Don’t be surprised, if you have read my post January Favorites, you saw that my favorites books for January are The Hunger Games Trilogy. As promised here are some good mathematical concepts that the books offer us. We just have to open our eyes and enjoy maths. So lets start understanding the concepts.
Firstly, I don’t want to say much about the books, because I believe most of you already know the story. There are 3 movies out and they are quite popular, so I am expecting most of you already know the story. In case, you saw only the movies, I totally recommend you to read the books. They give more information about the society, the games and the characters; also you will better understand the concepts I want to talk about next.
The first mathematical concept is presented in the explanation of how are children selected for the Games. In the 1st book, there is a paragraph that explains exactly how many times the names appear in the ‘lottery’. A first formula appears: names = a + (n-1)d – an arithmetic progression where names represents the number of times a child’s name appears in the ‘lottery’, a=1, n ranges from 1 to 7 (standing for the ages 12 – 18 years the children are allowed to participate in the Games) and d=1 ( d represents the common progressive difference, which in our case is 1). This is easy to understand with a specific example: a 14 years old child will have his/her name 1+(3-1)*1=1+2=3 times in the ‘lottery’. Moreover, things change a little if the child puts its name multiple times in for food (which is Katniss’s example – see the 1st book).
In addition, we have some probability theory in there. Think of the following situation: there are 12 children of 12 years old in a district, 6 boys and 6 girls. Since the boys and girls are drawn separately, in the 1st year they have a probability of 1/6 each of being chosen in the game. Assume there are no other children in the district, so one girl and one boy is selected for the Games, that means that the next year their names will not put in the ‘lottery’, thus the remaining children have a probability of 2/10=1/5 each to be selected. Observe that 1/6 = 5/30 is smaller than 1/5=6/30, so the probability to be chosen next year is bigger. On the next years the probability increases as follows: 3/12=1/4 at 14 years, 4/12=1/3 at 15 years, 4/8=1/2 which is 50% chance at 16 years, and 100% chance at 17 years. Observe that the chance of being chosen not only increases with time but does so at an increasing rate. This is an extremely easy example, but things can become complicated if you consider the number of children is in a district, and also if you consider the fact that they can choose to put their names more times for food. Considering this the example could be an excellent way to introduce students interested in the book to important mathematical topics such as graphs (both their construction and interpretation), difference quotients, and rates of change. These are all important steps toward the differential calculus.
In addition there is another area of mathematics that relates to families choices about whether to enter their children’s names more times in exchange for food – the mathematics of decision theory. (for more about this theory, check Wikipedia) This comes from the fact that families can choose to enter their children’s names into the game more times, in exchange for more food, which will increase their children’s chances of being chosen for the games. On the other hand if they don’t do this, they may be increasing their chances of starving to death. The problem stays in understanding and interpreting the probabilities – an old issues among mathematicians/statisticians about whether or not probabilities are “objective” or “subjective”. Thus, the book(s) are an excellent way of introducing this important debate to students and others interested in mathematics.
Last but not least – The Hunger Games. There are 24 children in the arena, thus the probability for one to win is 1/24, and the probability to lose is 23/24. From this comes their so popular words: “May the odds be in your favor!”. Considering this phrase mathematically, we observe that the odds for a child to lose the game are: (23/24) / (1/24) = (23/24) * 24 = 23. Therefore, a child is 23 times more likely to lose the game than to win it, certainly not favorable odds, assuming the kid would prefer not die in a Hunger Game. But the problem is not that easy. So figuring out the probability of a given child winning also depends on that child’s skill set and how their skill set compares to others. What we have here is a complicated exercise in calculating conditional probabilities, not a game that can be approximated by names being drawn from an urn.
Moreover, the Games have another mathematical concept hidden there: game theory ( which is about modeling interdependent decision making, where the outcomes of one’s decision depends on decisions made by others). One of the most known problem is The Prisoner’s Dilemma. This is problem is applied to the 1st part of the Games, when the participants form groups / alliances. To understand this concept think of the following question: ” How do members of Cato’s
coalition in The Hunger Games get any sleep at all?” and apply the prisoner’s dilemma.
This post is inspired from the paper “Mathematics and The Hunger Games” by Michael A. Lewis. He ends the paper as follows:
But what I have tried to show here is that [the book(s)] are a great source of mathematical inspiration, perhaps the best such source we have seen from popular culture in some time. It could, I believe, easily be used to turn students and others on to some of the different, but no less compelling, thrills that can be found in mathematics.
Hope you like this post, let me know if you would like to see more like this. Also, what is your opinion about the books and the mathematical concepts presented above? Enjoy the rest of the week. Thank you for reading. You can find me on Facebook, Tumblr, Google+, Twitter and Instagram. Don’t forget that maths is everywhere, even in ‘The Hunger Games’ ^_^ !