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 undestand

is the concept of
turbulent flow in fluid dynamics.

The German physicist
Verner 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 Asylumn

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 brush strokes

creates 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 my 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 executted

prominent brush strokes to capture
something strikingly real

about how light moves.

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

one of the unsolved problems in physics.

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

In ther 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 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.

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 aggetation

behave remarkably similar
to fluid turbulence.

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

show no sign of this correspondence.

And neither did other artists' work that
seemed equally trubulent 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,

its 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.