If you've ever been stuck in a traffic jam,

you may feel like you're in the middle of a clogged pipe.

And that intuition... isn't too far off from reality.

Scientists can model traffic flow using equations

originally invented for liquids in pipes.

This is actually a common thing in science:

Equations that were invented to describe one physical system

can end up being useful for something completely different.

In fact, fluid dynamics, the study of how liquids and gases

flow and evolve, is one area where this seems to happen a lot.

There are lots of scenarios where things that are remarkably

unlike liquids behave in pretty liquid-like ways.

Like birds.

And… bitcoin.

So by studying how liquids flow, we can learn a lot

about the rest of the world.

Here are three examples.

Crowds of humans can behave like fluids—

and I'm not talking, like, in a stadium where people are doing the wave.

People act like fluids without even meaning to.

It mostly happens when a bunch of people get really close together.

For instance, one 2019 paper looked at people lining up to start a marathon.

Since there are tons of these races around the world

each year, and they look pretty similar,

marathons are a great system to study.

And at the start of each race, you tend to see the same patterns.

Like, at the start of a marathon, there's typically a column

of thousands of people waiting to begin running.

But since the street is only so wide, only a few rows

at a time are allowed to pass the start line.

If you've seen a video of this happening,

you can see what looks like a wave moving back

through the line of athletes every time some runners are let through.

And in the 2019 paper, researchers wanted

to understand this pattern.

Their study was the first to look at a crowd of runners

as a whole rather than as a collection of individuals.

They found that the apparent waves actually

were waves of changing density and speed,

so as they passed through the crowd, the number of people

in a given area fluctuated and then settled back

into an even density — almost exactly like

sound waves moving through air particles.

And the amazing thing was,

this type of wave was predictable.

While the crowd was in equilibrium, the density of people

was pretty consistent.

It was actually pretty even from race to race, too.

But when waves did move through the crowd,

they moved at constant speeds.

Even from one race to another, one city to another,

the speeds of those density waves were similar worldwide.

Everything was so similar, in fact, that the researchers

were actually able to model the mass of people

as a continuous fluid, and they could accurately

predict the flow of runners.

That's right.

Using physics equations that describe fluids,

they were able to figure out how people would flow—

without knowing anything at all about what the individual people were doing.

Of course, marathon runners corralled at the start of a race

is a pretty contrived example of human crowds.

But lots of research has been done on other,

more erratic crowd movements,

and they behave like fluids, too.

For instance, one 2013 paper looked at people

thrashing around in mosh pits at heavy metal concerts.

By analyzing videos, they found that moshers

behaved remarkably like gas particles.

So they could actually model the movement of the moshers

using equations normally used to study gases.

Admittedly, this might not be the most useful application

of fluid dynamics in the real world — but it is very cool.

Still, research suggests that similar uses of fluid dynamics

could actually help us understand and prevent

crowd behavior that becomes dangerous.

Because, in tragic cases, erratic crowd movements

turn into stampedes, like the fatal one

at the Hajj in Saudi Arabia in 2015.

Stampedes like this don't happen because of how

individual people are acting.

They happen because people in crowds are part of a flow.

Typical crowds look like what's called laminar flow

of a liquid, where particles smoothly slip past each other

in clearly defined lanes.

But sometimes, as crowds get too dense, small perturbations,

like someone tripping, can cause the flow

to quickly become turbulent.

In a turbulent flow, movement becomes chaotic

and hard to predict, and people are pushed

in essentially random directions.

Situations like this can become more likely

if crowds are forced through bottlenecks,

like narrow emergency exits.

But there is a bright side:

By treating crowd flows as fluids, we can use fluid dynamics

to lower the odds of stampedes happening

and make crowds flow more smoothly.

For instance, simple measures,

like adding columns or other obstacles near emergency exits,

might actually speed up evacuations by reducing

the number of directions people approach from.

This is a technique also used for fluids, so even though

people aren't actually water molecules, it turns out

they can sometimes behave in pretty similar ways!

Now, a lot of individual species can act like fluids at times

—not just humans, but also birds in flocks or fish in schools.

And the language of fluid dynamics can be useful

for describing how they move, too.

But it can also be useful for describing how species

as a whole move across landscapes.

In 2018, some researchers wrote a paper doing exactly that.

Their goal was to understand how species

respond to changes in their environment

— especially human-made changes like

deforestation or habitat fragmentation.

Naturally, in a given landscape, species of animals and plants

spread out and populate different places.

So, first, the team wanted to understand

how quickly different species spread naturally.

They created a model using the equations

that describe how a fluid moves through

a porous material, like a sponge.

In fluid flow, the viscosity of a fluid tells you how resistant it is to flow.

And species have an analogous property, called mobility,

which measures how readily they disperse.

Like, you wouldn't expect rabbits to spread out over

a landscape at the same speed that, say,

lichen does—their mobility is different.

Then there's permeability, which describes

how readily a material lets fluids move through it.

So the researchers' model works out how permeable

a landscape is to different species that are

essentially “flowing” through it.

Using this model, they simulated a species spreading out

across a landscape from west to east.

Then they tested how different factors — like the mobility

of the species and the permeability of the terrain —

influence the rate of that spread.

And what's nice about this model is that it can be used

to test how species react to changes in their environments.

So we can use it to model what happens if, say,

the area becomes more urban and built-up.

And that can help us figure out how much humans

are interfering with species' habitats.

We can also use this model to work out how to keep

a population of a species connected when

human activity disrupts a landscape.

It's not a perfect analogy, because the spread of species

doesn't work exactly like a fluid.

For example, in fluids, permeability usually

only depends on the material itself,

nd not the fluid going through it.

But in this model, permeability depends pretty strongly

on the species, since a given terrain may be

much easier for a species of birds to spread through

than a species of trees.

So there are some limitations, but overall,

fluid dynamics give us a super useful way

to look at a species as a whole.

Finally, our third weird thing that acts like a fluid

isn't even in the physical world at all.

We're going to get digital and look at what in the world

cryptography has to do with fluid dynamics.

Cryptography is the science of sending information securely

—think “secret codes” and “cyphers.”

And the key to modern, online cryptography

is something called hashing, which is important

for everything from entering passwords

to paying people with bitcoin.

Basically, when you enter a password on a website,

you want to make sure no one who hacks

the website can get your password.

So any good site will use something called

a cryptographic hash function to convert your password

into what's called a hashed form—that's this weird gibberish

that only the computer can understand.

These functions typically use super advanced math,

but the basic concept isn't too tricky.

Overall, a hash function just needs to have

three properties to be useful.

First, it needs to be unique, meaning that you can

never get the same string of gibberish

from two different passwords.

Second, it needs to be repeatable, meaning that

any time you apply that function to the same password,

it will produce the same gibberish.

And finally, it needs to be one-way, meaning that the process

that turns it into gibberish is easy to do,

but really, really hard to undo

—like trying to flawlessly un-break a mirror.

If the hash function can do these three things,

the website never needs to store your password.

Instead, every time you enter the password,

it will just apply that function to make gibberish

from whatever you entered.

Then it'll compare that to the password-gibberish

that it stored when you made the password

to see if those two gibberishes match.

So, what's all this got to do with fluid dynamics?

Right.

So, in 2018, a scientist at Stanford figured out

that the equations of fluid dynamics can

behave like a hash function.

Which is a really abstract idea, but let's look at an example

that's much more familiar: a cup of coffee.

Think about what happens when you pour milk into coffee and stir it.

At first, the milk is a white drop in the coffee, but if you stir it,

the mix of coffee and milk gets these weird, random patterns.

Intuitively, you know that you'll never be able to recreate

those exact same patterns in a fresh cup of coffee.

But according to fluid dynamics equations,

it's not technically impossible.

If you drop the exact same amount of milk

in the exact same amount of coffee,

at the exact same temperature and pressure,

and stir it the exact same amount in the exact same direction,

with exactly the same all of everything,

then you will get the same pattern as before.

These are the initial conditions of the process.

And with the same initial conditions, the process is repeatable.

It's incredibly unlikely, and even tiny changes

in the initial conditions can completely mess it up,

but it is possible.

The Stanford scientist realized this and made two more intuitive leaps.

He knew that it's much easier to create a specific pattern

given the initial conditions than it is guess the initial conditions

by looking at the final pattern.

In other words, the process was one-way.

And he worked out that a particular pattern of milk and coffee

can only come from one exact set of initial conditions.

So the stirring process was unique.

And if it was repeatable, one-way, and unique,

that meant the process of stirring milk into coffee

had all the properties of a good hash function.

Essentially, the initial conditions are like the password,

the equations are like the hash function,

and the pattern produced is like the gibberish the website stores.

So now we know the complicated situations

in cryptography aren't just some weird digital thing.