The unexpected math behind Van Gogh's "Starry Night" - Natalya St. Clair

Neočekivana matematika iza Van Gogove "Zvezdane noći" - Natalija Sent Kler (Natalya St. Clair)

Prevodilac: Ivana Krivokuća Lektor: Mile Živković

Jedan od najizuzetnijih aspekata ljudskog mozga

One of the most remarkable aspects of the human brain

is its ability to recognize patterns and describe them.

jeste njegova mogućnost da prepozna šablone i da ih opiše.

Among the hardest patterns we've tried to understand

Među najtežim šablonima koje smo pokušali da razumemo

is the concept of turbulent flow in fluid dynamics.

jeste koncept turbulentnog protoka u dinamici fluida.

The German physicist Werner Heisenberg said,

Nemački fizičar Verner Hajzenberg je rekao:

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

"Kada sretnem Boga, postaviću mu dva pitanja:

why relativity and why turbulence?

zašto relativnost i zašto turbulencija?

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

Verujem da će imati odgovor na prvo."

As difficult as turbulence is to understand mathematically,

Koliko god da je turbulenciju teško razumeti matematički,

we can use art to depict the way it looks.

možemo koristiti umetnost da bismo dočarali kako ona izgleda.

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

Juna 1889, Vinsent van Gog je naslikao pogled tik pre izlaska sunca

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

sa prozora svoje sobe u azilu Sen Pol de Mazol

in Saint-Rémy-de-Provence,

u San Remiju de Provans,

where he'd admitted himself after mutilating his own ear

gde se sam prijavio nakon što je osakatio sopstveno uvo

in a psychotic episode.

tokom psihotične epizode.

In "The Starry Night," his circular brushstrokes

U "Zvezdanoj noći", njegovi kružni potezi četkice

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

stvaraju noćno nebo ispunjeno uskovitlanim oblacima i vrtlozima zvezda.

Van Gogh and other Impressionists represented light in a different way

Van Gog i drugi impresionisti su prikazivali svetlo na drugačiji način

than their predecessors,

od svojih prethodnika, čineći se da hvataju njegovo kretanje,

seeming to capture its motion, for instance,

na primer, kroz vodu prošaranu suncem,

across sun-dappled waters,

or here in star light that twinkles and melts

ili ovde u svetlu zvezde koje treperi i nestaje

through milky waves of blue night sky.

kroz mlečne talase plavog noćnog neba.

The effect is caused by luminance,

Ovaj efekat stvara osvetljenost,

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

intenzitet svetline boja na platnu.

The more primitive part of our visual cortex,

Primitivniji deo našeg vizuelnog korteksa,

which sees light contrast and motion, but not color,

koji vidi kontraste svetlosti i kretanje, ali ne i boju,

will blend two differently colored areas together

stopiće dve različito obojene oblasti u jednu

if they have the same luminance.

ako imaju istu osvetljenost.

But our brains' primate subdivision

Ali primitivni pododeljci našeg mozga

will see the contrasting colors without blending.

videće kontrastne boje bez mešanja.

With these two interpretations happening at once,

Sa ove dve interpretacije koje se dešavaju istovremeno,

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

svetlo u mnogim radovima impresionista

izleda kao da pulsira, treperi i čudno zrači.

That's how this and other Impressionist works

Tako ovo i druga dela impresionista koriste brzo povučene

use quickly executed prominent brushstrokes

istaknute poteze četkice da bi uhvatili nešto zapanjujuće stvarno

to capture something strikingly real about how light moves.

o tome kako se svetlo kreće.

Sixty years later, Russian mathematician Andrey Kolmogorov

60 godina kasnije, ruski matematičar Andrej Kolmogorov

furthered our mathematical understanding of turbulence

produbio je naše matematičko razumevanje turbulencije

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

kada je izneo da energija turbulentnog fluida na dužini R

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

varira u razmeri od 5/3 snage R.

Experimental measurements show Kolmogorov

Eksperimentalna merenja pokazuju da je Kolmogorov

was remarkably close to the way turbulent flow works,

bio zapanjujuće blizu načinu na koji turbulentan protok radi,

although a complete description of turbulence

mada potpuni opis turbulencije ostaje

remains one of the unsolved problems in physics.

jedan od nerešenih problema u fizici.

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

Turbulentni protok liči na sebe ako postoji kaskadna energija.

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

Drugim rečima, veliki vrtlozi prenose svoju energiju na male vrtloge,

which do likewise at other scales.

koji rade to isto u drugim razmerama.

Examples of this include Jupiter's Great Red Spot,

Primeri ovoga obuhvataju veliku crvenu tačku Jupitera,

cloud formations and interstellar dust particles.

formacije oblaka i međuzvezdane čestice prašine.

In 2004, using the Hubble Space Telescope,

2004. godine, koristeći Habl svemirski teleskop,

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

naučnici su videli vrtloge udaljenih oblaka

prašine i gasa koji okružuju zvezdu,

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

i to ih je podsetilo na "Zvezdanu noć" od Van Goga.

This motivated scientists from Mexico, Spain and England

Ovo je motivisalo naučnike iz Meksika, Španije i Engleske

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

da detaljno izučavaju osvetljenost na Van Gogovim slikama.

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

Otkrili su da postoji izražen šablon struktura turbulentnog fluida

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

blizak Kolmogorovoj jednačini skriven u mnogim slikama Van Goga.

The researchers digitized the paintings,

Istraživači su digitalizovali slike

and measured how brightness varies between any two pixels.

i izmerili kako svetlina varira između bilo koja dva piksela.

From the curves measured for pixel separations,

Na osnovu kriva koje su izmerene zbog razdvajanja piksela,

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

zaključili su da se slike iz perioda psihotične pometnje Van Goga

behave remarkably similar to fluid turbulence.

ponašaju neverovatno slično fluidnoj turbulenciji.

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

Njegov autoportret sa lulom, iz mirnijeg perioda Van Gogovog života,

showed no sign of this correspondence.

nije pokazivao znake ove podudarnosti.

And neither did other artists' work

A nisu ni radovi drugih umetnika

that seemed equally turbulent at first glance,

koji su izgledali jednako turbulentno na prvi pogled,

like Munch's "The Scream."

kao što je Munkov "Vrisak".

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

Mada je lako reći da je Van Gogov turbulentni genije

enabled him to depict turbulence,

omogućio da prikaže turbulenciju,

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

takođe je suviše teško precizno izraziti uzbudljivu lepotu činjenice

that in a period of intense suffering,

da je u periodu intenzivne patnje

Van Gogh was somehow able to perceive and represent

Van Gog nekako mogao da vidi i prikaže

one of the most supremely difficult concepts

jedan od krajnje najtežih koncepata

nature has ever brought before mankind,

koji je priroda ikada iznela pred čovečanstvo,

and to unite his unique mind's eye

i da ujedini oči svog jedinstvenog uma

with the deepest mysteries of movement, fluid and light.

sa najdubljim misterijama kretanja, fluida i svetlosti.