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."
Jedan od najizuzetnijih aspekata ljudskog mozga jeste njegova mogućnost da prepozna šablone i da ih opiše. Među najtežim šablonima koje smo pokušali da razumemo jeste koncept turbulentnog protoka u dinamici fluida. Nemački fizičar Verner Hajzenberg je rekao: "Kada sretnem Boga, postaviću mu dva pitanja: zašto relativnost i zašto turbulencija? Verujem da će imati odgovor na prvo."
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.
Koliko god da je turbulenciju teško razumeti matematički, možemo koristiti umetnost da bismo dočarali kako ona izgleda. Juna 1889, Vinsent van Gog je naslikao pogled tik pre izlaska sunca sa prozora svoje sobe u azilu Sen Pol de Mazol u San Remiju de Provans, gde se sam prijavio nakon što je osakatio sopstveno uvo tokom psihotične epizode. U "Zvezdanoj noći", njegovi kružni potezi četkice stvaraju noćno nebo ispunjeno uskovitlanim oblacima i vrtlozima zvezda. Van Gog i drugi impresionisti su prikazivali svetlo na drugačiji način od svojih prethodnika, čineći se da hvataju njegovo kretanje, na primer, kroz vodu prošaranu suncem, ili ovde u svetlu zvezde koje treperi i nestaje kroz mlečne talase plavog noćnog neba. Ovaj efekat stvara osvetljenost, intenzitet svetline boja na platnu. Primitivniji deo našeg vizuelnog korteksa, koji vidi kontraste svetlosti i kretanje, ali ne i boju, stopiće dve različito obojene oblasti u jednu ako imaju istu osvetljenost. Ali primitivni pododeljci našeg mozga videće kontrastne boje bez mešanja. Sa ove dve interpretacije koje se dešavaju istovremeno, svetlo u mnogim radovima impresionista izleda kao da pulsira, treperi i čudno zrači. Tako ovo i druga dela impresionista koriste brzo povučene istaknute poteze četkice da bi uhvatili nešto zapanjujuće stvarno o tome kako se svetlo kreće.
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.
60 godina kasnije, ruski matematičar Andrej Kolmogorov produbio je naše matematičko razumevanje turbulencije kada je izneo da energija turbulentnog fluida na dužini R varira u razmeri od 5/3 snage R. Eksperimentalna merenja pokazuju da je Kolmogorov bio zapanjujuće blizu načinu na koji turbulentan protok radi, mada potpuni opis turbulencije ostaje jedan od nerešenih problema u fizici. Turbulentni protok liči na sebe ako postoji kaskadna energija. Drugim rečima, veliki vrtlozi prenose svoju energiju na male vrtloge, koji rade to isto u drugim razmerama. Primeri ovoga obuhvataju veliku crvenu tačku Jupitera, formacije oblaka i međuzvezdane čestice prašine.
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.
2004. godine, koristeći Habl svemirski teleskop, naučnici su videli vrtloge udaljenih oblaka prašine i gasa koji okružuju zvezdu, i to ih je podsetilo na "Zvezdanu noć" od Van Goga. Ovo je motivisalo naučnike iz Meksika, Španije i Engleske da detaljno izučavaju osvetljenost na Van Gogovim slikama. Otkrili su da postoji izražen šablon struktura turbulentnog fluida blizak Kolmogorovoj jednačini skriven u mnogim slikama Van Goga.
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."
Istraživači su digitalizovali slike i izmerili kako svetlina varira između bilo koja dva piksela. Na osnovu kriva koje su izmerene zbog razdvajanja piksela, zaključili su da se slike iz perioda psihotične pometnje Van Goga ponašaju neverovatno slično fluidnoj turbulenciji. Njegov autoportret sa lulom, iz mirnijeg perioda Van Gogovog života, nije pokazivao znake ove podudarnosti. A nisu ni radovi drugih umetnika koji su izgledali jednako turbulentno na prvi pogled, kao što je Munkov "Vrisak".
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.
Mada je lako reći da je Van Gogov turbulentni genije omogućio da prikaže turbulenciju, takođe je suviše teško precizno izraziti uzbudljivu lepotu činjenice da je u periodu intenzivne patnje Van Gog nekako mogao da vidi i prikaže jedan od krajnje najtežih koncepata koji je priroda ikada iznela pred čovečanstvo, i da ujedini oči svog jedinstvenog uma sa najdubljim misterijama kretanja, fluida i svetlosti.