Introduction
Numbers as symbols have always attracted their hidden meaning, an essential meaning for a person. That may be why numbers often carry additional meanings in works of art and are not exhausted by the meanings lying on the surface. The symbolic meaning of a single number was not reduced to one meaning but instead represented a multi-layered, multifaceted, and unique semantic structure, the content of which in each particular case – depending on the objective and subjective factors of the context – could appear as more or less unambiguous. Symbolism is an important and, at the same time, very complex means of revealing the author’s position. The symbolism of numbers is one of the most complex and, at the same time, one of the most refined, extraordinary artistic techniques. The numbers often allow the reader to immerse themselves in the atmosphere prevailing in work to get closer to understanding the author’s idea.
Symbolic Meaning
The symbolic meaning of numbers calls for the study of symbolic systems (containing the knowledge of our ancestors), which constitute one of the areas of human self-knowledge. The use of numerical symbolism is a long-standing tradition that has survived to the present day and is able to reconstruct historical and cultural memory. The symbolism of numbers does not just convey a variety of characteristics of objects and phenomena, and it is not just designed to influence the reader from the point of view of emotional impact (O’Shaughnessy, Gibson, and Piantadosi 2021). It contains a meaning that depends on the context and the speech environment. The numbers in the text help to model unreal and real worlds, forming an exceptional picture of the world, and are integral exponents and symbols of national culture (O’Shaughnessy, Gibson, and Piantadosi 2021). They serve to show the complex world of emotions, thoughts, feelings, aesthetics, and ethical values.
Mathematics in Art
The Fibonacci sequence is a series of numbers in which the first two elements are 0 and 1, and all subsequent ones are equal to the sum of the previous two. It can be traced in some natural phenomena, science, architecture, and art. If one consistently divides one number of the Fibonacci series by the previous one, in the end (from dividing 89 by 55), the number 1.618 will begin to be obtained (Shannon and Power 2019). This coefficient is commonly called the golden ratio or the golden proportion. Moreover, if it is depicted graphically, then a golden rectangle will be obtained — the lengths of its sides will relate to each other as 1.618: 1 (Shannon and Power 2019). With the help of a golden rectangle, one can build a Fibonacci spiral.
Both the golden ratio and the Fibonacci spiral are interesting because they are often found in nature. For example, the seeds in the sunflower’s center are arranged in a spiral and go clockwise and counterclockwise (Schreiber and Pedersen 2022). The same applies to the shells of some snails and even the structure of the human ear. If it is calculated how the distance from the navel point to the knees and from the knees to the feet in the human body correlates, then the golden ratio will be obtained — 1: 1,618 (Schreiber and Pedersen 2022). The golden section and the Fibonacci spiral are often used in painting or architecture. Thus, this phenomenon opens the way for mathematics in art.
Jasper Johns
The artist owns a series of works with images of numbers in a variety of variations (“Gray numbers”, “from 0 to 9”, “0-9”), as well as many images of maps of the United States and various kinds of targets. All these symbols are part of the ordinary world, but in everyday life, it is common for layman to ignore their form, paying attention only to what they “mean” in their various combinations (“Gray Numbers, 1958 by Jasper Johns” n.d.). It is extremely rare to question the significance of a single number or letter, just as rarely does anyone talk about the shape of a flag or a map itself. Jones obviously ignores questions related to how individual letters or numbers interact with each other, creating language and meaning.
In his early work “Gray Numbers”, for example, he gives the entire canvas space to a grid filled with numbers. The numbers are stenciled, each in its own cell throughout the picture, with the exception of the upper left rectangle. They are arranged in a particular sequence, but it is not the meaning of each number that attracts attention but the form, structure, and order that the artist creates directly (“Gray Numbers, 1958 by Jasper Johns” n.d.). Flags, maps, targets, numbers, and letters remained Jones’ main objects for a long time, no matter what technique he worked in. For a while, Jones moved from painting to lithography, experimented with the maximum flattening of figures, simplifying forms and superimposing them on top of each other — in one of the works, for example, he depicted all nine digits one on top of the other (“Gray Numbers, 1958 by Jasper Johns” n.d.). Surprisingly, Jones did not repeat himself, and these experiments are interesting precisely because of the variety of creative ideas with a limited number of objects.
Marcel Duchamp
Marcel Duchamp, of course, was familiar with multidimensional mathematics. He was particularly interested in the fourth dimension and ways to show it through art. In his search, he went through the stages of cubism, displaying different angles, the depth of space, physical movement, and the flight of thought on one canvas. A genuinely progressive and unique in terms of multidimensionality is the Large Glass, on which Duchamp worked from 1915 to 1923 and also pondered and supplemented the text for several more years (Kuykendall 2019). The full title of the work is “The Bride Stripped Bare by Her Bachelors, Even” (Kuykendall 2019). Two large glasses are located one above the other. On the upper one, there is a three-dimensional projection of the Bride in the fourth dimension. On the lower glass, which symbolizes the three-dimensional world, nine figures of bachelors are depicted, resembling clothespins. A mysterious mechanism is depicted in the foreground. The work was done in a mixed technique – Duchamp used not only glass but also oil paints, varnish, wire, and dust.
The Bride, undressed by her bachelors, acquired the final look later. For artists, the fourth dimension has become a symbol of liberation, a source of ideas, a new language, and a new concept of space. The belief in the fourth dimension allowed artists to distance themselves from visual reality and completely abandon the method of perspective, which represented the three-dimensional Euclidean world (Kuykendall 2019). In addition, the interest in the fourth dimension was an alternative approach to the idealistic perception of higher reality underlying the new abstract art (Kuykendall 2019). Many were fond of the fourth dimension, although each movement and each artist chose different aspects for themselves: a rejection of the perspective method, movement, color, time, infinite space, memory, gravity, anti-gravity, and mysticism.
Salvador Dali
The theme of the fourth dimension, along with dreams and parallel universes, excites surrealists as well. The legendary Salvador Dali also turned to mathematics and was incredibly inspired by it. Moreover, he sought to bring to a common denominator the achievements of science, Catholic values, and canons of the painting by great masters. All this was reflected in the direction of Dali’s nuclear mysticism. The most striking picture of this period is the “Crucifixion (Corpus Hypercubus)” (History of Information n.d.). Jesus soared in the night sky, crucified on a hypercube sweep. The scene is enthusiastically contemplated by the wife and muse of the artist – Gala, in the image of Mary Magdalene.
There are no nails and suffering in this crucifixion, but there is humility and the passage of Christ into the four-dimensional world. Dali was the first to draw parallels between the unfolding of the tesseract and the cross. Dali’s monumental work generally does not obey the laws of three-dimensional measurement. Going beyond the usual boundaries, this canvas was able to reflect the new meaning of the traditional biblical scene (History of Information n.d.). In fact, the “Crucifixion” combines the classical image of Christ with a form that exists only in mathematical theory (History of Information n.d.). The artist tried to bring the image of three-dimensional space beyond the boundaries. The realization of this task became possible by superimposing two perspectives on one another.
Numbers in Everyday Life and History
Numbers have a particular significance for people not only in art but also in the surrounding reality. Historically, they are given different meanings and meanings that determine their essence and perception by people. As an example, the branding of people sent to a concentration camp can be carried out; it has become a symbol of violence, pain, and destroyed lives (Holocaust Museum 2019). For branding, a set of metal numbers-plates was used (Holocaust Museum 2019). The camp numbers were tattooed on the left side of the prisoner’s chest using a metal stamp, into which replaceable plates with needles several centimeters long were inserted, forming separate digits.
There is a whole system of beliefs about the mystical connections of numbers with physical objects, processes, and people’s lives and consciousness, which are interconnected and influence each other – numerology. In the modern world, a number or digit is associated with information (represented as a sequence of binary numbers), the development of human knowledge, and management (Ayonrinde et al. 2020). Numbers are perhaps the most primitive element of order in thought and are subconsciously used as an organizing factor. For Eastern countries in general and China in particular, figures play a special role in forming customs. In China, “seven” is consonant with the hieroglyph “confidence” (the sound in some dialects corresponds to the word “for sure”) (Ayonrinde et al. 2020). It symbolizes wisdom and virtue and is associated with unity. The seven has always brought prosperity and extraordinary luck in the world-famous Feng Shui teaching. Philosophers from different countries adhered to the tradition of making cardinal changes in their lives every seven years, bringing with them a surge of luck and prosperity (Ayonrinde et al. 2020). Numbers should be perceived not only in quantitative but also in qualitative terms. Each number is associated with a particular idea that comes from the higher worlds and is realized in the form of patterns in the earthly reality. In any phenomenon and event, the corresponding numerical formulas are enclosed.
Conclusion
Numbers are an essential component of people’s lives. As it was possible to determine, they surround the whole reality. Their peculiarity is the acquisition of additional meanings and meanings. They may also reflect the negative aspects of life associated with the infringement or belittling of someone. However, for the most part, numbers are present in everyday life. Historically, they have been associated with various phenomena that were designed to justify the features of a particular aspect of human life. Consequently, this theme was reflected by artists who sought to reflect the essence of numbers in their works. In the course of this essay, three artists were identified who view the world of numbers and their significance for people in different ways.
Speaking about Jasper Johns, it should be noted that he sought to draw the attention of art connoisseurs to the fact that even such a common and typical phenomenon for people as numbers can be perceived completely differently. Johns used unusual approaches that sought to transform the form and essence of numbers in every possible way, thereby giving a different meaning to everyday life. On the other hand, Salvador Dali and Marcel Duchamp were interested in a more profound topic. They used mathematical theories in their works to convey the fourth dimension in a static picture. Their unique approach and skill allowed them to discover new principles and forms in the visual arts that were not known before. Thus, their visionary vision and striving for knowledge of numbers and mathematics significantly advanced the capabilities of the artists. It is worth noting that numbers are important to people’s reality. In a sense, it affects harmony not only in the aspect of art but also in the whole of life.
References
“Gray Numbers, 1958 by Jasper Johns.” n.d. www.Jasper-Johns.org. Web.
Ayonrinde, Oyedeji A., Anthi Stefatos, Shadé Miller, Amanda Richer, Pallavi Nadkarni, Jennifer She, Ahmad Alghofaily, and Nomusa Mngoma. 2020. “The Salience and Symbolism of Numbers across Cultural Beliefs and Practice.” International Review of Psychiatry 33 (1-2): 179–88. Web.
History of Information. n.d. “Dali’s Crucifixion (Corpus Hypercubus): Surrealism and Four-Dimensional Geometry : History of Information.” Www.historyofinformation.com. Web.
Holocaust Museum. 2019. “Tattoos and Numbers: The System of Identifying Prisoners at Auschwitz.” Ushmm.org. 2019. Web.
Kuykendall, Lara. 2019. “Marcel Duchamp, the Bride Stripped Bare by Her Bachelors, Even (the Large Glass) – Smarthistory.” Smarthistory.org. 2019. Web.
O’Shaughnessy, David M., Edward Gibson, and Steven T. Piantadosi. 2021. “The Cultural Origins of Symbolic Number.” Psychological Review, June. Web.
Schreiber, Annelise, and Jennifer Pedersen. 2022. “Fibonacci Sequence and Art: The Measure of Utilization during Art Movements in European History.” Journal of Student Research 10 (4). Web.
Shannon, Anthony G, and Seamus A. Power. 2019. “Natural Mathematics, the Fibonacci Numbers and Aesthetics in Art.” Journal of Advances in Mathematics 17 (October): 248–54. Web.