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.