The Mathematics of Surviving Zombies - Numberphile

TL;DR

Math can explain the spread of zombies. Running away from them is a better strategy than trying to slow them down.

Transcript

The maths of zombies. Previously people didn't care if you  studied epidemiology through mathematics;   all they cared about was keep me healthy. And  so the way you'd sell it to people is okay,   let's talk about zombieism. It's the  same maths of flu, it's the same maths as   chickenpox, but it spices it up a little. And so  what we're going to c... Read More

Key Insights

• 🧟 The diffusion equation helps predict the movement and spread of zombies.
• 🧟 Slowing down zombies increases the time it takes for them to reach a target.
• 🧟 Doubling the distance between a person and a zombie quadruples the time it takes for the zombie to reach them.
• 🧟 Human encounters with zombies usually result in negative outcomes for the humans.
• 🧟 The zombie equation incorporates rates of zombie production, zombie killing, and zombie spread.
• 🧟 The speed of the zombie wave is determined by the square root of factors including zombie spread and the rate of zombie production minus the rate of zombie killing.
• ✳️ Isolating oneself or removing potential infected individuals can reduce the risk of infection.

Questions & Answers

Q: How is the movement of zombies related to the diffusion equation?

The diffusion equation helps predict the movement of zombies based on their random motion and speed. It takes into account the rate of change of zombies over time and the degree of random motion.

Q: What happens when a zombie meets a human?

When a zombie meets a human, there are three possible outcomes. The human can be killed by the zombie, the human can kill the zombie, or the human can get bitten and become a zombie themselves.

Q: How are the populations of zombies and humans affected by interactions?

The populations of zombies and humans change over time due to interactions. Zombies can increase through zombification and decrease through being killed by humans. Humans, on the other hand, can decrease through being killed by zombies and through dying.

Q: What happens when the equations are solved?

Solving the equations reveals that humans always lose population when encountering zombies. The zombie equation shows that if zombies are more infectious than the rate at which they are being killed, the infection will spread like a wave throughout the human population.

Summary & Key Takeaways

• The diffusion equation is used to predict the movement and spread of zombies, based on their random motion and speed.

• Time of first interaction with a zombie is proportional to the distance from them and the rate of zombie diffusion.

• Slowing down zombies doubles the time it takes for them to reach you, while doubling the distance quadruples the time.