Name: 【TED-Ed】The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair
Uploaded: 2014-11-30T12:57:08.000Z
Duration: 4 min 39 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

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 undestand

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:

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

where he'd admitted himself after mutilating his own ear

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,

or here in star light that  twinkles and melts

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

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

60 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

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

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

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 luminence 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.

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-portait with a pipe, from a calmer period in Van Gogh's life,

And neither did other artists' work that seemed equally turbulent at first glance,

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

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

Van Gogh was somehow able to perceive and represent

one of the most supremely  difficult concepts

with the deepest mysteries of movement, fluid and light.