- A branch of mathematics called chaos theory looks at how small changes in a system can lead to unexpected behavior.
- Chaos theory explains how complex systems work in multiple fields, including astrophysics, climate change, and neuroscience.
- Chaos doesn’t always mean that systems are completely unpredictable. The researchers identified patterns that help them predict general movements.

Did the flapping of butterfly wings in Brazil cause a hurricane in Texas? It might sound like the kind of question sci-fi explorers ask to reveal how dangerous time travel is, but it’s actually the title of the MIT Professor __paper 1972__ Presented in the Sheraton conference room for members of the American Association for the Advancement of Science.

Meteorologist Edward Lorenz wrote the research paper, and while the concept seems far-fetched, the analogy actually highlights the idea behind everything from planetary motion to climate change: chaos.

More precisely, this example serves to explain a type of mathematics called chaos theory, which looks at how small changes to the initial conditions of a system — such as an excessive gust of wind from a butterfly’s wings — can lead to seemingly unexpected behavior. (For example, a tornado in Texas.)

While mathematicians do not necessarily call themselves chaos theorists today, theory does play a role in the study of dynamical systems, which __Kevin Lane__an associate professor of mathematics at the University of Arizona, says it helps us study everything from climate change to neuroscience.

Lane explains: “Chaos is a fact of life…and part of the theory of dynamical systems.” *popular mechanics* in a letter. Some systems are inherently chaotic, while others are not. many [mathematicians] They are also interested in how certain systems display both types of behaviour, and the transition between these different systems under different conditions.”

**Chaos Theory Origins**

While Lorenz may be best known for coining the “butterfly effect” in relation to chaos theory, Lane says the discovery of chaos theory actually dates back to the 1890s and a mathematician and physicist named Henri Poincaré. In his relatively short life, Poincaré had an influence on a wide range of topics, 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 was that the system was sensitive to small, unpredictable disturbances…AKA, chaos.

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

Although not the first to come up with the idea, it was Lorenz’s discovery of chaos that “broke into popular culture”, __Mark Levy__professor and chair of the Department of Mathematics at Penn State, says *popular mechanics* in a letter.

Butterfly analogy aside, Lorenz was actually discovered when an early computer was used to study weather models. Rerunning the weather simulation from part of her computation, Lorenz was surprised to see that the same data and conditions somehow made wildly different predictions. As it turns out, the difference is down to the important numbers the machine uses for the computation, which shows that systems like weather patterns can be very sensitive to their initial conditions.

**Is chaos ****Always unpredictable?**

While many natural systems have chaotic behaviour, this does not necessarily mean that they are all unpredictable or non-deterministic. When studying how these systems work __stage space__A kind of multidimensional map of the states of a system over time Researchers have identified patterns that help them predict the system’s overall motion.

Like gravity that attracts planetary bodies or an ocean current that draws marine creatures, researchers have found that there are invisible “attractors” that chaotic systems are attracted to. These attractants look different for different systems, but often take the form of repeating fractal shapes.

Unfortunately, Levy says, finding an attraction for every kind of chaotic system is a pipe dream.

“Even ridiculously simple systems, such as an oscillating pendulum, are too chaotic and complex to fully understand – regardless of the movement of the atmosphere or oceans,” he says.

**How can chaos help us today**

Chaos theory may be somewhat theoretical at this point, but the study of dynamical systems is more realistic, says Lin. As part of his research, Lin uses dynamics to study how the random fires of neurons in our brains transform into complex information systems.

“The brain is an example of a system that is highly unpredictable when you look at it closely,” he says. “However, it works very reliably. And herein lies the mystery: How can something seemingly random can reliably encode and process information?”

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

Sarah is a Boston-based science and technology journalist with an interest in how innovation and research intersect with our daily lives. She has written for a number of national publications covering innovation news in *inverse*.

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