[music playing] Back in the day, sailors used to tell stories about these monster waves.

These waves were enormous, two to three times taller than the tallest average waves, even in stormy conditions, and big enough to sink ships as big as ocean liners and oil platforms.

They would talk about being battered by this giant wave and barely living to tell the tale.

And these waves would form in the open ocean, randomly, spontaneously, and without an obvious cause.

But people tend to exaggerate.

And scientists who study the ocean didn't buy it.

These tales of so-called rogue waves were happening far too frequently to be true.

And according to their calculations, rogue waves could form based on a wave phenomenon known as superposition.

When two waves combine crest-to-crest, the waves double in size.

Oh, and when they combine trough-to-crest they cancel out.

So if a bunch of normal waves happen to meet at the right place at the right time, they could create one monster wave.

This wave would break with a force of 100 metric tons per square meter.

That's like 15 elephants standing on your car.

Needless to say, your little boat would not fare well.

But according to superposition, these waves should be incredibly rare.

They should happen maybe once every few years.

And it took scientists until 1995, barely 20 years ago, to realize they were wrong.

On New Year's Day in 1995, a 25 and 1/2 meter wave crashed against an oil platform off the coast of Norway.

This wave was twice as high as any wave ever measured in that part of the ocean.

And it wasn't a tsunami or a tidal bore, which is caused when ocean tides meet river currents.

So for the first time, a rogue wave was measured and scientists could no longer deny their existence.

So they looked further.

A study by the European Space Agency in 2001 using satellite data found more than 10 high amplitude rogue waves occurring within a three week period.

So maybe all those ships of yore that disappeared into thin air were actually sunk by monster waves, because rogue waves aren't so rare after all.

Why were scientists so wrong?

Well, it turns out ocean waves are really complicated, more complicated than just superposition.

Imagine trying to explain a human to an alien, you might start with a stick figure, which is pretty good.

You've got the head, torso, and some limbs, but then try explaining the circulatory system.

Yeah.

In the same way, superposition can describe some aspects of ocean waves.

But it's just too simple to explain most phenomena like rogue waves.

So what's missing?

Well, waves formed due to many, many factors, wind, tides, the geology of the ocean floor, differences in temperature throughout the ocean, even varying amounts of salt can affect ocean waves.

And you end up with this complicated, unexpected, chaotic system of wave behavior.

You can see interdependent behavior like this in something as simple as a double pendulum.

Initially, it behaves pretty normally, but the pendulum's behavior soon becomes utterly unpredictable, because the motion of the bottom joint depends on the motion of the top joint.

So it turns to chaos.

Physicists call these weird behaviors non-linear effects.

Many of the processes that we're familiar with are linear processes.

Baking cookies for the most part is linear.

If you double your ingredients, you make twice as many cookies.

Similarly, when you use superposition to add two waves of the same size, the height doubles.

On the other hand, watering a cactus twice as much doesn't necessarily mean it will grow twice as high.

In fact, it might even die.

This is a non-linear process.

It means that increasing your input doesn't necessarily increase your output, well, linearly.

Some phenomena seem linear at first, but in fact become non-linear, like stretching a rubber band.

If you pull twice as hard, it will stretch twice as long.

But if you stretch it four, six, eight times as hard, it won't keep stretching proportionally.

It'll snap.

Despite the fact that the most common model of adding waves, superposition is linear, ocean waves are non-linear.

Physicists and mathematicians figured out that only by adding in these nonlinear effects could they figure out why rogue waves are so common.

It turns out that when you add two ocean waves, you don't necessarily double the height.

Waves are chaotic and hard to predict.

Depending on the scenario, you could have a bunch of normal waves passing by.

And then through non-linear processes, energy is passed between waves concentrated on one wave that becomes a giant monster rogue wave.

That's just scary.

So now that we know about nonlinear chaotic effects, does that mean that our superposition model is no good?

Well, no.

In certain circumstances, like calm water with small waves, you can use superposition to add and cancel out waves, just like with our rubber band.

It started out linear when you first start stretching it, it's only when you take it to the extreme that it becomes non-linear.

Just like Newton's laws of motion are great, until you move near the speed of light, then you need Einstein's relativity.

This is an excellent reminder that science is based on models and not absolute truths.

Scientists were wrong when they thought that they knew the entire picture about ocean waves, but it's exciting when scientists are wrong.

It just means that there are so many more details ahead in the nature that we have yet to discover.

Thank you so much for watching and happy physicsing.