ART experts have long marvelled at the emotional chaos apparent in the later paintings of the Dutch artist Vincent Van Gogh. Perhaps that is because the images reflect light in a way that mimics the physics of turbulence.
At least that鈥檚 the view of a team of physicists led by Jose Luis Aragon of the National Autonomous University of Mexico, who analysed several of Van Gogh鈥檚 later paintings, including Starry Night, Road with Cypress and Star (see below) and Wheat Field with Crows.
Mathematically, they studied how the luminosity, which is a measure of the total amount of visible light reflected off the paintings, varied across the canvas. Specifically, they analysed the likelihood that two points a distance D apart would have the same, or similar, brightness. In each of the paintings, they found that points further apart were statistically less likely to have similar luminosities.
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This in itself is not surprising. But this probability decreased in a very simple way, in proportion to the distance between the points, D, raised to some power.
This pattern is significant. The very same pattern characterises variations in fluid velocity at different points in a churning, turbulent liquid, a property called Kolmogorov scaling, after the Russian physicist Andrei Kolmogorov. 鈥淪ome art critics have said that Van Gogh鈥檚 paintings give the impression of looking through a turbulent atmosphere,鈥� says team member Gerardo Naumis. 鈥淏ut we were very, very surprised by the close link to Kolmogorov鈥檚 theory.鈥�
鈥淎 strong sense of turbulence appeared only in the paintings created during times when he was psychologically disturbed鈥�
Also surprising is the difference between Van Gogh鈥檚 later and earlier work. The pattern of luminosity in the paintings Van Gogh created during periods of emotional calm bears little resemblance to real-world turbulence. A strong visual sense of turbulence, apparent also in the mathematical analysis, appeared only in paintings created during times when he was psychologically disturbed. Van Gogh painted his famous Starry Night, for example, during a year spent in an asylum. In contrast, he completed his Self-Portrait with Pipe and Bandaged Ear in a state of self-described 鈥渁bsolute calm鈥�. Mathematically, this work lacks the signature of turbulence ().
Naumis speculates that there could be some link between fluid turbulence and the dynamics of neural processes in disturbed individuals, and that mathematics might provide a means for detecting psychic disturbance through the analysis of drawings. 鈥淭he work so far is only a first step,鈥� he says. 鈥淲e need to apply it to patients and see if it works.鈥�
