De wiskunde in The Fault in Our Stars

TFIOS-bankje-wordt-teruggezetNee, ik heb het hier niet over de film, waarin bovenstaand bankje aan de Leidsegracht (Amsterdam) een glansrol vervult, maar over het gelijknamige boek waarop deze film gebaseerd is.

In het boek, van John Green, zit enige wiskunde verstopt. Allereerst is daar de bekende paradox van Zeno, Achilles en de schildpad, die het verschil tussen actueel en potentieel oneindig verkent.

So Zeno is most famous for his tortoise paradox. Let us imagine that you are in a race with a tortoise. The tortoise has a ten-yard head start. In the time it takes you to run that ten yards, the tortoise has maybe moved one yard. And then in the time it takes you to make up that distance, the tortoise goes a bit farther, and so on forever. You are faster than the tortoise but you can never catch him, you can only decrease his lead.

Of course, you just run past the tortoise without contemplating the mechanics involved, but the question of how you are able to do this turns out to be incredibly complicated, and no one really solved it until Cantor showed us that some infinities are bigger than other infinities.

Dat oneindig wordt verder verkend via onderstaand citaat, waaruit wat zinnen zijn weggelaten. Let op: niet alles klopt! Wilt u meer over het begrip oneindig in de wiskunde weten, dan kunt u hier terecht.

I can’t talk about our love story, so I will talk about math. I am not a mathematician, but I know this: there are infinite numbers between 0 and 1. There’s .1 and .12 and .112 and an infinite collection of others. Of course, there is a bigger infinite set of numbers between 0 and 2, or between 0 and a million. Some infinities are bigger than other infinities. […] There are days, many of them, when I resent the size of my unbounded set. I want more numbers than I’m likely to get […]. But […], my love, I cannot tell you how thankful I am for our little infinity. I wouldn’t trade it for the world. You gave me a forever within the numbered days.