The Influence of the Perspectives of M.C. Escher
Only those who attempt the absurd will achieve the impossible — M.C. Escher
As a person, I really am all over the place. I love the concept of breadth — I want to know a little bit about everything. So, my liberal arts education works very well for me. While focusing on economics and the financial world, I can satisfy my curiosity by taking classes across a wide range of disciplines. Hence, when the opportunity to take a class called Geometry and the Emergence of Perspective came up, I was never going to let it go. Consistently working on just one thing is not my cup of tea, and this class was meant to be a perfect respite from my daily work. Little did I know how deeply this would interest me.
Our class focused on understanding historical geometry and the concepts used to create perspective — a mathematical tool used to create the effect of depth on a two-dimensional surface in art.
To understand the use of 1-, 2- and 3-point perspectives, one should refer to the image below. The different perspectives derive their name from the number of ‘vanishing points’ each contains — the number of final points that the lines used to render the figure can trace back to. These vanishing points, and the lines that can be drawn back to them, enable an artist to create depth in paintings by making the viewer look at their work from different angles — head-on, on the side, or from the top/bottom.
No conversation about mathematical art can be complete without discussing M.C. Escher. To many, Escher is the father of mathematical art. When I looked up Escher’s art out of personal interest, I was amazed. Escher’s talent was stretching the limits of his artistic tools.
Escher’s lack of formal mathematics training did not keep him from creating beautiful works based on the profound ideas presented above. In fact, he used the simple concepts of perspective and literally distorted reality. Case in point — his most famous work, Relativity.
The implication of this lithograph is the variability in human conception — each human has a different conception of horizontal and vertical, but they still may share the same experiences. For example, look at the staircase on the top — on a single staircase, one human walks down while the other walks up. Tilt your head clockwise, then anti-clockwise, and enjoy the distortion of reality!
Understanding the perspective in such a complicated work of art cannot be easy — it isn’t for me as well. So, here’s a diagram that helps explain the geometrical perspective:
One can only imagine the creativity, vision, and precision Escher needed to produce a work like this. Due to works like this, Escher came to be known as a mathematical artist, and not a traditional one. Yet, this is not the pinnacle of his work — Escher was one of the first to establish work with distorted perspective grids. He left the traditional rules of perspective behind and broke all the boundaries mathematical theory had placed on his tools. By using these grids, he managed to create reflective effects in his art — something that had rarely been done before. This is the most famous one:
Escher created this lithograph to have a better view of his surroundings. The work encompasses his entire world around him, and his head is the absolute center of the lithograph. By making himself the center of this work, he reminds viewers that his ego is the unshakable core of his world, as should be for others. He did this entire work, all using a grid that must have looked like this:
Escher’s work is clearly groundbreaking. He stretches the limits of the tools given to him and creates visionary works. Normally, these are the kind of works that influence people for years to come. You must be thinking — this is cool, but so what? Who uses this? Apparently, a bunch of popular cinematographers.
Many movies, music videos, and video games over the years have directly borrowed concepts that Escher created. The most famous one to do so has to be Harry Potter and the Sorcerer’s Stone. There is a scene in the movie inspired by Escher’s Relativity, and you can watch it here. The rotating staircases produce the same distorted reality effect that the lithograph does — can you see the similarities?
The most interesting application of Relativity, however, is in the third edition of Night at the Museum. The idea behind the movie is that all the artifacts in the museum come to life at night, and in this specific scene, the protagonists of the movie literally navigate the staircases in Relativity! While fighting, the characters also fall on flat surfaces in different dimensions. Just another example of the wonders of modern technology!
Inception, the 2011 Oscar winner for best visual effects, also plays on a concept of Escher’s. In 1960, Escher created Ascending and Descending by using the concept of Penrose Steps. Sir Kenneth Penrose created the Penrose Steps — steps that always looked like they were going up (or down, depending on your perspective)! Escher made this mathematical concept beautiful and created this masterpiece:
Inception recreated this exact effect in an office building. Through some creative camera work, the movie convinces its audience that this illusion exists in 3-D as well. Both use the effect to relay the same message — Walking in both directions on these steps is equally useless. Yet those who fail to take part in the seemingly futile exercise will be shown the error in their nonconformity.
Escher really was a maverick of his time. One cannot begin to imagine the masterpieces he could produce if he had the knowledge and technology we have today. However, we must take heart to the fact that Escher broke and re-wrote all the rules so that we could get the most out of them. Escher is gone, but his influence might never follow him.