Name: Zombies and Calculus
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<div class="rich-text">Zombies are wreaking havoc on the campus of a small college in New England. Mathematician Colin Adams says that calculus can help us understand the fluctuations in the numbers of people and zombies. Stay inside, stay safe, and study your derivatives.
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The zombie apocalypse is here, and calculus explains why we can't quite finish them off.

The zombie apocalypse is here, and calculus explains why we can’t quite finish them off.

Zombies and Calculus

<div class="rich-text">The zombie apocalypse is here, and calculus explains why we can't quite finish them off.</div>

Physics & Math

<div class="rich-text">
 OK, looks like the coast is clear. I’m Colin Adams and I’m making this video to try to help you to survive the zombie apocalypse, with all the…


 Oh, hang on a second. Ah, trouble folks, real sorry. Not gonna have time to do this right now. I’ll catch up with you later.


 OK, I think we’re good—let’s try this again. I’m Colin Adams, I’m here in my office. I’m a math professor at Williams College, or at least what’s left of it at this point.


 And I’ve been out there—it is bad out there right now. The number of zombies is through the roof—it’s growing really fast. The number of humans is dropping really fast.


 And this idea of numbers changing like that is an idea that comes up in calculus, and it’s called the derivative. So the derivative is measuring how fast quantities are changing. In this case, we’re interested in how fast the number of humans is changing and how fast the number of zombies is changing.


 So let’s think about what contributes to the number of zombies at any given time. And just for convenience, we’re gonna think of each zombie corresponding to a red lentil. So the total number of zombies will just be the total number of red lentils, and we’re gonna call that number
 
 Z
 
 .


 What can change that number? Well, first of all, zombies, if they can’t find anybody to eat, they will eventually starve to death, and that will decrease the number of zombies that we have. On the other hand, when a zombie interacts with a human, that zombie either gets sustenance by eating a person. Or that zombie can convert somebody into a zombie, which will also increase the number of zombies that we have.


 So now let’s talk about the total number of humans. And let’s represent each human with a brown lentil. So the total number of humans will be equal to the total number of brown lentils. And we’re gonna call that number
 
 H
 
 .


 Now, unlike zombies, as far as we know, humans can have babies. And that will increase the number of humans. If there’s a zombie-human interaction, the zombie can attack a human, kill the human, and therefore the number of humans will drop.


 Now, if there’s a lot of people and a lot of zombies, then there’s gonna be a whole lot of interaction. That is not gonna be pretty. I’ve seen it—it is awful.


 Ohhh, for the love of Newton. Things are looking bad out there. Don’t know how much time I have. I mean, this situation really reminds me of situations that occur in nature. Think about a wolf population and a deer population. The wolves are the predators, the deer are the prey. Very similar to the situation that we’re in, only the zombies are the predators and we’re the prey.


 So let’s think back to when this whole thing started, and there were lots of people and there were just a few zombies. But those zombies had lots of people to convert into zombies, and that meant that the number of zombies went up dramatically.


 As that was occurring, the number of humans was dropping precipitously. And eventually, we got to a state where there were very few humans left and lots of zombies. Now, that couldn’t last because of course the zombies no longer had people to eat, so the zombies started to starve to death. Until we reached a point where both the number of humans and the number of zombies was small.


 In that situation, the humans had a chance to recover, and the number of humans started to increase again.


 Now unfortunately, that meant the zombies again could convert a lot of people into zombies. And suddenly the number of zombies started to increase, and I think that’s the situation we’re finding ourselves in now.


 So it looks like this is just gonna repeat—the number of zombies will go up, the number of people will go down. The number of people will go up, and the number of zombies will go down. Like an endless cycle going on and on and on, unless we can be smart. And unless we can overcome them using our brains.


 Oh, I wonder who that is?


 Yeah, yeah, yeah, what’s up? Oh no!
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