Tag Archives: game of thrones

Always wear a helmet to a duel: network analysis shows Game of Thrones infamous murders were pretty predictable

Credit: HBO

George R.R. Martin’s Game of Thrones book series is renowned for its complex narrative featuring thousands of characters whose plot lines elegantly intertwine with one another. Now, a new study performed by an interdisciplinary team of scientists, including physicists, psychologists, and mathematicians, employed data science and network analysis techniques to reveal hidden connections between your favorite GoT characters.

The findings suggest that the interactions between the various characters in the epic saga are very similar to how humans maintain relationships in the real world. And, perhaps most surprising, the tragic murders for which the series is famous aren’t all that unpredictable or as random as they may seem at first glance.

“This study came about when keen personal interests in G.R.R. Martin’s writing intersected with an established research project called ‘Maths Meets Myths‘. This project has been using mathematical tools like network science to quantify and compare the structure of mythological epics. We thought it would be both fun and informative to apply these methods to A Song of Ice and Fire since it really stands out in terms of scale and complexity,” co-author Professor Colm Connaughton, from the University of Warwick, told ZME Science.

“I would say the main finding is that Martin’s writing, either consciously or subconsciously, reflects social and temporal patterns that we are cognitively familiar with from real life. We propose that this helps to keep the narrative both comprehensible and engaging despite its huge scope,” he added.

The social network at the end of the first book “A Game of Thrones”. Blue nodes represent male characters, red are female characters and transparent grey are characters who are killed by the end of the first book. Credit: University of Cambridge.

The researchers found that the over 2,000 named characters in the A Song of Ice and Fire series had over 41,000 interactions between them. But if you could only remember a handful, that’s just perfectly normal. According to an often-cited figure, known as Dumbar’s number, humans can only maintain 150 connections at a time and according to the new study, the most predominant characters in the book average out to have only 150 others to keep track of.

British anthropologist Robin Dunbar found this ‘magic’ number after studying the ratios between brain sizes and group sizes in non-human primates. When he applied the same technique to humans, Dunbar found a remarkable consistency around the number 150, which seems to be the upper limit to how much social complexity the human brain can handle. It’s quite fascinating to see the same number pop up in a fantasy world — in fact, this may partly explain why G.R.R. Martin’s books have been so successful.

“We propose that such consistencies help in making Martin’s world comprehensible to us regardless of whether or not we find realistic parallels in the story,” Connaughton told me in an email.

Many GoT fans have expressed their dismay when leading characters, whether loved or hated, were expeditiously killed off at the stroke of a pen. Some may think that these deaths are somewhat random in order to thicken the plot and keep the story interesting as it unfolds over thousands of pages. But the study shows that there is actually a pattern to them when the chronological sequence is reconstructed. According to the findings published in the Proceedings of the National Academy of Sciences, the untimely deaths actually reflect common historical patterns in the real world. And it’s this mix of realism and unpredictability that makes the books so engaging.

“Patterns in when deaths occur help to explain why many readers find the narrative to be full of surprises and often feel that no characters are ‘safe’ in Martin’s world. For example, I remember personally, being shocked at Eddard’s exit in book one and I certainly never saw the Red Wedding coming! At least now, I have a better understanding of why,” Connaughton explained.

GoT’s complex narrative and tangled web of characters just became a whole lot easier to understand now — but this work wasn’t straightforward. British researchers from  Coventry, Warwick, Limerick, Cambridge, and Oxford universities all contributed with their own unique set of expertise, and tying everything together was challenging, to say the least.

“The biggest challenge was figuring out how to get 7 authors with very diverse perspectives to agree on the final wording of the article. There are some sentences in there that took a day to write!” Connaughton said.

The same method can be used to perform literary analyses of other books. More such studies may tell us more about how complex narratives can be comprehensible and relatable. They also show that the greatest authors are those that reflect real life with their works.

“Narratives are centrally important to how we understand and relate to our social world.  While we can identify clear human preferences for simple narratives, many issues cannot be sensibly reduced to simple stories. It is surprising how little we understand about what makes for a successful complex narrative. Our work aims to help in this understanding,” Connaughton said.

Obsidian is one of the only few substanes that can kill the undead from Game of Thrones. Credit: HBO // YouTube

Why Game of Thrones’ Dragonglass is so deadly

Obsidian is one of the only few substanes that can kill the undead from Game of Thrones. Credit: HBO // YouTube

Obsidian is one of the only few substances that can kill the undead from Game of Thrones. Credit: HBO // YouTube

In Westeros, there are only two substances capable of killing White Walkers: Valyrian steel and Dragonglass. The Maesters, however, refer to Dragonglass as obsidian — a naturally occurring volcanic glass formed as an extrusive igneous rock.

In George R.R. Martin’s books, as well as in real life, obsidian can be extremely dangerous. Well-crafted obsidian blades can have a cutting edge many times sharper than high-quality steel surgical scalpels.

 A knife blade manufactured from mahogany obsidian. The craftsman also added a serrated edge. Credit: Al Braunworth // Geology.com

A knife blade manufactured from mahogany obsidian. The craftsman also added a serrated edge. Credit: Al Braunworth // Geology.com

Today, some surgeons use obsidian scalpel blades with the blade’s cutting edge only 3 nanometers thick or almost 30,000 thinner than human hair. However, the history of obsidian blades goes much farther back in time.

The finest of these prismatic blades were produced in Mesoamerica about 2,500 years ago, according to Dr. Don Crabtree who re-discovered the production technique in the 1970s. “The prismatic glass blade is infinitely sharper than a honed steel edge, and these blades can be produced in a wide variety of shapes and sizes,” wrote Bruce A. Buck in a paper published in 1982.

Motolinia, a 16th-century Spanish observer, left this account of prismatic blade production:

“It is in this manner: First they get out a knife stone (obsidian core) which is black like jet and 20 cm or slightly less in length, and they make it cylindrical and as thick as the calf of the leg, and they place the stone between the feet, and with a stick apply force to the edges of the stone, and at every push they give a little knife springs off with its edges like those of a razor.” Hester et al. (1971)

The volcanic glass is thought to be so sharp because of the way it breaks, a pattern geologists call a conchoidal fracture. This means the obsidian breaks into pieces with curved surfaces that are razor thin and extremely sharp.

Over time, ancient peoples learned to break obsidian into tools of various shapes. All sorts of prehistoric artifacts made from obsidian have been found by archeologists, including knives, arrowheads, spear points, and scrapers.

[panel style=”panel-success” title=”What’s Obsidian?” footer=”Source: Geology.com“]

Various obsidian tools and blades. Credit: The National Park Service

Various obsidian tools and blades. Credit: The National Park Service

Obsidian is an igneous rock that forms when molten rock material cools so rapidly that atoms are unable to arrange themselves into a crystalline structure. It is an amorphous material known as a “mineraloid.” The result is a volcanic glass with a smooth uniform texture that breaks with a conchoidal fracture

Black is the most common color of obsidian. However, it can also be brown, tan, or green. Rarely, obsidian can be blue, red, orange, or yellow. The colors are thought to be caused mainly by trace elements of inclusions. Source: Geology.com. [/panel]

Historians believe obsidian may have been the very first material actively mined and used to manufacture sharp tools at scale. Ancients may have transported these goods thousands of miles to trade for other goods and services.

Remarkably, obsidian tools may even predate humans! Researchers have found what they believe to be the oldest known stone-tipped throwing spears. The remains are so ancient that they actually predate the earliest known fossils of our species by 85,000 years. These spears were made from obsidian by either another species — which had to be extremely crafty and clever — or ancient humans. The latter possibility means that our species is at least 85,000 older than we believe.

Map showing the locations of some of the main obsidian sources in Mesoamerica. Credit: Wikipedia

Map showing the locations of some of the main obsidian sources in Mesoamerica. Credit: Wikipedia

The Pre-Incan civilization used brain surgery as an extensive practice as early as 2,000 B.C. with an inordinate success rate noted among patients, archaeologists say. These ancient doctors used brain surgery to treat a variety of diseases like mental illnesses, epilepsy, headaches, organic diseases, neuropathy treatment, osteomylitis, and head injuries. The surgical tools they used were made from bronze and shaped obsidian.

Despite the fact that obsidian is a very popular material used for mirrors, decorations, and even bogus energy trapping, the glass’ main use nowadays is still as a cutting tool.

Jon and Daenerys

Game of Thrones inbreeding: odds are stacked against Jon and Dany having a healthy baby

Jon and Daenerys

Credit: Game of Thrones / HBO.

During Game of Thrones’ previous season finale, viewers had the confirmation of Jon Snow’s true identity. As many die-hard fans of George RR Martin’s books have known, or at least suspected, for years, Jon Snow’s father is Rhaegar Targaryen, the young prince who secretly married Jon’s mother and Ned Stark’s sister Lyanna in the Tower of Joy.

There’s a big dilemma with this newfound insight, though. You see, it means that Jon Snow, or Aegon Targaryen by his birth name, is Daenerys Targaryen’s nephew. The two are now lovers which can only mean there’s a big risk any children the two might birth would be extremely disabled or messed up in some way.

A game of chance?

According to Jonathan Pettitt, a University of Aberdeen geneticist who actually calculated what are the odds of the baby being born with problems, the pair share 44 to 47.5 percent of their DNA. Siblings typically share 50 percent of their DNA while unrelated people ought to share zero.

As such, any child produced in this incestual union shouldn’t be healthy by our universe’s standards.

“Jon Snow is not so inbred as Dany, so their offspring would be less inbred. The inbreeding coefficient of any child of Jon and Daenerys would have an inbreeding coefficient (calculated as half of their relationship coefficient) of 22 percent. So, slightly less than that of Charles II of Spain, though not by very much,” Pettitt told Inverse

Targaryen family tree. Credit: HBO

Targaryen family tree. Credit: HBO

The fact that Jon is only half Targaryen softens things up a tad but Daenerys still has an extremely high coefficient of inbreeding of 37.5 percent since both her parents and her grandparents were siblings. She didn’t turn out too bad, of course, but unless genetics in R.R. Martin’s universe works fundamentally different, we can consider she was plain lucky.

Painting of Charles II of Spain (6 November 1661 – 1 November 1700).

Painting of Charles II of Spain (6 November 1661 – 1 November 1700).

Take Charles II of Spain, for instance. He was the last king of the Spanish Hapsburgs line, a dynasty where uncle-niece, first cousins and other consanguineous unions were prevalent. He died prematurely aged 39 but not before his imbecile behavior plunged his kingdom into chaos eventually leading to the War of Spanish Succession. This was the first world war of modern times with theatres of war in Spain, Italy, Germany, Holland, and at sea. It’s estimated the war resulted in 400,000 casualties. 

Here’s how one biography describes King Charles (Carlos) II:

“The Habsburg King Carlos II of Spain was sadly degenerated with an enormous misshapen head. His Habsburg jaw stood so much out that his two rows of teeth could not meet; he was unable to chew. His tongue was so large that he was barely able to speak. His intellect was similarly disabled. His brief life consisted chiefly of a passage from prolonged infancy to premature senility. Carlos’ family was anxious only to prolong his days and thought little about his education, so that he could barely read or write. He had been fed by wet nurses until the age of 5 or 6 and was not allowed to walk until almost fully grown. Even then, he was unable to walk properly, because his legs would not support him and he fell several times. His body remained that of an invalid child. The nature of his upbringing, the inadequacy of his education, the stiff etiquette of his court, his dependence upon his mother and his superstition helped to create a mentally retarded and hypersensitive monarch.”

Like Daenerys, Charles II was the culmination of generations of cousin and sibling marriages. Fortunately, the beautiful silver-haired Daenerys Stormborn of the House Targaryen, First of Her Name, the Unburnt, Queen of the Andals and the First Men, Khaleesi of the Great Grass Sea, Breaker of Chains, and Mother of Dragons, never inherited the famous Habsburg jaw.

We can’t rule out though that Charles’ faith won’t befall any offspring Dany and Jon have.

“They would still be predicted to be fairly sick based on real-world genetics,” says Pettitt. “So, overall, not likely to be great material for founding a future dynasty!”


The kill rate in Game of Thrones is actually quite realistic, a new study reveals

“When you play the game of thrones, you win or you die,” Queen Cersei said. Apparently, she was right.

Sorry, Jon. Your world is just as brutal as the real one was in Medieval times.

George R. R. Martin started writing the first Game of Thrones (GoT) novel in 1996. That’s right kids, A Song of Ice and Fire, as the fantasy series is called, started more than 20 years ago. But it definitely blew up when HBO turned it into a TV series. It was an instant hit. The drama, the strong, believable characters — and the violence. GoT stood out through violence, leaving many people wondering if they’ve gone too far. As it turns out, the answer is no — they haven’t gone too far. In fact, they haven’t really gone far at all. The fatality rates in the series match those in reality.

Celine Cunen, PhD student at the Department of Mathematics at University of Oslo has examined whether the mortality rate in GoT is higher than that of a real civil war from the Middle Ages. She compared the fantasy with  the famous War of the Roses, a civil war that ravaged England between 1455 and 1487, from which Martin took a lot of inspiration. Cunen found that mortality rates of main characters in the TV show match the mortality rate of the noble classes in the War of the Roses.

This might come as quite a shocker for most people, but we tend to forget just how brutal and unforgiving those times were. That a series which strikes us as incredibly violent is just normal for the Middle Ages says a lot about those times, as much as the ones we live in now.

Statistics for “important” people

Left: Graph of survival for GoT characters (red) and War of the Roses people (blue). The faster the arc falls, the higher the mortality rate. Right side: Graph of survival for noble GoT characters (dark red) and GoT commoners (light red) and noble historical people (dark blue) and historical commoners (light blue). Graph: Celine Cunen/UiO.

The Wars of the Roses was fought between supporters of two rival branches of the royal House of Plantagenet: the House of Lancaster and the House of York. This is mirrored in the GoT series as the Houses of Lannister and Stark (spoiler alert, in the real war, the Lancasters won). Although Martin mentions the lower classes more than other authors, it’s clear that the books are biased towards the higher echelons of society — that’s where all the cool things happen. The same can be said in the historical evidence of the War of Roses. The information we have is greatly skewed towards mentioning the nobles. In a world where rulers fight for the throne, there’s little place for commoners. So this is not a statistic made for the general population of the time, as Cunen herself mentions.

“The medieval wars were fought by the nobility and professional warriors. Furthermore, all historical data from these wars are completely fixated on so-called “important people”, meaning politicians or nobility. Consequently, this is not a comparison on these wars general mortality, but a comparison on the mortality between «important» people.”

The mortality rate in the War of the Roses and GoT, considering the sample, is very similar. Even without dragons, medieval noblemen managed to kill each other just as fine as Martin’s groundbreaking series. So remember, instead of cursing Martin or HBO for killing of your favorite character, you can just curse the reality who inspired them.

Cunen adds that she did all this for fun. She found that it’s a nice way of communicating statistics to a broad audience. Adding a layer of both historical and literary significance is just a bonus.

“I have to add: I did this just for fun. I am part of a group of researchers that wish to communicate statistics to the world. I regarded this as a good opportunity to do just that! However, it is of course impossible to obtain a correct statistical basis in a comparison between a TV-show and a historical war. But it might give you some idea of the realism of the show!”

Pheidole viserion, a newly discovered ant species from Papua New Guinea © OIST

Meet Viserion and Drogon: the new ant species named after the Game of Thrones dragons

Pheidole viserion, a newly discovered ant species from Papua New Guinea © OIST

Pheidole viserion, a newly discovered ant species from Papua New Guinea © OIST

The island of New Guinea is home to some of the rarest animals on the planet. Among them are over 800 species of ants with a diverse range of fascinating characteristics, each well-suited to their unique island habitat. Scientists estimate that around 60% of these ants are found only in New Guinea. In many cases, a single species originally colonised the island and then developed into multiple distinct forms.

Now two new species of ant have been discovered with the help of a major technique that uses 3D imaging technology to identify insects. The ants themselves have a particularly striking appearance thanks to their formidable spine-covered exoskeletons.

Perhaps just as notable as their appearances, though, are their names, Pheidole viserion and Pheidole drogon, inspired by the fire-breathing dragons from the fantasy series Game of Thrones. While not quite in the same size bracket as their mythical namesakes, the ants do have a strong resemblance to the dragons thanks to the distinct blade-like serrations adorning their backs.

Unlike the dragons of fantasy, however, these ants are a product of evolution. So what is the point of their ornate spines? The answer can be found by looking at the social structure of their colonies. The Pheidole group of ants comprises over 40 species that are widely distributed across the island’s rainforests.

Pheidole ants also have several different types or “castes” of worker, each physically specialised for performing specific tasks within the colony. There are smaller “minor” workers and larger “major” workers, commonly referred to as soldiers due to their role in defending the colony from predators and rival ants.

Not fire-breathing, but still pretty scary. Fischer et al

The spines could be seen as a defence mechanism for the soldiers, but this may not be the full story. Soldiers are often many times the size of minor workers and have disproportionately large heads that are packed with muscle, making them formidable adversaries. Their heads are so large, in fact, that they require special skeletomuscular adaptations just to support their extra weight. Results from a kind of imaging technique known as “X-Ray microtomography” have suggested that the ants’ spines are in fact a by-product of this muscular support system, rather than a kind of armour.

This novel imaging method is more like something from science fiction than fantasy, and is opening up the possibility that new insect species could be identified and catalogued much more easily than before. The process works by scanning a mounted specimen with X-rays while rotating it 360 degrees. This produces a 3D cross-section that can then be used to make a virtual model.

Time-saving technique

In this way, X-Ray microtomography allows scientists to capture precise 3D renditions of their specimens and then easily share them with colleagues around the world. This means insects can be compared and identified without the need to send physical samples back to a lab, saving time and reducing the risk of damaging them. Even more impressively, the technique also maps the internal structures of the insects so they don’t need to be dissected for scientists to understand their physiology.

In fact, X-Ray microtomography has the potential to eliminate the laborious tasks of labelling, fixing and dissecting insect specimens that are currently commonplace in science, replacing them with a simple and rapid exchange of data files. In this case, the process also enabled the researchers to uncover new information about the anatomical structure of the Pheidole ant spines, giving them further insight into their biological function.

Classifying plants and animals is still an important tool for studying and monitoring biodiversity. New Guinea in particular holds rich potential for the discovery of new and charismatic species, as the discovery of P. viserion and P. drogon demonstrates. The island comprises just 1% of the world’s land area but is estimated to harbour 5% of all plant and animal species, half of which are yet to be formally described.

Unfortunately, terrestrial ecosystems on the island are in decline, with logging and agriculture posing particularly severe threats. But there is growing interest in safeguarding New Guinea’s biodiversity and, though much progress is still to be made, descriptions of new species and techniques for identifying them are likely to bolster these initiatives.

If nothing else, the discovery of P. viserion and P. drogon, currently known only to New Guinea, may give Game of Thrones fans a reason to appreciate conservation efforts in this often-overlooked patch of the south Pacific.

Thomas O’Shea-Wheller, PhD Student, University of Bristol

This article was originally published on The Conversation. Read the original article.

The Conversation

Mathematicians show who is the the real main character in Game of Thrones

It’s probably not who you think it is – but this small guy casts a big shadow.

The books by George Martin and HBO’s subsequent series adaptation have stolen our hearts. Game of Thrones has become one of the most popular series of all time, with millions of people eagerly awaiting to see the developments of the new season. The narrative has several innovative features, including several major plot line, with numerous character arcs and intricate relationships. Most of the time, you can’t really tell who or what the story is about, because there’s just so much going on. With that in mind, two mathematicians, Andrew Beveridge and Jie Shan conducted a network analysis of the characters to see who stands out the most. Three characters stand out:

“Tyrion, Jon, and Sansa,” Beveridge and Shan write.

This in itself is a bit surprising. Jon is regarded by most people as the main character, despite his… let’s say precarious situation at the end of the last season. Tyrion is also well connected, but Sansa came as quite a surprise. Other fan favorites like Arya or Daenerys are a bit isolated from the main action, so they can’t be regarded as the main ones. So, who’s the main character after all?

“Acting as the Hand of the King, Tyrion is thrust into the center of the political machinations of the capitol city. Our analysis suggests that he is the true protagonist of the book. Meanwhile, Jon Snow is uniquely positioned in the network, with connections to highborn lords, the Night’s Watch militia, and the savage wildlings beyond the Wall. The real surprise may be the prominence of Sansa Stark, a de facto captive in King’s Landing. However, other players are aware of her value as a Stark heir and they repeatedly use her as a pawn in their plays for power. If she can develop her cunning, then she can capitalize on her network importance to dramatic effect.”

Now, for those of you who only watched the series, it has to be said that this study was conducted based only on the books – on the third book, to be more precise (A Storm of Swords). The action in the series has been slowly but surely diverging from that in the books, so the same might not stand for the series.

They laid out a diagram of how all the characters in the book were connected to each other, and if they were mentioned within 15 words of each other, they’re connected, regardless of how they feel about each other. They then mapped out all the relationships thusly defined, creating a type of “Page Rank“, similar in concept to the one used by Google. The “degree centrality” of the characters was measured based on how many connections they had and how many interactions within those connections. Researchers acknowledge that their work is trivial in purpose, but the technique can be applied in a myriad of other, more important areas.

“We have considered a fanciful application of network science to give an enticing taste of its capabilities. More serious applications abound, and network science promises to be invaluable in understanding our modern networked life.”

Network science is an academic field which studies complex networks… yeah, I know. It basically studies the relationships between things, whether it’s people, money transactions, biological relationships or anything else. It’s a growing field of data science, employing methods and elements from numerous other fields, including graph theory from mathematics, statistical mechanics from physics, data mining and information visualization from computer science, inferential modeling from statistics, and social structure from sociology.

The study was published in the April issue of the Mathematical Association of America’s journal Math Horizons.