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

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.

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

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.

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.

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.

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.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father 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.

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

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

Pareidolia: the cognitive bias of finding meaning in randomness

Many people equate "random" with "well-spaced," creating a cognitive bias that influences how people interpret events. This article explains how people tend to assume a generative force behind the patterns produced by randomness. This phenomenon, known as pareidolia, is seen in claims ranging from backward messages hidden in reversed audio recordings to tea leaf readings.

Researchers identify a hidden instability pattern in simple ocean wave models

Stokes waves—a solution to the mathematics of water waves—were once assumed to be stable. Italian mathematicians have proven disturbances cause these waves to collapse and such collapses follow an infinite repeating pattern. To complete the proof, the team offered a $100 donation to solicit online help.

How a competition honoring a king's birthday uncovered history's first chaotic system

A committee established a contest for King Oscar II's 60th birthday, featuring four unsolved problems in mathematics, including one on proving the stability of a system of more than two objects held together by gravity. Focusing on three celestial objects, Henri Poincaré won the prize for his proof, which he later learned was incorrect and, upon correcting it, instead proved these systems to be unstable.

How upheavals in accepted scientific theories helped popularize the term 'paradigm'

When Thomas Kuhn published "The Structure of Scientific Revolutions" in 1962, he described the history of science as comprising periods of "normal science" where these accepted frameworks—paradigms—gradually accumulate anomalies until they cannot describe nature. Revolutionary science, such as the development of a new theory, results in a paradigm shift, another term Kuhn helped popularize. (Some readers may experience a paywall.)

How a solar eclipse proved Einstein's theory of gravity

For hundreds of years, Isaac Newton's laws of gravity and motion accurately predicted every observation and measurement involving orbits. With the advance of technology, more precise measurements revealed anomalies, including the orbit of Mercury, which Albert Einstein's general theory of relativity could explain. This article details the two frameworks and how they went head-to-head during an eclipse for gravitational supremacy.

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.

Wilbur published key papers, gave speeches in the burgeoning aviation community

Much of the theoretical work is credited to Wilbur, whose scientific mind observed birds and early pioneers to discover the key problem to solve was control. This 1901 speech surveys the recent work in the field and showcases what the brothers worked on two years before their breakthrough flight.

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).

'It's those who lie outside ordinary experience who have the most to teach us.'

- Author Malcolm Gladwell (1963 - present)

The first algorithmic random number generator was developed in 1946

Although previous methods of randomness involved physical tools with limited outcomes, such as dice, or relied on chaotic variables for number generation, such as electronic noise, John Von Neumann's middle-square method turned the problem into a mathematical computation. It has since been replaced by methods that generate numbers from unique initial values, such as the time on a clock.

The 1978 prediction of the Kessler syndrome popularized the risks of space trash

A paper published by NASA scientists Don Kessler and Burton Cour-Palais described a scenario where the density of objects in orbit becomes so high that collisions between them create a cascading effect of runaway debris, preventing future space travel. The risks were confirmed from returned telescope parts showing debris impacts.

Meteorologists believe they know the weather that inspired the terror behind Munch's painting 'The Scream'

Helene Muri, a meteorologist at the University of Oslo, believes the clouds causing the man such terror are nacreous. "We do know that there were mother-of-pearl clouds in the Oslo area in the late 19th century," she said, though she was careful to note that it was still a hypothesis.

How one professor uses 'Walden' to study climate change

Richard Primack, a biology professor at Boston University, uses observations on Walden Pond's ecology from Henry David Thoreau's book to inform his study of climate change, noting that "Walden" is one of the oldest datasets available in the United States.

'Birds Aren't Real' parodies the way memes traffic conspiracy theories

Peter McIndoe claims the US government killed 12 billion birds only to replace them with drones. These statements have powered protests—and McIndoe's fictional campaign that highlights how conspiracies and their theorists are treated.

Writer William Gibson invented the term 'cyberspace'

The science-fiction writer coined the term in his 1982 short story "Burning Chrome" to describe "a consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts...A graphic representation of data abstracted from the banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data. Like city lights, receding."

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.

Exploring the Larry Bird punch that almost changed March Madness

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

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

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.

The name 'Silicon Valley' arose from the founding of Shockley Semiconductor Laboratory in Fairchild Semiconductor in 1956-57, founded near Stanford University in Palo Alto

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

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

After NASA's Voyager 1 captured Earth as a single pixel as it left the solar system in 1990, astronomer Carl Sagan used the image to reflect on humanity's fragility and the responsibility to protect 'the only world we've ever known.'

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Warren Buffett's former professor Benjamin Graham is known as the 'father of value investing,' a strategy in which investors seek to buy stocks trading below their intrinsic worth.

Planeterrellas create artificial auroras that mimic the atmospheric displays of light by setting up an electric field between two metal balls in a jar filled with a small amount of air.

Before writing 'Walden,' transcendentalist Henry David Thoreau nearly burned down his hometown with a campfire that grew out of control.

View the ten deadliest tornadoes in US history.

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.

Mid-century modern graphic designers, known for their bright colors and bold lines in advertising, also found success with children's books.

Salvador Dalí believed he was his own dead brother, who had died nine months before he was born

After 25 people used virtual reality headsets to practice flying with virtual wings—flapping their arms—their visual cortex responded to the wings almost as if they were real arms, treating them as body parts.

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.

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.

An investigation suggests a Scottish island became awash in forever chemicals via seafoam and seaspray—raising questions about what that means for the safety of other coastal areas.

Quincy Jones' 'Big Band Bossa Nova' helped introduce bossa nova—a jazz-influenced Brazilian genre—to the US