Divine Proportions
Photos and Text by: Jared Lloyd
Have you ever read Edgar Allan Poe’s Philosophy of Composition? Yes, that Poe. “Harks the Raven” Poe. I was assigned this in a writing class back in college and it completely revolutionized how I saw art from that moment on.
We all have those watershed moments in life. A point that we can look back to and realize there was the world, or at least our world view, before and after that experience. For me, with art, nothing would ever be the same again. The Philosophy of Composition revolutionized the way I saw and thought about art, in all of its many forms.
The premise behind this essay was to explain Poe’s personal artistic view on the composition of writing by dissecting what may be his most famous of all poems, the Raven. According to the Philosophy of Composition, every aspect of this piece could, in essence, be broken down to something of an almost mathematical formula. What had seemed like a poem so dark and painful and inspired, as if the writer had merely reached out into the ether and wrapped his fingers around lyrical greatness, could not be further from the truth.
Poe had always intended the Raven to stand as an example of his philosophy on writing. In his essay on the matter, he lays out a bold and provocative argument that quite upset the literary world at the time by completely dismissing the notion of artistic intuition. Writing, he explained, was logical, calculated, methodical, and unfolding almost like an equation – though he did not use the word equation. He claimed that no writer would ever admit to such a thing as they all benefited from the seemingly mysterious nature of their art.
The argument was a compelling one – at least when using his own work as example. Reading and rereading the Philosophy of Composition, and The Raven, slowly it began to make sense. I could see the calculating nature of the writer behind the words. And with this, a certain shroud of mystery was lifted.
The Philosophy of Composition was written in 1846 for Grahams American Monthly Magazine. This was revolutionary for the time. But it was not, as I would learn, revolutionary in the world of art. Though it was a new argument to be made for literature, the argument was thousands of years old in the realm of visual arts.
Photographers are not the only genera of artists to use so called “rules” in their compositions. Everyone reading this article is probably going to be intimately familiar with the Rule of Thirds, for instance. Maybe, if you’re a bit more savvy than the average bear, you have even caught wind of the Rule of Odds. This second one simply states that odd numbers of things are more interesting than even.
At the heart of these so-called rules is a thing that can give just about any artist a panic attack today: math. Start talking in terms of ratios and equations and your almost guaranteed to watch people’s eyes begin to glaze over. But it didn’t used to be like this. Historically, many of the world’s greatest artists were down right obsessed with math.
But when I say that artists were obsessed with math, this doesn’t mean all math. Most of the seemingly intangible stuff is relatively new in the history of us. Abstract algebra wasn’t introduced to Europe until the 16thcentury, and the world had to wait for Sir Isaac Newton to invent calculus in the mid-17th century. Instead, when I refer to math and the arts, it is geometry that I speak of.
Geometry, broken down into its ancient Greek origins means, literally, Earth Measurement. It is here, with the measurement of things, with the understanding of proportions, and dimensions and the patterns that can be found within such things that we find an almost Asperger’s like obsession in artists throughout history.
In our modern view of history, it is probably Leonardo de Vinci who comes to mind when we think of the combination of mathematics and art. Leonardo was positively consumed with the understanding of geometry and the natural forces that shaped it. When we think of Leonardo’s work, we tend to think of the Mona Lisa, maybe the Last Supper, or even Madonna of the Rocks. In all of these we find his obsession with such details at work. But more than any of his paintings or unrealized inventions, it was a sketch he made known as the Vitruvian Man that exemplifies the importance of what was then being called Divine Proportion.
Despite the fact that Leonardo de Vinci is best known for paintings such as the Mona Lisa, it was a simple sketch known as the Vitruvian Man that would become something of the poster child for blending art and science. Thousands of measurements of the human body went into this creation, making it the most anotomically correct sketch ever created at the time
We think that the Egyptians understood it in the creation and completion of the Great Pyramids. We know that the Greeks had a strong grasp of the concept of course, which can be found in creation of the Parthenon and in the writings of Plutarch and Plato. And for as long as people have written about it, we know that the whole of the concept was attributed to the gods and the creation of the cosmos.
Throughout history, people have discovered a certain kind of universal truth in the natural world through mathematics. Pythagoras said that God was number. Galileo claimed, “mathematics is the alphabet in which God has written the universe.” There is no one time and place that this occurred – despite the decidedly Western bias in the examples I have chosen here. Most likely it was discovered and lost, and independently discovered again elsewhere with a different people, culture, and time. At least, this would explain the many names we use to describe it all today. Names like divine proportions, sacred geometry, or the golden ratio.
Sometimes I think I was born a few centuries to late. Or, at least one century anyways. When I was in school with visions of being a biologist dancing in my head, I pictured 19th century biology when people set out into the unknown, Terra incognito if you will, to study and observe life in all its many and wonderous forms on Earth. This is not how things are done in the 21st century, however.
Back when observation was paramount to understanding, when it was thought that knowledge and enlightenment came from observing Nature (with a mandatory capital N of course), people noticed that patterns emerged everywhere they looked. Apparently, this was life before iPhones.
In some ways, this made sense. Everything that exists, from life to rocks to rivers, does so with a given set of parameters or rules that it cannot break. This isn’t hocus pocus. It’s called physics. Everything on Earth is effected by the same pull of gravity, the same rotation of the planet for instance – Einstein’s Special Relativity. And therefore, since the same physical properties are impacting everything that exists here, we should see patterns in how things are shaped or grow.
Examples abound. Take rivers and mountains for instance. From 35,000 feet, both take on the same shape. A river begins with tiny streams and creeks that come together forming the river, only to then itself spread apart and branch into a delta. Mountains have this very same look from the sky. So does a tree – with branches reaching towards the heavens, with a mirror image below the ground in the form of roots. And of course, all of this looks very much like our own circulatory system with arteries branching out to deliver blood to our most distant of extremities.
The Fibonacci spiral, also known as the golden spiral, mapped in three different ways across Leonardo da Vinci’s most famous of works, the Mona Lisa
But this isn’t the weird stuff. Take the creeks that form the river. A closer look reveals that they themselves take on the same pattern as the river from 35,000 feet, with countless paths of water running together to form them. Likewise, look at a single ridge of a mountain range and you will find the same pattern. Or take our tree and you will find that the branches themselves branch out to smaller and smaller twigs until you find leaves and then within those leaves the very same pattern on even smaller and smaller scales in the form of veins.
I can go on, but I won’t.
These are called Fractals: patterns that repeat themselves over and over on a seemingly never ending scale the closer or further away one observes the thing. And for some reason, you and I are drawn to these fractals on a subconscious level. We see them without seeing them. We are lured to them without knowing what we are even looking at.
Jackson Pollock, the whiskey swilling Wyoming artist that splattered paint on a canvas and made millions, has entranced countless with is non-objective art. Love it or hate it, people are drawn to it with little understanding of why. Though pollock himself would never come to know this, modern computer analysis of his work reveals that his most famous pieces show the very same fractal patterns that we find throughout the natural world.
Let’s go deeper.
Did you know that the distance between the base of your palm to your elbow is 1.6 times the length of your hand? Or that the distance between the middle section of your index finger is 1.6 times the length of the tip of your fingertip? Technically, from the tip of your finger to the start of your wrist, every section gets 1.6 times longer than the last. And your middle finger itself is roughly 1.6 times longer than your palm. The same goes for your leg from the knee to the foot. Or for you head and neck in proportion to your torso. Or the ratio of the distance between your eyes compared to the size of one of your eyes. Or from the floor to your navel and from your navel to the top of your head.
Confused yet?
Here’s a nauseating thought: our general interpretation of beauty can be measured in an almost exact mathematical formula. Change the measurements, change the distance of a fingertip to the knuckle or head and neck to torso, or distance between the eyes, and EVERYONE takes notice – though not usually on a conscious level. There is a grocery list of psychological studies of our perception of beauty that back this up. Time and again, academia has revealed that when test subjects are shown the faces of random strangers in photographs, the ones that are deemed the most beautiful are the ones that have the most perfect proportions of 1 : 1.6.
This ratio, this division of 1 to 1.6 (or really, 1.618) is the golden ratio – or what mathematicians refer to as phi (different than pi). This golden ratio is a fractal pattern in nature. I am using examples in humans because we are most intimately familiar with ourselves. When I mention the ratio of your hand to your forearm, you can look down and see this for yourself. But this same ratio is found EVERYWHERE. All animals fit this bill. All living things fit this bill to one degree or another.
Yet, it’s not just living things. The shape of hurricanes and the swirl of water caught within the vortex of a whirlpool follow suite. The packing of seeds in a pod, the spacing of leaves and flower pedals, all obey this rule. And then there is the sequence of numbers.
Around 1200AD, Leonardo Fibonacci discovered a numerical sequence that expressed the golden ratio. By its self, this was little more than a simple thought experiment. However, we would soon realize that not only did this pattern of numbers identically match many of the number patterns in nature, we also realized that when plotted out geometrically, it created the perfect spiral – intimately larger in one direction, and infinitely smaller in the other. And with a shape that matches that of hurricanes, and whelk / conch shells, and the unfurling of ferns, and the shape of pine cones to name just a few out of many thousands of examples. Today, these numbers are known as the Fibonacci Sequence.
0,1,1,2,3,5,8,13,21,35,55,89 and on and on and on it goes. Where it will stop, nobody knows.
A simplified explanation of this sequence is that each progressive number, moving left to right, is the sum of the two numbers before it added together. Just typing that is confusing. Look at it this way: 1+1=2 and 1+2=3 and 2+3=5 and 3+5=8 and 5+8=13.
The crazy thing about this is that these numbers can be found all over the natural world. Take flowers for instance. The number of petals on every species of flower ever known to have existed equals one of these numbers in the Fibonacci Sequence. Species within the sunflower family (Asteraceae), all have either 21, 34, 55, or 89 petals. Marigold has 13, delphinium has 8, columbine has 5, and iris have 3 – as a few more examples.
Biology is messy though. These numbers are perfect world scenarios. Just like not all humans are blessed with perfect golden proportions and get to strut around like Greek gods and goddesses, so to does mutation and genetic variation exist in everything from flowers to the bees that pollinate them. Thus, with the sunflower for instance, we find about 1 in 5 that does not fit this bill. Yet, what is interesting about this is that most of us would most likely notice this instantaneously (again, on a subconscious level) and move on to a different flower to photograph. Yes, your decision to chose one subject over another to photograph is most likely governed by these concepts as well.
All of this is a rabbit hole.
So, what does any of it have to do with art? Artists throughout history have asked themselves this very same question.
Beauty is something that cannot be defined. Yet we all know it when we see it. Finding another person attractive is one thing. This makes sense. Its biological. Its evolutionary. But why do we find sunsets beautiful? A tree? A mountain? A painting? Is it possible that the very same things that make us universally attracted to paintings such as Albert Bierstadt’s Rocky Mountain Landscape is the same thing that attracts us to Claude Monet’s Impression, Sunrise? And could it very well be the same things that make supermodels who they are, and hurricanes the way they are, and flowers what they are?
Want to go even further?
As wildlife photographers, as visual artists, it’s important for us to be infinitely curious about the world around us. From nature to the nature of other’s artwork, it’s through the never ending pursuit of knowledge that we grow. If you would like to learn more about the fascination way in which divine proportions and golden ratios play a role not just in art but also the natural world around us as well as our own definitions of beauty, then check out these books below.
