I’ve been thinking recently about patterns. I like patterns and I don’t think that is strange or unique, in fact I think it’s a very human thing. I’ve written previously about puzzles and about how they help us to spot patterns, but I’ve been thinking more about why it’s important to spot patterns and why we find them so pleasing.
Mathematician Marcus du Sautoy has summarised his work by saying: “My mind searches for patterns and structures as I contemplate the unexplored reaches of the mathematical landscape.” He is talking about how he sees a lot of mathematics as searching for patterns, whether it is patterns of prime numbers, or symmetry groups. But patterns are not just important in mathematics. Searching for patterns helps in a lot of contexts. For example chess Grand Masters memorising games, or concert pianists memorising music, usually rely on seeing a pattern and remembering that rather than each individual piece or each individual note.
So patterns are useful, but it’s not just that they are useful, I think there’s something more deeply human about why we like them. David McCandless puts this… erm… beautifully in his brilliant TED talk: “The eye is exquisitely sensitive to patterns and variations in colour, shape and pattern. It loves them, and it calls them beautiful. It’s the language of the eye. If you combine the language of the eye with the language of the mind, which is about words and numbers and concepts, you start speaking two languages simultaneously, each enhancing the other.”
McCandless turns complex data sets (like worldwide military spending, media buzz, or Facebook status updates) into beautiful, simple diagrams that tease out unseen patterns and connections. The way he sees it, finding patterns in data allows us to derive information or insight from raw data, and allows him to tell a compelling ‘story’ with the data. But it is important to him that there is a ‘beautiful’ pattern (in the language of the eye) at the heart of his story (in the language of the mind).
The point McCandless makes is that our eye finds patterns and symmetries beautiful; we like things tidy and we like patterns and it’s interesting to try to understand why that might be.
In his book Deviate, Beau Lotto talks about how our brains have evolved to seek for certainty in an uncertain world. The way he sees it: “Resolving uncertainty is a unifying principle across biology, and thus is the inherent task of evolution, development and learning”. Marcus du Sautoy makes a similar point in The Creativity Code: “Any animal’s ability to survive depends in part on its ability to pick out structure in the visual mess that nature confronts us with. A pattern in the chaos of the jungle is likely to be evidence of the presence of another animal… We are programmed to search for patterns, to make sense of the chaotic world around us. It’s what saved us from being eaten by wild animals hiding in the undergrowth. That line of yellow might be nothing, but then again it could be a lion.” Essentially it’s a complicated world and in order to make sense of it, we need to try and simplify it. One of the ways we do this is by looking for patterns; and we can see how our brains have evolved to seek simplicity (or certainty) and a complex (or uncertain) world. Applying this to learning, development and evolution, we could speculate that if an early human was better able to recognise the patterns of a migration of buffalo to improve hunting, or the patterns of the seasons to better manage farming, then that human would likely be more successful. And it’s not such a huge leap then to speculate that this could be why we are wired up to find patterns compelling or attractive.
And this leads us to appreciation of beauty and art. As du Sautoy puts it: “The human code is extremely good at reading patterns, interpreting how they might develop, and responding appropriately. It is one of our key assets, and it plays into our appreciation for the patterns in music and art.”
Undoubtedly we find things like patterns and symmetry pleasing. The composer Johann Sebastian Bach loved symmetry and used it to structure much of his music. Béla Bartók used Fibonacci numbers in his compositions. This BBC Three article cites a number of instagram and pinterest accounts dedicated to symmetrical pictures of buildings, symmetrical origami (which is quite close to my own heart), and even pictures of symmetrical breakfasts! Quoted in the article, physicist Alan Lightman writes in The Accidental Universe that: “Symmetry represents order, and we crave order in this strange universe we find ourselves in. The search for symmetry, and the emotional pleasure we derive when we find it, must help us make sense of the world around us, just as we find satisfaction in the repetition of the seasons and the reliability of friendships. Symmetry is also economy. Symmetry is simplicity. Symmetry is elegance.”
And this article discusses in more detail some of the reasons why we might find symmetry and order pleasing. There are some beautiful examples of symmetry in nature from starfish and flower petals to snowflakes and crystalline rock formations. Bridges and buildings with regular geometric structures and symmetry and generally stronger and more stable. Humans are (largely) symmetrical and research has shown that we find symmetrical faces more attractive than asymmetrical ones, the explanation being that symmetry is an easily observable sign of good genetics and good health. Essentially symmetrical structures are stable and efficient and (maybe) therefore we’re programmed to find symmetry and order reassuring and secure and therefore pleasing.
However, as the article also states “too much symmetry can be a tad boring.” Johan Wagemans, an experimental psychologist from Belgium, found that perfectly symmetrical designs are pleasing to the brain, but that they’re not necessarily more beautiful. We seem to prefer art that strikes an “optimal level of stimulation,” art that is “not too complex, not too simple, not too chaotic and not too orderly.” So maybe we like order with just a pinch of chaos? Marcus du Sautoy sums this up brilliantly in The Creativity Code: “Our brain responds to that tension between recognising a pattern and knowing it is not so simple that we can predict what will happen next. It is that tension between the known and the unknown that excites us.” Obviously I like this because it’s about balance isn’t it?
And as ever, there’s a Japanese word for it, the aesthetic principle called fukinsei, which is all about creating balance, using asymmetry or irregularity, and accepting that nothing is ever perfect and that the imperfections can be beautiful. Good (or at least relevant) examples are the Japanese arts of bonsai or ikibana, working with natural materials like trees or flowers means that there is always going to some irregularity, and this rather than being seen as an imperfection, makes art interesting and beautiful. It is like the grit in the oyster that forms a pearl, or the seed that helps a crystal grow, necessary to perturb the status quo and lead to something beautiful.
So there’s something beautiful about a bit of imperfection and in many cultures artists deliberately introduce some imperfection of flaw into their work. This article cites some examples in Navajo weaving and Islamic architecture. And another Japanese art form (this is becoming a bit of a thing with me isn’t it?) is Kintsugi, which is the beautiful art of putting broken pieces of pottery back together, and actually highlighting the ‘scars’ in the piece.
Thinking about how a pinch of chaos makes things interesting got me thinking about fractals, mathematically generated patterns with infinite complexity. As you zoom in on a fractal it doesn’t become simpler, but ever more ‘layers’ or complexity are revealed. The classic example is the Mandelbrot Set which is generated by iteration of relatively simple equations. So fractals are complex and beautiful, but also (in a manner of thinking) they are simple since they can be generated with simple equations.
This leads us to the concept of emergent complexity, the idea that dramatic and diverse behaviour can emerge spontaneously in a complex system. Think about the patterns in murmurations of starlings, or schools of fish avoiding a predator. These behaviours don’t necessarily derive from adding up the behaviours of the component parts of the system, which means that complex systems are chaotic and difficult to model or predict. Pretty much anything natural is a complex system, one where there are many moving parts, all interconnected to such an extent that you can’t really predict how they will all affect one another. Examples are ecosystems, stock markets, traffic in cities, and weather systems.
Now I like connections, and think that interesting things happen where things overlap, such as where art meets science. There are some great examples of this such as artist Nathalie Miebach who takes weather data from massive storms and turns it into complex sculptures that embody the forces of nature and time or into musical scores for a string quartet to play. Or the work of ‘data imaginist‘ Thomas Lin Pederson who creates beautiful artwork using the R programming language (which is more usually used for statistics and data analysis).
But this idea of beautiful things emerging from complex systems or from ‘big data’ got me thinking about negative capability, a phrase used by poet John Keats to explain the capacity of artists to perceive and recognise ‘truths’ without conscious reasoning, that is to sometimes create something without really understanding why they are creating it. As Keats himself put it: “With a great poet the sense of beauty overcomes every other consideration.” I think Keats is saying that great artists just make something beautiful and don’t overthink it… And maybe I’m overthinking this (wouldn’t be the first time!).
So I want to tie this up with a return to puzzles, and beauty and symmetry. I remembered one of Alex Bellos’s Monday puzzles in The Guardian from a few months ago about symmetry and patterns, and it also involved a bit of colouring in and was therefore right up my street! But even better, the puzzle was inspired by Beautiful Symmetry: A Coloring Book about Math, by computer scientist Alex Burke called. The idea is to provide a gentle introduction to mathematical ideas about symmetry through the process of colouring in, which I think is all kinds of wonderful!