Chapters

Even if you are not an avid fan, Game of Thrones (GOT, for short) has probably not escaped your notice. Every second person on the street you come across is discussing plot twists, new characters and other minutiae of the **hugely popular and commercially successful show from the house of HBO. **

## The Song of Ice and Fire

Indeed, GOT, adapted from the novels of George R. Martin has become a global phenomenon, having acquired a fiercely loyal fan base **(the GOT fans**) across the globe. The show has been at the centre of many passionate debates, one of the foremost being, **who is the show's main character?**

It is true that the saga contains a lot of characters and, judging by the growing number of characters, emanating from central ones each season, it is hard to keep track of the originals. The directors, it would appear, derive a sense of sadistic pleasure out of killing popular and much-loved characters, that too in the most brutal manner imaginable!

*“This is where mathematics can come in to help us uncover the lead character in the myriad of sub-plots.”*

**Mathematics in Game of Thrones**

Yep, you have read it right! Math teachers, A. Beveridge and J. Shan, of MacalesterCollege, wondered **if it would be possible to figure out the main character of GOT using a mathematical formula.** Their curiosity led them to employ a new science that is based on the mathematical formula of graphs.

They finally solved the problem with a **conclusion that might surprise you**, because as you know, the battle for the Iron Throne is seemingly never-ending and the answer to this mathematical problem could reveal a lot more about the rest of the show.

**SPOILER ALERT**!!!

## The World of Game of Thrones

Before we delve into the mathematical plots of GOT, it might be useful to get to know the storyline a little bit. **Game of Thrones is a television drama set against the backdrop of a fantasy-medieval universe. It was first released in the United States in 2011.**

*“To understand why mathematicians are interested in this television program, we must look at the story itself.”*

The story plays out in the imaginary continent of Westeros, under the governance of the Seven Kingdoms, lorded over by King Robert Baratheon. The different protagonists belonging to different ‘houses’ are revealed one by one, as the plot unfolds over multiple seasons. Alliances are forged and pacts are signed between these competing houses. However, they have one common goal – to usurp the Iron Throne.

Added to the internal strife is the constant external threat from the White Walkers – the ones made of ice and in possession of terrifying magical powers. They live ‘beyond the ice wall’, to the north of the kingdom.

*“Where there is magic, there are dragons. And, mathematics is never too far away!”*

**GOT – The Success Story**

Here are some statistics on the true magnitude of success that the HBO series has tasted.

- It has been
**broadcasted in 173 different countries.** - It also has the dubious distinction of being
**the most pirated series in history**. - It has
**won hundreds of awards**. - It has a
**budget of $ 100 million**to shoot the 10 episodes of season 6. - It has been
**filmed in 30 locations**around the world. - It has used approximately
**3,000 different costumes**. - GOT even
**invented a language called Dothraki**.

We are pretty sure even George R.R. Martin, with his remarkable imagination and storytelling prowess, could not envisage the sheer scale of the series’ success.

**Main Characters and Their Corresponding Houses**

- House Lannister: (the one that everybody loves to hate) with Cersei, Jaime, Tyrion, Joffrey Lannister.
- House Stark: They are the first introduced characters in the series. The Starks comprise Ned Stark, Robb Stark, Sansa Stark, Arya Stark, Bran Stark and, of course, the immortal Jon Snow.
- House Bolton: with Roose and Ramsey Bolton.
- House Greyjoy: with Theon Greyjoy.
- House Targaryen: with Daenerys Targaryen, "the mother of the dragons".

The above is not an exhaustive list as there are other characters central to plot points in the overall story. However, **those listed above are the most recurring ones.**

## Game of Thrones or a Network of Thrones?

Let us rewind and go back to the question we started with, rather Beveridge and Shan started with. **How to figure out the lead character in GOT using maths? How do the mysteries of math help to unravel the mystery of GOT?**

**The Mathematical Study of the Relations between the Characters**

The curious math teachers looked to a new field of mathematical study to solve their question. They did not rely on conventional branches such as geometry, algebra, some mathematical equations or even exponential functions.

*"They used a relatively new, but thriving research field: the science of networks!"*

**The Networks Theory**

The Network Theory, developed in 2007 in the United States, deals with **relationships, connections and interconnections between things**. Interdisciplinary studies have also been conducted using this theory in the fields of Physics, Biology, Information and Cognitive Sciences, and Social Networks.

*“Armed with the original novels and the Network Theory, the two teachers transformed the GOT universe into a gigantic network.”*

They used the **theory of graphs** (not your regular graphs that you struggle with, in class). They did not use abscissa, ordinates, curves, functions. Instead, they **studied the network of information flow between the different characters in the story.**

Intrigued much? **Read the rest of the story to give yourself a better chance of figuring out the statistical probability of your favourite TV characters getting killed/surviving.**

**Creating and Analyzing the Network**

To ensure accuracy in their results, the two mathematicians started out by listing all the interactions between the characters in the 3^{rd} novel in the series by R.R. Martin. They also counted the number of times these character names appeared. Following this, they used an algorithm to distribute the results in 7 distinct communities and to assign one colour to each. This is how the resultant network graph looked like.

There were **107 different protagonists** (called "vertices") connected by 353 connections (these are the "edges") in the above graph.

*“The research did not end there!”*

The researchers then proceeded to take several scales of measurement in order to **classify the characters according to their interactions with the most important characters. **This was done due to the fact that, in Beveridge’s own words, "A character can play a leading role in several ways."

**Measures of Centrality**

Several measures of centrality were studies in order to model the graph, including,

- The number of links of the character to the other protagonists.
- The number of interactions.
- The character's connections to the most important protagonists. Google's PageRank algorithm was used to define who the most important characters in the series were.
- The values of average distance, between the characters.
- The frequency of presence of a character.

**AND THE WINNER IS**…

*“Tyrion Lannister, mathematically speaking, was chosen as the main character of Games of Thrones!*

The experiment did throw up the names of Jon Snow and Sansa Stark as possible winners, Tyrion’s was the first of the first 4 centralities. Thus, a mathematical exercise, born out of plain curiosity, once again shows the enigmatic side of mathematics.

But, haters will be haters!

## Everyday Science of Networks

Very similar to the enduring legacy of Pi, the science of networks has always been with us. The advent of computer systems has largely made possible the evolution of the science of networks. On closer inspection, however, it would appear that **this** **science has always been around us, everywhere we look, **be it in the transportation we avail (road, air, rail, etc.), the natural networks (hydraulic, biological etc.), networks of infrastructure (water, gas, electricity, etc.), and the immensely popular social networks. Networks hold the key in politics, war and security, trade and every other imaginable aspect of our lives!

*“Can the study of networks act as a bridge between the different branches of science?”*

Historian M. Gribaudi and physicist J.P. Nadal have come together to answer this very question, with the help of researchers from across disciplines the world over - mathematicians, physicists, historians, linguists, sociologists, and many more. **This collaboration could be the first leap of faith needed for a great discovery in the future!**

On a friendlier note, go out there and **impress your friends in school by revealing the one true protagonist in GOT**. See their jaws drop as you explain, like a pro, how mathematics helped you figure this problem that has been the stuff of endless debates among GOT fans!

All said this exercise has been brought to you to help you understand how much fun learning math can really be. Calculations, fractions, geometric riders, quadratic equations only seem tough. You only have to feel their presence in your everyday life and they will appear more like friends to you, here only to make your life fun-filled and more exciting.