- You've probably heard this one before: a butterfly flapping its wings in one place can lead to a tornado in a whole other part of the world.

That's the butterfly effect, and chances are you've seen it everywhere, from Jurassic Park to TikTok.

But its roots run way deeper than that, because the butterfly effect isn't just about how some small choice or event changed your life years down the road.

It's about chaos, math, and just how well we can know our complex, unpredictable world.

We'll come back to the butterfly effect, but first we need to back up to Isaac Newton, because after he described the laws of motion in the 1600s, the universe seemed straightforward, knowable, and predictable.

Then Newton ran into what's known as the Three-Body Problem.

He found that he could use math to predict Earth's path around the Sun using the starting position and velocity of both bodies.

But once he added a third body, like the Moon, there were too many variables, so he couldn't predict their future position and velocity.

Newton never did find the answer to the three-body problem.

Two centuries later, no one else had either.

Eventually, French mathematician Henri Poincare theorized that the problem had no practical solution, because of a concept called Sensitive Dependence on Initial Conditions.

The idea was that in some systems, even small differences and where something starts can dramatically change where it ends up, making prediction all but impossible.

That concept is central to Chaos Theory, which says that we can't definitively predict the position and action of every single atom, and therefore there are limits to what we can know.

For example, say I'm going to knead some walnuts into a bread dough- or a Play-Doh, because mess.

The more I work the dough, the more things move around and I'll never make the same bread twice.

Even small differences in where the walnuts were in the first place, or how many times I fold the dough could push the walnuts into a completely different spot in the dough.

And we can see this type of chaos in all kinds of systems.

From the motion of gas molecules to the path of a double pendulum to the staple of office small talk, (thunder booming) the weather, which brings us back to the butterfly effect.

In 1961, MIT meteorologist, Edward Lorenz was using a weather prediction program to simulate earth's atmosphere using equations.

At the time, most people thought weather prediction should be pretty straightforward.

If we look at enough historical data, we should be able to predict what will happen in the future.

But one day, Lorenz wanted to take a closer look at some of his data, so he reentered some numbers into the computer and in the process, the number 0.506127 was rounded to 0.506, a seemingly minor difference.

For a while, the resulting numbers followed the same pattern as the original, but then they changed, eventually predicting completely different weather.

Lorenz tried all sorts of experiments to see if he could shift that trajectory and produce a run where small changes didn't ultimately lead to big differences.

But eventually he theorized that tiny actions could impact something dynamic, like weather forecasts resulting in large scale changes.

In 1972, Lorenz gave a presentation called "Predictability: Does the Flap of a Butterfly's Wings in Brazil Set Off a Tornado in Texas?"

And there you have it, the butterfly effect was born.

People have gone on to debate whether or not it's literally true that a butterfly can set off a tornado, but either way, it's a helpful analogy for describing sensitive dependence on initial conditions.

The butterfly effect helps us understand just how unpredictable systems like the weather can be.

Small changes or errors in the way a weather station measures temperature or humidity could lead to wildly different weather forecasts.

But that doesn't mean these systems are entirely unknowable.

There are mathematical tools that help us describe and find overall patterns and trajectories in chaos.

For example, differential equations relate one or more variables to the rate that the same variables change and fractals are complex repeating patterns created by repeating a process or equation over and over.

With these tools, we can visualize, analyze, and begin to make sense of unpredictable systems.

Which is why we have weather forecasts at all.

Since the 1950s, we've made huge technological advances in weather forecasting.

We've got satellites that help us track atmospheric trends and supercomputers that use complicated models and equations to simulate weather conditions and make predictions.

We also use ensemble forecasting where multiple models with slight variations are compared to estimate a range of possible outcomes.

The spaghetti plots you see during hurricane season are an example of how we can visualize this ensemble forecasting.

And when more of the outcomes look similar, the more confident forecasters are.

So the first three to five days of a forecast can usually give us a pretty accurate idea of whether we will need, say, a sweater or not.

Beyond that, things get complicated again.

More than 10 days out, there are too many variables, so forecasting is mostly guesswork.

And as we move even farther out into the future, and as climate change drives extreme weather events, even more variables are introduced and forecasting future conditions becomes even more complex.

But that's not to say we won't get there.

Our world is made up of intricate patterns and structures that can show us connections between seemingly random events, systems, and outcomes.

And these patterns can help make even the most complex unknowable problems, something we can continue to trace, model, consider, and try to understand.

So when it comes to our ability to solve the unsolvable and predict the unpredictable, who knows what the future might hold.

(light music)