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ANTHROPOLOGY APPLIED MATHEMATICS distinction between story time and discourse time. Story time nodes as the number of times the corresponding pair of characters interact refers to the order and pace of events as they occurred in the in the narrative. Fig. 1 is therefore a visual representation of the primary fictional world. It is measured in days and months, albeit using characters and their interactions. For example, the enduring importance of the fictional Westerosi calendar in the case of Ice and Fire. Dis- characters such as Eddard Stark and is clear, despite the course time, on the other hand, refers to the order and pacing of fact that both perished early in the story. To analyze the dynamics and evolution of the narrative we also use a events as experienced by the reader; it is measured in chapters second dataset. This is an approximate timeline of the events of Ice and Fire and pages. indexed by the Westerosi calendar date, compiled by fans and followers, We find the social network portrayed is indeed similar to and maintained by the Reddit user identified as PrivateMajor (https:// those of other social networks and remains, as presented, within www.reddit.com/r/asoiaf/comments/1c07jw/spoilers all most precise asoiaf our cognitive limit at any given stage. We also find that the timeline in/). This timeline makes a number of assumptions which are order and pacing of deaths differ greatly between discourse noted in the dataset. Many of these dates are educated guesses because no time and story time. The discourse is presented in a way that explicit in-story timeline is provided by the author. According to the Reddit appears more unpredictable than the underlying story; had it timeline, the opening events of A take place on 22 April been told following Westerosi chronology, the perception of ran- of the year 297, and the closing events of A Dance with take place on 8 February in the year 300. We used this second set of data to assign dom and unpredictable deaths may be much less shocking (22, an approximate date to each chapter of each book, allowing us to study 23). We suggest that the remarkable juxtaposition of realism events as they occur within the in-story timeline. In many cases, chapters (verisimilitude), cognitive balance, and unpredictability is to clearly span multiple days. In such cases we use the date corresponding to the success of the series. the earliest dated event occurring in that chapter. This allows us to order the data in two ways, the order in which the events happen (story time) Materials and Methods and the way in which the narrative is told (discourse time). To perform this investigation we draw on two datasets. The first was There are multiple measures of network architecture, nodal importance, extracted manually from Ice and Fire by carefully reading the text and not- and edge weights. To address the primal issue of societal topology we ana- ing interactions between characters. To facilitate comparisons to them, we lyze the full unweighted network. We assign a degree to each character follow methodologies developed for network analyses of medieval epics as the number of connections it has to other nodes of the network, and (16, 24–26) whereby characters are deemed to have interacted if they we track average values over story and discourse time. Studies have shown directly meet each other or it is explicitly clear from the text they knew that real social networks tend to have properties which distinguish them one another, even if one or both are dead by that point in the story. (To our from other complex networks (15). Notable among these is homophily—the knowledge, no automated method currently exists that has been proven tendency of people to associate with people who are similar to themselves to match this manual approach; see, e.g., ref. 27.) From this dataset we (28). One quantitative measure of homophily is assortativity, the extent to construct a network of all of the characters in Ice and Fire who interact which the degrees of pairs of connected vertices are correlated (29). A net- with at least one other. Characters are identified as nodes and interactions work which has a positive correlation is called assortative, and one with a between them identified as edges (links). We also gathered temporal data negative correlation is disassortative. on character deaths for interevent time analysis. As degree measures how connected a node is, centrality quantifies how Fig. 1 presents, for illustrative purposes, a subset of the network show- close it is to the core of the network. There are various measures, and ing the most predominant characters. SI Appendix contains a similar figure common examples are betweenness, closeness, page rank, and eigenvec- showing only those characters still alive at the end of the fifth book (the tor centrality. We use these tools holistically— tool gives a definitive survivor network). Predominance for these illustrations is measured by the characterization of verisimilitude or narratology, but together they build number of chapters in which a given character interacts with at least one a picture that we can compare to real networks (15) and to mythological other character, and nodes are sized accordingly. Each character in Fig. 1 (16), Shakespearean (17), and fictional literature (18). In the next section interacts in at least 40 chapters. The full network is far greater in extent. we present betweenness, which is a normalized measure of the number The thickness of the various edges represents the strength of links between of shortest paths (geodesics) between all other nodes that include the

Fig. 1. Network of the most predominant characters. For illustrative purposes we size nodes proportional to the number of chapters in which the characters interact. Edge thicknesses represent the numbers of times that corresponding pair of characters interact in the narrative.

2 of 7 | www.pnas.org/cgi/doi/10.1073/pnas.2006465117 Gessey-Jones et al. Downloaded by guest on September 26, 2021 Downloaded by guest on September 26, 2021 hpe-ycatreouino h endge,adFg 3B Fig. and degree, mean the of evolution chapter-by-chapter stability The remarkable green. indicates in curve depicted series. each the are throughout of book have growth fifth who linear Those the 2B. near by Fig. in died blue explicitly includ- in plotted not and is The to chapter) up given 35). a (introduced (34, ing characters centers of for research size number optimal literature cumulative and and (17) language the plays (contemporary) as Shakespeare’s English identified of in been size size also cast has typical typical It the (33). hunter-gatherers as within of subgrouping and around bands stable (32) at a as networks settles identified chapter social been intro- has per are value characters characters This main of 35. the number which the in to book, duced, up first chapter the first in of the growth 16 for chapter 7 from for in range 89 plotted numbers are These chapter 2 A. individual Fig. each in numbers appearing The of unfolds. characters discourse of how the identified, depicts as 2 Fig. evolve were once. numbers least character at characters another with 2,007 interact 1,806 which chapters, Structure. 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(212) Lannister Jaime 2. (214) Snow Jon 1. .Rb tr (158) Stark Robb 8. (161) Lannister Cersei 7. (175) Greyjoy Theon 6. (192) Stark Arya 5. (204) Stark Catelyn 4. 9 anrsTrayn(0)1.SmelTry(0.0207) Tarly Samwell 17. (103) Tarly Samwell 20. (104) Targaryen Daenerys 19. (106) Stark Bran 17. (108) Tarth of Brienne 16. (140) Stark Eddard 12. (156) Selmy Barristan 10. (156) Stark Sansa 9. .SnaSak(122) Stark Sansa 5. (135) Stark Arya 4. (149) Lannister Jaime 3. (150) Snow Jon 2. (162) Lannister Tyrion 1. (72) Seaworth Davos 51. 8 anrsTrayn(9 3 rnSak(0.0248) Stark Bran 13. (68) Stark Bran 20. (69) Targaryen Daenerys 18. (79) Tarly Samwell 12. (83) Tarth of Brienne 10. (86) Baratheon Stannis 9. (103) Selmy Barristan 8. (115) Greyjoy Theon 7. (120) Lannister Cersei 6. 8 ao ewrh(54) Seaworth Davos 38. nte osqec ftePVsyei h upeso of suppression the is style POV the of consequence Another values (with centrality betweenness and degree by ranked are Characters .Ay tr (0.0777) Stark Arya 3. 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ANTHROPOLOGY APPLIED MATHEMATICS AB

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Fig. 2. Number of characters in the narrative. (A) Number of characters appearing in each individual chapter. This shows significant fluctuations chapter by chapter and fluctuates around 35 by the end of .(B) Evolution of the cumulative number of characters appearing in the narrative by chapter (blue) and of characters introduced who have not yet died (green). Both curves grow approximately linearly throughout Ice and Fire. Labels AGOT, ACOK, ASOS, AFFC, and ADWD represent A Game of Thrones, , , , and , respectively.

initial growth period in the first book, assortativity fluctuates one chapter. We apply this criterion to avoid the inclusion of around 0, before dropping to a slightly negative value (−0.03) by the deaths of “cannon-fodder” characters whose main purpose in the fifth book. This is lower than most values measured in real the story is to die immediately after they are introduced. Fig. 4A social networks (15) but not by much. It is certainly sufficient to shows the number of significant character deaths by chapter (dis- endow Ice and Fire with a greater degree of verisimilitude than course time). Fig. 4B gives the same data ordered by date (story more egocentric networks such as Beowulf or the Tain´ Bo´ Cuail- time). It is striking how deaths appear far more clumped together gne (16). In comparative mythological terms, Ice and Fire has a in story time than in discourse time. The structure of Fig. 4A narrative networks more akin to those of the Icelandic sagas (24). helps explain the perception that death can occur unpredictably Therefore, despite the continuous introduction of new char- in the narrative, while Fig. 4B suggests extended safe periods acters, the author has managed to maintain a consistent social where no deaths occur. network structure. The number of these interactions is at the These observations can be quantified by examining the empir- upper end of the cognitive capacity of an average reader. Hence, ical distributions of the time intervals between deaths. Our data while there is a vast number of characters and even greater num- analysis follows the reasoning described in ref. 39, and all com- ber of interactions in Ice and Fire at any given stage of the putations are performed using the associated R package (40). narrative, the social network a reader has to consider in order To explore the (un)predictability of Ice and Fire timelines, we to follow the story is similar in scale to natural cognitive capacity. consider the conditional probability that the number of steps (chapters or days) to the next event exceeds n + m given that it has already exceeded m. If this is the same as the unconditional Distributions of Interevent Times for Significant Deaths. We now probability that the waiting time exceeds n, turn to consider interdeath story time and interdeath discourse time to reveal an interesting difference between the underlying P(X > n + m | X > m) = P(X > n), [1] chronology and how the narrative is presented. For this purpose we consider only deaths which we deem to be significant. These then the interevent time distribution is said to be memoryless. In are deaths of characters in the network who appear in more then other words, knowing the time since the last event provides no

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Fig. 3. Evolution of network properties by chapter labeled as in Fig. 2. (A) Evolution of the average degree. After a period of initial growth as main characters are introduced, the average degree stabilizes at around 16 for the network involving all characters and around 12 if only the living characters are included. (B) Evolution of the degree assortativity. After the first book (A Game of Thrones), the assortativity for the living-character network fluctuates around 0. While the assortativity of the full network (blue) also fluctuates, it stays slightly disassortative for the later books.

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ANTHROPOLOGY APPLIED MATHEMATICS AB

Fig. 6. Empirical distributions of interevent times for significant deaths by date (story time). Date here is measured using the fictional Westerosi calendar. Shown in blue is the best-fit discrete power law (Zeta) distribution.

uncertainties in the α parameter value which are much higher (47). Ice and Fire avoids this; although more than 2,000 char- than their discourse time counterparts.) The memoryless geo- acters appear, readers and TV audiences alike remain avidly metric model is therefore the superior description of interevent engaged. times in discourse. The findings reported here suggest that this is facilitated by In summary, the interevent time distribution for significant clever structuring such that each chapter is told by different POV deaths by discourse time is well fitted by a geometric distribu- characters, endowed with social networks containing only around tion indicating that such events can seem to the reader to occur 150 individuals. Moreover, there are only 14 major POV charac- almost at random intervals. However, when analyzing deaths in ters. These are frequent numbers in the structure of real social terms of story time, this is not the case, with significant events networks (32–34, 36–38, 48) and they allow the reader to work occurring in a more natural way. Portraying significant events by within natural templates; the story reflects experiences in the discourse time instead of as they happen appears to maintain the everyday social world and therefore does not overtax cognitive reader’s suspense. abilities that are evolved to match these scales (10). Our findings on the constraints on the size and structure of the Discussion cast of characters are not peculiar to this particular drama. Sim- is a prodigious modern epic of consider- ilar numerical constraints have been reported for Shakespeare’s able complexity that remains accessible to a vast congregation plays (17) and contemporary films (49). Much of this seems to of devotees. Among its appeals are the uncertainty and unpre- reflect natural limits on mentalizing competences—the cognitive dictability of its storyline as characters, including important ones, skills that underpin our ability to handle social relationships in can be killed off seemingly at random. Indeed, not even the the virtual mental sphere of the everyday social world (7, 10). POV characters are guaranteed safe passage from one book These are limited to five orders of intentionality and provide the to the next. Here we have shown that the network properties base from which the scaled layers of social networks are built of the society described in Ice and Fire are close to what we up (7); more importantly, neuroimaging studies have shown that expect in real social networks (16). Also, by relating the story competences in this respect correlate directly with the number from the points of view of different characters, the total num- of individuals in the 15-layer (50, 51). That this is important ber of interactions at any given stage remains within the average for storytelling has been demonstrated by a series of experimen- reader’s cognitive limit, making it possible to keep track of these tal studies showing that enjoyment of a story is greatest when relationships (19). the number of levels of mentalizing (effectively the number of The positioning of this paper relative to the context, initiatives, characters involved in a scene) is closest to the reader’s own and aspirations of digital humanities merits further comment. mentalizing abilities (52). Krems and Dunbar (49) showed that The recent review (46) identified some of its methods and Shakespeare, at least, seemed to adjust the number of charac- themes, developed in the context of comparative mythology and ters in a scene to the effect of remaining within the mentalizing traditional epic narrative cycles in particular (8), as one of four capacities of the audience. focal points in the extraction and analysis of character networks Also, the characteristic unpredictability of the narrative (the remaining three foci being literary analysis, video narra- appears in discourse time only, with associated interevent times tives, and computer science methods aimed at data extraction). for significant deaths well described by a memoryless distribu- Here we go beyond such character network considerations by tion. In story time the plot unfolds in an altogether different introducing two elements to quantitative narratology, namely, manner for, chronologically, many characters die in a way consis- the questions of cognitive limits and the interplay between story tent with regular human activities. The difference suggests that time and discourse time (10). Unlike historical, quasi-historical, the author structures the order and pacing of significant events or mythological chronicles of societies and events, a key require- (consciously or subconsciously) to make the series more unpre- ment for fictional storytelling in Ice and Fire is that it not spin dictable. The distinction between story time and discourse time out of control because of its enormous scale. Fictional narra- was first identified in the early part of the 20th century by the tives require widespread engagement for commercial success. influential Russian formalist literary theorists, notably cowork- Whatever the storyteller’s cognitive competences may be (7), ers Schklovsky and Propp (11). Their distinction between fabula he has to avoid overtaxing his reader’s ability to keep track of (story, or chronological sequence of events) and sjuzhet (plot) the action—itself related to the number of characters involved is essentially that which we draw here. Schklovsky, in particular, (10). If the story is allowed to become too complex, there emphasized the importance of defamiliarization (decoupling the is a threat of the average reader becoming cognitively over- temporal sequence of the plot from the chronological storyline) whelmed and the story becoming chaotic and unfathomable as a device for engaging the reader in the story. Our analysis

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Labatut, V. 46. in world” virtual a of “Analyses Thurner, S. Szell, M. Mryglod, O. murders Holovatch, Y. between intervals time 45. of study Statistical Roychowdhury, P. V. Simkin, V. M. killer. serial a 44. of modeling Stochastic Roychowdhury, P. V. Simkin, V. M. 43. T B. Vajna, S. 42. package. poweRlaw The Barab distributions: A.-L. tailed 41. heavy data. Fitting empirical in Gillespie, distributions S. Power-law C. Newman, J. 40. E. M. Shalizi, R. C. Clauset, A. 39. 0 .C rea,Asto esrso etaiybsdo betweenness. Gessey-Jones on T. based centrality 31. of measures of networks. set A in Freeman, social C. L. mixing in Homophily 30. Assortative feather: Newman, a of J. Birds E. M. Cook, M. 29. J. Smith-Lovin, L. McPherson, M. 28. 041.RK a diinlyspotdb oetyUiest iyof discussions. City for Platini University Thierry Coventry and Carney a James (grant by thank Council RPG-2018-014. We supported Research award. additionally narratives” Culture and European was the medieval conflict R.K. by “Women, early 802421). supported grant additionally in Curie was research number networks P.M. Marie Trust project Commission’s gendered Leverhulme Scheme” European peace: the Exchange the and Staff by 612707 and Research P.M., supported R.K., “International part grant. Action University in Coventry a were by J.Y. C.O. and College Fitzwilliam ACKNOWLEDGMENTS. github.com/colm-connaughton/ASOIAF-data-and Availability. Data genre, liter- periodicity, of fantasy. film, and areas television, history, literature, drama, other canonicity, including to study, approaches ary quantitative wider reader’s making may inspire methods the computational by through heighten unpredictability appealing cog- and to verisimilitude, nition, of more such as patterns of continuously so in identification The random it story engagement. seem make the events to of significant as timeline way the a manipulated has storyteller fhne–ahrrsca networks. social hunter–gatherer of sizes. group social size. group research size. health. and stability network (2020). diffusion, for cations (2003). artv rcsigo te minds. other of processing narrative in differences individual of study imaging An humans. size: network social predicts volume tex size. network social and 2011). others ( 1624–1629 of understanding predicts volume psychology. evolved of Constraints world. offline the in those mirrors networks Psychol. Evol. Cult. J. Surv. 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