I think I know what Escher dreamed of

If you've looked at some of the other posts in this blog, you'll have noticed that I am a huge fan of Escher's work. Almost every single one of my drawings has been influenced by him. He was an incredibly inspirational graphic artist to me, but this isn't just because of his work in itself. Yes, his work is beautiful, it conforms with his idiosyncratic style and it approaches technical perfection (for someone who never used computers). But I'm mostly inspired by how he continued to innovate and come up with new ideas and themes to play with, and what he might have created if he wasn't stopped by his death in 1972.

So what were these ideas and themes? Well in my mind I classify them differently to how literature generally classifies them. In literature, you'll mainly read about four themes in Escher's work as follows: (1) traditional, normal face-value representations of people, animals and landscapes; (2) metamorphic transitional images and tessellations; (3) playing around with perspective; (4) approaches to infinity, (again with tessellations). I classify them differently because I'm more interested in his "break points". That is to say, points in his life at which he discovered a new idea and brought that idea to the world through his prints. I won't attempt to put them in any order, but here is my list. It doesn't include category (1) above, because this wasn't one of his "ideas". In my opinion, that phase was just a formative era on his journey towards the development of his own style.

(1) tessellations, i.e. shapes that fit together like his famous print, 'Sky and Water I' below. This section also encompasses both his metamorphosis period and his "approaches to infinity" period. The reason I've grouped them all together is because this whole phase was based on just one "device", namely working out how to fit shapes together and creatively repeating the patterns you can create this way.

Sky and Water I (1938)

(2) perspective under the rules of traditional Euclidean geometry, i.e. perspectives built upon straight, ruler-drawn construction lines disappearing to their vanishing points, like his 'Tower of Babel' below. This period of Escher's work was a fairly unpublicised one and as soon as he started experimenting with perspective in non-Euclidean geometry (my next bullet point), he looked back on this phase with regret. He said the following about Tower of Babel in a lecture when he was about 72: "I was 30 years old then and now find it to be a typical example of youthful clumsiness and lack of understanding of perspective." The number of works from this phase are limited because he soon discovered non-Euclidean geometry. (Euclid was a Greek mathematician: some say the Father of Geometry).

Tower of Babel (1928)

(3) perspective under the rules of "non-Euclidean geometry", as in a study he did for 'House of Stairs', below. Unlike Euclidean geometry, where perspectives are built upon straight lines disappearing to their vanishing points, non-Euclidean geometry observes that the human eye doesn't actually see straight lines as straight, it sees them as curved. The brain receives the information from the eye and interprets those curved lines as straight. We actually see things as in a fisheye perspective, but it took us about 2,000 years to figure out that the brain was doctoring this information while the poor old eye had it right all along! (The 2000 years is from 300 BC when Euclid laid out his observations, up until the early 19th century when the first of many other non-Euclidean geometries was discovered). This section also encompasses all of his fisheye perspectives. I myself am significantly influenced by this period of Escher's work.

Study for House of Stairs (1951)

(4) regular solids and symmetrical spatial structures, mainly comprised of polyhedra, Möbius strips, torus knots and so on. A good example of this is 'Stars' (1948) below. I'm using Stars as an example to illustrate this category, but I don't really like it because in my opinion, it serves as a somewhat crude and passionless 'display platter' of Escher's skills. However, despite this criticism, I am heavily influenced by this period of Escher's work as well, (which you can see from my blog, although I really like mandalas as well. Escher didn't really play with mandalas). I really love the way computers had no involvement in Escher's work here, and I'm confident that even if he were alive today, he would resist the channel of temptation that so many others have fallen into, namely using computers to construct, develop and inspire this kind of work.

Stars (1948)

(5) "impossible" repeating / cyclical perspectives. In other words, depicting things that are three dimensional but breaking the rules of spatial 3D geometry. This is arguably the theme for which Escher became most famous. Often, if people say they haven't heard of Escher, I describe 'Ascending and Descending' below, with its perpetually rising / ascending staircase, or 'Waterfall', also below, with its forever flowing cycle of water. They're famous because they're fun, interesting and pretty. Plus, they make good student posters! But I like them because they are good examples of how Escher kept on coming up with new ideas. Interestingly, when discussing Print Gallery (1956) with a group of revered mathematicians, Escher was commended on his innovative adaptation of an extremely complex mathematical manifold called a 'Riemann Surface'. Escher told them he had no idea what they were talking about. He said that if he had created a Riemann Surface then he was very pleased, but he assured them that he had done so by complete accident! This proves Escher's genius in the field of interpreting spatial geometry through art, not mathematics. (By the way, I understand that in its simplest linear form, a Riemann surface can be likened to the "Droste Effect". I blogged about the Droste effect in an earlier post, where you can also see Print Gallery and the Riemann surface he created).

Ascending and Descending (1960) and Waterfall (1961)

This final theme is especially important to me, and so significant, because it encompasses many fascinating ideas. It best describes my point about how Escher consistently and tirelessly devised, experimented, conceptualised and dreamed. In my understanding, this is what drove him. Not his physical tools or his media, nor his quest for mathematical accuracy, nor his earnings through the trade of his art. Rather, it was new ideas, new ways of distorting existing preconceptions and the biggest one: his quest to discover an entirely new type of spatial geometry. Just like Euclid and the geometers of the early 19th century, I believe Escher dreamed of discovering a whole new framework upon which a new view of the world could be built. He tragically died before he got there, but he said himself near the end of his life, "I could fill an entire second life with working on my prints". I think of this quote so frequently because I feel part of a collective consciousness of Escher fans around the world who, in their own small way, attempt to carry forward the flame that Escher held.

"Not one of us needs to doubt the existence of an unreal, subjective space. But personally I am not sure of the existence of a real, objective space. All our senses reveal only a subjective world to us; all we can do is think and possibly mean that therefore we can conclude the existence of an objective world" (Escher, 1953)