If there is one thing that someone born in Pamplona, like the author of this article, can assure you, it is that being inside the Town Hall Square during the San Fermín "chupinazo" is a unique experience. It is the closest thing to being a tiny particle trapped in a dense, chaotic, and constantly moving space—except that the other 'particles' are wearing red scarves and have likely had more wine for breakfast than advisable. But what was once just a personal impression has recently gained scientific backing.

A study published in Nature by a team led by Denis Bartolo, a professor at the École Normale Supérieure de Lyon, in collaboration with Iker Zuriguel from the University of Navarra, has analyzed this phenomenon rigorously for the first time.

These researchers have conducted a meticulous four-year observation of how thousands of people (around 5,000), packed like sardines in the Consistorial Square during the chupinazo, end up moving in a coordinated manner without any explicit guidance. According to their analysis, when the crowd reaches a critical density threshold (about four people per square meter), it transitions from a disordered state to an emergent phenomenon of collective oscillations, in which hundreds of individuals synchronize into a swaying, orbital movement.

The significance of this discovery goes beyond a mere festive anecdote. The phenomenon observed in Pamplona is a benign version of what can happen in extreme danger situations, such as the 2010 Love Parade tragedy in Duisburg, where the researchers also identified the presence of these oscillations before the deadly stampede that claimed 21 lives.

The study does not stop at mere empirical description. Based on principles of fluid mechanics, the researchers have developed a model that predicts how these oscillations emerge and how they could be monitored in real time. Simply put: if we can determine the point at which a crowd stops behaving as a collection of individuals and starts acting as a single oscillating entity, we could identify when a controlled situation might escalate into disaster.

For those of us who have experienced the chupinazo firsthand and have a background in physics, the idea that the crowd’s pushes and movements can be described by differential equations is both fascinating and unsettling. However, the study of crowd dynamics not only helps us understand the frenzy of San Fermín but also allows us to identify behavioral patterns that could be crucial in anticipating and preventing accidents at large-scale events. Being able to monitor and predict these collective flows is essential for ensuring safety and optimizing the management of massive gatherings.

So next time someone asks me what it feels like to be at the heart of the chupinazo, I won’t have to resort to vague metaphors. Now I can answer with precision: "It’s a density-driven phase transition that gives rise to collective oscillations." And then, raise a toast to it.

This article is an excellent example of how experimental observations, computational simulations, and mathematical analysis complement each other in scientific research. The question at hand is simple and has two parts: Is it possible for a crowd to exhibit coordinated movements in the absence of external stimuli? And through what mechanism?

A starting point could be to abstract each person as an object that consumes energy to move in a particular direction—what is known as a self-propelled agent. Systems composed of such agents have been of special interest to the physics community because, despite their simplicity, they display various types of collective behaviors.

For instance, when these agents are introduced into an enclosed space, interactions between them can lead to circular trajectories, also known as oscillations. This phenomenon has been observed and modeled in various systems, from bacteria to self-propelled robots. Therefore, the researchers' observations of human crowds, along with their proposed model, align closely with existing literature on the subject and serve as a valuable complement to models that study movement in smaller groups. Notably, the methodology used to analyze data and images in this study is explained in detail and utilizes open-source code, making it easily applicable to new observations.

In short, the model suggests that the origin of these oscillations lies in a continuous mismatch between the direction a person wants to move and the direction they are actually moving—affected by being pushed or blocked by others and by the surrounding walls. The intention to move in a particular direction, unlike position and velocity, is difficult to measure experimentally as it involves psychological and environmental factors. To address this, the researchers constructed this variable following an established approach in physics: assuming that every individual in the crowd is identical to the others and that their environment is uniform. This approximation facilitates mathematical calculations and produces results that closely match real-world observations. As a possible extension, it would be interesting to study the effects of an environment with variations or the influence of ‘guide’ individuals who affect group behavior more strongly than the rest.

A key prediction of the model, which aligns with experimental observations, is that the emergence of these oscillations depends on the number of people per square meter, meaning a safety threshold could be established to prevent their occurrence. Another point highlighted in related studies—and suggested by this article as well—is that oscillations in enclosed systems depend on the geometry of the boundaries. Therefore, studying the design of spaces to dissipate unwanted oscillations could help minimize the risk of crush-related accidents.