We live in a three-dimensional world and our brains are trained to see three dimensions — height, width, and depth. This was formalized thousands of years ago in the year 300 B.C. by the Alexandrian Greek philosopher, Euclid, who founded a school of mathematics, wrote a textbook called the "Euclidean Elements," and is known as the "father of geometry."
However, several hundred years ago physicists and mathematicians postulated a fourth dimension. Mathematically, the fourth dimension refers to time as another dimension along with length, width, and depth. It also refers to space and the space-time continuum. For some, the fourth dimension is spiritual or metaphysical.
Many artists during the early 20th century, among them the Cubists, Futurists, and Surrealists, have attempted to convey the fourth dimension in their two-dimensional artwork, moving beyond the realistic representation of three-dimensions to a visual interpretation of the fourth dimension, and creating a world of infinite possibilities.
The idea of time as a fourth dimension is usually attributed to the "Theory of Special Relativity" proposed in 1905 by the German physicist Albert Einstein (1879-1955). However, the idea that time is a dimension goes back to the 19th century, as seen in the novel "The Time Machine" (1895) by British author H.G. Wells (1866-1946), wherein a scientist invents a machine that lets him travel to different eras, including the future. Although we may not be able to travel through time in a machine, scientists have more recently discovered that time travel is, in fact, theoretically possible.
"Picasso was particularly struck by Poincaré's advice on how to view the fourth dimension, which artists considered another spatial dimension. If you could transport yourself into it, you would see every perspective of a scene at once. But how to project these perspectives on to canvas?"
Picasso's response to Poincaré's advice on how to view the fourth dimension was Cubism -- viewing multiple perspectives of a subject at once. Picasso never met Poincaré or Einstein, but their ideas transformed his art, and art thereafter.
Although the Cubists did not necessarily know about Einstein's theory — Picasso was unaware of Einstein when he created "Les Demoiselles d'Avignon" (1907), an early Cubist painting — they were aware of the popular idea of time travel. They also understood Non-Euclidean geometry, which the artists Albert Gleizes and Jean Metzinger discussed in their book "Cubism" (1912). There they mention the German mathematician Georg Riemann (1826-1866) who developed the hypercube.
Simultaneity in Cubism was one way artists illustrated their understanding of the fourth dimension, meaning that the artist would simultaneously show views of the same subject from different viewpoints — views that would not normally be able to be seen together at the same time in the real world. Picasso's Protocubist painting, "Demoiselles D'Avignon," is an example of such a painting, since it uses simultaneous fragments of the subjects as seen from different viewpoints - for example, both a profile and frontal view of the same face. Other examples of Cubist paintings showing simultaneity are Jean Metzinger's "Tea Time (Woman with a Teaspoon)" (1911), "Le Oiseau Bleu (The Blue Bird" (1912-1913), and Robert Delaunay's paintings of the Eiffel Tower behind curtains.
In this sense, the Fourth Dimension concerns the way in which two kinds of perception work together as we interact with objects or people in space. That is, to know things in real time, we must bring our memories from past time into the present. For example, when we sit down, we don't look at the chair as we lower ourselves on to it. We assume the chair will still be there when our bottoms hit the seat. Cubists painted their subjects based not on how they saw them, but on what they knew of them, from multiple perspectives.
Futurism, which was an offshoot of Cubism, was a movement that originated in Italy and was interested in motion, speed, and the beauty of modern life. The futurists were influenced by a new technology called chrono-photography that showed the movement of the subject in still-photos through a sequence of frames, much like a child's flip-book. It was the precursor to film and animation.
One of the first futurist paintings was Dynamism of a Dog on a Leash (1912), by Giacomo Balla, conveying the concept of movement and speed by blurring and repetition of the subject. Nude Descending a Staircase No. 2 (1912), by Marcel Duchamp, combines the Cubist technique of multiple views with the futurist technique of the repetition of a single figure in a sequence of steps, showing the human form in motion.
Another definition for the fourth dimension is the act of perceiving (consciousness) or feeling (sensation). Artists and writers often think of the fourth dimension as the life of the mind and many early 20th century artists used ideas about the fourth dimension to explore metaphysical content.
The fourth dimension is associated with infinity and unity; the reversal of reality and unreality; time and motion; non-Euclidean geometry and space; and spirituality. Artists such as Wassily Kandinsky, Kazimir Malevich, and Piet Mondrian, each explored those ideas in unique ways in their abstract paintings.
The fourth dimension also inspired Surrealists such as the Spanish artist Salvador Dali, whose painting, "Crucifixion (Corpus Hypercubus)" (1954), united a classical portrayal of Christ with a tesseract, a four-dimensional cube. Dali used the idea of the fourth dimension to illustrate the spiritual world transcending our physical universe.
Just as mathematicians and physicists explored the fourth dimension and its possibilities for alternative realities, artists were able to break away from one-point perspective and the three-dimensional reality it represented to explore those issues on their two-dimensional surfaces, creating new forms of abstract art. With new discoveries in physics and the development of computer graphics, contemporary artists continue to experiment with the concept of dimensionality.
Henri Poincaré: the unlikely link between Einstein and Picasso, The Guardian, https://www.theguardian.com/science/blog/2012/jul/17/henri-poincare-einstein-picasso?newsfeed=true
Picasso, Einstein, and the fourth dimension, Phaidon, http://www.phaidon.com/agenda/art/articles/2012/july/19/picasso-einstein-and-the-fourth-dimension/
The Fourth Dimension and Non-Euclidean Geometry in Modern Art, Revised Edition, The MIT Press, https://mitpress.mit.edu/books/fourth-dimension-and-non-euclidean-geometry-modern-art
The Fourth Dimension in Painting: Cubism and Futurism, The peacock's tail, https://pavlopoulos.wordpress.com/2011/03/19/painting-and-fourth-dimension-cubism-and-futurism/
The painter who entered the fourth dimension, BBC, http://www.bbc.com/culture/story/20160511-the-painter-who-entered-the-fourth-dimension
The Fourth Dimension, Levis Fine Art, http://www.levisfineart.com/exhibitions/the-fourth-dimension