The unexpected math behind Van Gogh’s “Starry Night” – Natalya St. Clair
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The unexpected math behind Van Gogh’s “Starry Night” – Natalya St. Clair


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 star light
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 brains’ 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 5/3rds 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.

95 Comments

  • Maria: The Demon Barber of YouTube

    Someone had commented here: "I know nothing with certainty but the view of the stars makes me dream" and in the replies I had a conversation with a most interesting person. Thank you so much that you deleted your comment, now I have lost all that forever…

  • scott FAILING

    I bought on off his stary night painting.Yes the mind makes the star gas move.Play trick the mind.Scream painting guy looks like he shakes.I love his work.He can know how to make some of his painting move..Even Will Smith movie end of world virus called leagon.He has stary night painting over his fireplace in movie.So cool his work.Will be misssed

  • Robert Schlesinger

    Interesting that during van Gogh's periods of so-called psychosis, he also apparently had lucid insights into certain aspects of nature. This sort of deep insight during a psychological episode may be much more common than commonly thought. I can think of such examples from music, literature, poetry, art, and even mathematics. It has been said (by an ex-Harvard psychologist from the mid-60s) that to learn how to use your mind, you must first go out of your mind!

  • oneof theninetynine

    A bit of a huge supposition here like most TED talks. Somehow I suspect math had nothing to do with Van Gogh's genius but mathematicians would love to think so because math is so deadly dull. It's called artistic talent and to some extent practice. Pretending it has anything to do with math is silly jump of wishful thinking. Pls go back to making a computer fractals and pretending they're art

  • Vincent Gonzales

    A view from the asylum window?
    Yes and no.
    He painted Starry Night in his studio—incorporates views from his studio window and elements from the view from his asylum window.

    He painted 21 paintings of the view looking out his studio window.

  • super duper

    i think it’s not okay to romanticize mental illness. when someone is depressed or dealing with anxiety they don’t become some magical creatures capable of greater things, they’re just suffering. that may put things in perspective and make you appreciate the good moments, the small things, he said in his letters that he found peace in looking at the stars, that’s beautiful and that’s why he created such a delicate painting yet full of love and passion, but let’s not act like his internal struggle made him a better artist, that’s not it, we’re talking about an actual person who ended up killing himself, i’m sure his pain was no god given miracle

  • Allison

    I have visual impairments that cause me to see flowing type of kaleidoscopes similar to Van Gogh’s swirls. I wish I could paint them like he did. I wonder if he could have had a bit of neural path damage along with psychiatric symptoms.

  • Jer

    Ya know I draw these ‘turbulent’ lines all the time which is why I love Van Gogh and his most recognizable painting “ the starry night “ I draw these however because to me it expresses how my mind is , it’s messy but a neat messy, lines going everywhere, the flow never stopping

  • WVGIRL

    His friend artist Cut his ear when they were in a fight. Van Gogh did not cut it himself. He also ate his own lead paint, so his behavior should be questioned!

  • Limerence

    Artists have to be physicists without the knowledge of one. Some learn to draw straight lines and circles free hand. You need to do realistic perspectives without any math or measuring. You need to do colour without knowing the properties of light. How can a non-scientist brain recreate the laws of reality. It's because our brain is a scientist. Every time we take a step, our brain must measure the distance from your foot to the ground. We just don't have access to this marvelous calculator. But through art we can. We are part of nature and we must be able to understand it to live with it. The greatest artists will have access this primal computer. That's how Van Gogh understood Turbulence, the biggest mystery in physics, before it was even thought of in the academic sciences.

  • Leonard Ax

    Now I understand what you tried to say to me
    How you suffered for your sanity
    How you tried to set them free
    They would not listen, they did not know how
    Perhaps they listen now

  • Knowbrains

    Van Gogh is my favorite artist … his paintings not only captured the time and space of the eternal moment, but the energy as well … this is most apparent in The Starry Night … and is what gives life and meaning to his beautiful works … Thank you Vincent !!!

  • Marilia Tatone

    That reason I think people considerate with mental disease should be treat better and with more attention.. and some tribe when someone demonstrate different behavior like Van Gogh they put them for be spiritual consuler treat like someone with power and wisdom..

  • Zen Traveler

    Even through math we can find justification to why Van Gogh’s Starry Night is one of the greatest works of humankind

  • Chloë Lee

    I know it seems like Van Gogh probably didn’t consider any of this while creating his artworks but I do think there’s intellectuality behind his work since the Impressionism art movement was all about meticulously studying light

  • Sidhartha Sankar Sarma

    Now I think I know
    What you tried to say to me
    And how you suffered for your sanity
    And how you tried to set them free

    They would not listen, they're not listening still
    Perhaps they never will.

  • Narinka

    Говоря русским языком, завитушки в звёздной ночи расположены примерно так же, как волны в турбулентности? Я посмотрела картину внимательней, Винни писал жирными и частыми мазками в центре каждой завитушки и постепенно, по мере удаления от центра, делал мазки тоньше и дальше друг от друга. И плюс цвета сочетал, как тут сказано, контрастные. Вроде я поняла смысл ролика 🤔

  • I will post a video at 25 subscribers

    Off topic:
    As a Dutch person it kind of annoys me how English people pronounce van Gogh 😂

  • Alexei W.B.

    It has also been suggested that the medications he was on at the time to treat his condition, had a side effect of seeing light with halos like depicted in this painting, this has been shown in medical studies where Drs documented patients describing such visual hallucinations. we must also take into account what level of toxicity did his brain have from the medication and the large amounts of absinthe that he partook in as was common in that time.

  • Sebastian Messerer

    Van Gogh did not think up a painting, he felt it. This is an attempt to scientifically explain a poetic effort. The danger of this kind of imposed genius onto the work is it gives people the impression they need to be clever to paint, whereas the opposite is the case: Art is exactly an expression of the subconcious. If you conciously conceive of a work, it is not art but a sort of plastic science. This video may make someone think they need a clever thought to make a great work of art. When instead great works of art happen when the artist has managed to ignore his concious and establish a connection with his subconcious which dictates which colours are "right"… Of course you can impose all sorts of scientic explanations on the works after, but it is pointless and can distort.

  • Ted JustAdmitIT

    Yeah he had issues, but painted in asylum following the self-maiming incident. I'd bet he was on serious drugs. He was swirly….

  • Augh Bable

    He painted it by his skills and experiences. He knew what colors went well with what colors, the combinations within his various studies, which strokes compliments his paintings and I hope people know that make a living for being a painter is no laughing matter. Those oil paintings are not cheap. Now imagine you have to buy it repeatedly…and your painting is not sold. For what it is worth, you must paint beautiful and interesting subject. Beauty is strength….. maybe we're over analyzing?

  • Stephanie O

    Hmmm… I learned that in those days, people would use digoxin, a modern day medicine used for cardiac issues, as a tea. The side effects are halos around lights and that’s why his starry night painting looks different. That’s what I learned.

  • June Purple-Tea

    Van Gogh [vɑnˈxɔx] was a post-impressionist.
    If you what to know how his surname is pronounced in Dutch: https://forvo.com/word/vincent_van_gogh/

  • Déborah Lzrg

    It’s really interesting. I like making links between maths/science and Art. But please, don’t call Van Gogh and Impressionist. He is a Post-Impressionist. Impressionists are concerned about pure objective visual accuracy. While post Impressionists seek self-expression!

  • Aslans Angel

    You know WHY Van Gogh was able to paint "turbulence?" It's because he had Meniere's Disease. Ask any person who has this disease (it's an inner ear disease, and wow! He cut OFF his ear! hmmm), and they can tell you that we FEEL that turbulence, and it's extremely painful. The man was so in tune with this phenomenon, he could paint it. Instead, he was portrayed as some psychotic freak, and put in a mental asylum, and committed suicide. Sad what people do "in the name of medicine" to victims because they don't understand something.

  • Betty Iglesias

    I respect the work that Ted-Ed does, and probably using stereotyped racism should be topic for the next one. Wishing you could see a Mexican beyond the hat, poncho, huarache and cactus. Remember, mexico is rich in colonized tradition, stigmatized marijuana and violent cartels. Also it’s gastronomy, beaches and accessible medicine.

  • 5k subscribers with Jin's photo challenge

    I came here to understand the turbulence but the turbulence in the animation kept distracting me…

  • Ram Lathers

    It's shameful to think how one of history's greatest artists was mocked and derided and slowly driven insane. Yet from the depths of his sorrow and pain he birthed works of unrivalled cosmic power and beauty into the world.

  • Dangerfield

    Apart from the fact you used possibly the worst style of illustrator to depict this information, the rest is a substantial overreach which is fully exposed in the word ‘similar’. You could have said it in one dull line: Van Gogh’s work is a bit similar to turbulence.

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