ClassX Video Lessons Subjects Art The unexpected math behind Van Gogh’s “Starry Night” – Natalya St. Clair
One of the most fascinating abilities of the human brain is its knack for recognizing and describing patterns. Among the most complex patterns we encounter is turbulent flow in fluid dynamics. The renowned German physicist Werner Heisenberg famously remarked, “When I meet God, I’m going to ask him two questions: why relativity and why turbulence? I really believe he will have an answer for the first.” This highlights the enigmatic nature of turbulence, which remains a challenging concept to grasp mathematically. However, art can provide a unique lens through which we can visualize its appearance.
In June 1889, Vincent van Gogh painted “The Starry Night,” capturing the view from his room at the Saint-Paul-de-Mausole asylum in Saint-Rémy-de-Provence. This masterpiece, with its swirling clouds and stars, is a testament to Van Gogh’s ability to depict the movement of light through his circular brushstrokes. Unlike their predecessors, Van Gogh and other Impressionists portrayed light in a dynamic way, capturing its motion across landscapes and night skies.
The effect achieved in these paintings is due to luminance, which refers to the intensity of light in the colors used. Our visual cortex, which processes light contrast and motion, blends areas of different colors if they share the same luminance. Meanwhile, another part of our brain perceives the contrasting colors distinctly. This dual interpretation creates a pulsing and flickering effect in Impressionist art, making the light appear alive and moving.
Fast forward sixty years, and Russian mathematician Andrey Kolmogorov made significant strides in understanding turbulence. He proposed that the energy in a turbulent fluid at a certain length scale, R, varies proportionally to the 5/3 power of R. While Kolmogorov’s theory brought us closer to understanding turbulent flow, it remains one of the unsolved mysteries in physics. Turbulent flow is self-similar, meaning that energy cascades from larger to smaller eddies, a phenomenon observable in natural occurrences like Jupiter’s Great Red Spot and cloud formations.
In 2004, scientists using the Hubble Space Telescope observed eddies in a distant cloud of dust and gas that reminded them of Van Gogh’s “The Starry Night.” This observation led researchers from Mexico, Spain, and England to analyze the luminance in Van Gogh’s paintings. They discovered patterns of turbulent fluid structures that closely matched Kolmogorov’s equation, hidden within many of Van Gogh’s works.
The researchers digitized the paintings and measured brightness variations between pixels. They found that paintings from Van Gogh’s period of intense emotional turmoil exhibited remarkable similarities to fluid turbulence. In contrast, his self-portrait with a pipe, created during a calmer time, showed no such patterns. Interestingly, other artists’ works, like Munch’s “The Scream,” did not display this turbulent pattern, despite their chaotic appearance.
While it might be tempting to attribute Van Gogh’s ability to depict turbulence to his genius, it is profoundly significant that during a time of great personal suffering, he managed to capture one of nature’s most complex phenomena. Van Gogh’s unique perspective allowed him to unite the mysteries of movement, fluid, and light, offering us a glimpse into the intricate dance of turbulence through his art.
Examine a high-resolution image of Van Gogh’s “The Starry Night.” Identify and describe the patterns you observe that might represent turbulent flow. Consider how the use of color and brushstroke contributes to the perception of movement and energy.
Using Kolmogorov’s theory, create a simple mathematical model to simulate turbulent flow. Discuss how this model can be applied to understand the patterns observed in Van Gogh’s paintings. Present your findings in a group discussion.
Compare Van Gogh’s “The Starry Night” with another painting from his calmer periods, such as his self-portrait with a pipe. Analyze how emotional states might influence the depiction of turbulence and movement in art. Write a short essay on your observations.
Participate in a workshop that combines art and science. Collaborate with peers from different disciplines to create a piece of art that visually represents a scientific concept, such as turbulence. Reflect on the process and how each discipline contributes to a deeper understanding of the concept.
Engage in a virtual reality experience that simulates the turbulent patterns found in Van Gogh’s paintings. Explore how technology can enhance our understanding of complex phenomena like turbulence. Discuss the potential educational benefits of using VR in art and science education.
Here’s a sanitized version of the provided YouTube transcript:
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One of the most remarkable aspects of the human brain is its ability to recognize patterns and describe them. Among the hardest patterns we’ve tried to understand is the concept of turbulent flow in fluid dynamics. The German physicist Werner Heisenberg once said, “When I meet God, I’m going to ask him two questions: why relativity and why turbulence? I really believe he will have an answer for the first.”
As challenging as turbulence is to understand mathematically, we can use art to depict its appearance. In June 1889, Vincent van Gogh painted the view just before sunrise from the window of his room at the Saint-Paul-de-Mausole asylum in Saint-Rémy-de-Provence, where he had admitted himself after a personal crisis. In “The Starry Night,” his circular brushstrokes create a night sky filled with swirling clouds and stars. Van Gogh and other Impressionists represented light in a different way than their predecessors, capturing its motion across sun-dappled waters or in the twinkling starlight that flows through the blue night sky.
The effect is caused by luminance, the intensity of light in the colors on the canvas. The more primitive part of our visual cortex, which perceives light contrast and motion but not color, will blend two differently colored areas together if they have the same luminance. However, our brain’s primate subdivision will see the contrasting colors without blending. With these two interpretations occurring simultaneously, the light in many Impressionist works seems to pulse and flicker. This is how Impressionist artists use quickly executed brushstrokes to capture something strikingly real about how light moves.
Sixty years later, Russian mathematician Andrey Kolmogorov advanced our mathematical understanding of turbulence by proposing that energy in a turbulent fluid at length R varies in proportion to the 5/3 power of R. Experimental measurements show that Kolmogorov was remarkably close to describing how turbulent flow works, although a complete understanding of turbulence remains one of the unsolved problems in physics. A turbulent flow is self-similar if there is an energy cascade, meaning that larger eddies transfer their energy to smaller ones, which do the same at other scales. Examples include Jupiter’s Great Red Spot, cloud formations, and interstellar dust particles.
In 2004, using the Hubble Space Telescope, scientists observed the eddies of a distant cloud of dust and gas around a star, which reminded them of Van Gogh’s “Starry Night.” This inspired researchers from Mexico, Spain, and England to study the luminance in Van Gogh’s paintings in detail. They discovered a distinct pattern of turbulent fluid structures close to Kolmogorov’s equation hidden in many of Van Gogh’s works. The researchers digitized the paintings and measured how brightness varies between any two pixels. From the curves measured for pixel separations, they concluded that paintings from Van Gogh’s period of intense agitation exhibit remarkable similarities to fluid turbulence.
In contrast, his self-portrait with a pipe, from a calmer period in Van Gogh’s life, showed no sign of this correspondence. Other artists’ works that initially seemed equally turbulent, like Munch’s “The Scream,” did not exhibit this pattern either. While it may be tempting to say that Van Gogh’s turbulent genius enabled him to depict turbulence, it is also profoundly significant that during a time of intense suffering, Van Gogh was able to perceive and represent one of the most complex concepts nature has presented to humanity, uniting his unique perspective with the mysteries of movement, fluid, and light.
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This version maintains the essence of the original transcript while removing any sensitive or potentially distressing content.
Turbulence – A state of fluid flow characterized by chaotic changes in pressure and flow velocity – The study of turbulence is crucial in understanding how air flows over an aircraft’s wings.
Art – The expression or application of human creative skill and imagination, often in a visual form such as painting or sculpture – The art of physics can be seen in the elegant equations that describe the universe.
Light – Electromagnetic radiation that is visible to the human eye and is responsible for the sense of sight – The study of light and its properties is a fundamental aspect of both physics and art.
Fluid – A substance that has no fixed shape and yields easily to external pressure; a gas or liquid – Understanding fluid dynamics is essential for artists who work with materials like paint and clay.
Dynamics – The branch of mechanics concerned with the motion of bodies under the action of forces – The dynamics of a pendulum can be described using differential equations.
Patterns – Repeated decorative designs or regular arrangements of elements – The patterns in Van Gogh’s “Starry Night” can be analyzed using mathematical models of turbulence.
Van Gogh – A Dutch post-impressionist painter known for his vivid colors and emotional impact – Van Gogh’s use of color and brushwork has been studied in terms of both artistic technique and psychological expression.
Luminance – The intensity of light emitted from a surface per unit area in a given direction – Artists often manipulate luminance to create depth and focus in their work.
Mathematics – The abstract science of number, quantity, and space, used in physics to model and analyze phenomena – Mathematics is the language through which we can describe the intricate patterns found in nature.
Impressionism – An art movement characterized by small, thin brush strokes and an emphasis on the accurate depiction of light – Impressionism revolutionized the art world by focusing on the effects of light and color rather than detailed realism.
