Is the 2004 Ashton Kutcher vehicle *The Butterfly Effect* a good movie? Definitely not, no—but try telling that to me at age thirteen. And then wrap your head, once more, around the fact that if you *had* told me that, you might have set in motion the utter annihilation of the human race—the whole notion of the butterfly effect being that small-scale events (telling a credulous thirteen-year-old he has bad taste in movies) can generate massive, unforeseen consequences (World War III, nuclear apocalypse, etc.).

At least, that’s the version of the idea that has trickled down into popular consciousness. But the butterfly effect is technically a meteorological term, coined exactly half a century ago. What it actually is—and whether it still applies, or has since been superseded/discredited—is a whole different thing. And so for this Giz Asks, we reached out to physicists, atmospheric scientists and psychologists for the latest on how (or if) the butterfly effect actually works.

**Dale Durran**

*Professor and Chair, Department of Atmospheric Sciences, University of Washington, whose research includes the study of atmospheric predictability*

The Butterfly Effect was introduced by Edward Lorenz in the context of atmospheric predictability. He was actually talking about seagull wings in his paper—it wasn’t butterflies. The name The Butterfly Effect was proposed (by Dr Phil Meriless) as a title for a talk Lorenz gave soon after he published his paper in 1969.

The Butterfly Effect is real, in the sense that small changes at small scales can change the weather forever—but it’s doubtful that a butterfly could effect any kind of meaningful change in the weather. As an image that captures the imagination, it’s more or less okay—not the perfect example, but it’s illustrative. The problem is, butterflies are too small to really change anything.

But things that are just a little bit larger—an aeroplane, say, or a cumulus cloud—can have an eventual effect on the weather everywhere. The presence or absence of a cloud can change circulations around the cloud, which, as they change, will change slightly larger-sized circulations, which then change still-larger-sized circulations, and so you get this cascade of influence upscale from the very small scale. If we had two planets with exactly the same weather and put this cloud in one of them, over Illinois, and, except for the cloud, the other one was exactly the same, after several weeks the weather on these two planets would be as different as two random days selected from the same date in the weather pattern (i.e., two 18ths of May selected at random from two different years). That kind of difference would develop in a space of at least four weeks.

That said, it is not true that butterflies are spoiling our weather forecasts. Very small uncertainties about the weather over much broader regions also make nearly identical weather patterns diverge with time, and the uncertainties over larger regions (say a 100 mile rectangle) completely override any influence from butterflies.

### “The Butterfly Effect is real, in the sense that small changes at small scales can change the weather forever—but it’s doubtful that a butterfly could effect any kind of meaningful change in the weather.”

**Brian Swingle**

*Assistant Professor, Physics, University of Maryland, who studies the physics of quantum information*

The butterfly effect is definitely real: if you take a chaotic system and run two different experiments with slightly different starting points, you will observe the difference in behaviour growing rapidly with time. Mathematically, the differences between the two experiments will repeatedly double as time passes, until the differences are large.

A more confusing phenomenon is the quantum butterfly effect, which arises in systems that combine chaos with the weird physics of the quantum world. For these kinds of systems, there are notions of quantum chaos, but precisely the diagnosing the quantum butterfly effect is a topic of ongoing research. In some cases, we can identify an experimentally detectable property that is expected to repeatedly double as in the classical butterfly effect. But we don’t know whether it’s possible to make sense of this yet for general quantum chaotic systems.

The experiments that try to study this physics are also very interesting. They often involve special collections of atoms and photons which have been engineered to be highly controllable and isolated from the outside world. The experimenters attempt to run the system’s dynamics forward and backward in time, like rewinding and fast-forwarding a movie. The idea being that if we fast-forward then immediately rewind, we get back to where we started from, but if we fast-forward and make a small change before rewinding, then in a chaotic system we will quickly end up at a very different place than we started.

*“A more confusing phenomenon is the quantum butterfly effect, which arises in systems that combine chaos with the weird physics of the quantum world.”*

## David Pincus

*Professor, Clinical Psychology, Chapman University, who has studied chaos theory and the butterfly effect as they relate to human psychology *

Is it real? Yes. A confident yes. Then you can try to explore the question of, what does real mean? And that’s where the fun is.

The butterfly effect was first probably “discovered” back in the 1900s by Poincaré. He was trying to solve the problem of three interacting bodies—astrophysics. If you have gravitational interaction with two things in space it’s relatively simple to model: they impact each other mutually. But when you get to three it’s not really solvable. If you tie three tennis balls together, and swing the top string, the bottom tennis ball will move in a chaotic way. The bottom tennis ball’s motion demonstrates the butterfly effect—meaning it’s not random but it’s also not predictable, and if you make some small change at one point in time, a tiny change, the position of the tennis ball at a future point in time will be totally different.

One really clear example where it applies: fractal geometry. A fractal is a self-similar kind of branching structure that you see all over the place in nature, like trees and neurons and so on. If you look at systems that display the butterfly effect and are chaotic, they will produce fractal patterns—if you have 10,000 data points you can see the fractal patterns in terms of how they change over time, what you call trajectories. Complex systems where you have a tonne of different components all interacting in complex ways to produce coherent output, like the growth of trees and neurons and waves in the ocean and a million different things in nature, these tend to produce fractal patterns also.

I just published a study this January where we measured personality structure and found a fractal structure. It turns out you can measure personality with the same kind of measurement, and when people are more resilient and more healthy their personality structure is more branch-y; the structure is fuller and less rigid.

I have a colleague in Germany named Gunter Scheitek, and he in my opinion has done the most of anyone when it comes to applying chaos theory specifically to psychology, and he really focuses on trying to find the butterfly effect through a psychotherapy process. The gist of his work is that he’s built a mathematical model—the only one I know of—that applies to personality change during psychotherapy, and when you run the model it produces the butterfly effect, meaning small changes in psychotherapy can cause much different outcomes later on in time. His models are proof of concept that the butterfly effect might be central to processes of human change over time. He actually tracked the data of a client over time and the data matched really well to his models. So the butterfly effect is not only real in mathematical terms and across a lot of different areas of science, it’s true in psychological change and growth as well, it seems.

*“If you look at systems that display the butterfly effect and are chaotic, they will produce fractal patterns—if you have 10,000 data points you can see the fractal patterns in terms of how they change over time, what you call trajectories. Complex systems where you have a tonne of different components all interacting in complex ways to produce coherent output, like the growth of trees and neurons and waves in the ocean and a million different things in nature, these tend to produce fractal patterns also.”*

**Douglas Stanford**

*Associate Professor, Physics, Stanford Institute for Theoretical Physics, who studies quantum gravity, quantum field theory, and string theory *

The butterfly effect is real, but it’s sort of difficult to detect. To make it noticeable, we can imagine an experiment with a time machine. You go far back in time and change one tiny inconsequential thing, like the position of a single atom. Then, when you zoom forward to the present again, pretty much everything will have changed a lot, in a sort of random way.

This was basically the plot of the 1952 short story “A Sound of Thunder.” And the author Ray Bradbury got a lot right. But he underestimated how powerful the rearrangement of the present would be. A rule of thumb is that things about the present that would have been easy to predict in the past won’t change. But things that seem difficult to predict will be different.

*Featured image: Illustration: Angelica Alzona (Gizmodo)*

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