The weather forecast for three hours from now is very likely to be accurate. However, a forecast for next week is rarely confirmed. The difference lies not in the quality of the equipment or the amount of data, but in the characteristics of the atmosphere itself, which is influenced by many variables. This sensitivity is at the heart of chaos theory.

From it came the metaphor that crossed academic walls and reached cinema, literature, and everyday conversation: the idea that the flapping of a butterfly's wings in one place can trigger a tornado in another. The butterfly effect is now used to explain everything from ecosystems to economic decisions—and even to think about how individual choices can generate major effects on the environment.

What is chaos theory

First of all, it is necessary to separate the word from the theory. "When we look for the meaning of chaos in the dictionary, we find definitions like a state of complete disorder, generalized confusion, or a total absence of rules," explains Kelly Cristiane Iarosz, a physicist and professor at the Center for Natural and Human Sciences at the Federal University of ABC (UFABC), where she researches dynamic and complex systems.

The theory, however, is not about messiness. It is an area of science dedicated to phenomena that evolve over time and in which several elements interact simultaneously. "A chaotic phenomenon follows rules. The problem is that, in certain situations, it is so sensitive to initial conditions that almost imperceptible differences can be amplified, making it very difficult to predict exactly what will happen," the researcher details. This is known as sensitivity to initial conditions.

To translate the idea, Tiago Pereira, a professor at the Institute of Mathematical and Computer Sciences (ICMC) at USP in São Carlos and a member of the Brazilian Academy of Sciences, uses a culinary analogy. "Every physical phenomenon has a rule, and the rule is nothing more than a recipe," he says. The initial conditions would be the ingredients, and the evolution of the system, the preparation. "When the recipe is prepared following all the measurements and steps to the letter, it will reach the same result. But any small mistake along the way will leave the cake too sweet or too salty. That is chaos theory," the mathematician summarizes. "At first, it was believed that this type of rule could not exist. It took years to realize that most of nature's rules have this property," says Tiago.

The pioneering description of this behavior came from astronomy. At the end of the 19th century, the Frenchman Henri Poincaré (1854–1912) was investigating whether the Solar System would be stable in the long term. When calculating the trajectory of a tiny body, such as an asteroid, subjected to the gravity of the Sun and Jupiter at the same time, he found orbits that took radically different paths when he slightly adjusted the starting values. The calculations filled the volumes of Les méthodes nouvelles de la Mécanique Céleste, published between 1892 and 1899.

What is the butterfly effect

The expression originated from the work of Edward Norton Lorenz (1917–2008), an American mathematician who worked as a meteorologist and researched climate forecasting at the Massachusetts Institute of Technology (MIT). While rerunning a climate pattern simulation, he rounded one of the input values and typed 0.506 instead of 0.506127. "This small change caused his program to produce a completely different simulation," says Kelly. The discovery became a paper published in 1963.

The butterfly only entered the scene nearly a decade later. In 1972, Lorenz presented his work at a meeting of the American Association for the Advancement of Science, and it fell to meteorologist Philip Merilees, who was organizing the session, to suggest the title of the lecture: Predictability: Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?. The image stuck, and the term "butterfly effect" became established in 1987 with the book Chaos, by journalist James Gleick. "The butterfly flaps its wings, this effect grows, and it generates a typhoon somewhere else," describes Tiago.

When transforming the numbers from his simulations into a graph, Lorenz obtained two interconnected oval figures that resembled a butterfly's wings, now known as the Lorenz attractor. "It demonstrates that two close starting points can diverge rapidly. Each one forms a wing of the butterfly," explains Kelly.

The researcher makes a point of emphasizing that the phrase should not be taken literally; that is, no experiment has ever linked the flight of an insect to the formation of a tornado. "The idea isn't that a butterfly causes a hurricane. It's a way of saying that a small change can trigger increasingly larger shifts as the system evolves," she says.

It is worth distinguishing the two concepts, which often appear as synonyms. "They are not two independent phenomena, but you also can't say that one is the result of the other. Chaos theory is a broader field, while the butterfly effect is a simple and intuitive way to explain one of its fundamental characteristics," points out Kelly. For her, the popularity of the image has a practical explanation. "It is much easier to say a phrase like the one about the butterfly than to explain the concept of sensitivity to initial conditions," she observes.

How the butterfly effect is perceived in everyday life

The weather is the most direct example. In the atmosphere, elements such as temperature, pressure, humidity, winds, and solar radiation interact continuously, and a minimal deviation in any of these factors accumulates with each new calculation. "For near-term days, we can have a very reliable forecast, but the further away those days become, the greater the uncertainty of the answers," says Kelly.

This does not make forecasting useless, it just changes the type of answer possible. "Sometimes it's complicated to say whether it will rain or not, but you can say that the chance of going through a dry spell is high," Tiago exemplifies. The tools of chaos theory are also applied to ecosystems, animal populations, and biological signals, such as those of an electrocardiogram.

For Kelly, however, the field's most valuable contribution is something else. "Difficult to predict does not necessarily mean random. Sometimes there is a structure, there are rules behind that behavior, but the dynamics are so sensitive and involve so many interactions that we cannot precisely determine what will happen down the road," she explains. Hence her resistance to the idea that the theory could be used to predict the future. "It helps to understand patterns, identify changes, and recognize the limits of predictability."

What is the relationship between the butterfly effect and sustainability

Sustainability is the ability to meet the needs of the present without compromising the possibilities of future generations. "There isn't just today. The consequences of our today will come in a certain future," says Kelly.

The connection to chaos theory is established because the environment is a complex system. "It doesn't function as a collection of isolated parts. Water, soil, forests, and human activity are all interrelated and evolve together. A change in one of these parts can produce consequences in the others," she explains.

This interdependence helps us understand a phenomenon observed across different environmental fronts. "Many environmental changes happen gradually, but they can reach a point where their effects become much greater and much harder to reverse," warns Kelly. This is seen in the progressive loss of biodiversity and the advancement of climate change.

This was the image used by Elizabeth Gray, former global climate director at The Nature Conservancy (TNC), in an article published by the organization. For her, the possibility of small actions causing unpredictable results is both unsettling and encouraging, and it also applies in a positive sense. Conservation and restoration measures for forests, grasslands, and wetlands generate chain reactions that go beyond the climate, such as new jobs and public health gains. "The future of nature is our future," she writes.

The UFABC professor, however, adds a scientific caveat. "We cannot say that all small individual actions will necessarily trigger a major transformation. But a small action, inserted into a network of relationships, can participate in a sequence of events and produce greater consequences," she states.

The key lies in multiplication and accumulation. Kelly offers an everyday example: someone who decides to reduce water waste at home. "In isolation, this attitude may seem small. But when a person influences their family, they influence others. When these practices start to be incorporated by schools, companies, and absorbed by the community, we have a change in behavior that can take on a much larger dimension," she describes. The same applies to separating recyclables or choosing responsibly sourced products.

Conclusion: a world of relationships and interdependencies

Not everything is predictable, but that does not mean everything is disorder—and it is this distinction that chaos theory offers to those thinking about sustainability. "There is often a logic behind the complexity of things, and science seeks to uncover that logic," says Kelly.

Applied to the environmental debate, the metaphor carries a less immediate message than popular interpretation suggests. "The most relevant message is that we live in a world of relationships and interdependencies, in which our actions are part of larger networks. Sustainability is also a matter of time, connection, and collective responsibility. What we do today may not produce a visible transformation immediately, but it can change the paths we are building," the professor explains.

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