Black Square: Adventures in the Fourth-Dimension With Kazimir Malevich

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At first glance, the Black Square (1915) by Russian avant-garde artist and art theorist Kazimir Malevich (1879 — 1935) may come across as nothing special; the painting appears to depict exactly what its title suggests — a black geometric shape on a white background that seems impressively unremarkable. But, there are really good reasons as to why the work is internationally famous, featured in exhibitions hosted by respectable art institutions, and is regularly brought up for discussion in art history.

"Black Square" (1915) by Kazimir Malevich

The most obvious of these is that the Black Square is widely considered to be the first painting in the world to portray absolutely nothing in particular. It made its debut at the 0.10: Last Exhibition of Futurist Painting show, a scandalous event that rocked the art community and officially launched Malevich’s Suprematism art movement, which focused on pure geometrical abstraction by depicting basic forms — such as circles, squares, lines, and rectangles — in a limited range of colors.

“Up until now there were no attempts at painting as such, without any attribute of real life,” explained the artist in a text accompanying the work at the show. “In the year 1913, trying desperately to free art from the dead weight of the real world, I took refuge in the form of the square,” he elaborated years later in his The Non-Objective World (1927). “To the Suprematist the visual phenomena of the objective world are, in themselves, meaningless; the significant thing is feeling.”

But, the radically non-representational piece we know as the Black Square may not be just about feeling. Malevich was alive during a particularly exciting time in history: The world’s first commercial airline launched one year prior to the art exhibit. Einstein presented his Theory of General Relativity within months of its opening. And Russia was on the brink of a world-changing revolution. Developments in STEM provided exciting new frameworks for the exploration of novel ideas.

The title, 0.10: Last Exhibition of Futurist Painting, was chosen by Malevich and fellow Suprematist artist Ivan Puni (1892 — 1956). The “0” stood for a new beginning and 10 for the number of artists initially booked for the show. The “Last Exhibition of Futurist Painting” was a direct reference to Futurism, an artistic movement that originated in Italy and emphasized the “dynamism, speed, energy, and power of the machine and the vitality, change, and restlessness of modern life.”

"Airplane Flying: Suprematist Composition" (1915) by Kazimir Malevich

Malevich debuted his Airplane Flying: Suprematist Composition at the same show. The work does not, technically, depict an airplane, but is “intended to convey the sensation of mechanical flight using thirteen rectangles in black, yellow, red, and blue placed in dynamic relationships on a white ground.” A sense of “movement is created by the diagonal orientation of the rectangles in relation to the edges of the canvas… [and] ascension is implied by the point of the yellow rectangle centered at the top.”

The movement in the aforementioned work is particularly important since Futurists viewed “motion as the medium in which reality is formed and sought to represent that motion and the perception of time it elicited.” As Tommaso Marinetti put it in the Futurist Manifesto (1909): “All things move, all things run, all things are rapidly changing. A profile is never motionless before our eyes, but it constantly appears and disappears.” If traditional art ignored movement, Futurists wanted to make it central to theirs.

But, more importantly, Futurists also advocated “for a violent and decisive break from the past.” The controversial art show featured 39 Suprematist artworks by 14 different artists. Unlike in a usual gallery display, the paintings “did not form a neat line, but were dotted unevenly over the walls, from floor to ceiling, creating their own environment.” The Black Square, however, hung in a corner just beneath the ceiling, “precisely where an icon usually hung in the traditional Russian home.”

Over the years, there’s been a lot of speculation about why Malevich chose to hang the Black Square where he did. Some state that by doing so, the artist was rejecting the ideas historically posed by organized religion. Others argue that it was his tribute to supernatural phenomena, since Malevich “was [allegedly] searching for the barest essentials of art in an almost mystical manner, [and] considered the Black Square to be sacred: a symbol for a new, modern sort of spirituality.”

Considering that “mystical traditions [as well as] theories of multi-dimensional, non-Euclidean space were popular within artistic and literary circles in the early 20th century,” and that the notion of space featuring a fourth dimension was seriously considered in physics until 1919, a number of historians think that “Malevich was particularly interested in the mystical geometry of Peter Ouspensky, who believed artists were able to see beyond material reality and communicate their visions to others.”

Much like Immanuel Kant (1724 – 1804), Ouspensky (1878 – 1947) believed that all phenomena have a noumenal substrate or real nature.” But, unlike Kant, he also thought “that metageometrical laws could en-compass noumena, the key to intuitive knowledge of the universe.” Ouspensky was deeply influenced by the works of Helena P. Blavatsky (1831–1891) a writer and theosophist, who “asserted that mystical experience and doctrine were the means to attain true spiritual insight and authority.”

“The roots of connecting higher dimensions with a transcendental realm date back at least to Plato’s cave allegory, in which prisoners confined to a cavern observe two-dimensional shadows on a wall while being unaware of the three-dimensional world outside that produced them,” argues Paul Halpern, a professor of physics at the University of the Sciences in Philadelphia. Plato thought that three-dimensional beings may be unaware of a greater reality, but didn’t explicitly mentioned a fourth dimension.

Conceptual illustration of both 3D space and time distortion near a mass.

“As a concept the fourth dimension can trace its roots back to classical times,” writes Snezana Lawrence “but was developed in the nineteenth century by mathematicians, some of whom were either amateur mathematicians or stumbled upon it in their research related to a number of other sciences.” Mathematically speaking, “the fourth dimension refers to time as another dimension along with length, width, and depth” as well as space and the space-time continuum as put forth by Einstein.

But, as evidenced by Ouspensky and Blavatsky, it was also thought of as a supernatural and metaphysical realm; hence, the argument that Malevich’s painting references the fourth dimension does, in fact, appear to hold water. In fact, many of his contemporaries — including 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.”

Given the historical context, it may seem reasonable to assume that Malevich was making a statement against organized religion and used the Black Square as well as its strategic placement as a symbol of new understanding of spirituality. But, in A Man and His Square: Kasimir Malevich and the Visualization of the Fourth Dimension (2010), Stephen Luecking, former chair of the art department at Depaul University, provides some fairly convincing evidence to why that’s probably not the case.

First, Luecking eludes to Malevich’s investment in Futurism, who considered the Black Square Suprematism’s ground zero: “The square is not a subconscious form. It is the creation of intuitive reason. The face of the new art. The square is a living, regal infant. The first step of pure creation in art.” The masterpiece is “‘the embryo of all potentials.’ The other ‘paintings of geometric forms, including Airplane Flying, were implicitly generated from this basic form’” — they serve as “secular equivalents of Russian icons.”

Second, he dismisses the idea that Malevich was influenced by Ouspensky, writing: “Malevich and other artists were ambivalent if not hostile toward Ouspensky, since they viewed theosophy as a late 19th century fashion propagated among the elite.” Third, Luecking argues that the artist’s “primary interest resided in geometry at large, as influenced from his understanding of Nikolai Lobachevsky [1792 —1856], the Russian mathematician who first formulated a Non-Euclidean geometry and published his findings in 1829.”

Self-Portrait (1912) by Kazimir Malevich

According to the author, the mathematician believed “Euclidean geometry was simply a special case that ably described the middle scale of space between the astronomical and the molecular scales.” He realized that “geometry need have no connection to the real world, but could define spaces that existed only as mental constructs, as long as the geometry was logically consistent,” and he also correctly discerned that many geometries were possible when that prerequisite was met.

Luecking is convinced that to Malevich, “mathematics and specifically geometry offered formative systems, which may or may not possesses referents in nature, or even make conventional sense.” In other words, “the value of a fourth dimension was its virtue as a mathematical and artistic conceit, and not its necessary existence or… the beauty of its mathematical descriptions.” For Malevich, “geometry and the art it inspired possessed their own existence not predicated on the logic of a physical reality.”

Olga Rozanova, Kseniya Boguslavskaya and Kazimir Malevich at 0. 10: The Last Futurist Exhibition of Paintings (1915)

Furthermore, Luecking brings up another very interesting point. Out of the 39 works featured at the 0.10. exhibition, five of Malevich’s paintings had the following subtitle: "Colored Masses in the Fourth Dimension." Considering that the works had no observable difference in technique from the others, the addition seems rather perplexing. But “the author asserts... that Malevich's paintings could be viewed as actual visualizations of four dimensional geometry.”

To better understand why Malevich gave the paintings different subtitles, Luecking suggests we think of it like this:

“Though Malevich's paintings were normally depictions of forms afloat in a three-dimensional yonder, they could indeed also depict two dimensional shapes in space flattened to two dimensions, as well as portray a four dimensional phenomenon. In the case of Suprematism the space was not necessarily two-dimensional nor was it necessarily three-dimensional. Into this region three-dimensional masses from a fourth dimension would present as planes in the same manner as that same mass in a three-dimensional space intersecting a two dimensional space. In true alogical fashion paintings of these would appear the same.”

We may never know what, exactly, Malevich thought of his Black Square when he first displayed it at the art show, but we do know that mathematics played a pretty serious role in its conception.

Note* Gif made by Lucas Vieira Barbosa authored the original OGV. Selected frames (10% of the original) extracted and re-timed by Stigmatella aurantiaca, via Wiki Commons.