Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

The 'butterfly effect' is the informal name for chaos theory

In mathematics, chaos theory involves complex systems that are highly sensitive to their initial conditions. Originally discovered when analyzing weather data, slight variations in the data input into such systems create drastically different results, despite following known physical laws.

The origin of chaos theory, colloquially known as the 'butterfly effect'

The theory explains that systems following well-understood physical laws can still produce unpredictable outcomes due to small variations in their initial conditions. Originally identified in weather data, elements of chaos have been observed in stock market fluctuations, cardiac arrhythmias, and the evolution of online social movements.

The life of Edward Lorenz, who originally used a seagull in his 'butterfly effect' metaphor

By accidentally finding that rounding one variable to its third decimal place and re-running a weather simulation produced a drastically different two-month forecast, the American mathematician established the field of chaos theory. His paper—"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?"—introduced the well-known metaphor for the behavior of chaotic systems. (Some readers may experience a paywall.)

An explanation distinguishing the butterfly effect from causality, necessity, and sufficiency

In pop culture, the analogy has conveyed the impression that the flapping of a butterfly's wings has a cascading effect that directly produces a tornado somewhere else on Earth. However, butterfly-wing flapping alone is insufficient to cause tornadoes, as the complexity of atmospheric systems requires many more conditions to produce them, any of which can be the tipping point to initiate tornadogenesis.

View the Lorenz attractor, a graphical solution to chaotic equations that resembles a butterfly

The discovery of chaos theory came from Edward Lorenz's computer model of the atmosphere, which used three equations to quantify atmospheric circulation. However, the chaotic evolution of this system creates wandering figure-8-like shapes—some resembling butterfly wings—as it repeatedly attempts to settle on one of two values along unique trajectories.

Learn how natural systems exhibit characteristics of chaos theory

In biology, some mathematical models of ecosystem populations and heart irregularities show strong sensitivity to initial conditions, which scientists can simulate to determine quantitative tipping points at which these systems become unstable. Within the social sciences, crowd behavior and the virality of social media posts have shown how human behavior fits within the framework of chaos theory.

Mathematics proves turbulence's chaos creates super diffusion

Turbulent flow is responsible for the rapid scattering of dandelion seeds, volcanic ash, and untied balloons. Its swirling behavior accelerates particle scattering faster than other mixing methods, as particles acquire energy from the interactions of eddies.

How chaos helps explain why small market corrections can produce major economic instability

Oxford University complex systems professor Doyne Farmer discusses how predictions from many economic models are overly weighted toward simple relationships, such as supply and demand, and external shocks, such as the COVID-19 pandemic. However, real-world macroeconomic systems involve public and private actors interacting, producing feedback loops and cascading effects that resemble the oscillatory behavior seen in chaotic systems.

A mathematical and visual analysis distinguishing chaos from randomness

Random systems lack any underlying pattern or causal relationships, while chaos is mathematically deterministic because the behavior follows established laws of nature. In 3D plots, chaotic systems produce outputs that approximate a mathematical function, while random points appear as statistical noise.

The turbulence experienced in airplanes results from unexpected changes in airflow

Pilots rely on forecasts, onboard tools, and air traffic control to avoid regions of severe turbulence during flight. Turbulence is generally weaker for those sitting in the front of the main cabin and for morning flights that follow cooler nighttime temperatures.

Atmospheric processes amplify the strength of storms by coalescing clouds

Research has shown that turbulent mixing of air at the edges of clouds and other small-scale thermal activity beneath them help clouds group together, intensifying short bursts of rainfall, especially in tropical regions. Simulations reveal this produces more powerful storms than predicted by older models, though they may occur less frequently.

Unlike quantum mechanics, classical physics suggests free will does not exist

Models based on Newton's laws of motion suggest all actions are predetermined and must follow specific trajectories and outcomes, such that everything that will ever occur in the future has already been set in motion by past causes. However, quantum mechanics challenges determinism because it is based on probability, where no outcome is certain.

Accurate climate models incorporate calculus to account for complex feedback loops

The simplest models assume uniformity across the Earth, with incoming energy from the sun being offset by the planet's albedo, or reflectiveness, which prevents the radiation from being fully absorbed. Incorporating elements such as atmospheric layers, latitude bands, geographic variability, and emissivity yields coupled differential equations quantifying Earth's interconnected systems.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Tornado chasers include scientists conducting field projects

Research teams use drones, mobile weather stations, and radar systems to capture real-time meteorological data, better understand conditions that favor tornado formation, and improve forecasting models. As of 2022, model limitations result in roughly 70% of tornado warnings being false alarms.

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

What does the hurricane forecast cone really tell us?

Ever feel like hurricane forecasts change a lot? Hurricane forecast tracks might not mean what you think they do. Concentric circles are actually used to help form the forecast. Chief Meteorologist Bobby Deskins explains how you should really be reading these cones.

Meteorological v. astronomical seasons, explained

Meteorologists and climatologists define seasons differently from “regular” or astronomical spring, summer, fall, and winter. Traditional seasons reflect the movement of celestial objects, known as the astronomical seasons; meteorologists mark seasonal change based on temperature averages.

What types of extreme weather can be attributed to climate change?

For decades, it was impossible to say that a specific weather event was caused, or even made worse, by climate change. But advanced research methods are changing that.

Eruption forecasting relies on probabilistic methods resembling weather forecasting

While some volcanoes erupt with predictable signs, such as surface deformation from the build-up of underground magma pressure, others release magma at inconsistent rates. Extensive monitoring is needed to identify less clear patterns and indicators of future eruptions.

AI-powered models can provide low-cost, localized and accurate weather forecasting

These models can run on standard laptops, reducing the need for expensive supercomputers and expanding access to developing regions. AI forecasts can help farmers make informed planting decisions, improving crop yields and reducing costs.

The theory of chemtrails originated from misinterpreting a US Air Force paper

The document proposed a future weather modification system to achieve military objectives, but clarified that such a system "does not reflect current military policy, practice, or capability." Past testing of biological and chemical weapons has accelerated conspiracies about streaks of condensation trailing aircraft to be harmful chemical agents.

The weather time machine

A fun interactive on how old ships’ logs are giving scientists new insights into the past and future of the Earth’s changing climate (w/maps and pictures).

Temperature is a value that controls how predictable or creative an LLM's output is

In large language models, temperature adjusts the randomness in text generation by modifying how often words with lower probabilities are selected next in the sequence. Lower temperatures produce more obvious outputs while higher temperatures produce more creative responses.

Fearology, or the study of fear, explores the difference between stress and fear

Our brains involuntarily respond to our environment and signal alarm when that isn’t always needed, triggering responses that include goose bumps. But understanding fear and how to talk our brains into calming down can improve daily life.

Why being able to disprove explanations distinguishes scientific theories from pseudoscience

Introduced by philosopher Karl Popper, falsifiability holds that a scientific theory must make predictions that could be proven inaccurate by future observations. Explanations that cannot make such predictions are not scientific theories. It is scientists' jobs to seek out data to poke holes in scientific theories, thereby potentially strengthening them if they hold up to scrutiny.

Stars appear to twinkle because turbulence in the motion of molecules in Earth's atmosphere causes light to bend and wiggle rapidly on its way to the surface—a phenomenon called scintillation.

Hurricanes, which rely on air consistently spinning in the same direction, cannot cross the equator because air curves in opposite directions north and south of it.

Scientists can determine Earth's past climate conditions by analyzing air trapped in microscopic bubbles within ice cores—columns of compressed snow layers that build up over hundreds of thousands of years.

Dirty lightning is a thunderstorm created from friction between rising and falling flows of ash and smoke during volcanic eruptions.

Learn how your body is, scientifically, like a firework with its own slow, controlled burn.

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

El Niño, Spanish for 'the boy,' was named after Jesus Christ because the phenomenon resembled the weather changes observed around Christmastime.

The boiling temperature of water decreases with increasing elevation because the molecules need less energy to overcome the lower atmospheric pressure associated with thinner air.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

Researchers believe the brain consolidates memories, processes emotions, and plans for the future during dream states

View the ten deadliest tornadoes in US history.

Doctors differentiate between a phobia and fear by asking patients whether their fear interferes with their day-to-day activities.

Some Pokémon have been named after real and fictional organisms, while some real-world species have been named after Pokémon, such as Chilicola charizard and Binburrum zapdos.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

Poison ivy will likely become both larger and more resilient due to climate change.

How the most famous Ebola book, The Hot Zone, which sold 3.5 million copies and was translated into 30 languages, got aspects of the disease so wrong.

The power and influence of the American presidency have expanded significantly over time—far beyond what the founders envisioned.

American short story writer Flannery O'Connor raised 40 peacocks, which became potent symbols for her fiction's elegant violence

The hormonal disorder PCOS was renamed PMOS in 2026, a move designed to improve care and research by shifting the focus to the hormonal causes of this condition that affects 1 in 8 women.

Indefinite cloning of some endangered species may not sustain their longevity because cloning success rates decrease as genetic mutations accumulate.

When a Paris department store hesitated to sell Estée Lauder's perfume, she 'accidentally' broke a bottle, causing the smell to spread throughout the store and shoppers to start asking to buy the scent.

Existentialist writer Jean-Paul Sartre coined the famous phrase 'Hell is—other people' in his play 'No Exit'