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One of the most remarkable aspects
of the human brain

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is its ability to recognize patterns
and describe them.

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Among the hardest patterns
we've tried to understand

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is the concept of
turbulent flow in fluid dynamics.

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The German physicist
Werner Heisenberg said,

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"When I meet God,
I'm going to ask him two questions:

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why relativity and why turbulence?

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I really believe he will have
an answer for the first."

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As difficult as turbulence is
to understand mathematically,

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we can use art to depict the way it looks.

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In June 1889, Vincent van Gogh
painted the view just before sunrise

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from the window of his room
at the Saint-Paul-de-Mausole asylum

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in Saint-Rémy-de-Provence,

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where he'd admitted himself after
mutilating his own ear

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in a psychotic episode.

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In "The Starry Night,"
his circular brushstrokes

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create a night sky filled
with swirling clouds and eddies of stars.

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Van Gogh and other Impressionists
represented light in a different way

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than their predecessors,

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seeming to capture
its motion, for instance,

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across sun-dappled waters,

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or here in star light
that twinkles and melts

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through milky waves of blue night sky.

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The effect is caused by luminance,

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the intensity of the light
in the colors on the canvas.

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The more primitive part
of our visual cortex,

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which sees light contrast
and motion, but not color,

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will blend two differently
colored areas together

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if they have the same luminance.

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But our brains' primate subdivision

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will see the contrasting colors
without blending.

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With these two interpretations
happening at once,

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the light in many Impressionist works
seems to pulse, flicker and radiate oddly.

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That's how this
and other Impressionist works

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use quickly executed
prominent brushstrokes

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to capture something strikingly real
about how light moves.

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Sixty years later, Russian
mathematician Andrey Kolmogorov

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furthered our mathematical
understanding of turbulence

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when he proposed that energy
in a turbulent fluid at length R

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varies in proportion to
the 5/3rds power of R.

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Experimental measurements show Kolmogorov

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was remarkably close
to the way turbulent flow works,

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although a complete description
of turbulence

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remains one of the unsolved
problems in physics.

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

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In other words, big eddies
transfer their energy to smaller eddies,

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which do likewise at other scales.

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Examples of this include
Jupiter's Great Red Spot,

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cloud formations
and interstellar dust particles.

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In 2004, using the Hubble Space Telescope,

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scientists saw the eddies of a distant
cloud of dust and gas around a star,

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and it reminded them
of Van Gogh's "Starry Night."

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This motivated scientists
from Mexico, Spain and England

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to study the luminance
in Van Gogh's paintings in detail.

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They discovered that there is a distinct
pattern of turbulent fluid structures

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close to Kolmogorov's equation
hidden in many of Van Gogh's paintings.

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The researchers digitized the paintings,

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and measured how brightness varies
between any two pixels.

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From the curves measured
for pixel separations,

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they concluded that paintings from
Van Gogh's period of psychotic agitation

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behave remarkably similar
to fluid turbulence.

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His self-portrait with a pipe, from
a calmer period in Van Gogh's life,

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showed no sign of this correspondence.

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And neither did other artists' work

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that seemed equally
turbulent at first glance,

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like Munch's "The Scream."

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While it's too easy to say
Van Gogh's turbulent genius

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enabled him to depict turbulence,

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it's also far too difficult to accurately
express the rousing beauty of the fact

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that in a period of intense suffering,

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Van Gogh was somehow
able to perceive and represent

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one of the most supremely
difficult concepts

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nature has ever brought before mankind,

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and to unite his unique mind's eye

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with the deepest mysteries
of movement, fluid and light.