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.)

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.

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.

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.

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.

Understanding turbulence, which is characterized by growing chaos at multiple scales

As energy is lost in fluids undergoing turbulent, non-linear flow, particles will collectively form eddies, or whirlpools, of various sizes that mix together. The energy cascade of larger eddies becoming smaller ones before dissipating completely varies based on the initial conditions of the fluid, a characteristic feature of chaotic systems.

Climate models use complex equations and supercomputers to predict future climate

The equations apply the laws of thermodynamics, fluid motion, and radiative transfer to a 3D grid along Earth's surface. After solving them for each cell in the grid over a time interval, the results carry over to neighboring cells, and the process repeats into the future.

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.

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

The ingredients that make up severe weather

A seven-minute video illustrating how a storm is made. These factors—moisture, instability, lift, and shear—are explained through a series of data sets and creative, descriptive diagrams.

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.

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.

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

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.

Chaos gardening involves scattering seeds without any planning

The trend is intended to produce colorful, dense gardens by mixing various seeds. While encouraging experimentation and lower stakes, the success of these gardens depends on choosing plants with similar needs and incorporating native, nectar-rich flowers.

The origin of atmospheric science while testing nuclear weapons during the Cold War

The arms race between the US and the Soviet Union saw both countries stockpiling and detonating hundreds of bombs underground, underwater, and in the atmosphere. To better predict where nuclear fallout would travel after these tests, scientists developed models that would serve as a foundation for those used to explain atmospheric circulation.

What is the cone of uncertainty?

In hurricane forecasting, the cone of uncertainty results from connecting a set of circles representing where a hurricane is expected to be at 12-hour intervals. The size of each circle is two-thirds of the historical forecast error over the previous five years.

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.

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.

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.

Distinguishing between scientific theories and laws, and why both are on equal footing

Scientific laws describe outcomes of specific conditions, and scientific theories explain why those outcomes occur. Both are supported by observational and experimental data and can each inform one another, but neither can become the other. Instead, additional data can improve each towards more accurate descriptions and explanations of reality.

Time crystals are systems of atoms organized into periodic patterns of motion

Unlike traditional crystals—whose atomic structures cause them to look identical no matter how you look at them in space—time crystals exhibit this behavior through time, where the motion of atoms will bring them to the same positions relative to one another regularly.

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.

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.

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.

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.

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

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.

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.

View the ten deadliest tornadoes in US history.

Studies suggest when you sleep is as important as how much you get, and syncing with your circadian rhythms may lead to less fatigue and improved long-term health outcomes

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.

Hedge funds, the private investment firms that trade a wide swath of financial assets, make money by imposing steep fees on investors and from the fund's investment performance.

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.

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

The United States is one of only around two dozen countries with a fully federal system of government, in which power is divided between national and state governments.

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.

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

The Mona Lisa's celebrity status and repeated restorations have obscured what made the painting so revolutionary for its time

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

Search a massive database of over 4 decades of clues from the TV quiz show 'Jeopardy!'