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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 a lot 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 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 the 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 soundwaves 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 or thinking. 

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 study looked at people thrashing around in mosh pits at heavy metal concerts.  By analyzing videos, they found that moshers behaved remarkably like gas particles.  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 can turn into stampede, 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's 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.  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, many animals can act like fluids at times, not just humans.  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 like, a 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 infuenced 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 a species doesn't work exactly like a fluid.  For example, in fluids, permeability usually only depends on the  material itself and 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 has given 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 gonna 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 encryption, 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 that no one who hacks that 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 then 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 anytime 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 hard to undo, like trying to flawless unbreak 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 will compare that to the password gibberish it stored when you made the password to see if those two gibberishes match.  

So what's this all 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 makes it 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 then, as it expands or you stir it a little bit, the mix of coffee and milk gets these weird, kinda beautiful random patterns.

Intuitively, you know that you'll never be able to recreate those exact same patterns in a fresh cup of coffee.  It's just too random, 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 be able to 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 to 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 initial set of conditions, so the stirring process was also unique, and if it was repeatable one way and unique, that meant the process of stirring milk into coffee had all of 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 of cryptography aren't just some weird digital thing.  They crop up in the real world, too, and knowing that can help us think of new creative ways to study the properties of hash functions and think about cybersecurity, which is super important because cryptography is always an arms race between researchers and hackers, so any potential new source of hash functions is always useful.

So yes, the physics of coffee could potentially help us improve Bitcoin.  More broadly speaking, making analogies like the ones we've looked at here is a really important part of doing science.  It allows us to make connections you'd never otherwise think of and come up with innovative ways to solve problems, and there are tons of other systems out there that look at fluids, too, from electrons flowing in currents to galaxies flowing in space, it turns out lots of things in our universe like to go with the flow.

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