The Turbulent Twenties: What Van Gogh Teaches Us About the Mediation of Conflict
By Ambassador David L. Carden
The protracted conflicts in Ukraine, Gaza, and Myanmar, among others, reflect the challenge diplomats face in negotiating peace agreements. There are many reasons, among them the failure of those responsible for the negotiations to enter into, and be familiar with, physical spaces occupied by the combatants. This failure impacts their ability to speak the language of the parties and understand what is necessary on the ground to achieve a lasting agreement. The idea of entering into the world in order to fully understand how to resolve its challenges is something we intuitively understand. Yet, all too often we stand back.
It was with these thoughts in mind that I recently met with a colleague to discuss how to approach a resolution to the conflict in Ukraine. Following our meeting, I was invited to join a small group which was given a private, after-hours tour of the Van Gogh Exhibit at the National Gallery in London. My visit to the museum underscored the reason why physical presence and familiarity could make a positive contribution to resolving conflicts around the world.
Before we began the tour, the curator of the exhibit told us Van Gogh had predicted no one would understand what he was trying to do for a hundred years. Then, he added that it had not taken that long, as his paintings were widely appreciated shortly after his death in 1890. As I listened, I asked myself why Van Gogh thought it would take so long for his work to be understood, and whether the fact that his work had been appreciated more quickly really meant he had been mistaken.
I was interested because the process of understanding—what something means, what it requires of us, and why—is what connects us to the world, and to one another. It can create the opportunity for harmonizing hearts and minds. When we are not connected, it is difficult to build a peaceful, secure, prosperous world; the process of understanding is fundamental to our effort to create the world in which we want to live and to manage the inevitable conflicts that arise. As a mediator, I thought Van Gogh’s stated desire to speak the language of nature might offer some clues on how to approach the political, cultural, and religious conflicts among nations and within societies.
I was familiar with many of the paintings in the exhibit, but none more so than Starry Night. Starry Night is without doubt appreciated, and has been for a very long time. It is unquestionably one of the most famous paintings in the world, whose impact has been deeply felt, especially in the art world. It also has become iconic in popular culture, being reproduced on T-shirts, coffee mugs, mouse pads, eyeglass cleaners, and countless other objects. However, a 2024 mathematical analysis of Starry Night by Dr. Yongxiang Huang, of Xiamen University, suggests that although the painting has been appreciated, it has not been understood until recently.
Dr. Huang’s analysis of Starry Night revealed it depicts one of the most complicated and mysterious mathematical manifestations in nature—turbulence, which is characterized by chaotic changes in the movement of fluids and gases. Starry Night accurately reflects the underlying mathematics of “turbulence theory,” first articulated by Andrey N. Kolmogorov in 1941, fifty years after Van Gogh’s death. Kolmogorov’s theory posits the energy spectrum of turbulence is proportional, meaning larger eddies transfer their energy to smaller ones in a predictable ratio, approximately 5/3, or 1.6.
The ratio of energy transference in turbulence identified by Kolmorgorov is very close to the “golden” ratio of 1.618. Manifestations of the golden ratio are among nature’s languages, similar to Fibonacci spirals, which can be found in the human body, trees, leaves, pinecones, seashells, coastlines, and galaxies. Fibonacci spirals emerge from the math inherent in the “Fibonacci sequence,” in which any two adjacent numbers in the sequence sum to the one that follows them. Dividing any number in the sequence (other than in its first four iterations) by the number immediately preceding it (i.e., 34/21) always yields a number very close to the golden ratio of 1.618. Fibonacci spirals also are logarithmic, which means their curves are the same at every scale. This makes them fractals, which are self-similar, repeating geometric patterns.
I have not been able to find a mathematical analysis of any of Van Gogh’s other paintings, but the conclusion is inescapable that many of them reflect Fibonacci spirals and fractals. Notable examples include Wheatfield with Crows; Landscape with Wheat Sheaves and Rising Moon; The Sower; Irises; and Wheatfield with Cypresses. These paintings, as well as Starry Night and many others, are “full of fractals.” They also share another quality—they appear to move. The motion draws the viewer near, offering an invitation to enter into the world it depicts.
Mr. Huang’s analysis revealed how Van Gogh accomplished this illusion of motion. First, his brush strokes are segments of Fibonacci spirals. Second, different areas in the canvas have differences in luminance, the measure of the amount of light emitted or reflected from a particular object, or, in the case of a painting, area. The primitive part of our visual cortex, which does not see color, apprehends differences in luminance. It discerns contrast. When it does so, it blends areas with different luminance together. As this is happening, the occipital lobe sees the color of the areas but does not blend them. The result of this is the illusion of motion. Thus, the sky in Starry Night, which also is filled with large and small whorls reflecting Kolmogorov’s “turbulence ratio” of 5/3, appears to whirl and flicker.
Van Gogh’s efforts to “speak the language of nature” necessarily require us to consider the mathematical quality of the language that nature speaks. As Galileo observed, “[n]ature’s great book is written in mathematical language.” But, understanding turbulence has remained elusive. Thus, Richard Feynman, the Nobel Laureate physicist, called turbulence the most important unsolved problem in physics. Another Nobel Laureate physicist, Werner Heisenberg, observed: “When I meet God, I am going to ask him two questions: why relativity? And why turbulence? I really believe he will have an answer for the first.”
So how did Van Gogh manage to accurately depict turbulence if it is not fully understood? Dr. Huang has said the painting “reveals a deep and intuitive understanding of natural phenomena.” But calling it an understanding may be an overstatement. A more plausible answer is that Van Gogh’s “intuitive understanding” was the ability to observe and appreciate the natural world, thus enabling him to accurately depict what he had seen. We all try to do the same unconsciously, as we engage the world and one another. As A.N. Whitehead once said, “[a]ll knowledge is derived from and verified by direct intuitive observation.”
Was it Van Gogh’s effort to speak the “language of nature” that led him to believe he would not be understood for a century? It is impossible to know. But there is evidence beyond Dr. Huang’s findings that it was, and that the invitation the artist offered to the world to enter into his paintings suggests what it will take for us to manage our conflicts more successfully.
In a letter to his brother Theo, Van Gogh wrote of “the eternal law that everything changes.” Turbulence is one of the most visible proofs of the truth that nothing is permanent. Unsurprisingly, impermanence, like turbulence, has commanded the attention of mathematicians and physicists. Einstein’s observation that “[t]ime and space are modes by which we think, not conditions in which we live” is one example of this interest. Van Gogh, like Einstein, understood that time and space are not static, but rather a series of “happenings.” Everything is in motion, a truth he captured in his canvases that create the illusion of movement.
Additional support can be found in Van Gogh’s interest in Ukiyo-e, a genre of Japanese art from the 17th through 19th centuries that has been translated as “pictures of the floating world.” Van Gogh asked Theo to collect hundreds of Ukiyo-e prints and paintings, and even experimented with painting in a similar style. He admired one painting in particular, Hokusai’s famous The Great Wave off Kanagawa, painted in 1831. A quotation from Hokusai reveals why Van Gogh might have been so interested in The Great Wave, and why he thought it would take so long for him to be understood:
“When I was 50 I had published a universe of designs, but all I have done before the age of 70 is not worth bothering with. At 75, I’ll have learned something of the pattern of nature, of animals, of trees, birds, fish and insects. When I am 80, you will see real progress. At 90, I shall have cut my way deeply into the mystery of life itself. At 100 I shall be a marvelous artist. At 110, everything I create—a dot, a line—will jump to life as never before.” (emphasis added)
Like Starry Night, the mathematical structure of The Great Wave has been analyzed, revealing turbulence, Fibonacci spirals, and fractals. Some have argued Van Gogh was inspired by The Great Wave when he painted Starry Night.
Although neither Van Gogh nor Hokusai could have understood turbulence, Fibonacci spirals, or fractals, it is quite likely that they observed them. Both painters accurately “spoke” the language of nature. Because they did, they enabled those who see their work to see the world beyond themselves. Art has the capacity to harmonize hearts and minds because it allows us to get beyond ourselves. This has been a goal of art since Leon Baptiste Alberti, who in his book On Pictures, outlined the mathematics of linear perspective. The result was to pull people into canvases, to enter into the worlds artists create. Brian Greene, a Professor of theoretical physics and mathematics at Columbia University, suggested how powerful this process is when he observed that interest in mathematics, the science “behind the universe,” can lead to a more fulfilling life because its immutability allows us to transcend impermanence. The poet John Keats’ concept of negative capability in the art world is based upon a similar observation.
What, if anything, does this say about how we can manage our relationships with the world, and with one another? Just this—the magnetism of mathematics is undeniable, and its effect palpable, even when not fully understood. It is the mathematics of nature that puts us inside the frames of the worlds we observe. The mathematics Van Gogh captured, which pulls us into his paintings and out of ourselves, provides some idea of how we could engage the world, and one another, more successfully. The key is in observing the world of others more closely, and in creating spaces we can share and occupy together.
Van Gogh’s work, with its mathematical foundations, suggests that it is necessary to enter into physical spaces if we are to fully understand the world and one another. Understanding requires us to move, to enter into, and to occupy the spaces around us. Failure to do so is a failure to speak the language of those affected by the conflict being addressed. Reaching a long-term resolution of conflicts around the world, or within our own social, political and religious communities, requires nothing less than negotiators learning the language spoken on the ground. The failure to reach lasting accords in places like Gaza, Myanmar, and Ukraine reminds us what happens when they do not.
The same is true of our daily conflicts including commercial and domestic disputes. The architecture of any negotiations to manage such conflicts also would benefit from the lessons offered by Van Gogh and Hokusai—we are more likely to reach an accord if we allow ourselves to be pulled into the spaces inhabited by those with whom we are attempting to reach agreement. When we do so, we are able to be more empathetic and better able to understand what must be understood to find a resolution.
Van Gogh was a close observer of the natural world. As a result, he intuitively understood the language spoken there. It is a language we all share, offering us the chance to resolve our conflicts and find a common cause. The way to peace is for us to follow where Van Gogh tried to take us—to understand the empathy he encouraged with his art, the empathy found only in geographies beyond ourselves.
David L. Carden served as the first resident U.S. ambassador to the Association of Southeast Asian Nations. He is the author of Mapping ASEAN: Achieving Peace, Prosperity, and Sustainability in Southeast Asia and has written for Foreign Policy, Politico, the SAIS Review of International Affairs, the Guardian, the South China Morning Post, and Strategic Review, among others. He also is a mediator and serves on the Board of the Weinstein International Foundation, which promotes the use of mediation around the world.
Van Gough - Self Portrait 18 is by Michael Jones and is licensed under CC BY-NC-SA 2.0.
