Physics to understand the unpredictable

Writing / Irene Vega

Multistable systems are those that present several stable solutions depending on the initial conditions. Their application includes problems as diverse as predicting which side a coin or die will land on, elucidating whether a given species will become extinct or survive in a specific ecosystem, or knowing whether a gene will express a given protein or not under certain conditions.

A group of physicists from the URJC has been studying these systems for years and, as a result of all this research, has been invited to publish an article on these complex problems in the prestigious journal Physics Today. The work can be consulted at the magazine website.

“Nonlinear dynamics has been studying this type of problem for decades and creating tools to quantify its unpredictability,” says Miguel AF Sanjuán, leader of the Nonlinear Dynamics and Complex Systems Group. “The difficulty in prediction is fundamentally associated with the appearance of fractal structures,” says the URJC professor.

Fractals are geometric objects, such as triangles or spheres, but unlike these they present complexity at different scales, as happens, for example, with a coastline in which nooks and crannies appear as it grows. zoom meeting. This recurring complexity means that increasing precision does not necessarily mean improving prediction. “Fractals are the geometry of chaos,” says Álvar Daza, professor of Physics at the URJC and associate professor of the Harvard Physics Department.

The difficulty in obtaining a prediction makes it necessary to develop new techniques that allow these structures to be classified and their associated unpredictability to be quantified. “In some situations, the slightest numerical or experimental error can make it impossible to calculate the final state of the system, even though the equations that describe its evolution are completely deterministic,” describes Daza, who adds that “there is a whole zoo of different fractal structures with surprising properties.”

Can we predict whether it will be heads or tails?

Tossing a coin or a die may seem like a fair method for making a random decision, but to what extent do we have control over the outcome of the toss? “Newtonian mechanics predicts with great accuracy the motion of macroscopic objects such as projectiles, so in principle it can also be used to describe what happens to a coin or a die. Any second-year physics student is able to write the classical mechanics equations that model the motion of a disk or a cube. In fact, by being careful when tossing, by dropping the coin from a small height and without letting it spin, for example, it is quite easy to guess the final result,” says Miguel AF Sanjuán.

However, the difficulty in prediction makes coins and dice paradigms of randomness. Therefore, a thorough understanding of these systems allows us to use chaos to select the final result. “It is possible to use the sensitivity of chaotic systems to control them through small but well-directed actions,” says Alexandre Wagemakers, professor of Physics at the URJC. In addition, these theoretical tools can be applied in a multitude of contexts that go far beyond simple coins and dice. “Multistability is a phenomenon that appears in scientific disciplines ranging from genetic networks to general relativity or neuroscience,” says Wagemakers. “Investigating its foundations can help the development of areas apparently as far apart as artificial intelligence or ecology,” he concludes.

Image: Fractal attraction basin in which each color represents a possible final state of the system (like the faces of a die).

In some areas, the slightest error can lead to completely wrong predictions.