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.

1. The unexpected math behind Van
Gogh's "Starry Night" - Natalya St.
Clair
https://youtu.be/PMerSm2ToFY
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.
1.- Where was Vincent van Gogh located when he painted "Starry Night"?
AIn Paris
BIn an asylum
CIn a church
DIn a university
2.- Who proposed statistical theory of turbulent patterns?
AA. Kolmogorov
BM. Damon
CR. Crowe
DV. van Gogh
3.- True or false: A complete description of turbulence is to this day an unsolved
problem in physics.
ATrue
BFalse
4.- What is meant by the idea of self-similarity?
AA line segment that goes on forever
BExponentially growing yaks
CSquaring derivatives on both sides of the equation
DObjects that have the same pattern, such as smaller versions of larger shapes

2. 5.- What are some examples of turbulence?
APlanetary hurricanes
BIntense oceanic currents
CInterstellar movement of gas and stars
DAll of the above
6.- Write a short paragraph (3-5 sentences) that summarizes the history of Vincent
van Gogh. What challenges did he encounter as a painter?
7.- Write a short paragraph (3-5 sentences) that summarizes the history of
turbulence. How would you describe the scientific problem-solving processes
described in the video?
8.- Research the idea of statistical self-similarity. What are some examples of
turbulence that are not shown in the video?
Additional Resources for you to Explore
A few lesson plans exist for teaching visual arts and self-similarity (objects that
have the same pattern) that could be used after showing this lesson. Shodor has
some free lesson plans for students in grades 4 through 8. High school students
can learn recursion algorithms to create the Koch curve using Scratch for free.
Educational technologist Dylan Ryder has also written about creating fractals. A
beautiful app worth checking out is Starry Night Interactive App by media
artist Petros Vrellis. Download it to your tablet and create your own version
of Starry Night. Finally, don’t forget to check out TED-Ed’s original The Case of
the Missing Fractals. Can you solve the case?
Really interested in mathematics? If you live in the New York-area, visit
the Museum of Modern Math for more on math and visual arts.
Turbulence, unlike painting, is mostly a time-dependent phenomenon, and after
some time, breaks statistical self-similarity that Kolmogorov predicted in the
1960s. To learn more about Kolmogorov’s predictions, Terry Tao provides a great
overview of Kolmogorov’s power laws for turbulence.
In fluid mechanics, since we can't often solve the equation for flow patterns, we
develop a system of scaling between the physical properties. This is called
dimensional analysis. Want to find out more about the five-thirds law that
the video references? Scroll through this website and learn

3. There are a few articles that outline patterns of turbulence in Van Gogh’s Starry
Night. Flow by Philip Ball (p. 164-178) provides an excellent overview of the
concept for a broad audience. Nature featured this article: Van Gogh painted
perfect turbulence. Discover Magazine in 2006 featured another article on this
topic called A Turbulent Mind. Learn how accurate Van Gogh’s turbulence was in
his paintings. Finally, this article entitled: Troubled Mind and Perfect Turbulence,
gives a great description of several of Van Gogh’s paintings. It also discusses how
the impact of the painting on the viewer was measured using the concept of
luminosity.
Acknowledgements
Natalya St. Clair would like to thank those who helped contribute their feedback
to the script of this piece at Countryside School, Harvey Mudd College, Princeton,
and University of Illinois in Urbana-Champaign, and, including Chris
Antonsen, Arthur Benjamin, Andrew Bernoff, Wendy Cho, Likith Govindaiah, Jon
Jacobsen, Carolyn Meldgin, Aaron Williams, and her students and colleagues.