LARGE DEVIATIONS

EMERGENCE

Flocks of birds sweeping across the sky in perfect harmony, a colony of ants collaborating to build intricate nests, the precise choreography of fish in a school—such natural phenomena can leave us marveling at their complexity. What dictates them? And who is the masterful director behind it all?

In scientific terms, the study of scenarios where many individuals interact in a larger entity is related to the field of complex systems. The key concept here is emergence: complex, collective behavior emerges from simple, individual rules. Surprisingly, in many cases, collective behavior is not led by a single leader or guided by a master plan. Instead, it naturally builds up from individuals cooperating, sharing simple messages with neighbors, and adapting to the response of the surroundings. These informational feedback loops and small-scale communications quickly spread to the entire group, creating a kind of group intelligence.

Take again the example of a flock of birds. Each bird follows a few basic rules—stay close, avoid collisions, move with nearby neighbors—yet the outcome is a unified, fluid movement. Ants, too, follow simple chemical trails left by their fellow workers to create complex networks of tunnels and paths, optimizing their colony's efficiency. Even in human crowds, when the density reaches a certain point, we naturally organize into orderly queues without any explicit instruction or directive—simply by following our peers and adapting to our surroundings.

Metaphorically, something similar occurs when people gather together to run together. The collective energy and rhythm of the group create an experience greater than the sum of individual efforts. Synchronized strides, shared goals, visual cues, and mutual encouragement emerge naturally from participants' interactions, transforming the crowd into a single, cohesive entity.

These patterns emerge from the interactions of each individual, without laws from the outside or central plans, yet displaying a bottom-up collective purpose and intelligence. In this sense, emergence reveals that simplicity gives rise to beautiful complexities, where elementary underlying structures leverage order within the disorder.

METASTABILITY

It is hard to stand still on a single leg. Yet we do it every day when going for a walk, a jog, or playing any kind of sport. At each step, we purposely lose our balance to move in space. Let’s take a step back.

Take a system. The notion of stability is related to what happens when it is perturbed in some way: does it go back to its original configuration, or will it drift away from it? Consider a pendulum. Once set in motion, it oscillates, gradually slowing down over time until it comes to rest. From that point onward, the system will forever remain identical to itself unless perturbed again. This behavior reflects the tendency of each physical system to move toward an energy minimum, where perturbations cannot alter its configuration.

However, equilibrium points don’t always correspond to the lowest energy state. Imagine a wavy landscape with slopes, peaks, and valleys, and a ball rolling across it. When the ball sits at the top of a hill, it is in unstable equilibrium—any small disturbance will cause it to roll away. Conversely, if it settles in a valley, it reaches a stable state.  What if it gets stuck in a place that is not the absolute lowest? These are metastable points: the system is not where it “would like to be”, but remains stable under small perturbations. In a world of countless complexities and factors acting together, metastability is an unavoidable effect encountered in nature.

A typical example of metastability might have occurred in your freezer. If the water is sufficiently pure, it can avoid reaching the state with minimum energy and instead remain in the metastable state of supercooling—staying liquid even at temperatures below 0°C. However, if a strong enough perturbation occurs, such as a shake or the act of pouring the water, the system can rapidly transition to its stable equilibrium, forming ice crystals almost instantly.

The ability to shift between equilibrium states enables systems to adapt, respond to stimuli, and reorganize without collapsing. For example, neural circuits in the human brain operate in metastable states: stable enough to store memories yet plastic enough to adapt to new inputs and information. A similar concept applies to evolutionary processes, as proposed in the theory of punctuated equilibrium. Over generations, small mutations act as perturbations to a metastable state, typically being reabsorbed unless they confer a significant advantage in natural selection. When such a beneficial change occurs, it often triggers a rapid transition to a new equilibrium.

Metastable equilibrium represents the continuous tension between stability and transformation, between maintaining a form and opening up to new possibilities. In this sense, for any living system, movement is never just moving through space, but also a creative condition, a state of passage in which each being finds its individuality in its continuous process of change.

GLOBAL POSITIONING SYSTEM

GPS, short for Global Positioning System, is a satellite-based network that enables precise tracking of locations, distances, and movements. Not only it guides us through unfamiliar cities but it also plays a role in transportation systems.

The location is retrieved using a method called trilateration. This technique determines the position of a point in space by measuring its distance from at least four reference points, which in this case are the GPS satellites. Each distance measurement defines spheres centered on the respective satellites, and the intersection of these four spheres pinpoints the target’s exact location. To ensure global coverage, the satellites orbits are designed so that nearly every point on Earth is always within range of at least four satellites.

Once a receiver (our smartphone or a GPS watch, for example) establishes a connection, it calculates distances using the information transmitted by the satellites. Each sends signals traveling at the speed of light accompanied by a time-stamp indicating the exact emission time. The receiver compares the time with its own clock: this time delay, typically measured in the microsecond range, is then used to compute the distances.

The most significant correction accounts for atmospheric delays, as signals slow down when passing through different layers of the atmosphere. Relativistic effects are also critical; according to General Relativity, satellite clocks tick faster than those on Earth due to their weaker exposure to Earth's gravitational pull. Additionally, multipath effects—caused by signal reflections off surfaces—are mitigated through advanced receiver algorithms. Although the system has been operational since the 1990s, it requires continuous monitoring and adjustments by ground stations to apply these corrections, ensuring GPS accuracy within a few meters.

Isn’t it possible that GPS comes from our own insecurity and fear of disorientation? It is a relief to that feeling, making the world feel just a little smaller and more within our grasp.