give the visual appearance of an unfolding, rounded form, floating in an [ambiguous] space.”
If you look at a cube from directly overhead, it looks like a square. What happens to its depth? Turn your head to the side a bit and more surfaces appear. How can an artist show that the cube is an object in space, rather than just one surface? Representing three-dimensional space using two-dimensional media is sometimes an artist’s most difficult task. Imagine trying to sculpt a solid as it moves through time. Such a task is as daunting now as the idea of perspective was before the 1400’s. Euclidean Geometry defines two lines as being parallel if they never meet. Lines drawn in perspective, however, do eventually converge at what is called the “vanishing point.” If an artist presents a scene from a view parallel to one axis, any parallel lines drawn in that direction will converge at some vanishing point, thereby creating a sense of depth. If the scene were not drawn in perspective, how would those lines coming straight toward us be drawn? Edwin Abbott Abbott’s book, Flatland: A Romance of Many Dimensions, is an excellent discourse on dimensions and perspective
A Brief History of Perspective
Before the use of perspective, art was almost entirely inspired by religion. From Byzantine art, most famous for its icons, to Early Christian art, the emphasis was placed on the most important religious character(s) in the scene. Figure 3 shows the lack of space and depth in Byzantine painting. Perspective was “discovered” sometime in the early 1400’s by Florentine architect, Filippo Brunelleschi. Quite by accident, Brunelleschi noticed the way the outlines seemed to converge in his painting of a building on a mirror. Leonardo da Vinci took it one step further by describing the effect of distance on color and the sharpness of outlines. Figure 3: Lamentation of Christ (1164) The Science of Art -7- Jodie Webb Giotto di Bondone was the first artist to attempt the use of perspective in his work. A geometric detail of Giotto’s Jesus and the Caïf, shown in Figure 3, reveals that, though there is an illusion of depth, there is no common vanishing point. The problem with Giotto’s perspective was his use of an algebraic method to determine the placement of his lines.4 The European Renaissance painters further developed the concept of perspective and actually began using it as a basis for their work. Figure 5 shows the use of perspective to create only one scene, in which the viewer’s eye is drawn in to the vanishing point. Figure 4: Giotto di Bondone, Jesus and the Caïf Figure 5: Piero della Francesca, View of an Ideal City. In 1436, Leone Battista Alberti wrote the first ever account detailing the mathematics of modern perspective. His work, titled De Pictura (On Painting), offered a geometric approach to the painting of objects using linear perspective to indicate correct space and scale. De Pictura was almost a step-by-step guide to the use of vanishing points, horizon lines, and other concepts behind linear perspective.
In some very special cases, artists can use perspective to create an ambiguous image. What allows this ambiguity is the phenomenon of multistable perception, which occurs when we perceive a “two-state” image. In Figure 6, the brain cannot see both interpretations at once, so it flips back and forth between the two. Ambiguity is also a very important component of Op Art. Knot Theory Warped perspective allows objects that are impossible in three dimensions to seem possible when drawn in a plane. Such objects are known as “impossible objects.”
Knot Theory, a somewhat esoteric branch of mathematics, and in particular the concept of “knots and links,” provides a mathematical explanation of impossible objects. Figure 7, “Penrose Stairs,” depicts a never-ending staircase, a knot created by “embedding one… closed curve… in 3D space.”
Perhaps the most famous creator of ambiguous art is Maurits Cornelis Escher, better known as M.C. Escher. Though his well-known work has an obvious mathematical influence, he had no formal training in mathematics. M.C. Escher’s lithograph in Figure 8, Ascending and Descending, is an artistic elaboration on the Penrose Stairs, which appear on the roof of
Escher’s building. The monks on the stairs seem to move in an unending loop.
Phi: The Golden Ratio
The Greek letter phi is a mathematical name for the golden ratio, also known as the golden section, golden mean, or golden number. Phi … is an irrational number that “expresses the relationship that the sum of two quantities is to the larger quantity as the larger is to the smaller.” Equation 1 is an algebraic definition of phi. The idea that adding 1 to a number returns that same number squared is hard to comprehend. Through some algebraic manipulation, we get Equation 2, an expression of phi we can better understand.
Life, the Universe, and Everything
The golden ratio appears throughout nature in plants, lightning, and even the human body. In these expressions, we see the golden ratio as a mathematic extension of the Fibonacci sequence. Nautilus shells, galaxies, and hurricanes are nature’s illustration of what is known as the golden spiral. In a golden spiral, each quarter-turn of the spiral increases in width by a factor of phi. Figure 9 is a cut-away of a nautilus shell revealing the spiral within.
Art and Design
Since the ancient Greeks, people have used the golden ratio in art and architecture. The lines overlaying the photograph of the Parthenon in Figure 10 indicate that the structure was built in close approximation to the golden ratio, seen here as golden rectangles. Artists have applied the golden ratio to their works to bestow in them a sense of beauty. The three-volume volume work called De Divina Proportione, written in 1509 by mathematician Luca Pacioli, was a key influence for the application of phi “to yield pleasing, harmonious proportions.”
Leonardo da Vinci
One of Luca Pacioli’s closest friends was Leonardo da Vinci, the quintessential “Renaissance Man.” In fact, Leonardo illustrated his De Divina Proportione. One of his illustrations, shown in Figure 11, demonstrates the application of the golden ratio to the human face. Some claim that Leonardo used the golden ratio to proportion the Mona Lisa. Though it seems in retrospect that his paintings are actually based on phi, he would never disclose whether it was true.
Space and Time
In 1905, Albert Einstein proposed his “special theory of relativity.” Within it, he described the “relativity of simultaneity,” which states that simultaneous events viewed by one observer may not be simultaneous to another observer. In 1907, Pablo Picasso was experimenting with what we now call Cubism. Cubist art allows the viewer to see all side of an object simultaneously, rather than having to move through space to see them. Figure 12, Picasso’s Girl with a Mandolin, exemplifies his treatment of simultaneity. A later movement, called Futurism, explored time as an artistic model. Their 1905 manifesto proclaimed, “Time and Space died yesterday.”9 This statement is actually what is called a “Strange Loop,” a paradoxical self-referencing statement. The futurist proclamation begs the question, “If time died, then what is yesterday?” The futurists also played on the idea of simultaneity. Though they had no experience with Einstein’s theories, they developed a very similar concept in their artwork. In relativity, as an observer travels at speeds closer and closer to the speed of light, time slows down and actually stops when the speed of light is reached. Futurist artwork often depicts an event as it happens at one instance in time, as if time has stopped.
As discussed in the section on perspective, three dimensions can be hard to represent on a two-dimensional plane. Filmmakers have attempted to bring depth to a plane, a movie screen, using the process of stereoscopy. We are very familiar the results of this process, better known as 3-D films. In a three-dimensional world, though, doesn’t it make sense to use all three spatial dimensions for our creative endeavors? Sculpture is a natural expression of the world around us. Since the beginning of human history, artists have used sculpture to communicate emotions and chronicle history. Moving Sculpture Alexander Calder was an American artist and sculptor who invented the mobile, a type of “kinetic sculpture.” Kinetic sculpture is a physical form of kinetic art, which is art that either moves or gives the appearance of movement. Figure 13 is a photograph of one of Calder’s mobiles, Totem. The nature of sculpture dictates that it must adhere to the laws of physics. Kinetic sculpture, in particular, employs such principles as center of mass and kinetic energy. My favorite Calder piece is the mercury fountain, pictured in Figure 14, that he designed as a tribute to his good friend and contemporary, Joan Miró, who was credited for the invention of gas sculpture. The use of fluid substances in sculpture presents a sense of life within inanimate objects.
Four Dimensions and Beyond
The Surrealist movement was possibly the most concerned about space and time than any other artistic movement. Like cubists and futurists, surrealists utilized Einstein’s theories as a basis for their art. Unlike the other two movements, though, surrealist art was actually meant to be nonsensical. Was it a coincidence that at the same time when art started to make no sense, the public became unable to understand science? Two of the most recognizable surrealist artists are Salvador Dali and René Magritte. They were both very familiar with and had a great deal of respect for modern physics, which was proven in their work. René Magritte Magritte’s Time Transfixed, shown in Figure 15, is based on Einstein’s postulate that time slows dramatically as the speed of light is approached. Magritte actually exploits the same imagery that Einstein himself used to demonstrate time dilation, a clock and a train.
Magritte was also fond of creating visual imagery of Einstein’s conclusion that space becomes infinitely flat as speeds approach that of light. Similar to the Cubist treatment of dimensions, Magritte painted impossible scenes in which opposite faces are seen simultaneously. Displayed in Figure 16, La Blanc Seing gives the viewer a glimpse of both the front face and back face of the scene, just as we might see it if space were compressed to two dimensions. Salvador Dali Perhaps Dali’s most famous work is The Persistence of Memory, shown in Figure 17. Here he uses the imagery of melting clocks to symbolize time dilation.
Maybe the reason this painting leaves a lasting impression is because we always seem to be searching for a way to stop time or at least slow it down. Dali stepped boldly into the realm of spacetime with his controversial painting Corpus Hypercubus. He was the first artist to attempt a representation of four dimensions on a planar medium. Dali explores the idea that, just as three dimensional objects cast two dimensional shadows, perhaps four dimensional objects cast three dimensional shadows. The “cross” to which Christ is not bound in Figure 18 is called a hypercube, a hypothetical four dimensional projection of a cube. Modern sculptors and other artists have also produced representations of hypercubes in their work.
Summary and Conclusion
The Science of Art provides students with deep knowledge and understanding of art and science through their relationship to each other, allowing them to see the world around them in a whole new way. The basis for all visual art is light and color. Moreover, without light and color, we would be unable to see artists’ great works of beauty. My course allows students to delve into light and color through the study of electromagnetic radiation and the visible spectrum. Mathematical analysis of art through such concepts as perspective and the golden ratio gives students a medium with which to investigate the more mysterious aspects of art and math. Whether or not artists have used the golden ratio consciously is a great subject for further research. There is also the conundrum that the Cubist, Futurist, and Surrealist movements developed with no conscious knowledge of Einstein’s theories. However, as surrealism grew, artists like Salvador Dali and Rene Magritte began to apply Relativity Theory to the creation of their work. If you need more information, I’ve offered some suggestions for further reading throughout this paper. The possibilities of The Science of Art are practically endless…
Axis: An imaginary infinite straight line in a particular direction used as a reference to determine position, distance and direction. Center of mass: The specific point at which an object’s entire mass appears to be concentrated. Fibonacci series: A recursive sequence where the first two values are 1 and each successive term is obtained by adding together the two previous terms.
Irrational number: A number that cannot be expressed as a ratio of two integers.
Kinetic energy: The energy of motion.
Nanometer (nm): A length equivalent to10-9 meters, 10 ångströms, or 3.94-8 inches.
Plane: A two-dimensional surface.
Space: An unlimited three-dimensional realm.
Spacetime: A four-dimensional system in which space makes up the first three dimensions and time, the fourth.
Figure 1: Electromagnetic Spectrum. Source: http://www.yorku.ca/eye/spectru.htm.
Figure 2: Stanczak, Julian. Spacial (1986). Source: http://www.artincontext.org.
Figure 3: Lamentation of Christ (1164). Source: http://www.wikipedia.org.
Figure 4: Giotto di Bondone. Jesus and the Caïf. Source: http://www.ski.org/cwt/CWTyler/Art%20Investigations.
Figure 5: Piero della Francesca. View of an Ideal City. Source: http://www.eyeconart.net/history/Renaissance/early_ren.htm
Figure 6: Source: http://www.wikipedia.org.
Figure 7: Penrose Stairs. Source: http://www.wikipedia.org.
Figure 8: Escher, Maurits Cornelis. Ascending and Descending (1960). Source: http://www.wikipedia.org.
Figure 9: Source: http://www.space.gc.ca/asc/eng/satellites/fuse.asp.
Figure 10: Source: http://www.wikipedia.org.
Figure 11: Source: http://www.wikipedia.org.
Figure 12: Picasso, Pablo. Girl with a Mandolin (1912). Source: http://artchive.com/artchive/P/picasso/tellier.jpg.html.
Figure 13: Calder, Alexander. Totem. Source: http://www.chrysler.org/20century01.asp.
Figure 14: Calder, Alexander. Mercury Fountain. Source: http://www.ics.uci.edu/~eppstein/pix/bar/miro.
Figure 15: Magritte, René. Time Transfixed (1935). Source: http://www.artchive.com.
Figure 16: Magritte, René. Le Blanc Seing (1965). Source: http://www.kahlil.org.
Figure 17: Dali, Salvador. The Persistence of Memory (1931). Source: http://www.virtualdali.com.
Figure 18: Dali, Salvador. Corpus Hypercubus (1954). Source: http://www.msgr.ca/msgr-4/dali_gallery.htm.
Hofstadter, Douglas R, Gödel, Escher, Back: an Eternal Golden Braid, New York: Basic Books, Inc., 1979.
Shlain, Leonard, Art and Physics, New York: Morrow, 1991.
“Alberti – ‘On Painting’.” Notebook: Context for Understanding Visual Art References and Resources. December 13, 2006, 1993. http://www.noteaccess.com/Texts/Alberti.
Wikipedia: The Free Encyclopedia. December, 2006. http://www.wikipedia.org.
1 “Light.” Dictionary.com. December 2, 2006 http://www.dictionary.com.
2 “Electromagnetic radiation.” Wikipedia. December 2, 2006 http://www.wikipedia.org.
3 Art in Context Center for Communications. December 4, 2006 http://www.artincontext.org.
4 “Perspective.” Wikipedia. December 5, 2006 http://www.wikipedia.org.
5 Yevin, Igor. “Ambiguity and Art.” Ambiguity and Art http://www.mi.sanu.ac.yu/vismath/igor/index.html.
6 Cerf, Corinne. “A family of impossible figures studied by knot theory” Impossible World. December 7, 2006 http://im-possible.info/english/articles/knot/knot.html.
7 “Golden ratio.” Wikipedia. December 8, 2006 http://www.wikipedia.org.
9 Shlain, Leonard, Art and Physics, New York: Morrow, 1991, p.207.
10 Ibid., p.222.