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A Song of Graphs and Quants.

Why were the novels of Game of Thrones so popular?

I don’t know, ah—okay, so, an experienced wordsmith well-connected in both the publishing and entertainment industries had the good fortune to have put out the third book of his well-enough received epic fantasy just as it became clear Peter Jackson had bottled a rather prodigious quantity of lightning with his filmic adaptation of Tolkien’s epic fantasy, leading to just about every half-viable piece of epically fantastic IP getting optioned by this production company, or that; being well-connected, but also experienced, said wordsmith was able to negotiate the sort of deal with the sort of people more likely than not to make a passably decent go of it; said go was made, a television serial, in time to catch enough of the lightning coming down from Jackson’s movie high, hungry for more, that it was given time enough and clout to build on that audience: thus, popularity, to such a degree that now everyone refers to “the novels of Game of Thrones,” which is the name of the since-concluded television show, and not “the novels of A Song of Ice and Fire,” which is the name of the as-yet unfinished series of books.

A new study from @PNASNews suggests one reason why @GRRMspeaking’s A Song of Ice and Fire was such a hit—the average number of social interactions main characters have, chapter-to-chapter, is just like real life.

Or, sure, okay. Maybe that’s it.

There’s lies, damn lies, statistics, and then there’s stuff like this, which has gone through a couple of waves of popular acclaim in the sorts of circles on social media that go for, you know, network science, and data analytics, and doorstopping wodges, and premium cable sexposition. —It doesn’t lie, no, and certainly there’s not the faintest whiff of damnation about it, but a whole lot of mathematical wheels are set to spinning with a great deal of show and rapid-fire patter, and the crowd does cheer for a moment or a tweet to see it run, but it doesn’t get us much of anywhere at all when the dust settles.

Significance: We use mathematical and statistical methods to probe how a sprawling, dynamic, complex narrative of massive scale achieved broad accessibility and acclaim without surrendering to the need for reductionist simplifications. Subtle narrational tricks such as how natural social networks are mirrored and how significant events are scheduled are unveiled. The narrative network matches evolved cognitive abilities to enable complex messages be conveyed in accessible ways while story time and discourse time are carefully distinguished in ways matching theories of narratology. This marriage of science and humanities opens avenues to comparative literary studies. It provides quantitative support, for example, for the widespread view that deaths appear to be randomly distributed throughout the narrative even though, in fact, they are not.

Eh. —Two empirical claims are made: that the cast of characters and the social networks formed within the books therefrom comport with the sorts of networks observable in the real world, and theoretical cognitive limits of association such as Dunbar’s number; and that the distribution of the deaths of notable characters appears random within the discourse time of the story, but comports with a power-law distribution when charted against the fictional calendar of story time, similar in value to those of real-world human activities. —From these, an implication is drawn: that the perceived quality of the books is due at least in part to how they fulfill these two claims. (Oh and but also: our research is cool and worthwhile and you should cite it so we can do more of it, but that usually goes without saying.)

The first claim, then, which is based on a dataset “extracted manually” by one of the authors “carefully reading” the books over several months, noting each character and every interaction between them, and entering the data into spreadsheets divided per book and chapter; interactions being defined as either a meeting portrayed in the text, or when the text makes it clear that the two characters had at some point interacted. (“In case of doubts regarding the data,” we are told, opinions were “calibrated through discussion. Consensus assured that no automated calibration method was required.”) —This process resulted in a network graph you might’ve seen running around:

Fig. 1.

All told, 2,007 unique characters were tabulated from the five books written to date, of which 1,806 have interactions with at least one other character, which raises any of a number of questions about those 201 solipsists, like who were they, and what were they up to, and do they raise any questions themselves about the methodology used to determine and count up interactions, but we breeze right by these to learn that the average number of characters appearing in any chapter fluctuates quite a bit, but averages around 35, the typical size of (contemporary) bands of hunter-gatherers, the cast of your run-of-the-mill Shakespeare play, or an English literature department; that main characters tend to have larger networks of interactions than other characters (or is it that characters with larger networks of interactions become main characters?); that the networks of point-of-view characters tend to average right around 150 or so: pretty much Dunbar’s number; and that these networks tend to have a high degree of assortativity, a quantitative measurement of homophily—a feature of real-world social networks, like liking like—but assortativity’s measuring pretty much whether nodes with lots of links tend to link to other nodes with lots of links, and not so much, you know, whether the node’s from Westeros, or the Free Cities, or whose point of view is the chapter they’re in at the moment.

I’m not here to quibble with their figuring—I can barely tell a python script from a hypnotized snake. What I’m here to quibble with is what’s done with them, or rather what’s thought to have been done with them: after all, as we’re told, the paper suggests the books are a hit at least in part because the number of social interactions entertained by the main characters mirrors those you’d see in real life—but. But:

  1. It’s not demonstrated that this quality is necessary for works to be popular;
  2. it’s not demonstrated this quality’s unique to these books, or to popular books as a general rule.

We’ve got a dataset, and a description of a dataset, and some gestures towards comparisons with other, possibly maybe similar sets, but in very limited contexts: we are pointed toward Shakespeare (always a sign of Quality), but only in comparing the average number of characters per chapter to the average cast list of two hours’ traffic of a stage; we are pointed toward the social networks to be found in more mythic sources such as Beowulf, the Táin, the Iliad, various Icelandic sagas (mostly to the detriment of Beowulf and the Táin)—aaand that’s about it.

The study “suggests,” perhaps, to be sure, but no work’s done toward such a suggestion. —Perhaps instead it’s true that, much as with plots, or dialogue, a certain degree of simplification and stylization in the social networks of sprawling casts turns out to be a hallmark of popular serials and epics, and A Song of Ice and Fire succeeds in spite of its verisimilitude on this point, and not because of it. —Perhaps instead it’s the case that this vaunted verisimilitude is basically an epiphenomenon: that (without conscious effort otherwise) things built by human brains tend to comport to the patterns and limits inherent to things human brains can build. Without directly comparing this dataset with other datasets also “manually extracted” from other works, we can’t even begin to know which way to turn, much less begin to suggest we hare off in that direction.

Instead of comparing the average cast sizes of chapters and plays, why not more directly compare the network graphs of these books with those generated by the intertwining casts of the history plays from Richard II to Richard III–plays directly about, after all, one of the stated inspirations for Ice and Fire. Instead of borrowing the glory of such stonkingly obvious Paragons of Quality (mythology! Shakespeare!), why not compare them against those of other epic fantasies: Tolkien, sure, okay, but also Ice and Fire’s far more direct progenitor, or neighbors such as Eddings, Jordan, Donaldson, Lackey, Elliott, Hobb, or Kurtz. —Hell, we’re splashing about in the digital humanities: imagine what we might’ve learned by comparing the network graphs of the books, with those generated by the television show!

There are even implications within their dataset that could be teased out into something more than a suggestion. We’re told, for instance, two kinds of interaction were noted: either explicit, or implicit. What’s the overall distribution of these two types—more of the one, or the other? About even? Are there characters whose networks buck these averages? If so, which way, and by how much? And are these characters of a certain type? —We don’t know. (Peering at the data itself, it looks like they didn’t record whether an encounter was explicit or implicit—but they did note whether an encounter was friendly, or hostile, which raises further questions admittedly beyond the scope of this already sprawling epic.) —And there’s a rather definite bobble in their network graphs just after [SPOILER] the Red Wedding, described as a “suppression of assortativity,” but it’s mostly written off as a side effect of the close third person: “The deflated degrees of the masses relative to POV characters decrease homophily,” which, well. Is a degree of wistfulness I hadn’t expected to encounter in such an objective paper.

The second claim, regarding the distribution of the deaths of notable characters in discourse time as opposed to story time, is far less interesting—far more a case of looking for your car keys under the streetlight, or measuring only what the ruler you have in your hand can measure, and not what you need, or what’s actually there. To be sure, the distinction between discourse time and story time is an important one, thank you, Russian formalism, and it’s a useful crowbar to pry at Ice and Fire with, given its interwoven back-and-forth structure. And deaths, even in epic fantasy, are usually precise and unambiguous events—easily totted up. But the butcher’s bill of this study starts off at a steep discount:

We now turn to consider interdeath story time and interdeath discourse time to reveal an interesting difference between the underlying chronology and how the narrative is presented. For this purpose we consider only deaths which we deem to be significant. These are deaths of characters in the network who appear in more then one chapter. We apply this criterion to avoid the inclusion of the deaths of “cannon-fodder” characters whose main purpose in the story is to die immediately after they are introduced.

“The kings, the princes, the generals and the whores,” as Martin himself said at one point; “But few of any sort, and none of name,” to drag Shakespeare back into this for a moment. —But much as you have to start somewhere, you have to stop somewhere else, or you’ll never be able to count it all, and the attentions that must be paid to protagonists over and above the spear-carriers and supernumeraries are injustices also beyond the scope of this too, too sprawling post. So we will accept their limitation, it’s precisely defined, not subject to subjective notions of significance, however much we might rankle at “cannon-fodder.” —In terms of story time, the deaths are fixed to a timeline compiled by fans, thank you, crowd-sourcing, with necessary assumptions and approximations as noted; in terms of discourse time, though, the deaths are indexed according to, uh, which chapter they appear in. —That’s it. In terms of the “memorylessness” (a term of art doing a lot of unfortunate work in this context) of the interevent discourse time between one death and the next, it’s entirely down to the number of chapters between them. And I mean choosing whether to put an event in this chapter, or that? Is definitely a choice to be made, with effects to consider—but it’s considering structure at a strikingly crude level.

It is one that’s easily tabulated, though.

I mean, we know why the authors of this study went with character deaths, and tried to find some objective measurement of shock, or surprise, when analyzing Ice and Fire. They tell us why, themselves:

A distinguishing feature of Ice and Fire is that character deaths are perceived by many readers as random and unpredictable. Whether you are ruler of the Seven Kingdoms, heir to an ancient dynasty, or Warden of the North, your end may be nearer than you think. Robert Baratheon met his while boar hunting, Viserys Targaryen while feasting, and Eddard Stark when confessing a crime in an attempt to protect his children. Indeed, “Much of the anticipation leading up to the final season [of the TV series] was about who would live or die, and whether the show would return to its signature habit of taking out major characters in shocking fashion.” Inspired by this feature, we are particularly interested in deaths as signature events in Ice and Fire, and therefore, we study intervals between them.

“Signature events,” rather like the chintzy mint on the pillow provided by a chain hotel as part of its Signature Service, or the ghastly Signature Desert the front office wants waitstaff to push this month. —Let’s face it: there are really only two deaths, or death-laden events, in Ice and Fire that shock above and beyond the usual thrills and chills expected of any blood-soaked melodrama: the [SPOILER] Red Wedding, and the execution, at the end of the first book/season, of Eddard “Ned” Stark. And I guaran-damn-tee you, it wasn’t the memorylessness of the interevent discourse time that led to the surpassing jolt of either of those events: it was the fact that the sprawling epic had taken the time and effort to set up Ned, and Robb and also Catelyn, as protagonists, with all that that implies; the implicit promise of the stories we thought they were going to get was suddenly and rather brutally forestalled—and it’s that violation that juices the shock. The trick of it is to lend a patina of that shock to all the other deaths that are dealt in the course of the story; the bind is that, as the story progresses, the “real” protagonists become clear—and it’s clear what won’t be happening to them. —That bind’s an enormous part of why so much tension evaporates from the later seasons of the show; it’s also quite possibly one of the barriers to finishing the books at all.

But this is all my subjective opinion, though. It’s not like I’ve measured it objectively or anything.

But enough of this! (Too late! wail the punters; I tip my hat.) —If I’m hungry for more analysis of these books, I’ll more than likely to turn to something more like this in-depth analysis of the depiction of the Dothraki than any more network analysis. Once again, I’d aim a kick at this unfortunate XKCD strip:

Imposter, reprinted under the auspices of a Creative Commons Attribution-NonCommercial 2.5 License.

Working with objectively measurable quanta is not only easy, it’s sometimes deceptively useless.

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