Study finds that starry sky painted by Van Gogh obeys the law of physics

Some say the starlight and swirling clouds in the painting “The Starry Night” by Vincent van Gogh reflect the artist’s tumultuous state of mind when he painted the work in 1889.

Now, a new analysis by physicists from China and France suggests that the artist may have had a deep and intuitive understanding of the mathematical structure of turbulent flow — a physics term that describes the chaotic movement of fluids.

A common natural phenomenon observed in fluids—moving water, ocean currents, blood flow, billowing storm clouds, and plumes of smoke—turbulent flow is chaotic and unpredictable as larger eddies form and break into smaller ones.

It may appear random to a casual observer, but turbulence follows a cascading pattern that can be studied and at least partially explained using mathematical equations.

“Imagine that you are standing on a bridge and watching a river flow by. You will see eddies on the surface, and these eddies are not random. They organize themselves into specific patterns, and these types of patterns can be predicted by physical laws,” said Yongxiang Huang, lead author of the study published Tuesday (16). in the scientific journal Physics of Fluids. Huang is a researcher at Xiamen University in southeast China.

“The Starry Night” is an oil painting on canvas that, the study noted, depicts the view of the sky just before sunrise from an east-facing window of the artist’s bedroom in Saint-Rémy-de-Provence, in southern France, where Van Gogh had been hospitalized after mutilating his left ear.

Using a digital image of the painting, Huang and his colleagues examined the scale of its 14 main swirling shapes to understand whether they aligned with physical theories that describe the transfer of energy from large- to small-scale eddies as they collide and interact with each other.

“The Starry Night” and the theories of turbulence

The atmospheric motion of the painted sky cannot be measured directly, so Huang and his colleagues precisely measured the brushstrokes and compared the size of the brushstrokes to the mathematical scales expected from turbulence theories. To assess the physical motion, they used the relative brightness or luminance of the varying paint colors.

They found that the sizes of the 14 eddies or vortices in “The Starry Night” and their relative distances and intensities follow a physical law governing fluid dynamics known as Kolmogorov turbulence theory.

In the 1940s, Soviet mathematician Andrey Kolmogorov described a mathematical relationship between fluctuations in the velocity of a flow and the rate at which its energy dissipates.

Huang and the team also found that the ink, at the smallest scale, mixes with some background eddies and gyres in a way predicted by turbulence theory, following a statistical pattern known as Batchelor scaling.

The Batchelor scale mathematically represents how small particles, such as seaweed drifting in the ocean or bits of dust in the wind, are passively mixed by turbulent flow.

“This is cool. In fact, this is the kind of statistic you would expect from algal blooms being swept up by ocean currents, or dust and particles in the air,” James Beattie, a postdoctoral researcher in the department of astrophysical sciences at Princeton University in New Jersey, said in an email. Beattie was not involved in this study but has conducted similar research on the artwork.

“In my article, I only really looked at the big [redemoinhos da pintura]so I didn’t see that second relationship,” he said, referring to the Batchelor scale.

“An incredible coincidence”

Of course, Huang said, Van Gogh would not have had theoretical knowledge of such equations, but he probably spent a lot of time observing turbulence in nature.

“I think this physical relationship must be ingrained in his mind, so when he made this famous painting ‘The Starry Night,’ it ends up imitating the real flow,” Huang said.

Beattie agreed: “It’s an incredible coincidence that Van Gogh’s beautiful painting shares many of the same statistics as turbulence,” he said.

“This makes some sense — the models were built to try to capture the statistics of eddies at multiple scales, with each eddy communicating with other eddies through the turbulent cascade. In a sense, Van Gogh painted something that represents this phenomenon, so why shouldn’t there be some convergence between the theoretical models and Van Gogh’s eddy statistics?” he added.

The study team performed the same analysis and detected the same phenomenon in two other images, one of which is a painting, “Chain Pier, Brighton,” created by British artist John Constable in 1827, and a photograph of Jupiter’s Great Red Spot taken by NASA’s Voyager 1 space probe on March 5, 1979.

“Unlike ‘The Starry Night,’ this painting [“Chain Pier, Brighton”] does not have well-defined swirl patterns, but the clouds are rich in structures with different scales, reminiscent of those often seen in the sky,” noted the study of Constable’s work.

On display at the Museum of Modern Art in New York, “The Starry Night” is a hugely popular artwork that has been recreated using Lego bricks, drones and dominoes.

Huang said scientists have long struggled to describe turbulent flow in fluid dynamics in a way that allows them to predict the phenomenon and that a complete explanation remains a prevailing mystery in physics. A complete understanding would help in predicting weather, flight turbulence and many other processes, he said.

“Even after more than 100 years of study, we still don’t know how to define this complex phenomenon,” Huang said. “It’s extremely important, but it’s extremely difficult.”

The fact that “The Starry Night” matches statistical models of turbulence, even though the artwork does not move, may suggest that statistical methods and tools are less accurate than scientists may have thought, Beattie said.

The paint cannot be measured accurately because “it’s not actually turbulence… It has no kinetic energy,” he said.

However, Beattie said he was a big fan of the artwork and that it reflected the universality and beauty of turbulence.

“I deeply love the fact that I can take my understanding of plasma turbulence between galaxies and apply it to turbulence between stars, between the Earth and the Sun, or in our own lakes, oceans and atmosphere,” he said.

“What I take away from studies like this is that [van Gogh] captured some of that universality in the beautiful painting,” Beattie added. “And I think people know that. They know that something wonderful has been embodied in that painting and we are drawn to that.”

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This content was originally published in Study finds that starry sky painted by Van Gogh obeys the law of physics on the CNN Brasil website.

Source: CNN Brasil