Maths in the society / Maths is fun

A turbulent mind

Recently I described my FameLab exprerience. In the Polish edition as well as in the London heat I was talking about air turbulence and how it’s influenced by climate change. I was a bit surprised when some journalists approached me afterwards saying: “Oh, you’re the one who gave a presentation about van Gogh!”. Even though famous Vincent featured in my speech as well, I intended to talk abouth maths and physics rather than art 🙂


I didn’t wear this pretty T-shirt just to stand out – I decided to illustrate my speech by the masterpiece “The Starry Night”. This choice was inspired by a short TED-Ed video by Natalya St. Clair. Although I had always known that this picture shows patterns resembling turbulence, only after watching this film I learned that van Gogh really depicted a turbulent flow. And that’s not even the most mind-boggling thing about “The Starry Night”…

Intuitively, turbulence can be defined as some zigzags and eddies imposed on the main direction of the water or air flow. We encounter tubulence in everyday life, for example in a cigarette smoke (but stop smoking, for the love of van Gogh!), in a strong water flow from your tap, air flowing out of your lungs or on the plane. You might think that with such an abundance of experimental opportuinities scientists should have been able to explain this phenomenon ages ago. Unfortunately (or maybe fortunately) turbulence remains a mystery. If you happen to know the solution to Navier-Stokes equations describing this type of fluid behaviour, e-mail Clay Institute and win one million dollars – but when you’re rich, don’t forget who inspired this idea 🙂

Mathematicians and physicists still struggle to undestand turbulence. However, artists don’t care. More precisely, Vincent van Gogh didn’t care. One summer day in 1889, just before the sunrise, he looked out of the window in Saint-Paul-de-Mausole asylum, where he stayed because of his mental health problems, and painted what he saw. The result has become one of the most well-known pieces of art: “The Starry Night”.

About sixty years later a Russian mathematician Kolmogorov suggested the mathematical relation between variations in the speed of a turbulent flow and the rate of change of its energy. His idea was confirmed by experiments and followed by a more detailed theory was developed – but we still don’t know exactly what’s going on when turbulence occurs.

Let’s now fast forward to 2004, when the Hubble Space Telescope sent a picture of a distant star surrounded by a cloud of dust and gas. Eddies present in this cloud reminded the scientists from Mexico, Spain and the UK of “The Starry Night”, so they decided to approach this piece of art… scientifically.


“Light Echo” Illuminates Dust Around Supergiant Star V838 Monocerotis (V838 Mon) ; source:

Two years later they published a paper, in which they studied this painting in detail. In particular they were interested in so-called luminace, the intensity of the light emitted from the picture. A skilful use of this phenomenon allowed van Gogh, as well as many other Impressionists, to give the impression of movement, flickering or blinking of the image.

After digitalizing the paintings, scientists measured the difference of brightness between pixels. They found out that the patterns present in van Gogh’s works closely resemble a turbulent fluid. However, this concerns only pictures painted while he was struggling with the mental illness. For example, the smoke from the pipe in his famous self-portrait is similar to the real turbulence only at first glance – closer analysis doesn’t confirm this hypothesis.

Did van Gogh’s illness enable him to “see” more than even scientists do? I doubt it. However, this is just another piece of a turbulent jigsaw puzzle that we still cannot solve.


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