Chaos theory explains why life gets so incredibly messy

  • A branch of mathematics called chaos theory examines how small changes to a system can lead to unpredictable behavior.
  • Chaos theory explains how complex systems work in multiple fields, including astrophysics, climate change, and neuroscience.
  • Chaos doesn’t always mean systems are totally unpredictable. Researchers have identified patterns that help them predict global movements.

“Does the flapping of a butterfly’s wings in Brazil trigger a tornado in Texas?” It may sound like the type of question science fiction explorers ask to reveal the insecurity of time travel, but it’s actually the title of an MIT professor. 1972 paper presented in a Sheraton conference room to members of the American Association for the Advancement of Science.

Meteorologist Edward Lorenz wrote the article, and while the concept seems far-fetched, the analogy highlights an idea underlying everything from planetary motion to climate change: chaos.

Specifically, this example helps explain a kind of math called chaos theory, which examines how small changes to the initial conditions of a system, like the extra gust of wind from a butterfly’s wings, can cause behavior seemingly unpredictable. (For example, a tornado in Texas.)

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While mathematicians would not necessarily call themselves chaos theorists today, theory plays a role in the study of dynamical systems, which Kevin Linassociate professor of mathematics at the University of Arizona, helps us study everything from climate change to neuroscience.

“Chaos is a fact of life…and part of dynamical systems theory,” Lin told Popular mechanics in an email. “Some systems are inherently chaotic, while others are not. Many [mathematicians] are also very interested in how certain systems can exhibit both types of behavior and the transition between these different regimes under different conditions.

The origins of chaos theory

While Lorenz might be known for inventing the “butterfly effect” in relation to chaos theory, Lin says the discovery of chaos theory actually dates back to the 1890s and a mathematician and physicist named Henri Poincaré. During his relatively short life, Poincaré had an impact on a wide range of subjects, from gravitational waves to quantum mechanics.

These efforts also included explaining why the famous three-body problem – which attempts to explain the motion of three planetary bodies orbiting each other – could not be solved. Chief among these reasons was that the system was susceptible to small, unpredictable disturbances…AKA, chaos.

sun, moon, earth and star field

photovideostock//Getty Images

“Before Poincaré, mathematicians who studied dynamics, that is, the behavior of systems governed by differential equations…focused on one solution at a time,” Lin says. “Poincaré introduced concepts and tools for thinking ‘globally’ dynamics, that is, how entire sets of solutions change over time.”

Although he was not the first to the idea, it was Lorenz’s discovery of chaos that “erupted into popular culture”. Marc Leviprofessor and head of the math department at Penn State, says Popular mechanics in an email.

Aside from the butterfly analogy, Lorenz’s discovery was actually made while using an early computer to study weather patterns. When re-running a weather simulation halfway through his calculation, Lorenz was surprised to see that the same data and conditions somehow made drastically different predictions. Ultimately, the difference came down to the significant digits used by the machine for the calculation, demonstrating that systems such as weather can be very sensitive to their initial conditions.

is chaos Always unpredictable?

Although many natural systems exhibit chaotic behavior, this does not necessarily mean that they are all unpredictable or non-deterministic. By studying the behavior of these systems in phase space— a sort of multidimensional map of system states over time — researchers have identified patterns that help them predict the overall motion of a system.

lorenz attractor, artwork

Artwork of a Lorenz attractor, named after Edward Lorenz, who developed a system of ordinary differential equations. The Lorenz attractor is a set of chaotic solutions of the Lorenz system which, when plotted, look like a butterfly or a figure eight. For the sensitivity of the system to initial conditions, Lorenz coined the term butterfly effect. This effect is the underlying mechanism of deterministic chaos.

PASIEKA//Getty Images

As gravity pulls planetary bodies or an ocean current directs sea creatures, researchers have discovered that there are invisible “attractors” that chaotic systems are drawn to. These attractors look different for different systems, but often take the form of recursive fractal shapes.

Unfortunately, finding an attractor for every type of chaotic system is a bit of a pipe dream, says Levi.

“Even ridiculously simple systems, like a pendulum with a swinging pivot, are chaotic and too complex to fully understand, let alone the motion of the atmosphere or the oceans,” he says.

How Chaos Helps Us Today

Chaos theory may be quite theoretical at this point, but the study of dynamical systems is much more tangible, Lin says. In his research, Lin uses dynamics to study how seemingly random firings of neurons in our brains transform into complex information systems.

“The brain is an example of a highly unpredictable system when you look at it up close,” he says. “Nevertheless, it works very reliably. Therein lies a conundrum: how can something seemingly random reliably encode and process information? »

Scientists and mathematicians don’t yet have a clear answer to this question, but Lin says he’s enjoying the ride through the chaos. “At least for me,” Lin said, “it’s fun!”

Sharon D. Cole