- A branch of mathematics called chaos theory examines how small changes to a system can cause 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 overall movements.
“Does the flapping of a butterfly’s wings in Brazil set off a tornado in Texas?” It might sound like the kind of question science fiction explorers ask to reveal the precariousness of time travel, but it’s actually the title of an MIT professor 1972 card 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 sounds far-fetched, the analogy actually highlights an idea behind everything from planetary motion to climate change: chaos.
More precisely, this example works to explain a type of mathematics called chaos theory, which examines how small changes made to the initial conditions of a system, such as the extra gust of wind from a butterfly’s wings, can result in seemingly unpredictable behavior. (For example, a tornado in Texas.)
More from popular mechanics
Although mathematicians today would not necessarily call themselves chaos theorists, theory plays a role in the study of dynamical systems, which Kevin Linassociate professor of mathematics at the University of Arizona, says it helps us study everything from climate change to neuroscience.
“Chaos is a fact … and it’s part of dynamical systems theory,” Lin explains Popular mechanics in an email. “Some systems are inherently chaotic, while others are not. lot of [mathematicians] they 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 may be known to have coined the “butterfly effect” in connection with chaos theory, Lin claims that the discovery of chaos theory actually dates back to the 1890s and to a mathematician and physicist named Henri Poincaré. In his relatively short life, Poincaré had an impact on a wide range of topics, from gravitational waves to quantum mechanics.
These efforts also included explaining why the famous three-body problem, which seeks to explain the motion of three planetary bodies in orbit relative to each other, could not be solved. Chief among these reasons was that the system was sensitive to small, unpredictable perturbations … AKA, chaos.
“Before Poincaré, mathematicians who studied dynamics, that is, the behavior of systems governed by differential equations … focused on one solution at a time,” says Lin. “Poincaré has introduced concepts and tools for thinking about dynamics ‘globally’, or how entire sets of solutions evolve over time”.
While he wasn’t the first to come up with the idea, it was Lorenz’s discovery of chaos that “broke into popular culture”, Marco Levisays the professor and head of the Penn State math department Popular mechanics in an email.
Butterfly analogy aside, Lorenz’s discovery was actually made using one of the first computers to study weather models. When he again ran a weather simulation from part of his calculation of him, Lorenz was surprised to see that the same data and conditions had somehow made drastically different predictions. Apparently, the difference boiled down to the significant figures used by the computational machine, demonstrating that systems such as weather models can be very sensitive to their initial conditions.
it’s chaos Always unpredictable?
Although many natural systems have chaotic behavior, this does not necessarily mean that they are all unpredictable or nondeterministic. When studying how these systems behave phase space—A kind of multidimensional map of system states over time — researchers have identified patterns that help them predict the overall motion of a system.
As gravity attracts planetary bodies or an ocean current directs sea creatures, the researchers found that there are invisible “attractors” that chaotic systems are attracted to. These attractors look different for different systems, but often take the form of recursive fractal shapes.
Unfortunately, finding an attractor for any kind of chaotic system is a pipe dream, says Levi.
“Even ridiculously simple systems, such as a pendulum with a swinging pivot, are chaotic and too complex for a complete understanding, no matter the movement 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. As part of his research, Lin uses dynamics to study how the seemingly random activations 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 closely,” he says. “However, it works very reliably. Here is a conundrum: How can something seemingly random encode and process information reliably? “
Scientists and mathematicians still don’t have a clear answer to this question, but Lin says he is enjoying the journey into chaos. “At least for me,” Lin says, “it’s fun!”
Sarah is a Boston-based science and technology journalist interested in how innovation and research intersect with our daily lives. She has written for numerous national publications and deals with innovation news on Reverse.