The butterfly effect in five minutes
The butterfly effect is the idea that a very small difference at the start of a process can grow into a very large difference later. The name comes from a question the meteorologist Edward Lorenz put in the title of a 1972 talk: does the flap of a butterfly's wings in Brazil set off a tornado in Texas? Lorenz was not claiming that it does. He was making a point about forecasting. In some systems, a tiny error in what we know about today makes long-range prediction impossible.
The idea belongs to chaos theory, the study of systems that follow exact rules and still behave in ways that are very hard to predict. It also became one of the favourite plot engines of fiction, which is why it has a place in the History of Science Fiction.
Three points to keep in mind:
- Small causes can have big effects. This happens in some systems, not in all of them.
- Chaos is not randomness. The rules are exact. If you knew the starting state perfectly, the result would be fixed.
- We never know the starting state perfectly. That is why long-range prediction hits a wall.
Where the butterfly effect came from
Edward Lorenz (1917–2008) was a meteorologist at the Massachusetts Institute of Technology. In the winter of 1961 he was running a simplified weather model on an early computer. To save time, he restarted one run from the middle, typing in numbers from an earlier printout. The printout showed three decimal places (0.506), while the computer had been working with six (0.506127).
A difference of about one part in a thousand looked harmless. Lorenz expected the new run to follow the old one closely. For a short while it did. Then the two simulated weather patterns drifted apart, and within a couple of months of model time they looked nothing alike. The model was magnifying tiny differences, and Lorenz realised what that meant for real forecasting.
In 1963 he published the paper "Deterministic Nonperiodic Flow" in the Journal of the Atmospheric Sciences. It used a model with only three equations and showed the same sensitivity. When the solution is plotted, it traces two linked loops that look a little like a pair of wings. This shape is now called the Lorenz attractor. Many people think it gave the effect its name, but the name came later, from a talk, even if the picture helped it stick.
In December 1972 Lorenz spoke at a meeting of the American Association for the Advancement of Science. The title, "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?", was suggested by the session organiser, Philip Merilees. Lorenz had earlier used a seagull in the same example. The butterfly won.
The real science
What is established
Scientists call the effect "sensitive dependence on initial conditions". It has been shown mathematically and in many models and experiments. How fast two nearly identical starting points drift apart is measured by a number called the Lyapunov exponent. When it is positive, the gap grows roughly exponentially, which means it keeps multiplying instead of growing in a steady line.
Weather is the standard example. We can never measure every point of the atmosphere exactly, so small errors in the starting data grow as the forecast runs forward. Detailed forecasts lose their skill after about one to two weeks, even with strong models and many satellites. The French mathematician Henri Poincaré had already noticed similar sensitivity in the three-body problem of planetary motion in the 1890s.
Not every system is chaotic. A swinging pendulum with friction slows to a stop, and small differences in how you start it fade away. The butterfly effect belongs to systems that stretch small differences instead of shrinking them.
What is speculation
Whether a real butterfly has ever caused a real tornado cannot be tested. The atmosphere is full of small disturbances, and no one can trace a single storm back to one flap. Lorenz himself said that a butterfly could just as easily prevent a tornado as cause one, and that nobody could tell which. The famous question is a way of describing limits on prediction, not a claim about a specific cause.
Chaos is not luck
Chaotic systems are deterministic. Nothing random is added to them. The unpredictability comes from the fact that we cannot know the starting values to unlimited precision. A computer that reruns the same model with exactly the same numbers will get exactly the same answer every time.
Where it shows up in fiction
Spoiler note: the first story below is described through its ending.
Ray Bradbury's short story "A Sound of Thunder" (Collier's magazine, 1952) came twenty years before Lorenz's talk, yet it is the classic fictional version of the idea. In 2055 a company sells time-travel hunting trips to the age of the dinosaurs. Hunters must stay on a floating path and touch nothing. A hunter named Eckels panics, leaves the path and, without noticing, crushes a butterfly. Back in the present, the language is spelled differently and the result of a presidential election has changed. One small death in the distant past has bent everything after it.
Many time-travel stories borrow the same logic: change one small thing and the future shifts. Our page on time travel paradoxes looks at what that does to cause and effect. Stories of branching worlds use it too, since a small difference can send events down a different path, as in our page on the parallel universe.
Michael Crichton's novel Jurassic Park (1990) brought chaos theory to a wide audience through the mathematician Ian Malcolm, who argues that a park built on complex systems cannot be kept under control. On the non-fiction side, James Gleick's book Chaos: Making a New Science (1987) explained Lorenz's work to general readers. A 2004 film titled The Butterfly Effect also carries the name.
Common misconceptions
- "A butterfly causes a tornado." No one has shown that. The point is that long-range prediction fails, not that one insect is to blame.
- "Every small change has huge effects." Most small changes fade out. Chaotic sensitivity is a property of particular systems such as weather, not of everything.
- "Chaos means random." Chaotic systems follow exact rules. They are predictable in principle and hard to predict in practice.
- "Fiction shows it accurately." Stories usually give a neat chain from one small act to one big result. In real chaotic systems the effects spread in countless directions and cannot be traced back to a single cause.
Why it still matters
Modern weather services respond to the butterfly effect instead of fighting it. Rather than running one forecast, they run many, each with slightly different starting values, and see how far the results spread. When the runs agree, the forecast can be trusted. When they scatter, forecasters know the situation is hard to call. The percentages you see in a forecast partly come from this method.
The same thinking helps in other fields where small differences grow, such as fluid flow, some electrical circuits and certain population models. Knowing a system is chaotic tells you what to stop expecting: you cannot predict it for ever, but you can still describe its general behaviour and its limits.
Read next
- Time travel paradoxes: see what happens to cause and effect when someone changes the past.
- Parallel universe: explore the idea that small differences could branch into other worlds.
- History of Science Fiction: follow how ideas like this one travelled from science into stories.
