The Scream Painting: Exploring Art and Mathematics

Introduction

Collaboration can be active and intentional - like scientists working together on a project - and it can also be passive when the experience of another is taken to synthesize knowledge that is not based on their personal experience. Since there is reliance on shared knowledge to validate personal knowledge, the production of knowledge is always collaborative in nature. The development of knowledge builds on the shared knowledge of others and so must be collaborative. The collaborative nature of knowledge can be traced back to Bernard of Chartres in the 12th century who stated that humankind are 'dwarfs standing on the shoulders of giants”. This metaphor explains that the work of predecessors (giants) serves as the basis of modern human civilization (dwarfs). My examples to illustrate the collaborative nature of knowledge are Edvard Munch’s The Scream painting and Srinivasa Ramanujan’s mathematical discoveries. 

The Arts are a Way of Knowing because they convey information about the artist, the world, and context in which the artist worked. Knowledge is produced through the interaction between the observer and the artists work. Therefore, we need to be aware of the origins and context of any piece of art. For example, Renaissance art can only be understood within the context of the Renaissance period that took place between the 14th and 17th centuries. In the case of The Scream by Munch, we need to place it in context to understand what inspired him to paint the distorted face of a genderless ma, and how this originated in the vision he had when he saw the sunset.

The Scream, 1893 by Edward Munch

He described seeing the “air [which] turned to blood” and the “faces of my comrades [which] became a garish white-yellow”. He felt vibrations in his ears caused by “a huge endless scream course through nature”. These hallucinations have two implications – art can be a product of sense perception and memory, two WOK’s. They show that inspiration leads to the creation of the artist, which shows that the production of knowledge through art is not solely from the individual, as it is influenced by outside experiences and the shared knowledge from others. 

However, a counterclaim can be made against the theory that art is collaborative is that the expression of knowledge in art is the task of the individual. This is a characteristic of artists which makes them separate from artisans who merely copy art and technique. Regarding the role of Munch’s personal sense perception and memory in creating The Scream, it is evident that he based his artwork on his imagination and personal experience, which constitutes as personal knowledge. The implication here is that artwork, as a real foundation, has the ability to convey an original and personal message about, and from the artist, which cannot be exactly copied by other artists. On the other hand, imagination itself is conveyed through artistic techniques, which are collaborative. Munch was influenced by “painters such as Paul Gauguin and Vincent Van Gogh”, (whose works inspired him) “to use bright color to flatten his form” (and) “dark outlines” (to make his drawings stand out). This suggests that art is never completely original, as painting techniques can be traced to individuals other than the artist himself. 

Exploring Ramanujan's Mathematical Collaborations

Srinivasa Ramanujan’s mathematical discoveries are a further example. Ramanujan is famous for his contributions to the Theory of Numbers and his works on “elliptic functions, continued fractions, and infinite series”. His educational background involved only one year in college. He was largely self-taught and made many of his mathematical discoveries in isolation with little interaction with other mathematicians. At first glance, Ramanujan appears to have been an isolationist whose mathematical discoveries were the product of the individual.

It is important to note, however, that Ramanujan credited his mathematical discoveries to God. There have been experts in the past who have “ascribed mystical and religious origins to Ramanujan’s thinking”. Many of Ramanujan’s discoveries were original, but some modern mathematicians regard them to be “highly intuitive and undisciplined”. In the past mathematical discoveries were related to mysticism, as mathematicians could experience an “esoteric and heightened sense of mind” which would allow someone to discover truths that would be inaccessible to someone who is not in an altered state of consciousness. This argument that Ramanujan’s mathematical knowledge was due to his sense perception, arising from his religious beliefs implies shared knowledge rather than solely individual thinking. 

Moreover, Ramanujan’s discoveries were based on the previous mathematical knowledge or others. Biographers claim that Ramanujan certainly read several mathematical books written by famous mathematicians, such as G.S. Carr’s book, A Synopsis of Elementary Results in Pure and Applied Mathematics. In fact, in five of Ramanujan’s published papers, Ramanujan “cited theorems from the second part of Carr’s book” showing that Ramanujan’s discoveries were not original, and therefore a product of shared knowledge, as the reasoning behind them were based on prior mathematical knowledge derived from other mathematical experts. 

This statement carries the implication that Ramanujan was actively synthesizing mathematical knowledge from other mathematicians to create his own discoveries. The flaw of this argument is that prior mathematical knowledge as the basis of Ramanujan’s discoveries cannot be established for certain. A causal relationship cannot be drawn between the knowledge that Ramanujan derived from outside sources and his own mathematical discoveries. However, it can be stated that Ramanujan’s ability to synthesize his own existing mathematical knowledge with his own genius enabled him to produce knowledge that can be rendered as original. While the mathematical techniques that Ramanujan employed were not original, the reasoning which led to the discoveries were certainly innovative. It was conspicuous that Ramanujan’s lateral thinking led to his unorthodox method of proving mathematical theories. This implication takes on the theory that while the process of mathematical induction is collaborative in nature, the reasoning which leads to the discoveries is original and individualistic.

Conclusion

In both examples, different reasons for why the production of knowledge is collaborative in nature were explored. It was deduced that outside influences which contributes to sense perception and memory show that the creation of knowledge in artwork is collaborative in nature. It was also seen in Ramanujan’s mathematical work that mathematical discoveries themselves are not merely a product of the individual, as they rely on mathematical techniques produced by other mathematicians. It is important to note, however, that the expression of knowledge and the reasoning which leads to knowledge are the products of the individual. This shows that the foundation of knowledge can never be truly original, but it is in the hands of the artist or the mathematician to confront the existing knowledge to create their own original product.

Moreover, in the development and progress of knowledge in any area there also needs to be the inspiration and imagination of the individual. In some areas this comes from imagination and in others it comes from a sense of doubt and questioning. We know what we know through experience, personal and shared. In the Arts, the artist expresses him or herself, but this is based on experience which is shared and common to all humanity. It is expressed in language, given that art is a form of language, and this needs to be collaborative in order to create understanding between the art work and the viewer. In the same way, the language of mathematics is a shared basis to understand knowledge, even through the mathematician can discover and express and new truth about mathematics, there is still a collaborative element. Thus, with reference to the arts and mathematics, the production of knowledge is deduced to be collaborative in nature, while the final body of knowledge represents the essence of an individual.

References

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