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In 1888, Vincent van Gogh cut off his earlobe. Biographers and psychiatrists have been trying to explain this act ever since. But mathematicians approached the mystery differently: they measured how the artist's feelings changed in his letters and how the 'nervousness' of his brushstrokes grew, and they saw a clear signal of impending trouble.

A swing that gets pushed usually swings and quickly calms down. But if the swing is nearly broken, each swing lasts longer, and returning to rest becomes harder. The same principle—'critical slowing down' (prolonged return to equilibrium)—is what scientists looked for in Van Gogh's mental state. They ran 727 letter fragments through a computer program, assessing how often words about melancholy, desire for death, or fear appeared. In parallel, for 569 paintings, they calculated the fractal dimension — simply put, they measured how densely and restlessly the lines on the canvas intertwine. The higher the number, the more fine details and 'jitter' in the composition.

The most striking signal came from the 1888 incident. A few months before it, three indicators at once (readiness for dangerous acts, attraction to death, and visual complexity of the canvases) spiked sharply and began to fluctuate wildly. And a couple of weeks before the crisis, the fluctuations suddenly subsided, as if the system froze for a moment before the breakdown. After the event, the indicators stabilized again, but at a new, more alarming level. This picture closely resembles the behavior of a sick ecosystem before collapse or climate before a sharp regime shift.

This approach could be useful not only for history. If we learn to detect 'slowing down' in a person's language, behavior, or creativity in advance, we might predict severe psychological breakdowns, and intervene before the swing breaks.

Original abstract

as written by the authors arXiv:2607.23457

Vincent van Gogh's prolific artistic output and personal correspondence offer a unique window into the psychological trajectory of a 19th-century artist. This study applies computational methods to analyze emotional patterns across van Gogh's final decade through sentiment analysis of over 700 letter segments and fractal dimension analysis of 569 paintings. Using critical slowing down (CSD) theory from dynamical systems, we examine whether van Gogh's psychological system exhibited mathematical signatures of approaching tipping points. Our analysis reveals a statistically significant correlation between visual complexity and death sentiment ($$r = 0.193, p < 0.001, n = 524$$), alongside evidence for CSD patterns in multiple psychological dimensions before major crises. The 1888 ear incident shows coordinated variance spikes across acquired capability, desire for death, and visual complexity preceding the event, followed by stabilization before the crisis. These findings demonstrate that mathematical approaches can detect psychological transition signatures in historical figures while revealing the complex multi-modal nature of psychological systems.