Weird Symmetry

AS AN ARTIST interested in science I’ve always been fascinated by symmetry. As a silhouettist I rely on symmetry, my art would literally not exist without it. I’d like to share some of that fascination by exploring a the symmetry which infuses all our lives. Symmetry is so commonplace we mostly don’t see it, but when you really start to look it does begin to seem rather weird.

A Search into Weird Symmetry

Profilles are not symmetrical
The profile view exists because of symmetry

Human faces are symmetrical. As a silhouettist I rely on this simple truth. In a silhouette the face is always seen in profile: that is, at 90º to the axis of symmetry. This is what defines a silhouette, and why faces in silhouette appear the same whether they face right or left. If our faces were not symmetrical, my job would become impossible. Which angle would we call the “profile”?

Although useful, I’m aware that our faces are not designed symmetrically to make my life easier. The simple phrase “faces are symmetrical” prompted me to think about the weird symmetry of our faces more deeply. Is it an accident of evolution? Could our faces have evolved some other way?

So I embarked on a search into the human symmetry which makes my job possible.

Symmetrical Faces

Face-on silhouette of a bald man with the axis of symmetry marked
His axis of symmetry is easy to see, including the bow tie!

My first observation was that our faces are only symmetrical in one plane. Seen from the front, the symmetry is obvious; the axis of symmetry runs vertically from top to bottom, bisecting the forehead, nose, mouth and chin. Whatever appears on one side of the axis is reflected on the other: the right eye mirrors the left, one ear for each side. This same symmetry is also apparent from the back. However, when seen from the side (the silhouettist’s-eye view) this symmetry disappears. Nothing about the profile is symmetrical. Yet, it’s this view I use as a silhouettist. The profile, in silhouette, is where the likeness lies.

My second observation was that our faces are not exactly symmetrical. When posing for a silhouette, people often comment that they have a “best side”. They tend to cite, as justification, that human faces are not symmetrical! Of course I cannot comment on whether or not my clients really do have a best side, but there is no doubt that their symmetry is imperfect. One ear may be different to the other, or one eyebrow more pronounced. Perhaps a scar, or other mark, may alter their natural symmetry. So perhaps I should have started this section by writing:

“human faces are imperfectly symmetrical”.

Four silhouettes in almost exact symmetry
Which is my best side?

Symmetrical Bodies

Thirdly, I realised that it isn’t just the face; this weird symmetry extends to our whole bodies. From head to toe a single vertical axis of imperfect symmetry bisects us: one hand reflects the other, one leg, the other. Every external organ that the axis bisects is itself symmetrical. Thinking about bodies, this imperfect symmetry even continues inside. Our skeletons and musculature are symmetrical. Those organs lying on the axis of symmetry (eg: our lungs and brains) appear symmetrical. Others (eg: our heart and bowels) are not.

Symmetrical Animals…

Kittens take symmetry for granted

Fourthly, I began to look around. I realised it isn’t just people. Every animal that walks, trots, crawls or swims has the same axis of weird symmetry. Always a single axis, always vertical, always imperfect and always seen from the front. All living beings are symmetrical when seen from the front and asymmetrical when seen in profile. Why is this? Is there some immutable law of nature that all living beings should be symmetrical?

Well, no, there are exceptions. Some species of crab, for instance, have highly asymmetric claws. Some species of bottom-dwelling fish, such as plaice, have taken to swimming on one side. Their bodies have evolved asymmetrically, with both eyes on one side (now the top). 

… and asymmetrical crabs

The odd-looking Fiddler Crab has evolved a highly-asymmetric set of claws.
Its weirdness emphasises how unusual this is in nature

Single clawed crabs are interesting partly because they look so odd. Nature, it seems, does experiment with asymmetrical forms from time to time. Yet – presumably driven by natural selection – it always returns to symmetry in the end. Why? Does symmetry offer some deep intrinsic advantage over other forms? Or is symmetry somehow encoded into the laws of evolution itself?

Even insects, with their capacity for rapid evolution, rarely stray from the symmetrical straight and narrow. They all have six legs, arranged three-each-side of a single vertical axis. Why so few exceptions? 

In looking for exceptions I’m not just looking for asymmetric animals. The rule of symmetrical weirdness is actually three rules. Nature seems to require that the axis of symmetry be single, vertical and imperfect:

  1. A single axis of symmetry: who can show me a creature with double or multiple axes of symmetry? That is, a creature that symmetrical both from the front and the side?
  2. A vertical axis of symmetry: have you ever seen a creature with a horizontal axis of symmetry? That is, where the bottom of the animal reflects the top?
  3. An imperfect axis of symmetry: who can show me any object in nature which is exactly symmetrical, without a single mark or hair to mar its perfect symmetry? Conversely: have you ever seen an animal without any trace of symmetry? Even odd marine animals don’t do this. The Fiddler Crab, with its single odd claw, does have a redundant small claw to balance it on the other side. Its symmetry is simply more than usually imperfect.

Imperfection itself seems to be an important part of the formula.

Symmetrical Trees

Silhouette of a sprouting plant: more weird symmetry
Will I be big or little?

Next, I asked if the rule applies outside the animal kingdom. Plants, at first sight, appear highly asymmetric. But, with my artist’s eye, I looked again.

Plants live their lives by growing. It’s only through growth that they can move at all; that they can adapt their lives to their environment and the things which happen to them. The pattern of their growth is highly symmetric. All plants, whether great or small, begin as a sprout with two identical leaves. As they grow they form a central trunk with branches either side, each branch balanced by another.  True, the branches grow in all directions, to wherever they can find light. The whole plant may quickly become lop sided, or even wind itself around other plants, yet the overall design is a symmetrical one. Plants seem to grow with a kind of distorted symmetry.

Next, I looked at the leaves. Each leaf is an essay in symmetry, a central stem with a web-like pattern either side, each half reflecting the other. Flowers and fruits are all beautifully, but imperfectly symmetrical.

Plants certainly bend the rule, but a symmetrical weirdness does somehow infuse their very being.

Our Own Symmetrical World…

Finally I began looking outside the natural world, at the world we’ve created. 

Motorcycle and sidecar combination
Riding an asymmetric Ural motorcycle and sidecar combination is an interesting lesson in weird symmetry!

Pause, for a moment, to look at the human-made objects around you. In front of me is my laptop, itself symmetrical. My laptop is clearly bisected by a single axis of imperfect symmetry (imperfect because the keyboard is not exactly symmetrical). My laptop sits on a symmetrical table, whilst I’m sitting on a symmetrical chair. In front of me is a glass of wine, a bowl of fruit, and a knife on a plate. All are symmetrical. Outside is my car, imperfectly symmetrical from the front, with a clear profile shape to the side.

As I thought about it I realised that the rule of symmetrical weirdness extends to every car, lorry, motorcycle of bicycle on the road. It applies to the aeroplanes in the sky and the ships on our seas. As with our bodies, the axis of symmetry always appears from the front, is always vertical and always imperfect. 

There are exceptions, of course. It’s easy to find specialised pieces of equipment which need to ne asymmetrical to function. The pantograph is one such piece of equipment, much loved by silhouettists of the eighteenth and nineteenth centuries. In my drive I keep a highly asymmetric motorcycle and sidecar combination; it has three wheels, none of which are a pair to another. Driving it is an object lesson in asymmetrical handling. I love it for its idiosyncrasy and plain oddness. It’s easy to see why many engineers would consider it a design dead end.

Whenever possible, however, we prefer our human-made objects to be symmetrical. Anything else appears specialised, alien or just plain quirky.

What’s going on? Does the same pressure that drives nature towards symmetry also drive the evolution of our own designs? If so, why? Where’s the advantage? Or is symmetry so implanted in our very being that we simply cannot help making symmetrical objects?

… & Other Worlds too

It isn’t just people. There aren’t many creatures on earth which make things, but those which do – birds building their nests for instance – tend to make them symmetrically. Humans began by making imperfectly-symmetrical stone tools and pottery, objects we can find in the rubbish tips of ancient settlements. Today, we make more things than we can count. Even the plastic rubbish accumulating in our oceans tends to be symmetrical.

Asymmetrical Aliens?

One of the questions I would most like to ask, if we ever discover complex life on another planet, is:

“Is life there subject to the same rule of symmetrical weirdness as here?”

If so, that would seem to me truly weird. But if not, what questions would it pose about the evolution of life on earth?

Ask a child to draw an alien and they will often draw you a wonderfully-asymmetric creature. But give an adult the same task and all you get is weird symmetry. It seems we cannot imagine anything else, even when tasked with drawing something beyond our wildest dreams.

Symmetrical Art

Strangely, despite its prevalence, artists and designers are taught to be cautious in using symmetry. Many art students arrive at art college very enamoured with symmetry, perhaps having used it successfully in their designs at school. They need to be gently guided away from this.

Portrait drawing on cut paper.
A recent experimental portrait using a combination of drawing and cutting. When drawing I rarely confront symmetry head on.

Portrait artists rarely paint their subject head on, where the symmetry is most obvious, but tend to prefer a more nuanced three-quarter or not-quite-profile view. This was certainly my approach when working in Covent Garden. Today, I like to experiment with combinations of drawing and cutting to make portraits. However I rarely draw the face either in symmetry or in profile.

Architecture too, has a very symmetrical past. Yet, modern architects strive to move away from this, exploring alien, asymmetric forms instead.  These make us look again and ask questions about our environment.

In art, the depiction of symmetry is at its best when hinted at, rather than stated openly. A portrait can suggest movement by suggesting that the axis of symmetry is “over there”, away from the viewer’s gaze. A building can hold our interest if the front, symmetrical aspect is always felt to be around the next corner. Yet, on rounding the corner, it somehow never appears. A sculpted figure is more interesting when twisted, seeming to move in a way which hides the natural symmetry of the human body.

Asymmetrical Hands

One of the hardest objects in nature to draw (or in my case, cut) is the human hand. Hands are important because they communicate so much. This is obvious if you watch a speaker speak, or look at hands in a classical painting. The reason hands are hard to depict is because they’re asymmetrical. Hands do form part of the symmetry of our bodies – the right reflects the left – yet one hand, considered on its own, has no symmetry at all. 

This means that a hand does not have a natural profile. There is no one point of view at a 90º angle from a vertical axis of symmetry. There is no axis, nor is there any sense of vertical. Which part of a hand is the top?  Which angle is the profile? A hand turns and moves in a multitude of ways. This makes it difficult to visualise the silhouette. In learning to cut silhouettes of hands I’ve have no option but to study them from every conceivable angle, never knowing which one a subject may present.

Three silhouettes of hands, no weird symmetry here.
Cutting silhouettes of hands with scissors is notoriously hard. Which angle is the profile?
Are these right or left hands? Are they seen from above or below?

Can You Explain it?

The study of hands and faces is how my interest in symmetry began. Since then, thinking about symmetry has made me realise that it infuses every aspect of life on earth. Bizarrely, it also infuses most objects created  by life on earth. From bird’s nests and the earliest stone tools, to the rubbish currently accumulating in our oceans, almost everything is imperfectly symmetrical. In the visual arts, including my own art of the silhouette, the use of symmetry has to be carefully considered.

To me, this all seems like weirdness. I can conceive of no plausible reason why symmetry should be so completely embedded in our lives. Can you?

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