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You may have heard of the butterfly effect, where butterflies flapping their wings somehow cause tornadoes. But that can't be right.

Butterflies flap their wings all the time all over the world. And clearly they're not all causing extreme weather. But it's also not entirely wrong.

It turns out that butterfly wings can affect the weather, just not in the way you might think. The idea that small changes in the past can have big consequences in the future, like an alternate universe where JFK survived, is what people often mean by the butterfly effect. And to explain how this idea works, we need to go back to the dawn of the computer age in the 1960s, and the beginning of the modern science of weather prediction, or meteorology.

See, our weather is caused by the flow of currents of air and water. Everything from breezes to hurricanes can be explained by looking at how these fluids flow. But predicting that weather is hard, because fluid dynamics is hard.

The equations that govern fluid flow are notoriously difficult to use, and their solutions tend to be messy, complicated, and tricky to calculate. So, until the 20th century, weather prediction was more art than science. But when computers arrived at universities in the 1960s, researchers quickly took to using them to solve these equations to make more accurate predictions.

And almost immediately, they ran into a problem that would change math and physics forever. When you want to simulate a physical system, whether it's the weather, or a particle accelerator, you need to solve what are called differential equations: the equations that govern how a system changes over time. You always need to give the equations some initial conditions.

Basically, you tell it what everything is like initially, and then the equations let time play out to see what things will look like later on. One of the first people to use the new computer-based methods to predict the weather was Edward Norton. Wait, Edward Norton?

Oh, Edward Norton Lorenz, the American mathematician and meteorologist, not the guy from Fight Club. His strange discovery came one day in 1961 when he was doing a simulation of a simplified weather system. He found he was getting two different predictions from the same equations, with the same initial conditions.

Which is pretty weird, right? I mean you'd think if you had the same initial conditions and the same equations, surely you would get the same outcome. After looking more closely, he saw that the two inputs weren't exactly the same.

In one, he'd rounded the number 0.506127 down to 0.506, thinking it wouldn't make a difference. But it did. And the predictions didn't end up being 0.1% different, the differences doubled in size every four days of simulated time, and became unrecognizably different after a month or so.

The conclusion was that small changes in initial conditions can lead to vastly different outcomes. Lorenz illustrated this point in a lecture titled “Does the flap of a butterfly's wings in Brazil set off a tornado in Texas?” And the idea of the butterfly effect was born. But Lorenz was careful in his talk to not say extreme things like ‘all tornadoes are caused by butterflies' or all butterflies generate tornadoes.

All he said was that some small events “can be instrumental in generating a tornado”. If you imagine two planets which are identical except for one extra butterfly in one of them, then it's technically possible that one planet will grow a tornado and the other won't. That's the amazing truth of the butterfly effect.

But Lorenz's work also strongly suggests that there's no way for us to know which butterfly wings' flap, if any, is the one that changed the weather. There are just too many tiny influences for us to trace back to one without infinite computing power. And, in fact, the butterfly is just as likely to prevent a tornado.

These discoveries eventually led to the invention of a new branch of mathematics: chaos theory. It deals with systems, like weather, that are extremely sensitive to initial conditions, where small changes in the past have big effects in the future. People call it a new field of mathematics because it seems to happen everywhere.

You see it in the gravitational interactions of the rings of Saturn, in the swinging of a double pendulum, in the flipping of Earth's magnetic field, and even in parts of macroeconomics. And the really wild thing is that all these systems, despite being chaotic by nature, actually have a lot in common. There seems to be some universal behavior, and some structure, hiding in the chaos.

For example, if you make graphs of their properties you often see fractals, these amazing, infinitely repeating patterns. But what does all this mean for weather prediction? Well, it's gotten a lot better over the last few decades.

Thanks to better input data from satellites and the like, along with far more powerful computers and better algorithms, we can now predict weather events with more confidence and further into the future. And a better understanding of chaos theory helps a lot, too. And yet, anything beyond a few days from now is still obscured by the ‘fog of war' chaos theory creates.

Like with quantum mechanics, the laws of physics seem to impose strict limits on our ability to forecast. Whether it's the flow of air, or the tides of history, chaos is all around us, so it's definitely worth trying to understand it. Thanks for watching this episode of SciShow!

If you want to be better at understanding the science of meteorology, you might want to check out our episode explaining what a 50% chance of rain actually means. And if you don't want to miss any of our daily episode, be sure to click on that subscribe button below the video. And ring the notification bell! [ ♪ Outro ].