The Starry Night and Turbulence: What the Science Really Found

The Starry Night and Turbulence: Art, Measurement and Limits

Does Van Gogh's The Starry Night really show turbulence? In a statistical sense, partly yes. Studies in 2006 and 2024 measured the brightness patterns in his swirling sky and found they follow the same scaling laws physicists use to describe turbulent fluids. But a painting is not a moving fluid, Van Gogh knew none of this mathematics, and the match says nothing reliable about his mental illness. The interesting story is how a hand-painted sky ended up sharing a pattern with nature.

How The Starry Night was made

Vincent van Gogh painted The Starry Night in June 1889 at the asylum of Saint-Paul-de-Mausole in Saint-Rémy-de-Provence, in the south of France, where he had admitted himself the previous month after a series of breakdowns. The oil-on-canvas work, about 74 by 92 centimetres, now hangs at the Museum of Modern Art in New York, which acquired it in 1941.

It was not a literal view of one night. Van Gogh's room looked east over a walled wheat field towards the Alpilles hills, and he painted that view many times. For this canvas he worked during the day in his ground-floor studio rather than at the window at night. The village and its church spire are imaginary, based on a sketch made from a hillside above Saint-Rémy, and the sky was turned into a rolling sequence of spirals. In letters to his brother Theo he mentioned watching the morning star from his window before sunrise; Venus was indeed bright in the eastern sky that spring.

Van Gogh himself was unconvinced by the picture; in a letter to Émile Bernard later in 1889 he called it a failure. Today it is one of the most reproduced paintings in the world.

A spiral from an Irish telescope

Lord Rosse's 1845 sketch of the spiral nebula M51, now known as the Whirlpool Galaxy.

The swirls in Van Gogh's sky have often been compared with one of the first drawings of a spiral galaxy. In 1845 William Parsons, the 3rd Earl of Rosse, an Anglo-Irish astronomer, used the "Leviathan of Parsonstown", a 72-inch reflecting telescope he built in the grounds of Birr Castle in Ireland, to observe the object catalogued as M51. It remained the largest telescope in the world until 1917. Through it he could see that some fuzzy nebulae had a spiral structure, and his drawing of M51 was widely reproduced in astronomy books.

Some writers have suggested Van Gogh saw one of those reproductions, perhaps in popular astronomy books of the period. That is a plausible guess, not a documented fact; no letter or note from Van Gogh confirms it. (Older versions of this story also said the telescope was installed inside the castle. It stood outside, between two massive masonry walls.)

Why the stars seem to flicker: luminance

A popular TED-Ed lesson by animator and educator Natalya St. Clair, The unexpected math behind Van Gogh's "Starry Night", explains two separate ideas: how the painting appears to move, and how its swirls relate to turbulence.

The first idea comes from vision science, notably the work of Harvard neurobiologist Margaret Livingstone. Our visual system processes colour and brightness partly through different pathways. One older, colour-blind pathway handles contrast, motion and depth; another sees colour. When two neighbouring colours have almost the same brightness, or luminance, the colour-blind pathway struggles to tell them apart, while the colour pathway clearly sees the difference.

The result is an unstable impression: edges seem to shimmer or slide. Impressionist and Post-Impressionist painters often placed colours of similar luminance side by side with quick, visible brushstrokes, which is one reason their water, light and skies look alive. Van Gogh's blues, greens and yellows in The Starry Night use the same effect.

What turbulence is, and Kolmogorov's rule

Turbulence is the chaotic, swirling motion of fluids, from smoke rising off a candle to storms in Jupiter's atmosphere. It is famously hard to describe mathematically; a full theory of turbulence is still counted among the major unsolved problems of physics.

In 1941 the Soviet mathematician Andrey Kolmogorov proposed an influential statistical description. In a turbulent flow, large eddies break into smaller ones, passing their energy down a cascade until it is finally lost as heat at the smallest scales. Kolmogorov showed that, in an idealised flow, the distribution of energy across eddy sizes follows a predictable law. In its best-known form, the energy spectrum falls off with wavenumber to the power of minus five-thirds. Put simply, there is a fixed relationship between how big an eddy is and how much energy it carries. (The TED-Ed narration simplifies this to energy varying with the five-thirds power of a length; physicists usually express the rule through a wavenumber spectrum, or as velocity differences scaling with distance to the one-third power.)

Real measurements in wind tunnels, oceans and the atmosphere follow Kolmogorov's law remarkably well over a wide range of scales.

What the studies of the painting found

A Hubble Space Telescope image of swirling dust and gas around a distant star, widely reported to be the 2004 light echo of V838 Monocerotis, reminded many people of The Starry Night. That comparison helped inspire physicists José Luis Aragón and Gerardo Naumis of the National Autonomous University of Mexico, with colleagues in Spain and the UK, to test Van Gogh's paintings directly. Their work was first released in 2006.

They digitised the works and measured how much the brightness differs between pairs of points at different distances apart. In The Starry Night, Wheat Field with Crows and Road with Cypress and Star, the statistics came close to Kolmogorov-type scaling. His Self-Portrait with Bandaged Ear and Pipe, painted after he had recovered and in what he described as a state of calm, did not show it. The researchers linked the turbulent-looking works to periods of psychotic agitation in Van Gogh's life, an interpretation that went beyond what the numbers alone can show, as Naumis himself acknowledged.

In September 2024 a team including Yongxiang Huang of Xiamen University, with colleagues in China and France, published a more detailed analysis in the journal Physics of Fluids. They measured the sizes, spacing and brightness of the painting's 14 main whirls and found they matched Kolmogorov's scaling, while the finest brushstroke textures fitted Batchelor's scaling, a law describing how a substance mixes in turbulence at very small scales. Princeton astrophysicist James Beattie, who was not involved, told CNN the painting "has no kinetic energy" and called the shared statistics an amazing coincidence rather than real turbulence.

What the comparison does and does not prove

It does show that a careful observer of nature, painting quickly with thick strokes, produced patterns with statistics similar to real turbulent flow. Van Gogh spent years watching wind in cypresses, wheat and clouds, and his technique of building forms from layered, directional strokes naturally creates structure at many scales.

It does not show that he understood fluid dynamics, that the painting solves any physics problem, or that mental illness "unlocked" a vision of turbulence. A brightness measurement is not a velocity field, and a painting does not change over time as a flow does. Romantic claims that suffering produced genius are not supported by these studies, and modern scholars caution against reading his art mainly through his illness. His letters show a deliberate, thoughtful artist making conscious choices about colour and form.

The best way to enjoy The Starry Night may be to hold both views at once: a masterpiece of expressive painting, and a reminder that the patterns of nature can show up in unexpected places, including a sky invented in an asylum room in Provence.

Sources: MoMA: The Starry Night; Aragón, Naumis, Bai, Torres and Maini, Turbulent luminance in impassioned van Gogh paintings (arXiv); Plus Magazine on the 2006 study; AIP Publishing on the 2024 Physics of Fluids study; CNN, 19 September 2024; Wikipedia: The Starry Night; Wikipedia: Leviathan of Parsonstown; TED-Ed lesson by Natalya St. Clair (video above); first shared via I Heart Intelligence, written by Raven Fon.

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