position at some point in the future, you might think it’d be relatively simple.

We should be able to predict that with the known laws of motion, right?

But this calculation is actually so complicated that it requires a relatively powerful computer.

And even if you did do this calculation, and then are offered slightly different initial

conditions, you would think that the output might also only be slightly different.

But instead, you get....chaos. Specifically, deterministic chaos.

See, as humans, we’re always trying to know more about how our world works, so we make

models.

For example, we have a bowling ball.

We know the weight of the bowling ball, the effect of gravity, the density of the air,

and the height of the balcony from which the bowling ball is to be dropped, and we can

put all those things together into a system of equations that we could use to tell us

things like how fast the bowling ball would fall, or the force with which it would impact

the ground.

That means we can also reasonably predict what might happen if any of those variables

were to change.

This is a deterministic system—the behavior of certain variables is determined by their

known characteristics. But not a lot of the world is like the bowling ball example.

It’s a whole lot messier.

Take the weather.

Just think about all the things that go into making weather—temperature, humidity, wind

strength and direction, rotation of the earth, I mean the list is exhaustive.

We do have models for how all these many variables behave, but a perfect weather prediction would

require highly accurate measurements of all of the contributing variables over every square

inch of the piece of atmosphere we’re looking at. In a system like this, little measurement

errors can result in HUGE fluctuations of our calculated result.

Tiny changes of the input mean a LARGE variation of the output. Now don’t get me wrong—the

system is still deterministic.

The variables behave the way we expect them to based on their physical properties, so

it’s quite different from something that is ‘random’.

But it’s highly unpredictable and subject to vast variations.

The system may look disorganized, but there is a set of rules that apply to the chaos.

Deterministic chaos—you may have also heard of it as chaos theory or the butterfly effect.

Weather is actually how chaos theory was first discovered.

Edward Lorenz, a meteorologist at MIT, was performing an early weather simulation in

the 1960s, when he took a shortcut and used input numbers rounded to the nearest thousandth.

He expected to get slightly different results from the version with the full numbers...but

what he got instead was completely different. His investigation into this unexpected outcome

led to the birth of chaos theory, or the idea that chaotic systems magnify even the tiniest

changes in the component parts of that system.

Chaos can make it impossible to accurately predict the behavior of such a system at a

faraway point in time.

You know how you like to complain that the weather report is always wrong?

Blame chaos.

We can never measure the initial conditions precisely enough to accurately predict the

weather past a certain point in time.

That tiny bit off that we will always be is enough to produce a wildly inaccurate prediction

as the system progresses. If sensitivity to initial conditions is one defining factor

of a chaotic system, the other is something called a strange attractor.

Which is just as odd and exciting as it sounds.

Lorenz and his team found that when they ran the weather simulation over and over with

slight variations in input resulting in vastly different results, when you visualize these

patterns, the paths never overlapped.

But at the same time, the paths seemed to circle these empty areas of space—this pattern

is an example of what’s called a strange attractor and one thing that differentiates

a chaotic system from random behavior. With Lorenz’s particular chaotic example, the

visualization starts to look a bit like a butterfly.

The phrase ‘if a butterfly flaps its wings in Brazil it could cause a hurricane in Texas’

is not what the theory is named after, it’s just a memorable example.

This first chaos work required some innovative computing, and although Lorenz typically gets

all the credit for being the ‘father’ of our modern chaos theory, he actually did

this work with two young mathematicians, Margaret Hamilton and Ellen Fetter.

Hamilton later went on to develop the math that got Apollo 11 to the moon, and is credited

with coining the term ‘software engineering’.

So many natural systems are chaotic, like the climate as a whole, the dynamics of clouds,

population dynamics, the patterns of the stock market...the way your milk swirls into and

combines with your coffee?

That’s chaos theory in fluid dynamics. These systems may be chaotic and have seemed impossibly

daunting in the past.

But the math of chaos theory is now small potatoes to the huge supercomputers that we

can use to calculate the progression of chaotic systems like the climate with more accuracy

than ever before.

Even outside of modeling, chaos theory proves exceptionally useful in other fields...like

encryption. And as we move into brave new worlds of exascale computing, quantum computing,

machine learning and other kinds of artificial intelligence, it’ll be exciting to see just

how far we can push chaos theory to help us predict the behavior of chaotic systems...essentially

looking further into the future than we ever have before.

If you want more on unusual math, check out our video on fractals over here, and subscribe

to Seeker for more deep dives into tangled topics like this.

Let us know what math subject you want us to tackle next in the comments below, and

as always, thanks for watching.