Visualizing the Temporal Space of Narratives

Introduction
This paper studies the graphs which are created when a narrative's fabula (the timeline of events within its story) is plotted along the vertical axis of a coordinate plane and its syuzhet (the order in which these events are presented to readers) is plotted along the horizontal axis. Such graphs were recently dubbed "time maps" by William Nelles and Linda Williams, and though time maps offer a new means for the study of narrative, they have received minimal scholarly attention. To remedy this, I survey the relevant theoretical landscape, outline a methodology for generating time maps, and theorize on the myriad forms they may take. Time maps are particularly relevant for temporal narratologists because they visualize the ordering framework Gérard Genette developed in
Narrative Discourse. But instead of simply tracking the order of a scene's position in the fabula, as Genette and others have done, I incorporate numerical values from the text to create time maps of unrivaled accuracy.

Theory
Many contemporary studies visualize literary complexity.
Their most direct forerunner is Kurt Vonnegut's framework for graphing the emotional arcs of stories. Vonnegut also plots syuzhet along the horizontal axis, but plots emotional valence along the vertical axis. Vonnegut created qualitative sketches that captured the essential shapes of several stories and predicted that most narratives could be described by a few patterns. His work inspired independent studies by Matthew Jockers and Andrew Reagan which implement automated machine learning techniques to quantitatively construct this same structure for a large number of texts. In sync with Vonnegut's prediction, Reagan's group found that six basic shapes account for the emotional arcs of approximately 95% of the texts in Project Gutenberg.

Franco Moretti and the Stanford Literary Lab have also generated a number of papers in this vein. I highlight one, written by Maria Kanatova's group. They studied patterns of anachrony in recent mystery films to conclude that a new subgenre has emerged, which features heavy use of analeptic flashbacks that are external to the fabula's principal reach. Complementing these studies of time, last year's Digital Humanities conference also featured a number of projects which digitally documented the spatial worlds within texts. Of particular note is Randa El Khatib's survey of
Paradise Lost's moral geography, as well as the anotational mapping that Gimena del Rio Riande, Romina De León, Nidia Hernández, and Leif Isaksen have done with Recogito 2.

Other researchers have more directly studied time maps. Perhaps most famously, Steve Aprahamian published a time map of
Memento to the film's Wikipedia page. Daniel Aureliano Newman created a time map of Aldous Huxley's
Eyeless in Gaza, using it to interpret the novel in terms of the biological concept of neoteny. Elisa Pezzotta created similar graphs for several science fiction films featuring time-travel. David Wittenberg has also performed a detailed study of time travel narratives which included a time map of Heinlein's "By His Bootstraps." The most comprehensive study of time maps to date, though, was the aforementioned analysis by Nelles and Williams. Yet their work is still limited in scope, merely concluding that narratives are inherently anachronous. My findings are in accordance with Nelles and Williams, yet I reach further. I formulate a general theory of time maps, outline a systematic methodology for creating them, and use them to perform interpretive work.

Methodology
Genette's scheme for organizing the scenes of disordered stories is a precursor to my work. He assigns each scene a letter, corresponding to its placement in the syuzhet, and a number, corresponding to its order in the fabula. The key difference is that I represent each scene as a line segment, instead of a point. This adds many layers of difficulty to data collection, since each scene now requires four pieces of information instead of two, but also allows for distinguishing scenes of varying durations.
The n-th line segment has its origin at

(s
ni
, f
ni)

where s
ni
denotes the scene's initial location in the syuzhet and f
ni
denotes the scene's initial location in the fabula. The terminus of this line segment is at

(s
nf
, f
nf
)

where s
nf
denotes the scene's final location in the syuzhet and f
nf
denotes the scene's final location in the fabula. A narrative's time map is simply the complete set of these line segments and, consequently, the study of time maps is a geometric approach to narratology.

Each line segment will have its own values for s
ni
, f
ni
, s
nf
, and f
nf
. In my data sets, each scene corresponds to a row containing all of these values, along with secondary columns which track the temporal cues essential to the compilation process. The works in my corpus were chosen because they contain a large number of temporal cues. My data sets for works such as
Infinite Jest
,
A Visit from the Goon Squad
, and
House of Leaves
are several hundred lines each. Machine learning techniques may eventually be implemented to collect this information, but entry currently requires a large amount of human input due to the fluid nature of fabula timeflow in narrative and the myriad ways it may be represented.

Analysis

I begin my analysis by examining the time map of
Rashomon
, which is shown in Figure 1. This film is particularly interesting because it simultaneously demonstrates two kinds of parallel storytelling. The first features three storylines being simultaneously told in the syuzhet, though they are nested in the fabula. These storylines manifest as three groups of line segments vertically displaced from one another: the red corresponds to the framing narrative of the monk and the woodcutter stranded on a rainy day; the green corresponds to their recollections of a trial; and the remaining colors sync up with the witness's accounts of the crime. The second form of parallel storytelling in
Rashomon
is what Genette called repetition, which occurs when a single scene is revisited. Repetition is central to
Rashomon
because each witness recalls the same crime, but narrates the events differently. This film highlights the capacity for time maps to track narratological complexity for viewers. It also serves as a theoretical model: stories with multiple timelines will be vertically offset from one another, while those with repeated events will contain line segments which are horizontally offset.

Hitchcock’s
Rope
, portrayed in Figure 2, is a perfectly linear narrative and stands in contrast to
Mrs. Dalloway
, which is approximated in Figure 3 by plotting the singular tolls of Big Ben that occur throughout the novel. The latter's time map is nearly linear, but thrown off by Woolf's extended discussion of the characters' actions at lunchtime. This demonstrates a key difference between the camera and the written word: cameras can easily produce purely linear stories through the use of real-time filming, but this is extremely difficult to achieve in writing, due to the slippery nature of language.

Figure 4 displays the time map for
Citizen Kane
, which is very nearly a triangle. Its sides are the vertical green dots on the left, the horizontal black line on top, and the multicolored line segments below. These respectively correspond to the opening newsreel, the reporter's interviews, and the events of Kane's life as recounted by the interviewees. The film notably features several narrators, whose spans of syuzhet are demarcated by vertical gray lines. Yet because these narrators recall Kane's life in almost exactly the order it unfolded, they produce a hypotenuse which is very nearly linear. As a result, almost every scene from
Citizen Kane
lies along the perimeter of this triangle, with one glaring exception: when Kane is forced to sell controlling interest of the
Inquirer
to Thatcher. This loss quite literally lies at the center of the film — and, thus, the viewer's understanding of Kane's life — albeit in a complex way which can only be recognized by plotting its time map. The interpretive inroads multiply when the corners of the triangle are taken into consideration. The film opens in the top left corner with Kane's last word, the bottom left corner depicts an early memory of him sledding as a child, and the top right corner shows that same sled being thrown into a furnace. Just as a triangle is geometrically defined by its three endpoints, Kane's life — or at least the audience's view of it — is defined by Rosebud. Inverting the trope of having an "inner child," Kane's core is failed ambition which is padded by memories of simpler times.

Conclusion

In short, time maps reveal many types of complexity, ranging from interpreting individual texts to formulating narratological theory. In addition to the works discussed in this abstract, I have created and studied many others. Their elaborate structures require more space to unpack than is available here. In the future, natural language processing may be used to algorithmically generate time maps, but my experiences unpacking the ambiguities of temporal language lead me to believe that this would be a herculean undertaking.

Figure 1: Time map of
Rashomon

Figure 2: Time map of
Rope

Figure 3: Time map of
Mrs. Dalloway

Figure 4: Time map of
Citizen Kane

Bibliography

Aprahamian, S.
(2017) ‘Memento’,
Wikipedia
. Available at:

https://en.wikipedia.org/w/index.php?title=Memento_(film)

(Accessed: 26 October 2017).

Danielewski, M. Z.
(2000)
House of Leaves
. 2nd edition. New York: Pantheon.

del Río Riande, G.
et al.
(2018)
Getting to Grips with Semantic and Geo-annotation using Recogito 2/ Cómo abordar la semántica y la geoanotación con Recogito 2
.

Egan, J.
(2011)
A Visit from the Goon Squad
. 1 edition. New York: Anchor.

El Khatib, R. and Currell, D.
(2018) ‘Mapping the Moralized Geography of Paradise Lost’, in Currell, D. and Issa, I. (eds)
Digital Milton
. Cham: Springer International Publishing, pp. 129–152.

Genette, G.
(1980)
Narrative Discourse: An Essay in Method
. Translated by J. E. Lewin. Ithaca, New York: Cornell University Press.

Hitchcock, A.
(1948)
Rope
.

Jockers, M. L.
(2014)
A Novel Method for Detecting Plot
. Available at:

http://www.matthewjockers.net/2014/06/05/a-novel-method-for-detecting-plot/

(Accessed: 26 October 2017).

Kanatova, M.
et al.
(2017)
Broken Time, Continued Evolution: Anachronies in Contemporary Films
.
Stanford Literary Lab Pamphlets
. Available at:

https://litlab.stanford.edu/LiteraryLabPamphlet14.pdf

.(Accessed: 16 October 2018).

Kurosawa, A.
(1951)
Rashomon
.

Moretti, F.
(2013)
Distant Reading
. 1 edition. London ; New York: Verso.

Moretti, F. and Piazza, A.
(2005)
Graphs, Maps, Trees: Abstract Models for a Literary History
. n Second printing edition. London ; New York: Verso.

Nelles, W. and Williams, L.
(2018) ‘Narrative Order in the First-Person Novel’,
Poetics Today
, 39(1), pp. 131–158.

Newman, D. A.
(2016) ‘“Education of an Amphibian”: Anachrony, Neoteny, and Bildung in Huxley’s Eyeless in Gaza’,
Twentieth-Century Literature
, 62(4), pp. 403–428.

Pezzotta, E.
(no date) ‘Personal Time in Alternative and Time Travel Narrative: The Cases of Groundhog Day, Twelve Monkeys, and 2001: A Space Odyssey’,
Alphaville: Journal of Film and Screen Media 2
.

Reagan, A. J.
et al.
(2016) ‘The emotional arcs of stories are dominated by six basic shapes’,
EPJ Data Science
, 5(1), p. 31.

Vonnegut, K.
(1981) ‘The Sexual Revolution’, in
Palm Sunday
. New York: RosettaBooks LLC.

Vonnegut, K.
(1995)
The Shapes of Stories
. Available at:

https://www.youtube.com/watch?v=oP3c1h8v2ZQ

(Accessed: 26 November 2017).

Wallace, D. F.
(1996)
Infinite Jest
. New York: Back Bay Books.

Welles, O.
(1941)
Citizen Kane
.

Wittenberg, D.
(2013)
Time Travel: The Popular Philosophy of Narrative
. Fordham University Press.

Woolf, V.
(1959)
Mrs. Dalloway
. New York: Harcourt, Brace and Company.