Week 2 Math and Art

Artists, making use of the concepts of mathematics, are able to represent the world better. The first idea I learned from this week’s lecture is the formulation of linear perspective, which allows   artists to represent three dimensional objects on a two dimensional canvas. The idea is based on the mathematical principles of optics and associated with a “vanishing point”. By proper scaling of objects at different distances, we are able to create a visually three dimensional image.


The second concept is the golden ratio or the divine ratio, which is obtained by dividing a line so that the ration of the shorter part to the longer part is the same as that of the longer part to the whole line. This idea has been implemented widely throughout history, including the pyramids, ancient Greek sculptures and da Vinci’s paintings. The golden ration produces a harmonic effect that is also existent in nature.


The third aspect is about dimensions. Artists became intrigued by the idea of a fourth dimension in the twentieth century, where they sought for new illustrations of the world. The concept of dimensionality is widely used in mathematics and it led to echo on the art side. Since we live in a three dimensional world, higher dimensions are undetectable for us and visually representing them became the romance among artists.

                                                                                
Projection of a 4D cube

So in general, mathematics on one hand provides the fundamentals of the nature that allow artists to better interpret the world, and on the other hand inspires them to pursue new perspectives. To further illustrate the idea of inspiring artists, let’s look at the figure below.    

A closer look at the picture will tell you that something is wrong, since such sculpture cannot exist in real life. It violates the physical law and is not logical, while the picture seems coordinated at first glance. So logic, being part of mathematics, inspires artists to create illogical elements that would otherwise not exist in nature.

Mathematics is the language of truth and filled with idealizations. It forms the fundamentals for most of the science and inspires artists to create better interpretations of the world. And the need for innovations in arts and science requires development of mathematics. So the coalitions between mathematics, art and science make them flourish.





Reference
Henderson, Linda, The Fourth Dimension and Non-Euclidean Geometry in Modern Art: Conclusion, Leonardo, Vol. 17, No. 3. (1984), pp. 205-210.
Abbott, Edwin, Flatland: A Romance of Many Dimensions, Seeley & Co. London, 1884.
Escher, M. C., The Mathematical Art of M.C. Escher, N.p. N.d.Web.
 <http://platonicrealms.com/minitexts/Mathematical-Art-Of-M-C-Escher/>.
Vesna, Victoria, “Mathematics”, N.p., N.d. Web.
<https://cole2.uconline.edu/courses/684222/pages/unit-2-view?module_item_id=11226140>
Unknown, Hypercube, Web.
< https://en.wikipedia.org/wiki/Hypercube#/media/File:Hypercube.svg>


Comments

  1. UnknownApril 19, 2017 at 10:10 PM

    Your mention of the illogical paintings remind me of the unprovable statements in mathematical logic. Godel's Incompleteness Theorem states that in any sufficiently complex logic system there must be some valid statement which cannot be proved within the system, which corresponds to the paintings that illustrate architectural structures that cannot exist in the real world. In my opinion, mathematics is the abstraction of our reality, while art being the reflections of the reality. Thus, artworks inspired by mathematical findings and theorems gain their aesthetic value in a unique way of applying the schemes of reality as reflections.

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