The Math Behind Van Gogh's "Starry Night"

Physicist Werner Heisenberg said, “When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.” As difficult as turbulence is to understand mathematically, we can use art to depict the way it looks. Natalya St. Clair illustrates how Van Gogh captured this deep mystery of movement, fluid and light in his work.

Lead in

Draw some flowing water. How can you represent something fluid, with static lines?

Lead in: What do you think makes this picture so well loved?

Look at the title:

“The unexpected math behind Van Gogh’s ‘Starry Night’ by Natalya St. Clair:

What do you think the article will say about the picture?

 

Read the article and find out:

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 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 difficult as turbulence is to understand mathematically, we can use art to depict the way it looks.

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’d admitted himself after mutilating his own ear in a psychotic episode.

In “The Starry Night,” his circular brushstrokes create a night sky filled with swirling clouds and eddies of stars.

Van Gogh and other Impressionists represented light in a different way than their predecessors, seeming to capture its motion, for instance, across sun-dappled waters, or here in starlight that twinkles and melts through milky waves of blue night sky.

The effect is caused by luminance, the intensity of the light in the colors on the canvas.

The more primitive part of our visual cortex, which sees light contrast and motion but not color, will blend two differently colored areas together if they have the same luminance.

But our brain’s primate subdivision will see the contrasting colors without blending.

With these two interpretations happening at once, the light in many Impressionist works seems to pulse, flicker, and radiate oddly.

That’s how this and other Impressionist works use quickly executed, prominent brushstrokes to capture something strikingly real about how light moves.

Sixty years later, Russian mathematician Andrey Kolmogorov furthered our mathematical understanding of turbulence when he proposed that energy in a turbulent fluid at length R varies in proportion to the five-thirds power of R.

Experimental measurements show Kolmogorov was remarkably close to the way turbulent flow works, although a complete description of turbulence remains one of the unsolved problems in physics.

A turbulent flow is self-similar if there is an energy cascade.

In other words, big eddies transfer their energy to smaller eddies, which do likewise at other scales.

Examples of this include Jupiter’s Great Red Spot, cloud formations, and interstellar dust particles.

In 2004, using the Hubble Space Telescope, scientists saw the eddies of a distant cloud of dust and gas around a star, and it reminded them of Van Gogh’s “Starry Night.”

This motivated scientists from Mexico, Spain, and England to study the luminance in Van Gogh’s paintings in detail.

They discovered that there is a distinct pattern of turbulent fluid structures close to Kolmogorov’s equation hidden in many of Van Gogh’s paintings.

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 psychotic agitation behave remarkably similar to fluid turbulence.

His self-portrait with a pipe, from a calmer period in Van Gogh’s life, showed no sign of this correspondence.

And neither did other artists’ work that seemed equally turbulent at first glance, like Munch’s “The Scream.”

While it’s too easy to say Van Gogh’s turbulent genius enabled him to depict turbulence, it’s also far too difficult to accurately express the rousing beauty of the fact that, in a period of intense suffering, Van Gogh was somehow able to perceive and represent one of the most supremely difficult concepts nature has ever brought before mankind, and to unite his unique mind’s eye with the deepest mysteries of movement, fluid, and light.

 

Go to Ted Lesson:

The math behind Van Gogh's "Starry Night"

1. Who admitted van Gogh to a mental asylum?

2. What is an energy cascade?

3. What is turbulence?

4. What is relativity?

5. What is the Hubble telescope?

6. What is amazing about van Gogh's 1889 Starry Night painting?

Discuss

1. Is it important that Van Gogh seems to have accidentally represented turbulence? Why?

2. If we can just take photographs or films of fluid things, why bother trying to represent them through painting or drawing? 

Descension

1. One key ability of the human brain is recognizing _________ and being able to describe them.
2. Among the most difficult patterns scientists study is ________ in ________ dynamics.
3. The physicist _________ once said he would ask God about _________ and _________.
4. In June 1889, _________ created a painting based on the view from his room in an asylum in _________.
5. In The Starry Night, _________ brushstrokes form a sky full of swirling _________ and starry eddies.
6. Impressionist artists showed _________ in a new way, capturing its _________ in scenes like water or the night sky.
7. This visual effect comes from _________, meaning the intensity of _________ in the colors used.
8. In 1941, _________ suggested that energy in turbulent flow depends on the _________ power of length.
9. In turbulent flow, an _________ cascade occurs, where larger eddies pass energy to _________ ones.
10. Researchers later found that the luminance patterns in Van Gogh’s paintings resemble _________, especially during times of _________ agitation.

Hannah Gadsby: Nanette | The Sunflowers

lead in:


Who painted this?

If I give you "unsolicited" advice, does it mean the advice is...
A) poorly researched?
B) unasked for?
C) not from a lawyer?
D) not advice that I follow myself?

Discuss

1. Should people who suffer from mental illness take medication or try to cope without it?

2. Is there a connection between artistic talent and mental instability?

3. How might the medication van Gogh was taking have actually been partly responsible for the Sunflowers?


Guide questions

1. According to the man, why should artists not take medication for mental health problems?


Kahoot Quiz

The Math of Starry Night