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We develop a new method to create maps that chart changes across a cinematic narrative. These are unlike narrative spaces previously discussed in the literature -- they are abstract, holistic, dynamic representations based on objective criteria. We consider three films (All About Eve, Inception, and MASH) by analyzing the co-occurrence of main characters within scenes, and one (12 Angry Men) by analyzing their co-occurrences within shots. Our technique combines the statistical methods of correlation, multidimensional scaling, and Procrustes analysis. We plot the trajectories of characters across these spaces in All About Eve and Inception, plot regions for characters in Inception and MASH, and compare the physical arrangement of jurors with their dramatic roles in 12 Angry Men. These maps depict the changing structures in the visual narrative. Finally, through consideration of statistical learning, we explore the plausibility that these maps mimic relations in the minds of film viewers.
a represents two paths across the four acts of the film. The relations of Eve and Margo, to each other and to the rest of the company, are the focus of All About Eve, and indeed they move most through the computed narrative space. Normalized to the distances moved across acts by the other characters (that is, giving them an average value of 1.0, the movements of Eve (1.72) and of Margo (1.87) are nearly twice as large. This suggests that their characters have changed most across the course of the film. Notice that initially Margo is in the center of the space, and indeed the flashback in the film starts centered on Margo. In terms of the data generating this position, Margo appears about equally often in scenes with each of the other characters. Alternatively, Eve generally co-occurs with only a subset of the characters, is computationally an outsider, and indeed a social outsider as well. During the second act, however, Eve insinuates herself into the center of the space and Margo is ejected. Margo is in crisis as she begins to realize, across this act and the development to follow, that she is no longer suited to play the roles of younger women. Most important, through the filmmakers' choice of depicting the various characters in the scenes, great distance is placed between Eve and Margo. This is the case both in the computation of co-occurrences and in the narrative itself. Finally, some of the tension-at least for Margo-is relaxed in the last act. This is, in large part, due to her improved relations with Bill. The Margo-Bill spatial relations are shown in Figure 2b. Initially, Margo and Bill are quite close in space, and indeed quite close in their relationship as depicted in the film. As Eve drives Margo into crisis, the distance between Bill and Margo dramatically increases during the complication and development. Indeed, Bill goes to Hollywood for a while and returns to a party in which sparks fly in all directions around Margo. In a memorable quote Margo warns: "Fasten your seatbelts, it's going to be a bumpy night." In the last portion they come close together. They occupy the same spot in the map. Bill is going to marry Margo, and Margo has accepted her inappropriateness for ingénue parts. Figure 2c shows the relative constancy of two more minor characters, Lloyd and Karen. They too end in the same spot, and in close proximity to Bill and Margo, but they have never moved very far. This reflects not only their co-occurrences in the scenes but also in their relationship within the narrative. Figure 2d shows the co-occurrence mappings of Addison and Eve. The narrative mirrors these relations: Addison is initially at some distance from Eve, tracks and helps her progress in the theater, both increasingly separated from Margo and the other characters. 11 Finally, and in the same panel, Phoebe arrives in the
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Projections Volume 7, Issue 2, Winter 2013: 80–107 © Berghahn Journals
doi: 10.3167/proj.2013.070205 ISSN 1934-9688 (Print), ISSN 1934-9696 (Online)
Mapping Narrative Space
in Hollywood Film
James E.Cutting, Catalina Iricinschi,and Kaitlin L.Brunick
Abstract: This article presents a new method to create maps that chart
changes across a cinematic narrative. These are unlike narrative spaces previ-
ously discussed in the literature—they are abstract, holistic, dynamic repre-
sentations based on objective criteria. The analysis considers three films (All
About Eve,Inception,and MASH) by counting the co-occurrences of main char-
acters within scenes, and 12 Angry Men by counting their co-occurrences
within shots. The technique used combines the statistical methods of corre-
lation, multidimensional scaling, and Procrustes analysis. It then plots the tra-
jectories of characters across these spaces in All About Eve and Inception,
regions for characters in Inception and MASH, and compares the physical
arrangement of jurors with their dramatic roles in 12 Angry Men. These maps
depict the changing structures in the visual narrative. Finally, through consid-
eration of statistical learning, the article explores the plausibility that these
maps mimic relations in the minds of film viewers.
Keywords: characters, film, maps, multidimensional scaling, narrative space,
scenes, shots, statistical learning
What is narrative space? In both writing and in film, it refers to any
space in which a narrative can take place. This space does not nec-
essarily have to be always physical: it can be emotional, psycholog-
ical. Many films take use of these intangible narrative spaces to
create moods and tones.
—Miss Yujin (9 October 2009)
This article offers a new way to map narrative structure and to show how it
changes across the shots and scenes of a film. It does so by looking at four
quite different Hollywood films—All About Eve (1950), a studio-era drama
with a well-defined sequence of scenes that can be placed neatly within four
roughly equal-length sections; Inception (2010), a much more complexly struc-
tured action film whose scenes we divide across six acts; MASH (1970), an
episodic comedy without traditional film structure but whose scenes can be
allocated to a setup and five major episodes; and 12 Angry Men (1958), a drama
with little traditional scene structure and with almost all of the story taking
place over continuous time within one room with a constant set of characters.
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In the context of film studies our method of mapping narratives is unusual
and only tangentially related to the broader concept of narrative spaces found
in literature and film.
There are at least six reasons for this contrast. First, we
really do mean maps —two-dimensional graphic representations of relations
among main characters across the course of a film. Second, most of our maps
have nothing to do with the physical spaces that are portrayed in films. Third,
we ignore entirely the verbal content of the film—screenplay, dialog, plotline.
Fourth, our maps are objective; they are generated by computer algorithms
from inputs based on the visual presentation of the characters as they co-
occur within scenes and shots and accumulate over portions of film. Fifth, our
maps are holistic. They consider relations among all major characters simul-
taneously, not just a select few. Finally, we create them multiple
times across the length of the film. Comparisons across such maps
reveal some of a film’s dynamic narrative structure. We believe that
these maps show the close relationship between how filmmakers
compose shots and how the verbal content of the narrative unfolds.
Narrative dynamics of almost any popular film can be portrayed in a
sequence of two-dimensional maps.
We create maps that are representations of the narrative structure of a
film, not its structure in the mind of the viewer. Nonetheless, as the result of
statistical learning, we claim that filmgoers encode the co-occurrences of
characters and build dynamic representations of character relations that are
consistent with these maps. We claim further that this knowledge, as it is ac-
quired, helps them understand the story of the film.
Making Maps
The essence of any map is that it presents distances between things in a con-
tinuous space. Consider a concrete example. The top left panel of Figure 1
shows a schematic map of six major cities in Western Europe—Berlin, Geneva,
London, Madrid, Paris, and Rome. The air distance in kilometers among these
cities is noted. If these fifteen numbers are entered into a multidimensional
scaling program, one can reconstruct the array of cities, shown in the top right
panel. This is a two-dimensional display of the distances among the cities.
There are several peculiarities about the production of this scaling solu-
tion, or simply map. First, the “proper” orientation of the map is not known to
the scaling program or represented in its output. In particular, the algorithm
does not know about north, south, east, or west. Thus, with such a scaling so-
lution, one is free to rotate the map however one wishes, although clearly the
map shown at the upper right is oriented in the generally accepted way. The
second peculiarity of this procedure is that it could be mirror reversed with
Berlin to the left of London, and Rome to the left of Madrid. In other words,
from the input distances the algorithm does not know that one usually looks
Narrative dynamics of
almost any popular
film can be portrayed
in a sequence of two-
dimensional maps.
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down at such a map, rather than up through it. Thus, one also has the free-
dom to flip the map over as if it were transparent. Despite these constraints,
the program allows one to recover the map from the distances. In this case the
map is essentially exact.
Surely, this does not seem very impressive: one inputs distances and gets
back the map from which one obtained the distances, and one does not even
Figure 1.The creation of three maps through multidimensional scaling.The top panels use the
distances in kilometers among Western European cities; the middle panels use the ranked order of
distances among them; and the bottom panels use round trip flight costs from 2002.Adapted
from Cutting (2006).
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know its orientation or which side is face up. Distances in this first case were
given in kilometers, which are measured on what is called a ratio, or metric,
scale. The aggregation of their collective relations is called metric multidi-
mensional scaling. But there are other ways to scale the data without this re-
sult, and these are much more interesting.
Consider: rather than mark intercity distances in kilometers, one might
simply rank them from closest to farthest. This is done in the middle left panel
of Figure 1. Here, London and Paris are ranked the closest, Paris and Geneva
second, Geneva and Rome third, and so forth, with Madrid and Berlin the far-
thest apart. Notice that the distances between Paris and Madrid and Paris and
Rome are very nearly the same, so these are given ranks of 9.5 (the average of
rank 9 and rank 10). Using nonmetric multidimensional scaling, which uses
only such ordinal ranks as input, one can also create a new map. This one is
shown in the middle right panel of Figure 1.
In this process of comparing all possible ranks, the algorithm tries to cre-
ate a map with the distance between London and Paris as the shortest link,
that between Berlin and Madrid the longest, and the rank order of all the dis-
tances between cities the same as given in the middle left panel. The scaling
result is impressive. Notice that this map, despite its nonmetric origin, is al-
most the same as the metric one in top right of Figure 1. Oriented and flipped
appropriately, it is very difficult to tell the difference. Scrutiny reveals that
Berlin is perhaps a little bit too close to Rome, having slid somewhat south.
It is fun to make such maps, and one quickly realizes that aerial distances
are not the only thing that might be considered. The lower panels of Figure 1
show the creation of a different kind of map. Shown on the left are costs in US
dollars to fly roundtrip between the same fifteen pairs of cities according to™. These data are old but instructive,
and all seasoned travel-
ers will be familiar with these types of results. Notice that it was cheaper to
fly from Paris to London to Berlin and back than to fly roundtrip between Paris
and Berlin directly. The same is true from Geneva to London to Madrid, com-
pared to roundtrip flights between Geneva and Madrid. Moreover, it is almost
the same price to fly through London to most other cities from most other
cities. This is a peculiarity of air hubs, routing, and heavily trafficked links be-
tween certain cities. And notice also that usual hubs of Frankfurt and Amster-
dam were left out of this modeling.
Contemporary travelers understand these situations well, but rarely con-
vert their intuitions into a map. Nonetheless, one can easily do so through
nonmetric multidimensional scaling. If we start with the costs of travel as the
“distances” between cities rather than the kilometers that separate them, we
can create a new map of Western Europe. The scaling results are shown in the
lower right panel of Figure 1.
This map shows why, in terms of monetary
cost—although not total trip time or connection aggravations—London is on
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the way from Paris to Berlin, and why London is between Geneva and Madrid.
In other words, if airfare prices were the only consideration for the traveler, he
or she could use such a map of Europe to plot business or vacation trips.
Deriving Character Distances and Making Maps of Film Narratives
As suggested in the cases above one can use many different sources of infor-
mation as “distances”—kilometers, ordinally ranked distances, airfares, and so
forth. One can also use correlation values as distance measures. That is, be-
cause correlations vary from 1.0 through 0.0 to –1.0, one can assert that items
with correlations of 1.0 are very close to each other (indeed in the same loca-
tion), those with correlations around 0.0 are at middling distance; and those
near –1.0 very far apart. In this manner, one can use correlations as numbers
on an ordinal scale, relating objects (in this case characters in a film) to one
another, and then scale them nonmetrically to make a map.
Correlations come in several varieties and with different tweaks. The one
we use is called Cohen’s kappa, or κ. The distance measure we use is 1 – κ,
yielding a set of possible distances between 0.0 and 2.0.
Cohen’s kappa is
usually used to measure the agreement between two people making judg-
ments in psychological experiments. Here we generalize it to the appearance
of any two characters as they appear across scenes of a film.
Consider four cases, the first three from Santa Fe Trail (1940). First, Windy
(Guinn Williams) and Tex (Alan Hale) are characters of comic relief. Like Twee-
dledum and Tweedledee they always appear together in a scene. More con-
cretely, they appear together in twenty-six scenes, Windy never appears
without Tex, or Tex without Windy, and neither appears in 109 other scenes.
The “distance” between Tex and Windy, then, is zero (κ = 1.0; distance = 1.0 –
κ = 0.0). Second, Jeb Stuart (Errol Flynn) and George Custer (Ronald Reagan)
are main characters in the film and present a different relation. The film be-
gins as a “bromance” between the two at West Point and then in Kansas in
the 1850s, but shifts as Stuart begins to win over Kit Carson Holliday (Olivia de
Havilland). Stuart and Custer appear together in sixty-nine scenes, Stuart ap-
pears without Custer in twenty-five, Custer without Stuart in only one, and
neither appears in forty scenes. Thus, κ = .64 and thus the distance measure
is .36. Third, Kit’s father Bob Holliday (William Lundigan) and John Brown (Ray-
mond Massey) appear together in only one scene, the last of the film where
Brown is to be hanged. Holliday appears in twelve scenes without Brown,
Brown in thirty-six without Holliday, and neither appear in eighty-seven
scenes, yielding a distance of 1.15.
Finally, for a distance of 2.0 one must imagine a film in which two charac-
ters appear across all scenes, but they never appear together. There are likely
a number of experimental films that have this composition, but the closest
popular movie may be Sliding Doors (1998). It depicts Helen (Gwyneth Paltrow)
s5_PROJ-070205 9/4/13 9:47 AM Page 84
living in two separate realities. In one she catches a train and discovers her
lover in bed with an ex-girlfriend. In the other she misses that train, is
mugged, and comes home to her lover alone in the shower. The film goes back
and forth between the two realities as they progress, but clearly the two He-
lens (one now with short hair having jettisoned her partner, and the other re-
taining long hair and having kept him) cannot appear in the same scene.
one or the other appears in all scenes their “distance” would be 2.0 [κ = –1.0;
distance = 1.0 – (–1.0) = 2.0].
Given n characters in a given film, there are n*(n–1)/2 distances to consider.
Thus, if there are four characters, there are six distances among them to scale;
8 characters, 28 distances; and 15 characters, 105 distances. Critically for this
effort the more characters the more difficult it will be to fit them easily into a
two-dimensional space.
Film Units,Small and Large
We had a number of viewers parse twenty-four films, three per film. Their in-
structions were to track “events” in the film (without having been given an
overt definition of an event) and to mark frame numbers that began new
events. Handily, these events generally obey continuities of space and time,
particularly space. That is, viewers generally coded a new event as occurring
when the film shifted to a new locale. Thus, these events map reasonably well
onto scenes and subscenes in film structure (Cutting et al. 2012).
For three of
the films we investigate here—All About Eve, Inception, and MASH—these
parsed events are our “small” units. We started with the original scene-pars-
ing data, going through each film again and generally tracking where at least
two viewers agreed on an event boundary. We then recorded each character
that was shown within each scene, entering a value of one for each into a
large matrix. All characters not shown in that scene were given a value of zero.
Because our fourth film, 12 Angry Men, does not have a traditional scene struc-
ture, we shifted our “small” unit to the shot, analyzing the co-occurrence of
characters in all shots of the film, with 1s and 0s in a large matrix for all shots.
The constructed matrix was then the input for a Matlab computer program
that computed the kappa-based distance measures among all possible char-
acters across all scenes or shots in the film. It then generated a nonmetric
scaling solution in two dimensions. We call this the base map and used it as a
backdrop against which to compare other maps from that film.
Next new maps were computed independently for each of the “large”
units of each film. We use here the term act as a technical term for All About
Eve and Inception, which in our analyses contained four and six of these large-
scale units, respectively. For All About Eve our acts seem to correspond to the
structure promoted by Thompson (1999), who divided most films into roughly
four equal-length acts, although she allowed longer films to have more. We
s5_PROJ-070205 9/4/13 9:47 AM Page 85
make no claim that she or others would parse these films in the same way as
we have. What is important here is the serial nature of these units across the
film, each one following directly on the previous, and that they are of roughly
equal length. For a third film, MASH, we abandoned the notion of an act and
substituted the term episode.Act structure implies coherence across the arc
of a film, and this simply does not apply to a film like MASH. And finally, in 12
Angry Men we divided the film according to juror votes. For lack of a better
term, we call these larger units sections.
Our analytic method for the larger units is this: we first scaled the charac-
ters in each film portion, creating a new map, and then used a statistical tech-
nique called Procrustes analysis. This procedure rotates, shifts, expands or
contracts, and possibly flips the newly scaled solution to best fit the base map.
We followed this procedure for each larger portion of a given film—act,
episode, or voting segment—matching its solution back to the base map so
we could cross-register the separate maps and gain insight into character re-
lations as they might change across the film.
All About Eve (1950):Tracing Paths in a Narrative Space
We chose All About Eve as the first film for our analysis. This drama presents
the story of a small cross-section of mid-twentieth-century New York City the-
ater society, taking place mostly within a flashback. The core of the story pits
an established actress, Margo Channing (Bette Davis), against newcomer Eve
Harrington (Anne Baxter). It also involves Margo’s partner, Bill Simpson (Gary
Merrill), a playwright and screen writer; another couple, Margo’s director
Lloyd Richards (Hugh Marlowe) and his wife Karen (Celeste Holm); a theater
critic, Addison DeWitt (George Sanders); Margo’s housekeeper, Birdie (Thelma
Ritter); and the producer, Max Fabian (Gregory Ratoff), of Margo’s play. We
omit discussion of Birdie and Max, although their appearances were used in
the construction of the base map and subsequent maps.
An Analysis of Acts
Following Thompson, the first act is a setup (here 31 minutes long). It intro-
duces the characters at a banquet in honor of Eve, and then flashes back to a
beginning with Eve lurking in an alley and having done so after every perform-
ance of a play in which Margo stars. The plot then progresses through to the
point where Karen introduces Eve to the theater crowd, Eve charms them with
her (fictitious) personal story, moves in with Margo, becomes her personal as-
sistant, and arranges—against Margo’s knowledge and remembrance—for
her to have a midnight phone call with Bill for his birthday.
The second 31-minute act in our segmentation, the complication in
Thompson’s terms, has Margo growing increasingly fed up with Eve, while Eve
insinuates herself among the others and into all matters of the theater pro-
s5_PROJ-070205 9/4/13 9:47 AM Page 86
duction in which Bill, Lloyd, Max, and Margo are involved. In the third act, the
development (36 minutes), Margo learns that Eve is now her understudy,
Karen arranges that Margo miss a performance, Eve performs well, and Addi-
son writes a glowing review. In the climax act (33 minutes, including a 5-
minute epilogue), the two couples meet at a restaurant, with Eve and Addison
at a nearby table and, after an opening in New Haven and a behind-the-
scenes tussle between Addison and Eve, the narration eventually flashes for-
ward to the banquet that opened the film, celebrating the success of Eve.
Then, in an epilogue an aspiring young actress, Phoebe (Barbara Bates), has
talked her way into Eve’s empty hotel room and, after Eve arrives, sets herself
up to become a new Eve.
The four panels of Figure 2 lay out the co-occurrence relations of the players
across the four acts of the film, with the different colors distinguishing them.
Again, each map is oriented and fitted to the base map (not shown) and the
directions in these spaces are arbitrary: distances up the map are no different
than distances to the right. These are abstract spaces that encode only the
scaled distances among characters. Critical, however, are the distances
among points, which represent eight of the characters.
Figure 2. Four maps showing the trajectories of characters in a narrative space across the four acts
of All About Eve. Different colored dots represent the characters in the different acts.The layouts
are based on the co-occurrences of characters in scenes (measured by Cohen’s κ), with those values
multidimensionally scaled and brought into register by Procrustes analyses.
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Figure 2a represents two paths across the four acts of
the film. The relations of Eve and Margo, to each other and
to the rest of the company, are the focus of All About Eve,
and indeed they move most through the computed narra-
tive space. Normalized to the distances moved across acts
by the other characters (that is, giving them an average
value of 1.0, the movements of Eve (1.72) and of Margo (1.87)
are nearly twice as large. This suggests that their charac-
ters have changed most across the course of the film.
Notice that initially Margo is in the center of the space, and indeed the flash-
back in the film starts centered on Margo. In terms of the data generating this
position, Margo appears about equally often in scenes with each of the other
characters. Alternatively, Eve generally co-occurs with only a subset of the
characters, is computationally an outsider, and indeed a social outsider as
During the second act, however, Eve insinuates herself into the center of
the space and Margo is ejected. Margo is in crisis as she begins to realize,
across this act and the development to follow, that she is no longer suited to
play the roles of younger women. Most important, through the filmmakers’
choice of depicting the various characters in the scenes, great distance is
placed between Eve and Margo. This is the case both in the computation of
co-occurrences and in the narrative itself. Finally, some of the tension—at
least for Margo—is relaxed in the last act. This is, in large part, due to her im-
proved relations with Bill.
The Margo-Bill spatial relations are shown in Figure 2b. Initially, Margo and
Bill are quite close in space, and indeed quite close in their relationship as de-
picted in the film. As Eve drives Margo into crisis, the distance between Bill
and Margo dramatically increases during the complication and development.
Indeed, Bill goes to Hollywood for a while and returns to a party in which
sparks fly in all directions around Margo. In a memorable quote Margo warns:
“Fasten your seatbelts, it’s going to be a bumpy night.” In the last portion they
come close together. They occupy the same spot in the map. Bill is going to
marry Margo, and Margo has accepted her inappropriateness for ingénue
Figure 2c shows the relative constancy of two more minor characters, Lloyd
and Karen. They too end in the same spot, and in close proximity to Bill and
Margo, but they have never moved very far. This reflects not only their co-oc-
currences in the scenes but also in their relationship within the narrative. Fig-
ure 2d shows the co-occurrence mappings of Addison and Eve. The narrative
mirrors these relations: Addison is initially at some distance from Eve, tracks
and helps her progress in the theater, both increasingly separated from Margo
and the other characters.
Finally, and in the same panel, Phoebe arrives in the
The relations of Eve and
Margo, to each other and to
all of the rest of the company,
are the focus of All About Eve,
and indeed they move most
through the computed
narrative space.
s5_PROJ-070205 9/4/13 9:47 AM Page 88
epilogue, a young outsider hard-bitten on the ladder of success, much like Eve
at the beginning of the story.
We claim that the spatial layouts of each of the four panels make sense in
terms of the narrative in All About Eve. We hasten to add that these panels
were constructed without consideration of any verbal content within the film.
Instead, they were compiled based only on visual appearance in the film’s
scenes. Also, to be clear, we make no claim that this is the only way to create
a narrative space, but we do think that many similar schemes will converge on
these same results. For example, if one weights the character co-occurrences
by the duration of each scene, the results are almost identical to those in Fig-
ure 2.
Most important, we claim that this set of results makes narrative
Inception (2010): Character Regions and Paths across a Narrative Space
Tracking the co-occurrences of characters in All About Eve yields an inter-
pretable set of maps across the four portions of the film. One could argue,
however, that dramatically this is a fairly straightforward older film and that
perhaps those attributes contribute to the interpretability of the maps we
have generated. Thus, we next look at Inception, a much more complex film
with a much more complex structure. We divided Inception into six larger
units, which we also call acts.
An Analysis of Acts
The first act is a prelude (21 minutes). The action that takes place mostly in
two dream environments—a very large, Asian wooden building at one dream
level, and a hotel room with a revolution going on outside at another. It then
erupts into a nondream environment with the main characters on a fast train.
It continues until Saito (Ken Watanabe), an industrial magnate in his private
helicopter, drops off Cobb (Leonardo DiCaprio), the main dream controller, and
Arthur (Joseph Gordon-Levitt), his major assistant. It is then that Saito offers
Cobb a job in exchange for his heretofore-impossible repatriation to the
United States.
The second act is a first setup (23 minutes) in which Cobb assembles his
team. The team includes Arthur, Ariadne (Ellen Page) as the dream architect in
Paris, Eames (Tom Hardy) as the impersonator, and Yusuf (Dileep Rao) as the
chemist (or druggist) both in Mombasa, and with Saito tagging along, “pro-
tecting his investment.” The third act is a second setup (20 minutes) during
which the team, back in Paris, plans the inception —the insertion of an idea
into the controlled dream of Robert Fischer (Cillian Murphy), the son of Saito’s
chief global competitor. This portion ends as the inception team and Fischer
drop off in a drugged sleep in first-class compartment of a transcontinental
flight from Asia to Los Angeles.
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The fourth act is the complication (20 minutes), where the team and Fis-
cher arrive in the first dream level in an urban setting to rain, a train careen-
ing through cars down an avenue, a small enemy army consisting of Fischer’s
mental “projections” firing at the inception team, and Saito being shot. It con-
tinues in a warehouse, through a continued battle with projections, until all
members drive off in a van and Cobb hatches the revised plan called “Mr
Charles,” a gambit in which Fischer is informed he is dreaming within a dream.
The fifth act is the development (21 minutes). It begins at the second
dream level in a hotel bar and continues upstairs while at the first dream level
Yusuf dodges the small army and continues to drive the van with its sleepers.
This act ends when the van drives through the bridge railing, triggering the
beginning of the sixth and final act, the climax (35 minutes).
At the first dream level the climax shows the slow motion of the van drop-
ping to the water. Because time is increasingly dilated at successively deeper
dream levels in the film, this provides different amounts of time to the same
deadline at which events must come to fruition at dream levels two (the ho-
tel), three (the winter fortress and hospital), and four (limbo, and the city de-
signed by Cobb and his dead wife Mal, Marion Cotillard). At the end of the
climax, the epilogue (three minutes) has the group returning to cinematic re-
ality in the airplane, Saito assuring Cobb’s repatriation with a phone call, Cobb
passing through immigration, and Miles (Michael Caine) taking him to see
his kids.
By our counts Inceptionhas 2,755 shots and 355 scenes and subscenes, most of
the latter are quickly cut back and forth in parallel action, particularly in the
climax. These numbers vastly outstrip All About Eve, which we count as hav-
ing 775 shots and 90 scenes and subscenes. Thus, rather than simply tracking
the progress of characters across acts as we did in Figure 2, we will set up lo-
cal narrative regions in which most of the characters exist, and then plot the
trajectories of three other characters through these narrative spaces.
unlike the arrays in Figure 2, we have left in place the large array of across-act,
colored points, circles, and crosses for each of ten characters. This presents
what might appear to be chaos, but to create order we have drawn in colored
ellipses around all the locations of a given character across all the acts in
which he or she appears. These are shown in Figure 3a for Mal, Cobb’s chil-
dren, Miles, Arthur, Eames, Yusuf, and Saito.
Notice that Mal, the children, and Miles all appear on the one side of the
map in quite distinguishable regions. Contrasting with them and on the op-
posite side are Eames, Yusuf, Saito, and Arthur. They form highly overlapping
set of regions with Arthur, the only team member to appear in the prelude, ex-
tending considerably downward. The high degree of overlap of these four sug-
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gests that, as is true in the narrative, these characters are a team working to-
gether and are largely intersubstitutable in the larger story structure. The
multidimensional scaling solutions of characters within and across scenes
clearly separates the overlapping work of the Inception team from the separa-
ble narrative niches of Cobb’s family.
Figure 3b shows the clockwise trajectory of Ariadne across the last five acts
of the film, at and beyond her recruitment at the lower center of the map in
the first setup, and then entering the sphere of Mal in the second setup, when
she accompanies Cobb on his dreams/memories of
her. Ariadne then becomes more integrated into the
team and in the last two acts winds up at the center
of the computed configuration. Indeed, she is the
center of the film when dream levels collapse and the
van crashes into the water in the climax. We follow
Ariadne, but not the other characters, up through the
dream levels. Figure 3c shows the counterclockwise
The multidimensional scaling
solutions of characters within and
across scenes clearly separates the
overlapping work of the Inception
team from the separable narrative
niches of Cobb’s family.
Figure 3.The upper left panel shows the scaled narrative space for seven characters as they co-
occur in the scenes of Inception. Each ellipse encloses the scaled locations for each character across
the acts of the film in which he or she appears.The locations of these ellipses show the nonoverlap
between Cobb’s family and his co-workers.The other panels show the trajectories of Ariadne,Cobb
(who is near Ariadne,shown as small unfilled ellipses in three acts of the film), and Fischer.
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trajectory of Cobb, who starts out at the center of the space as he organizes
everyone, then moves downward towards Ariadne (the points surrounded by
open ellipses) and Mal in the last four acts of the film. His movement across
the mapped space is 1.32 times greater than the normalized average (1.0) of
the other characters. Finally, Figure 3d shows the trajectory of Fischer: he
starts as the target dreamer outside the team in the second setup; is held cap-
tive in the complication, essentially joins the team in the development at
dream levels two, three, and four; and then drifts to the outside during the cli-
max. His across-act average movement is the greatest of all the characters
(1.5). These normalized movement values suggest that Cobb and Robert are
the characters that have changed the most across the film.
Again, these maps were constructed based only on visual character co-oc-
currence within scenes. Nonetheless, we claim they make narrative sense and
generally depict more than a few aspects of plot relations among characters.
But again, we make no claim that these are the only possible narrative maps.
MASH (1970):Regions of Narrative Space across Film Episodes
Our analyses of All About Eve and Inception demonstrate that objective narra-
tive maps can be constructed for quite different films from quite different
eras in the face of both content and structural dissimilarities. Although our
analysis gives more acts to Inceptionthan most accounts might for Hollywood
films, we claim that both films have a tightly coherent narrative structure,
with cause and effect relations pervading them. This is not true for MASH, an
episodic film that takes place in and around a remote Mobile Army Surgical
Hospital in a war zone in Korea, standing in for Vietnam. In such a film, there
is less temporal coherence and only a smattering of cause and effect relations
across episodes.
An Analysis of Episodes
We divided the film into a setup and five episodes. In the setup (26 minutes),
we are introduced to the main characters as they arrive in camp—the sur-
geons, Hawkeye Pierce (Donald Sutherland), Duke Forrest (Tom Skerritt), and
finally Trapper John McIntyre (Elliott Gould). Those already in camp include
surgeon Maj Frank Burns (Robert Duvall), nurse Lt Dish (Jo Ann Pflug), Father
John Mulcahy (René Auberjonois), Col Henry Blake (Roger Bowen), and Cpl
Radar O’Reilly (Gary Burghoff). Episode 1 (23 minutes) begins with the arrival
of head nurse Maj “Hot Lips” Houlihan (Sally Kellerman) with ideas of enforc-
ing a strict regimen in camp and in the operating room. She begins a short
passionate affair with Frank Burns, the sounds of which Radar and Trapper
John broadcast over the camp’s loudspeaker system. The next day Hawkeye
taunts Frank, who then attacks him, and the episode ends with Frank taken
away in a straightjacket.
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We consider episodes 2 and 3 together (27 minutes), with the former cen-
tered on the Last Supper event and the latter on the Hot Lips shower event.
Troubled with manliness issues after failing to consummate an ad hoc fling
with a nurse, the camp oral surgeon Capt Painless Waldowski (John Schuck)
decides to commit suicide. He is thus the protagonist of a staged false suicide
scene that humorously replicates Leonardo’s Last Supper ensemble. Accom-
modating a request from Hawkeye, Lt Dish helps Painless regain his manly
confidence on her last night in the camp. Her departure the following morn-
ing closes the episode. The shower sequence begins with camp helper Ho-
Jon’s (Kim Atwood) and Radar’s endeavors over a device that successfully
lifted the women’s shower tent and revealed naked Hot Lips.
In episode 4 (12 minutes) Hawkeye and Trapper John are summoned to Japan
for surgery. They befriend another doctor, Me Lai Marston (Michael Murphy),
and outrage then dupe Col Merrill (James Douglas). Episode 5 (22 minutes)
sets up and enacts a football game between the MASH team and that of Gen
Hammond (George Wood). Hawkeye and Trapper John arrange for the trans-
fer of a heart surgeon and former professional football player, Spearchucker
Jones (Fred Williamson) to the MASH unit. Spearchucker then leads the MASH
football team to victory. A short epilogue (4 minutes) after the game declares
the war suddenly over for the main characters.
One aspect of a film like MASH is that, because the episodes have little
causal connection, the cast of characters shifts dramatically. Frank Burns dis-
appears after episode 1, and Lt Dish after episode 2, and Painless is not seen
after episode 3. With Hawkeye and Trapper John spirited away to Japan, the
rest of the MASH crew does not appear in episode 4 and two new characters
Unlike most feature films, the episodic structure of a film like MASH can af-
ford to relax the cause-effect plot connections. Such weak interepisodic causal
connections allow (and account) for the continuous shift in the cast of charac-
ters. Frank Burns disappears after episode 1, Lt Dish after episode 2, and Pain-
less is not seen after episode 3. With Hawkeye and Trapper John in Japan, the
rest of the MASH crew does not appear in episode 4 and two new characters
appear. Episode 5 introduces Spearchucker Jones in the context of the football
game. The only characters who traverse all episodes are Hawkeye and Trapper
John, the latter being introduced only three minutes from the end of setup.
By our analysis MASH has 962 shots and 153 scenes and subscenes. As for
other movies in our study, we created a base map, this time involving 15 char-
acters. We then fit to the base map the scale solutions of the setup and the
episodes, interpret the resulting structure.
Again, we left the markers for
each of the characters on the map displays. Figure 4a shows the layout of the
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characters in the setup. The three main characters form a small coherent
group in the middle left of the space, the regulars of the MASH unit (Col Blake,
Radar, Painless, and Mulcahy) are to the right, and Frank Burns and Ho-Jon,
whom Burns teaches to read English by reading the Bible, are near the top of
the space. Ho-Jon quickly disappears with a soft-porn magazine given to him
by Hawkeye, and he does not reappear until the end of episode 3. The separa-
tion of these three groups of characters makes narrative sense; the main sur-
geons are distanced from Burns, and the camp regulars are off to the side and
generally undistinguishable from each other as they each provide idiosyn-
cratic color.
Figure 4. Narrative regions for characters in scenes of MASH across the setup and five episodes as
determined by multidimensional scaling.
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Figure 4b shows the layout for episode 1, where Frank and Hot Lips get to-
gether. Notice that they now form a tight spatial group, that the camp regu-
lars (Col Blake, Radar, Painless, and Mulcahy) form another tight group, and
that the three surgeons (Duke, Trapper John, and Hawkeye) who provoke the
episode intercede between these two. This arrangement is consistent with
the content of the narrative.
The separation of episodes 2 and 3, both shown in Figure 4c, is revealing. It
allows a contrast between the Last Supper and Hot Lips shower episodes. In
the former, Painless is now separated from the remainder of the camp regu-
lars and tucked behind the space of the major surgeons. Spread around the
surgeons are Dish, who ends the episode; Father Mulcahy, who has doubts
about issuing last rights for a suicide and Radar, who helps the surgeons
arrange the Leonardo tableau. More striking, this Last Supper space contrasts
sharply with that of the shower episode. The major surgeons generally remain
relatively stable in their positions. However, Ho-Jon and Radar, who make
arrangements for the lifting of the tent sides around the shower, drift away.
Hot Lips, outraged, rushes to Col Blake, who is in bed with one of the nurses.
Most important is that Hot Lips has moved from her remote spatial position
with Frank Burns in episode 1, to an even more remote position from the ma-
jor surgeons and the camp regulars in episode 3.
Episode 4 takes place in Japan with only two of the surgeons, Hawkeye and
Trapper John, participating. They befriend Me Lai Marston and run afoul of
Col Merrill, and the triangular distances among them are consistent with the
plotline. Notice also that Hawkeye and Trapper John have become a single
point in Figure 4d. The reason for this, as with Windy and Tex in our discussion
of Santa Fe Trail, is that they appear in all scenes in this episode, and all scenes
together, never separately.
Episode 5 returns to the MASH camp and preparations for a football game
against the team of Gen Hammond. The three surgeons appear together
in nearly all their scenes and thus again become a single point in Figure 4e,
representing the players in the game; Col Blake, Radar, Mulcahy, and Hot
Lips appear in nearly all of their scenes together on the sidelines and also
become a point. Spearchucker appears at equal distance from the surgeons
and the camp regulars since he appears about equally often with both, and
the General appears at some distance from all of this since he is on the op-
posite sidelines. Thus, Figure 4e is a schematic representation that accu-
rately captures the four entities involved in the football game episode: Spear-
chucker, the MASH players, and the fans on the two sidelines. The General’s
team consists of individuals who are unknown and therefore not really
The narrative movement of Eve and Margo in All About Eve and of Cobb in
Inception is quite different than that for Hawkeye and Trapper John. The pro-
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tagonists of MASH move less across episodes, 0.67
and 0.69, respectively, compared to the normalized
average of 1.0 of the other characters. Our analysis
shows that Hawkeye and Trapper John have not
changed much across the film; instead they have or-
chestrated the people in the episodes as they take
place around them. This idea fits well with the narra-
tive of the film. Finally, even with 15 characters across
disjointed episodes, the plot of the narrative space of those episodes in MASH
seems reasonable based on the co-occurrence of characters that come in and
out of those episodes. In this manner, we claim increasing generalization of
this technique across different kinds of films—classic standards, complex con-
temporaries, and episodic gambits.
12 Angry Men (1957):From Diegetic to Narrative Space
Our co-occurrence analyses of the characters in All About Eve, Inception, and
MASH were carried out within scenes and then compared across all acts or
episodes of the film. Most films have more or less readily defined scenes and
subscenes, and characters change as the narrative shifts across time and
space. Some films, however, take place in continuous time—for example, My
Dinner with Andre (1981), 12 Angry Men,High Noon (1952), and Rope (1948).This
constraint allows few chances for standard scene change. Moreover, the cen-
tral core of first two films takes place in a single location with a constant set
of characters. Thus, with no time jumps, no location shifts, and no character
changes one could argue that there are no real changes of scene. The latter
fact might suggest that our type of analysis could not be used for such films.
Thus as a strong test of our method, we attempted to construct a dynamic
narrative space for 12 Angry Men, shifting methodological gears and looking
only at the characters seen in consecutive shots. In our analysis of the film we
found 362 shots and all but 10 of those take place in the jury room and an ad-
joining bathroom.
An Analysis by Votes
Ignoring the prologue in the courtroom followed by jurors milling around the
jury room (eight shots, nine minutes) and epilogue outside the courthouse
(two shots, one minute), we divided the whole of the jury deliberation se-
quence by the votes that were taken. Section 1 (22 minutes) begins with a pre-
liminary vote. This reveals that Juror 8 (Henry Fonda) is on the short end of an
11-1 guilty verdict. Unanimity would entail a death sentence for a young
Puerto Rican accused of killing his father. Discussion follows with almost
everyone sitting around the table focusing on the reticence of Juror 8. After a
long while and in desperation he calls for another vote.
Our analysis shows that Hawkeye
and Trapper John haven’t changed
much across the film;instead they
have orchestrated the people in
the episodes as they take place
around them.
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Section 2 (13 minutes) begins with a surprise: the vote is 10–2. The oldest
member, Juror 9 (Joseph Sweeney), has joined Juror 8. That outcome is unpre-
dicted by the previous discussion or by the camerawork. More discussion and
displeasure accrue, and the jurors start to walk around, and in some cases
simulating events of the murder.
Section 3 (15 minutes) begins with a new vote. Juror 5 (Jack Klugman), who
like the defendant grew up in a slum, changes his mind. Juror 11 (George
Voskovec), an immigrant who knows the difficulties of being out of the main-
stream, soon follows. The vote is then 8–4 and more discussion, anger, and
perambulations ensue.
Section 4 (11 minutes) begins with Jurors 2 (John Fiedler) and 6 (Edward
Binns) changing their votes, deadlocking the jury at 6–6. This is followed by a
pause in the proceedings, the start of rain and cooling temperatures outside,
then further discussion, and a demonstration of a switchblade fight.
In Section 5 (17 minutes) the deliberation begins with Juror 7 (Jack Warden),
and then Jurors 1 (Martin Balsam) and 12 (Robert Webber) changing their
votes without the apparent conviction of the others. This tips the vote to 3–9,
and further discussion ensues.
Juror 10 (Ed Begley) disqualifies himself for
bias, Juror 4 (E. G. Marshall) changes his vote on a reconsideration of evidence,
and Juror 3 (Lee J. Cobb) finally relents after a dramatic protestation.
The layout for the whole film and the maps of our five sections are shown in
Figure 5.
The base map is shown in Figure 5a. In the jury room the 12 jurors
sit at a rectangular table and they are numbered clockwise around it; the fore-
man (Juror 1) at the head and Juror 7 at the other end. If they all remained at
the table and shots simply showed a discussant and his near neighbors the
scaled arrangement would likely be an ellipse. However, during the course of
deliberation all jurors get up and walk around. This dissolves their diegetic
arrangement placing jurors nonadjacent at the table within the same shot
while sometimes omitting the jurors in between. Nonetheless, some aspects
of the table arrangement remain. We have placed a dot at the origin of the
plot (the center of gravity around which all jurors are placed) and drawn lines
from the origin to each of the jurors.
Notice that the clockwise order of the jurors perfectly mimics the order of
the jurors as they sit around the table. The diegetic space in 12 Angry Men is
apparent in our base map, merged with its computed narrative space. As to
the former, despite juror perambulations over the course of
the film there are a sufficient number of co-occurrences of
adjacent jurors in the shots to preserve their ordinal rela-
tions at the table. Yet overlaid on this order there are devi-
ations that are consistent with the narrative. Obvious
The diegetic space in 12 Angry
Men is apparent in our base
map, merged with its
computed narrative space.
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outliers are Jurors 8 and 3. Juror 8 (Fonda) is the first to vote for acquittal and
Juror 3 (Cobb) is the last. There is an important sense in which these two ju-
rors act as polar opposites in the film. The reason for their separation from the
others and from each other is the large number of shots in which they are iso-
lated, appearing without others in the shot. We call these one-shots—shots
depicting only one character. These reduce co-occurrence measures with all
other jurors, increasing their distance from them. There are 54 one-shots of
Juror 8, mostly near the beginning of the film; and 58 one-shots of Juror 3,
mostly near the end.
Figure 5b depicts the scaled solution from the first vote to just before the
second vote. The number of Juror 8 is colored in red because he has voted for
acquittal. Notice that he is an outlier (23 one-shots in this segment), but that
the general, ordinal arrangement around the table has been preserved. Across
Figure 5.Narrative spaces for 12 Angry Men as determined by multidimensional scaling co-
occurrences of characters in shots of the film.
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this section of the film there are only a few shots where individual jurors have
walked around. Notice too that at this point Juror 3 is not so extreme (only
four one-shots throughout the segment), and in the narrative neither he nor
the others is convinced of the innocence of the defendant.
Figure 5c depicts the film portion between the second and third votes. At
the beginning Juror 9 (three one-shots) has joined Juror 8 and their relative
positions could be predicted by proximity alone. Juror 3 (five one-shots) and
Juror 5 (two two-shots and appearing with Juror 3 in all others) become more
extreme. Juror 5 will soon change his mind and vote for acquittal. His isolation
in the scaling solution seems to anticipate his new view based on his knowl-
edge of switchblades, the implement of the murder, and how they are used.
Figure 5d depicts the portion between the third and fourth votes, showing
that Juror 5 has changed his mind and now migrating more towards the cen-
ter of the solution, no longer an outlier (and with only two one-shots in the
rest of the film). In addition Juror 11, the immigrant (six one-shots in the re-
mainder of the film), joins the still-minority view. During this sequence the ju-
rors have walked around quite a bit and the ordinal relations of the jurors at
the table is now no longer apparent. Notice that the jurors voting for acquit-
tal generally occupy more central positions in the solution.
The period between the fourth and fifth votes (see Figure 5e) is spatially
chaotic as jurors have continued their perambulations. There is no residual co-
herence of order around the table, no apparent visual structure in the co-oc-
currences of characters in shot, and no coherence of opinion as Juror 2
(convincingly) and Juror 6 (unconvincingly) have joined the emerging trend.
Overall opinion is unclear in the narrative, and co-occurrences in shots reflect
that lack of clarity.
Figure 5f shows the shot co-occurrences between the fifth vote and the
end of the film. Shown in black are the last three jurors to change their minds.
Juror 10 is the first to recant his position, essentially through embarrassment
at his own racist monolog. It was a little surprising to us that his position is so
central, but the depiction in this scene is of other jurors removing themselves
from the table as he speaks, facing away from him. The cinematography re-
tains all of jurors within the same camera purview in a long shot. Juror 4 is the
most reason-driven holdout and is shown in five one-shots as others counter
his claims. Eventually he is convinced that one of the key eyewitnesses could
not possibly have seen the murder. Juror 3 soon self-destructs in a tirade
against his son, himself, and the world. As he does so he is shown in 24
one-shots, many of them tight close-ups. Notice the cluster of votes for ac-
quittal is bound together, but has completely lost its spatial order around the
Ta ken as a group, we think these scaling solutions built on the character
co-occurrences in shots show the dynamic pattern of the narrative as rela-
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tions develop and change over the course of the film. Moreover, their diegetic
arrangement in the jury room—as might be predicted by the base map—sys-
tematically changes and is incrementally replaced by a more abstract narra-
tive space based on votes.
A powerful numerical trend concerns the distances of the characters from
the center of the space as each vote is taken. The center of the space can be
taken as neutral, particularly as the spatial layout around the table disinte-
grates. When Juror 8 casts the only vote for acquittal (Figure 5b), his distance
from the center is 1.79 times the average distance of those of the guilty votes.
He is a true outlier and this distance is due to the large number of one-shots.
But after being joined by Juror 9 (Figure 5c) the mean distance of the two dis-
senters is only 1.25 times the average of the majority. And after Jurors 5 and 11
join making the vote 8–4 (Figure 5d), the average distance from the center of
the characters with votes for acquittal is less than for those with guilty votes,
with a proportion of 0.83. When vote is deadlocked (Figure 5e), the distance of
those voting not guilty continues to decrease and is only two-thirds (0.68)
that of those jurors voting guilty. And with the vote 3–9 (Figure 5f) the mean
distance of those voting not guilty is about half (0.57) that of those voting
guilty. Thus, the sequence of mean spatial distances of characters voting for
and against acquittal anticipates the outcome of a unanimous verdict of not
guilty. And again, all of this stems from what is shown in the camera; no dia-
log is considered. What the visual narrative shows in its shots very much cap-
tures the dynamics of what the film is about.
Discussion:The Visual Narrative and the Viewer
We are getting closer and closer to the techniques of narrative ...and
to the description of association networks ... In this fusion of qualita-
tive literary qualities and the power of quantitative treatment, we ex-
pect a renewal of methods and explanations in the humanities. There
is no more powerful explanation than the analysis of the contingent
circumstances of association networks.
—Geneviève Teil and Bruno Latour (1995)
What is the import of our results? Consider four intellectual gains. The first
three are concrete but modest, and the fourth more tenuous but we believe is
of considerable importance. First, in reading the wider literature, we have
found previous accounts of narrative space in films and novels to be some-
what vague and unhelpful. Some are tied to an analogy between linear per-
spective in Renaissance art and narrative space in film, with separate shots
contributing to a mental construction of a physical space. Others abandoned
aspects of this idea but resuscitated it through an appeal to cognitive maps.
Such accounts seem incomplete, overly tied to physical space, and static even
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when discussing a moving camera and shot/reverse-shot depictions. Our first
contribution allows such spaces to be objective, explicitly mapped out, and
largely freed from physical space. Moreover, our analysis over separate por-
tions of films allows for the interpretation of dynamic changes in those
spaces. Nonetheless, we admit that clearing up some of the problems or va-
garies in ideas found elsewhere is not earthshaking science. What we have
found here does not really add to our understanding of the narrative in each
film. Instead, it adds objective depictions that are coherent with it.
Second, by bringing statistical rigor to the analysis of shots and scenes
across larger units of film, we show a coupling of layout and changes in the
visual content of the film to the relationships and changes in its story line.
That is, our methods demonstrate that filmmakers sculpt the presentation of
characters in a way that comports amicably with the narrative itself. Again, it
is good to know that this can be done from objective data, but it is hard to
imagine that the result could be any other way. Surely the visual narrative of
a film must be tightly connected to the narrative itself.
Third, a major purpose of this article is to introduce a new method for the
visual analysis of films. The mappings we have offered are concrete and
largely deterministic.
One possible use might be in making narrative com-
parisons across a film. If it were important to an argument to assert that the
relative amount of narrative change in the relationship of one particular pair
of characters was greater than that of another pair, ours would be a method
that could affirm or disconfirm of such an assertion. Similarly, if it were impor-
tant to suggest that one character is more distant from the general flow of
the narrative than another, this too could be tested with our method. And fi-
nally, as we have done here, if it is important to measure the amount of spa-
tial change in a character compared to other characters as an index of
narrative development, our method allows this too.
We regard the fourth gain, although more tenuous than the first three, to
be quite deep. It concerns our analysis of the visual film structure and the
viewer. As suggested by Teil and Latour (1995), the human mind—among its
many other attributes—is an engine driven by associations. Indeed, the mind
can be described as a Humean machine (after David Hume); it builds up
knowledge through associations among things that co-occur in the world
across our individual lifetimes. Moreover, co-occurrence commonalities within
a culture create the consistency of cultural knowledge across individuals as
each of us absorbs them. This is not the only means to knowledge gain but it
is a very powerful one. Moreover, units of the nervous system—often called
Hebbian units (after Donald Hebb)—function this way as well. The oft-quoted
phrase is that “neurons that fire together, wire together.”
In this manner,
from basic neurophysiological processes to the attainment of knowledge and
culture, our brains and minds seem to follow associative mechanisms.
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For filmgoers we claim that part of their comprehension process is the
same: to understand the narrative over the course of a film a viewer must
build up representations of the relations among the characters and their
goals. Understanding how this is done and how films manipulate this build-
up are important tasks within cognitive film theory. As a preliminary sketch of
this process, Bordwell (1992: 184) suggested that:
the process of understanding many things in films is ...likely to draw
upon ordinary,informal reasoning procedures ...Presented with a set of
circumstances (flat tire,man opening trunk), you categorize it (Driver
Changing Flat Tire) and draw an informal, probabilistic conclusion,
based on a structured piece of knowledge about what is normally in-
volved in changing a tire.
For our purposes the key ideas in Bordwell’s analysis concern probability and
the making of meaning out of what one sees. Although surprise is always a
possibility in life and in movies—think of the endings in The Usual Suspects
(1995) and Atonement (2007)—the filmgoer’s aggregation of probabilistic in-
formation from a lifetime of experience with what she has seen in a film up
to the moment creates an evolving set of mental representations of the char-
acters and story. These accruing structures allow for reasonably accurate pre-
dictions about what will happen next. Again, violations of our filmic expec-
tations can be delightful, surprising, even horrific, and they can keep one riv-
eted to the narrative, but the ability to predict a good bit of what will happen
over the intermediate course of a film is central to its comprehension. More-
over, this ability to use the comparative probabilism from pieces of experience
is the essence of what is called statistical learning.
It occurs over lifetimes
and also over minutes.
More formally, statistical learning is a branch of machine learning and cog-
nitive science. It explores how learning can occur in computers and in hu-
mans, and in the latter has been particularly used to explore language
learning and visual learning by infants (Kirkham et al. 2002; Saffran et al.
1996). Particularly interesting and most relevant to our analysis is unsuper-
vised statistical learning. In this domain, a computer or human is typically ex-
posed to repeating sequences of nonsense items and passively learns about
the structure of the co-occurrences that are presented. Thus, to use an overly
simple example, if a red star is followed by a green triangle 60 percent of the
time in a long sequence of varied items of various shapes and colors, adults
and infants would likely come to expect that, given the presentation of a red
star, the next item is likely to be a green triangle. Most interesting about this
expectation is that it is typically learned without awareness. In more complex
situations, viewers often have no insights concerning their predictions and re-
gard them as just guesses. This learning is essentially nonconscious. More-
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over, this learning occurs not only for sequential items, but also for features
that co-occur in the same arrays and for complex aspects of static visual
scenes (Brady and Oliva 2008; Fiser and Aslin 2001).
We are quite sure that no one has experimentally studied the statistical
learning of co-occurrences of characters in a film. Nonetheless, given the
wealth and breadth of demonstrations of statistical learning, we have no
doubt that this occurs for filmgoers and that, for the most part, it also occurs
nonconsciously. People fascinate us, we pay attention to them to a greater de-
gree than anything else, and we do so from a very early age. Moreover, they
are the prime objects that we look at in movies (Mital et al. 2011; Smith et al.
2012). We follow them, remember them, and that we likely encode their ap-
pearances with other characters seems uncontroversial. Otherwise we could
not understand movies.
We make no direct claim that the diagrams shown in figures 2 through 5
are actually “in the head” of a viewer who watches these films. These dia-
grams are representations of the character relations in the films. Nonetheless,
our data demonstrate that character co-occurrence relations by themselves
can yield narrative insights, a fact heretofore not known. We claim that these
maps should bear some recognizable similarity to the relations among char-
acters in the minds of viewers, and by themselves could guide some coarse
understanding of the film without a necessary comprehension of verbal
events across the film.
James E.Cutting is Susan Linn Sage professor and chair of the Department of
Psychology at Cornell University where he has taught courses on perception
for over 30 years. He has written two books, Perception with an Eye for Motion
(1986) and Impressionism and it Canon (2006) and published more than 100
scientific articles on form, motion, depth, and related areas of perception.
Catalina Iricinschi is a graduate student in the Department of Psychology at
Cornell University. Her interests include psycholinguistics, narrative process-
ing, and language development.
Kaitlin L. Brunick is a graduate student in the Department of Psychology at
Cornell University. Her interested include film, TV, and children’s cognitive
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The discussion of narrative space in film studies begins with Heath (1976), who de-
scribed its creation through camera work. This space is the implied physical space within
which action takes place in the film, specifically carved by the filmmakers to promote the
story in its specific location. With modifications Cooper (2002) reviewed and continued this
idea. Zoran (1984) discussed several types of narrative space, including a chronotopic level
representing space and time within a film. Similarly in literature, Bjornson (1981: 59) sug-
gested that narrative spaces are created by “piece-by-piece construction of an image which
maps the imaginary space described in the text” and Ryan (2003) discussed cognitive maps
that are built up over the course of a story. O’Toole (1980) came closest to our approach, even
using two dimensional matrices to depict relationships among characters in episodes of sto-
ries but he never attempted further statistical analysis. Multidimensional scaling, which we
employ here, has been used to generate cognitive maps (Kosslyn et al. 1974), but these map
back to physical spaces. Throughout empirical psychology, however, multidimensional scal-
ing has been used to create conceptual spaces, and following Miss Yujin (2009), our maps
are abstract and do not typically reflect the depicted physical space in a film.
Film viewers intuitively claim that the verbal behavior displayed onscreen carries more
of the plot than visual information. In addition, research on content analysis in film regards
the plotline as a combination of dialog and action, where action is a mixture of verbal and
nonverbal visual input. See, for example, Rosenfeld et al. (2003).
With multidimensional scaling solutions one typically computes the stress of the solu-
tion, sometimes called “badness-of-fit.” The lower the stress value the better the solution
captures the relational patterns in the data. It is not surprising that the stress for the solu-
tion of the data for six European cities is very low—0.004.
These costs were gathered on 10 September 2002 for flights to be taken on 1 October
2002. These are the average of round trips each way: for example, Paris-London-Paris and
London-Paris-London. A more expansive discussion of these data can be found in Cutting
(2006). We also note that, as its name suggests, multidimensional scaling is not confined
to two dimensions. If there are more objects to scale, the algorithm can easily handle the
data in three or more dimensions. We have confined ourselves to two dimensions both be-
cause it yields more understandable maps and because the two-dimensional solutions gen-
erally provide reasonable and interpretable fits to these data. Notice that the more typical
hubs of Amsterdam and Frankfort were left out of this analysis. Finally, taking flight costs
for June 2013 into account, we found that London had lost its centrality in the mapping, but
that strong deformations from veridical maps still exist.
Nonmetric multidimensional scaling routines automatically convert metric informa-
tion into nonmetric ranks. Again, the stress is reasonable for this solution—0.095.
Cohen’s κ in this context corrects for chance co-occurrences, which Pearson’s r does
not. Also, unlike other correlations, it is typically confined to a range between 0 and 1.
Nonetheless, the calculation easily generalizes to a range of –1.0 to 1.0, which we use here.
The number of scenes was determined by aggregating the results of three different
viewers who parsed Santa Fe Trail (1950) for a different project (Cutting et al. 2012).
One could also argue that such a film would need two narrative spaces that are quite
separate from one another. We have no stake in either interpretation, and use this as an ex-
ample only.
Bellour (1976) called scenes and subscenes by the terms segments and subsegments.
The stress of the base map for the nine characters in All About Eve was rather high—
0.144—indicating a less than optimal fit. The stresses for maps of the act 1 and act 3 maps
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were also high, 0.127 and 0.13, respectively. The stress for act 2 was more reasonable—0.08,
and that for act 4 very good—0.0001. Despite the relatively high stress in these scaling so-
lutions, we claim it is their utility in making sense of the narrative that matters in this con-
text. Interpretability is an important criterion in multidimensional scaling (Kruskal 1964).
The climax representations in Figure 2 of the two heterosexual couples—Margo and
Bill, and Karen and Lloyd—contrast with Eve and Addison. It is worth reconsidering an argu-
ment concerning this film and classical Hollywood’s treatment of homosexuality. White
(1999) and Corber (2005), for example, proposed that Eve and Addison, and particularly Eve,
are portrayed as characters of diminished fulfillment and happiness because of their homo-
sexuality. Most provocatively in one short scene, Eve enlists a female companion to assist
her with a phone call in a plot concerning Lloyd. After that call, she and Eve walk up a stair-
case in bathrobes, arms around each other’s waists. Thus a lesbian reading seems not inap-
propriate. Nonetheless, it is worth noting that Eve also tries to seduce all three male leads
in the film, and late in the film Addison confronts her with her past, which involved a rela-
tionship with married man and a quick, paid departure from her hometown. We think that
Eve is essentially omnivorous, rather than simply lesbian. In addition, Addison seems asex-
ual rather than homosexual. He asserts to Eve in a climactic scene: “After tonight you will
belong to me,we both “have a contempt for humanity, an inability to love and be loved . . .
We deserve each other.”
After Procrustes analysis the correlation of coordinates is extremely high, r = .993, t(14)
= 31.5, p < .0001.
The stress for the base map for the 10 characters in Inception was adequate—0.099, and
that for the six separate acts was 0.005, 0.048, 0.076, 0.032, 0.107, and 0.099, respectively.
We did not consider Robert Fischer’s dying billionaire father, Maurice Fisher, nor his ex-
ecutive assistant Peter Browning as sufficiently important characters to include in this
analysis or in constructing the base map. The father appears in only 13 shots across the film
and, although Browning appears in 38 shots, Eames is impersonating him in 24 of them. In
our assessments Eames was always counted as present when impersonating any character.
By contrast Miles, the character with the smallest role in our analysis, appears as himself in
31 shots.
The correlation between the two base map solutions, one for simple scene coding ver-
sus another that weighted co-occurrences by the duration of each scene, was again ex-
tremely high, r= .9993, t(18) = 113.3, p < .0001. Thus, the two procedures yield the same results.
Tacked on to the end of the shower sequence is a short episode of Ho-Jon and Hawk-
eye at a Korean clinic (two minutes), but we did not consider it separately.
The stress of the base map for MASH was generally high—0.19, but this value is under-
standable given as many as 15 characters scaled in only two dimensions. The stress for the
setup was 0.126, and in the subsequent plots of episodes 0.058, 0.175, 0.001, and 0.001,
The correlation for MASH between the solutions of the unweighted co-occurrence
codes versus those weighted by scene duration was not nearly as impressive as those for All
about Eve and Inception: r = .799, t(28) = 7.05, p < .0001. This is undoubtedly due to the rela-
tively high stress in both two-dimensional solutions.
Juror 12 actually changes his vote back to guilty and then later back to not guilty.
Stress values of the six panels of Figure 5 for 12 Angry Men are 0.082, 0.051, 0.130,
0.065, 0.089, and 0.062, respectively. Moreover and again, weighting the shots by their du-
ration does not change the overall layout of the base map. The correlation between the
character positions in the map generated weighting the shots equally versus weighting
them by their duration was very high, r = .989, t(22) = 31.4, p < .001.
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Heath (1976), in comparing photography and cinema, suggested that space was built
up in a manner not unlike Renaissance perspective. Cooper (2002) suggest that this view
was passé, but resuscitated aspects of the approach in an analysis of physical space in Sleep-
less in Seattle (1993), and how it might be lit. Ryan (2003) switched gears towards the ob-
server and suggested that a mental space was built up in the form of a cognitive map.
The running of algorithms of multidimensional scaling yields a certain amount of
variability. As these programs iteratively run, cycling through possibilities, shifting points in
space, and remeasuring the goodness of fit, they can often reach what is called a local min-
imum and stop. This process is somewhat analogous to water running downhill and getting
caught in a puddle that will not allow it run down to a lower elevation. To keep this from
happening one typically starts the algorithmic process with a number of different random
positionings of the to-be-scaled points and selects the outcome “that runs downhill the far-
thest,” yielding the lowest stress. When several different starting configurations reach the
same stress level, one can be satisfied that what is called a global minimum has been reached.
See Cutting (2003, 2006) for an analysis of how an artistic canon might be built up
from shared experiences within a culture. And Doidge (2007: 427) attributes a first version
of the “wiring together” phrase to Carla Shatz, a neurobiologist at Stanford.
Prior to the evolution of statistical learning, script theory (Schank and Abelson 1997)
relied on the accumulation of probabilities for the buildup of information as in Bordwell’s
changing-tire example. See also Gernsbacher (1990).
Bellour, Raymond. 1976. “To Analyze, to Segment.” Quarterly Review of Film Studies 1(3):
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Bjornson, Robert. 1981. “Cognitive Mapping and the Understanding of Literature.” SubStance
10(1): 51–62.
Bordwell, David. 1992. “Cognition and Comprehension: Viewing and Forgetting in Mildred
Pierce.Journal of Dramatic Theory and Criticism 6(2): 183–198.
Brady, Timothy, and Aude Oliva. 2008. “Statistical Learning Using Real-World Scenes: Ex-
tracting Categorical Regularities Without Conscious Intent.” Psychological Science 19(7):
678–685, doi: 10.1111/j.1467-9280.2008.02142.x.
Cooper, Mark Garrett. 2002. “Narrative Spaces.” Screen 43(2): 139–157, doi: 10.1093/screen/
Corber, Robert J. 2005. “Cold War Femme: Lesbian Visibility in Joseph L. Mankiewicz’s All
about Eve. GLQ:A Journal of Lesbian and Gay Studies 11(1): 1–22.
Cutting, James E. 2003. “Gustave Caillebotte, French Impressionism, and Mere Exposure.”
Psychonomic Bulletin & Review 10(2): 319–343.
Cutting, James E. 2006. Impressionism and Its Canon. Lanham, MD: University Press of
Cutting, James E., Kaitlin L. Brunick, and Ayse Candan. 2012. “Perceiving Event Dynamics and
Parsing Hollywood Films.” Journal of Experimental Psychology: Human Perception and
Performance 38(6), 1476–1490
Doidge, Norman. 2007. The Brain That Changes Itself. New York: Viking Press.
Fiser, József, and Richard N. Aslin. 2001. “Unsupervised Statistical Learning of Higher-Order
Spatial Structure from Visual Scenes.” Psychological Science 12(6): 499–504.
Heath, Stephen. 1976. “Narrative Space.” Screen 17(3): 19–75.
Gernsbacher, Morton A. 1990. Language Comprehension as Structure Building. Hillsdale, NJ:
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83(2): B35–B42, doi: 10.1016/S0010-0277(02)00004-5.
Kosslyn, Stephen M., Herbert L. Pick, and Griffin R. Fariello. 1974. “Cognitive Maps in Children
and Men.” Child Development 45(3): 707–716.
Kruskal, John B. 1964. “Multidimensional Scaling by Optimizing Goodness of Fit to a Non-
metric Hypothesis.” Psychometrika 29(1): 1–27.
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Schank, Roger C., and Robert P. Abelson. 1977. Scripts, Plans, Goals, and Understanding: An
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... Moreover, the whole mental process-shifting attention with the change in scenes and updating mental models-is undoubtedly related to executive function (see, for example, Miyake, Friedman, Emerson, Witzki, & Howerter, 2000). Much of how this is done, of course, remains a mystery (Graesser, Millis, & Zwaan, 1997, p. 181), although see Cutting, Iricinschi, and Brunick (2013) for a small attempt at clarification. Here, however, we focus only on segmentation and the requirements of updating representations, not on the underlying mental models. ...
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Popular movies present chunk-like events (scenes and subscenes) that promote episodic, serial updating of viewers’ representations of the ongoing narrative. Event-indexing theory suggests that the beginnings of new scenes trigger these updates, which in turn require more cognitive processing. Typically, a new movie event is signaled by an establishing shot, one providing more background information and a longer look than the average shot. In our analysis of 24 films we reconfirm this and show that, when returning to a previously shown location, the re-establishing shot reduces both context and duration while remaining different than the average shot. In general, location shifts dominate character and time shifts in dictating film form. Nonetheless, over the last 70 years shifts to previously seen locations and characters, as opposed to new ones, have become more like the average shot. Such results suggest that film form is evolving to suit rapid encoding of narrative events.
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The way people interact with space appertains to the idea of territory. Territory is claimed by people all the time in communication. This article will explore how the lead actor, Joaquin Phoenix, of Joker (2019) develops Arthur Fleck and the story with the support of Method Acting, territorial theories and film techniques. More specifically, the study will consider (a) how Arthur interacts with other characters and narrative space in different territories naturalistically and (b) how Method Acting, territorial theories and film techniques facilitate Arthur’s characterisation and the story development. The study of Arthur reveals that he undergoes a metamorphosis during resisting his tormentors in the story. The study of Arthur also shows that it is meaningful to introduce territorial theories to film analysis and Method Acting.
Vertov’s works always revolved around the documentary, for it was only here that for him both the truth and the essence of the people in the Soviet reality were revealed. The fact that the film-maker turned precisely to film and did not, for example, work as the editor of a daily newspaper may be happenstance, or it may be traced back to Vertov’s active interest in new media. It is, however, just as plausible to assume that Vertov recognised in film the potential for revealing his processes without detracting from their effect – on the contrary; the director felt that films could actually gain in fascination through the demonstration of the processes of craftsmanship. Vertov transmitted the idea of film work as a demonstrative activity and accentuated the professional abilities of his film team. Above all, in his early films he also presented his colleagues on the screen, where they were shown practising their professions in a manner almost reminiscent of folk art: “The activity of a ‘filmer’, e.g. the cutter at work editing the material shot is expressly equated with the finishing of textiles and the sewing of fabric parts” (Drubek-Meyer and Murašov 2000: 8). This comparison runs through the history of editing and is also mentioned by Walter Murch, who sees it as a possible reason for the high proportion of women in the editing profession (Wright 2009).
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The purpose of this study is to present a general model of the structuring of space within the narrative text. The term space is used here to mean specifically the spatial aspects of the reconstructed world. This seems natural and rather obvious, but the term can be applied to the literary text in various ways and is, itself, far from unambiguous. It is.necessary, then, to examine the whole range of problems arising from the use of the term with regard to the literary text. If this task as a whole lies outside the scope of the present study, we can at least clarify one essential aspect of it: the relationship between space and time in the narrative text. 1. THE ASYMMETRY OF TIME AND SPACE IN THE NARRATIVE
At a climactic point in Hitchcock’s Suspicion, Lina (Joan Fontaine) receives a visit from two police inspectors come to inform her of the death of a friend in circumstances which cannot but increase her fears concerning the probity — the rectitude — of her husband Johnnie (Cary Grant). The scene finds its centre in a painting: the massive portrait of Lina’s father which bears with all its OEdipal weight on the whole action of the film — this woman held under the eye of the father (the name as crushing as the image: General MacLaidlaw), sexuality in place as transgression (‘Lina will never marry, she’s not the marrying sort... Lina has intellect and a fine solid character’, declares the General early on in the film), as radically ‘impossible’ (leaving her father for Johnnie, Lina is henceforth racked by doubt, a suspicion that is irresolvable, for her and the film) — and before which she now positions herself to read the newspaper report of the friend’s death and to gather strength enough to face the scrutiny of the law, the look relayed from portrait to police and to portrait again (Stills 1, 2, 3, 4).
During the past twenty years, much of the impetus for theoretical speculation in literary studies has come from non-literary disciplines. Yet, despite the intensity of this activity and the polemics associated with it, there has been relatively little attempt to elaborate a generally comprehensible explanation of how the writing and reading of literary texts relate to the more universal problem of how people orient themselves in the world where they are obliged to live. What is needed is a plausible epistemological model capable of integrating information and methodological strategies from various disciplines without contradicting the best available knowledge about how the human mind actually operates. Such a model should not be bound to the terminology or problem-setting techniques of a single discipline, nor should its applicability be restricted to the characteristic mental behavior of a single culture or ideology. The need to address this problem is particularly acute at a time when politically and intellectually conservative forces are threatening to discredit the genuine theoretical advances of the 1960's and 1970's by attacking their excesses and their limitations.' Although pluralism offers a tempting solution to the dilemma of competing interpretations, it too is ultimately unsatisfying, because, if people are to conceptualize their world and act in it, they must either choose among alternative explanations or synthesize a new one.2 A more promising point of departure might well be a serious consideration of cognitive function and its relationship to the creation and comprehension of literary texts.3 Any involvement with literature is necessarily embedded within the larger context of all human activity, and it seems plausible to assume that the same mental operations which allow people to make sense of their physical environments are also called upon when they seek to understand the verbal universes they encounter in literary texts. Furthermore, there is an undeniable carryover of information from lived experience to literature, and from literature to lived experience.4 To avoid the contradictions inherent in drawing absolute boundaries between the world of words and the