Van Gogh – not just a painter

November 22, 2022

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Van Gogh is undoubtedly one of the most famous painters of all time, but perhaps it’s time to consider him a mathematician.

Starry Night is one of Van Gogh’s most renowned paintings, depicting just that: a starry night. With a bright moon on the right, and Venus in the centre left, the sky is dominated by illuminating stars shining above the view from Van Gogh’s window at the mental asylum in Saint-Rémy, France. This painting is often considered a true depiction of modern art’s embracement of expressionism, mood and symbol. One of the most iconic features of this painting is Van Gogh’s capturing of movement in the night sky. It almost seems like the stars are swirling about – a sense of movement is indisputable. But what is this movement? Where does it come from? What does it represent?

An art enthusiast may believe that this “swirling” movement is how Van Gogh saw the world, since at the time Van Gogh was in an asylum, troubled by his own mental state. The movement in the sky is therefore often seen as his view of the world, through welled eyes. Whilst this is fanciful idea, scientists and mathematicians have taken a different, and somewhat more extraordinary, view: the starry sky is a perfect depiction of turbulence in fluid motion.

Turbulence is one of physics’ most complicated phenomena; to this day, scientists are still struggling to fully understand it.  It is characterised by fluid motion caused by chaotic changes in pressure and velocity. We all know what it feels like, in an aeroplane – it’s the thing that causes your tummy to flip due to a sudden movement. Turbulence occurs in every system containing moving fluids, not just air. It occurs in the blood flow of our arteries, waves along a beach, or even in the tea you’ve just stirred. Yet how it is really modelled remains somewhat of a mystery.

To piece together how turbulence is suggested to work, we begin with particles. Movement in gases and liquids is comprised into two categories: laminar flow (which is stable and smooth), and turbulent flow (which is made up of random swirls). An easy way to visualise this is through the smoke coming from an incense stick. At first the smoke is easy to follow, easy to predict how it will move, but the further the smoke moves from the base, the faster its billows in chaotic swirls and directions. Let us note that chaotic in this sense does not mean random. Random implies that turbulence is not sensitive to any changes from outside, but, in fact, turbulence is highly sensitive to changes, making its movement chaotic. If we were to waft our hand past our incense stick, the smoke patterns will be very different each time. This is partially what makes it so difficult to model and predict its movement.

Going back to our incense metaphor, have you ever noticed that the swirls produced at the end by the smoke are never the same size? The different sized swirls are known as eddies, and these can be all kinds of sizes and shapes. They interact with each other, breaking up until they are so small that the movement, or kinetic energy, converts to heat energy. This is known as an “energy cascade”. For those of you paying close attention, you might already realise how Van Gogh’s Starry Night comes into it. Mathematicians have struggled to model these energy cascades for over a century, yet in 1941, soviet mathematician Andrey Kolmogorov came the closest. He proposed that energy in a turbulent fluid at length R varies in proportion to the 5/3rd’s power of R. Modelling this leads to the closest mathematical model of turbulence to date, although it is still not perfect.

This did aid in helping scientists identify more forms of turbulence, as a way of trying to understand how it works. Notably, cloud formation on Jupiter, as seen through NASA’s Hubble Space Telescope, is another example of turbulence. This is where Van Gogh truly comes in. When scientists identified turbulence patterns on Jupiter, it reminded them of Van Gogh’s Starry Night. The turbulence in the clouds was a striking resemblance of the swirls depicted in the painting. Intrigued, scientists digitised Starry Night and analysed the swirl patterns. To much surprise, this almost exactly aligned with Kolmogorov’s mathematical model, as complex as it was.

So, how on earth did Van Gogh do this? Art is often regarded as beauty only in the eye of the beholder, but this mathematical aspect unquestionably impresses everyone. Some may say it’s chance that Van Gogh happened, yet analysis of his other paintings reveals similar patterns, for example his sunflower paintings. Strangely enough, however, all the paintings in which a visualisation of turbulence occurs, are from Van Gogh’s unstable time in an asylum. Analysis of fluid motion in his other paintings from a more stable period in his life, for example a selfportrait with a smoking pipe, does not include it. How is this then possible? A rather emotive commentary suggests that within his own mental turmoil, the rest of the world and its strange phenomena became clear. Perhaps the only way to understand such complex ideas is if we ourselves are in a complex state. In any case, the fact that Kolmogorov’s ideas from 1941 are portrayed in a painting from 1889, in a completely different country, is remarkable.

We often see art and mathematics as worlds apart, however, in a case such as this, we see that art and maths are one and the same. Starry Night has proved that art can be a compelling means to depict some of the most complicated phenomena. This can help to explain how the world works – after all, in every physics lesson diagrams are the best way to understand something. Whether Van Gogh is considered a mathematical genius or not, he remains one of the world’s best painters to this day. If scientists truly uncover the way turbulence works, then we might be able to confirm Van Gogh’s ingenuity.  

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