week two blog | JohnnyleungDESMA9

From the lectures and readings, I learned that mathematics and the arts are closely related and overlap in their spatial understanding of reality. While there are many concepts that are shared by both fields, the most representative example is the usage of geometry and shapes in both linear perspective art and abstract art.

Pablo Picasso's cubist painting, Guernica. Retrieved from Pablo Picasso - The 1930s | Britannica

Diagram overlaying Brunelleschi's experiment with linear perspective. Retrieved from Gaining Perspective | Nelson-Atkins

All visual art includes shapes, lines, and other geometric figures intrinsically, however art that works towards reproducing a single-point perspective of reality is "completely mathematical" (Alberti) as it stems from a visual pyramid with a single vanishing point. From this avenue of art-making, the artists incorporate mathematical concepts and produces a harmonious blend between the two fields. Moreover - despite the abstract art movements' intention to challenge the traditional, perspective-based representation of reality in art, these avenues still incorporated geometric shapes and lines that produced a dialogue and connection between art and mathematics, just from a different perspective (Vesna 00:28:00-00:28:17). 

Tony Robbin's acrylic painting visualizing higher-dimensional space, 1979-7. Retrieved from Tony Robbin A Retrospective: 1977-2018

Furthermore, Henderson's paper, "The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion" shows how the change in the modern art movement from perspective to abstract was also aligned with the development of non-Euclidean geometry - which had introduced hyperbolic shapes and the fourth dimension. Although the mathematicians and artists did not have the same goals and desires stemming from the knowledge of non-Euclidean geometry and the fourth dimension, it fundamentally changed how they both approached the future of their studies.

Henderson quotes Tony Robbins, "'Artists who are interested in four dimensional space… are motivated by a desire to complete our subjective experience by inventing new aesthetic and conceptual capabilities. We are not in the least surprised, however, to find physicists and mathematicians working simultaneously on a metaphor for space…'" (209). Through this quote, Henderson reinforces the conclusion that artists and mathematicians are alike in that their fields are closely intertwined and shows that the development/progression in one field can also heavily impact the course of the other.

While more can be said about the integration of mathematical concepts like the golden ratio and fractals, I think the most important takeaway from this week's content is that the barrier between mathematics and art is artificially imposed, and that the concepts and development within both fields are highly interconnected.

Works Cited

Alberti, Leon Battista. On Painting: Revised Edition. Vol. 175. Yale University Press, 1966.

Diagram demonstrating Filippo Brunelleschi's Perspective Technique from a Lost Painting of the

Battistero di San Giovanni. Drawing from an Unknown Artist. Kunsthistorisches Institut in 

Florenz, Max-Planck-Insitut, www.nelson-atkins.org/gates/gaining-perspective.html

Henderson, Linda Dalrymple. The fourth dimension and non-Euclidean geometry in modern art. 

Mit Press, 2018. 

Picasso, Pablo. Guernica. 1937. Museo Reina Sofia, Madrid. 

www.britannica.com/biography/Pablo-Picasso/The-1930s.

Robbins, Tony. 1979-7. 1979. Tony Robbin A Retrospective: 1977 2018. 

www.retrospective.tonyrobbin.net/

Vesna, Victoria."Mathematics-pt1-ZeroPerspectiveGoldenMean.mov" YouTube, YouTube, 9 April 

2012, https://www.youtube.com/watch 

v=mMmq5B1LKDg&t=923s&ab_channel=UCOnlineMathematicspt1-

ZeroPerspectiveGoldenMean.mov