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

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 '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 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.)

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

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.

In a tornado outbreak, a single severe weather system can spawn multiple twisters

By maintaining the ingredients for tornadoes—differences in wind speed and direction across altitudes, moisture, and rising air—for long periods of time as it moves across a region, a severe thunderstorm can continuously produce tornadoes by lifting multiple columns of horizontally rotating air.

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.

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.

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.

Because some models of the universe do not incorporate time, it may be an emergent property born from our limited perception of the universe, rather than a fundamental property of reality.

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.

Tornadoes, or twisters, have been seen on every continent but Antarctica

Because tornadoes require rising warm air to form, some meteorologists have suggested that urban environments—locations where human landscape modification has introduced materials that trap thermal energy—can enhance the conditions needed for tornado formation. Tornadoes have been reported to cause ear "popping" due to drastic changes in air pressure.

Tornado formation relies on wind shear to create a tube of rotating air

Once a horizontal vortex is created by air circulating between winds of different directions and speeds, an updraft, such as those seen in powerful thunderstorms, tilts the vortex vertically. The updraft then strengthens the vortex, which becomes a tornado upon touching the ground.

Fast-changing conditions during their formation make tornado forecasting difficult

The final steps of tornadogenesis—the process of forming a tornado—depend on near-surface details, such as local geography, which are difficult for radar to observe and affect how funnel clouds make contact with the ground. Inconsistencies in storm behavior have limited the amount of advance warning people receive before tornadoes touch down.

Within quantum physics, the order of events across time may not follow causality

Although time is considered a fixed, ordered mapping of events, where the past affects the future, quantum superposition breaks down causality, suggesting that future events can occur simultaneously with past ones. Within the quantum model, the notion of cause and effect is not a fundamental feature of our universe.

Turbulence has been called the most important unsolved problem in classical physics

Despite being the most common type of fluid flow in our world, scientists have struggled to model turbulent flow accurately. Though behaving unpredictably, understanding inertia and viscosity can help determine whether turbulence will occur.

Explore the effects of tornadoes of different scales

In this simulation, users can adjust the tornado's diameter and rotation speed to see its impact as it passes through a series of trees and a one-story home.

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.

The first known instance of a fire tornado occurred in 2003

During pyro-tornadogenesis, many processes that create thunderstorms from wildfires, such as rising hot air and steam from evaporated water in forests, fuel the formation of a fire tornado. The increasing rates of wildfires due to climate change are expected to make this phenomenon and other extreme weather more common.

Turbulence is needed to make airplanes more stable and golf balls fly farther

Vortex generators—small fins placed along airplane wings—create small eddies that prevent airflow separation, maintaining lift and preventing stalls. Golf balls have dimples that create a turbulent boundary layer on their surface, minimizing drag forces.

Hurricanes spin due to differences in air and ground speed as they move across Earth

The movement of an object across latitudes causes it to take a curved trajectory because its speed no longer matches that of the ground beneath it. This phenomenon, called the Coriolis effect, explains why hurricanes spin counterclockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

Airplanes generate enough lift to fly by accelerating air faster over their moving wings, which makes the pressure above the wings lower than the pressure below.

During a trophic cascade, the disappearance of a keystone species, which plays an indispensable role in ecosystems, triggers a domino effect within food webs that disrupts the populations of many more species.

Bomb cyclones can produce heavy rain, blizzard conditions, and intense winds

Known as "bombogenesis" in meteorology, these systems get their colloquial name from their rapid intensification over a 24-hour period—a phenomenon seen in some tropical cyclones. They occur most commonly along the coasts of the Northeast and Northwest US when there is a severe temperature difference between colliding air masses.

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.

Unlike hurricanes, tornadoes are not ranked based on measured wind speed

Technological limitations prevent direct measurements of wind speeds where tornadoes make contact with the ground. Instead, the Enhanced Fujita scale assigns a rating with a range of speeds based on how much damage a tornado caused to various types of structures. These types are more extensive than the original Fujita scale.

The 'Lindy effect' is a theory that says the longer things that don't physically wear out (like ideas, brands, or institutions) have been around, the more likely they are to exist for longer.

Some tectonic plates move faster than their underlying convection currents

Like a chain slipping off a ledge, as tectonic plates sink, their weight can pull the rest of the trailing plate forward, accelerating their movement. Plates can also break apart and fall, creating a suction effect that drives movement, resembling leaves following a passing car.

The field of attribution science seeks to determine whether specific phenomena, such as melting glaciers, droughts, and hurricanes, are driven by Earth's natural climate cycles or by human-caused climate change.

Though less common, tornadoes can form without the presence of thunderstorms

Supercell tornadoes involve rising warm air—updrafts—from the strongest type of thunderstorm—supercells—to help turn horizontally rotating tunnels of air into vertical columns. In non-supercell tornadoes, which are generally weaker as a result of forming within less energetic systems, vertical rotation is present from the start near ground level.

Explaining the many-worlds interpretation

A mind-bending, jargon-free account of the popular interpretation of quantum mechanics, helping to explain how something can be in two states at once.

The arrow of time—the concept that time only moves in the forward direction—is thought to result from the universe progressing toward greater disorder, or entropy.

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.

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.

In the 1950s, Alan Turing developed a mathematical model to explain why animals have stripes, spots, and other patterns based on differences in how quickly two interacting chemicals spread throughout a developing organism.

Tornado myths include suggestions to hide beneath a bridge or to open windows

Winds can accelerate due to a tunneling effect as they pass under a structure, making seeking shelter from a tornado in a mobile home or recreational vehicle highly discouraged. Significant tornado damage results from debris being picked up and hurled by strong winds, making it unsafe to be near windows that may shatter.

Turbulence is crucial to the formation of stars in molecular clouds

Within simulations of these clouds, gravity, jets, supernovae, and galactic motion-induced stirring have been shown to develop turbulence that creates shocks. These turbulent shocks move quickly in low-density regions and slow in high-density areas, forming lumps of matter with sufficient gravitational force to collapse and initiate fusion, birthing a star.

An interview with James Yorke, the man who coined the mathematical term 'chaos'

Along with co-author Tien-Yien Li, the former University of Maryland mathematics department chair published the paper, "Period Three Implies Chaos" in 1975. "Chaos" then became the terminological placeholder for systems with sensitive dependence on initial conditions, which had been well known to mathematicians for over a decade.

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.

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.

When experiencing turbulence, fluid elements undergo stretching and folding

Simulations show patches of fluid particles, such as splashes of milk, bend under turbulent flow, creating curvature that grows linearly then exponentially. This accelerated deformation enhances folding and mixing faster than other methods, such as stirring or beating.

Within quantum mechanics, the Heisenberg uncertainty principle limits how precisely one can simultaneously know the values of pairs of complementary properties for an object, such as position and momentum.

The centrifugal force is associated with the feeling of being pushed outward when moving in a circle, but it is a fictitious force arising from objects' tendency to move in straight lines.

Horsehead-shaped features seen on the sun and the clouds of Earth and Jupiter are examples of Kelvin-Helmholtz instabilities, where a faster-moving fluid rolls atop a slower-moving fluid.

Butterfly populations have declined by 22% from 2000 to 2020

Research suggests that one in every five butterflies is lost due to pesticide use, habitat loss, and climate change. Playing a vital role in pollination, their declining populations threaten plant reproduction and the health of ecosystems.

All hurricanes have a central eye, where no extreme weather occurs, surrounded by intense winds and thunderstorms.

Tachyons are theoretical particles that travel through space faster than light

The equations of special relativity require these objects to possess imaginary mass, and they would travel faster the more energy is taken away from them. The existence of tachyons would necessitate an unknown form of matter and lead to paradoxes involving information that can hypothetically travel backward in time.

There are lots of weird ideas about dinosaur extinction, like hungry, hungry caterpillars

One of the great historical puzzles is this: why did the dinosaurs go extinct? Whether an asteroid, poison plants, volcanos and climate change, or something else, it's still a mystery. Scientists have been debating this question for almost a hundred years. One insect scholar suggests that caterpillars are the culprits.

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.

Wind is the movement of air caused by the sun's uneven heating of Earth

The tilt, curvature, and variations in Earth's surface composition across the globe cause different regions to receive different amounts of solar radiation. As the Earth spins and tries to achieve thermal equilibrium, air masses move and interact, creating wind.