10.54103/2036-461X/16785
This paper examines the meaning potential of directed forces or vectors in cinema. The first part draws on the pioneering work of Rudolf Arnheim to highlight the prominent role of vectors in the visual structuring of meaning in paintings. In the second part, we move on to explore the semantic significance of motion vectors in cinema. To this aim we first define and diagram the filmic space in which vectors may articulate themselves visually. Having firmly grounded this spatial framework in film theory, we adopt the terminology of Herbert Zettl to further distinguish between three types of motion vectors: primary motion vectors (elicited by motion of visual objects), secondary motion vectors (elicited by camera movement) and tertiary motion vectors (elicited by editing). We conclude this paper by applying the proposed conceptual tools of this paper to three filmic case-studies in which the relation between narrative meaning and motion vectors is further discussed and illustrated.
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Maarten Coëgnarts
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Cinéma & Cie. Film and Media Studies Journal
Vectors
The Meaning Potential of Motion Vectors in Cinema
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2022-06-27
2021-11-27
2022-12-30
2022-12-30
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Cinéma & Cie
Maarten Coëgnarts
2022/06/27
10.54103/2036-461X/16785
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Vectors
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The Meaning Potential of Motion Vectors in Cinema
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                                                                                       The Meaning Potential of Motion Vectors
                                                                                       in Cinema
                                                                                       Maarten Coëgnarts, Universiteit Antwerpen




                                                                                       This essay examines the meaning potential of directed forces or vectors in cinema. The              Keywords
                                                                                       first part draws on the pioneering work of Rudolf Arnheim to highlight the prominent         Camera movement
                                                                                       role of vectors in the visual structuring of meaning in paintings. In the second part, we
                                                                                       move on to explore the semantic significance of motion vectors in cinema. To this aim
                                                                                                                                                                                              Editing
                                                                                       we first define and diagram the filmic space in which vectors may articulate themselves     Embodied cognition
                                                                                       visually. Having firmly grounded this spatial framework in film theory, we adopt the                Film style
                                                                                       terminology of Herbert Zettl to further distinguish between three types of motion                       Forces
                                                                                       vectors: primary motion vectors (elicited by motion of visual objects), secondary motion               Vectors
                                                                                       vectors (elicited by camera movement) and tertiary motion vectors (elicited by editing).
                                                                                                                                                                                                 DOI
This work is licensed under a Creative Commons Attribution 4.0 International License




                                                                                       We conclude by applying the proposed conceptual tools of this essay to three filmic
                                                                                       case-studies in which the relation between narrative meaning and motion vectors is                 10.54103/
                                                                                       further discussed and illustrated.                                                          2036-461X/16785




                                                                                                                                              In memory of Stephen Prince

                                                                                       INTRODUCTION
                                                                                         Research in cognitive science increasingly shows that meaning is not just a
                                                                                       matter of a transcendent disembodied view of logic at the level of sentences (or
                                                                                       propositions), nor is meaning a matter of truth-conditions or referential relations
                                                                                       only. Rather, meaning is highly dependent upon our bodily disposition and the
                                                                                       way we physically interact with the world.1 One way in which scholars have
                                                                                       tried to make sense of this theme of embodied cognition is by showing how the
                                                                                       semantics of certain linguistic concepts are metaphorically grounded in gestalt
                                                                                       patterns, so called ‘image schemas’, that arise in and through our sensory-
                                                                                       motor experience.2 This idea is central to the field of cognitive linguistics and the
                                                                                       theory of Conceptual Metaphor Theory as it was first proposed by George Lakoff
                                                                                       and Mark Johnson in 1980.3 One pattern in particular that has been argued
                                                                                       to play a pivotal role in the structuring of meaning in language is the ‘force’
                                                                                       image schema.4 This schema arises in and through our physical interaction with
                                                                                       objects and persons in our environment and functions as an important source
                                                                                       domain for metaphorically structuring the abstract target domain of (emotional)


                                                                                       Cinéma & Cie vol. 22 no. 38 2022 · ISSN 2036-461X                                                       19
     causality (‘The home run threw the crowd into a frenzy’, ‘He drove her crazy’, or
     ‘She pulled me out of my depression’).5
      It might not come as a surprise that both Lakoff and Johnson took inspiration
     from the work of the famous theorist of visual art Rudolf Arnheim in order
     to develop the image schema of force and its structuring role in language.6
     Even long before the embodied view gained foothold in the cognitive sciences,
     Arnheim believed that sensory perception structures and informs thinking. His
     notion of ‘visual thinking’ served as the key concept to signify this non-dualist
     interplay.7 Informed by the principles of Gestalt psychology, he considered visual
     percepts to be prominently dynamic and therefore as intrinsically meaningful
     and expressive. 8 Consequently, he extended this view to the realm of art by
     showing, through various inspiring case studies, how non-temporal media
     such as paintings and sculptures are able to portray the (abstract) dynamics of
     human life ‘as a closed system in which all relevant forces are shown together
     in configuration, each in its characteristic direction and appropriate strength’.9
      One concept in particular that plays a highly significant role in Arnheim’s work
     on dynamics in the visual arts is the concept of a ‘vector’. Vectors are the ‘forces
     generated by the shapes and configurations of visual objects’.10 As such, they
     are the ‘carriers of dynamics’, that is, ‘the directed tension perceived in visual
     objects’.11 It is through the configuration of vectors in the composition of a work
     that Arnheim believed that artists are able to communicate themes and narrative
     meaning in a purely visual way. More recently, the semantic role of a vector
     has also become a crucial component in Kress and van Leeuwen’s account of
     the grammar of visual representation in which the authors merge concepts
     from Arnheim’s theory of visual dynamics in art with concepts from Halliday’s
     functional-semantic theory of language.12 In both the works of Arnheim and
     Kress and van Leeuwen, however, the meaning potential of vectors has been
     predominantly analysed with respect to fixed images such as photographs,
     sculptures and paintings. Only limited attention has been paid to moving
     images. It is the goal of this essay then to demonstrate the semantic potential of
     vectors in narrative cinema. To this aim the essay follows a threefold structure.
     In the first part we provide a brief case study from Arnheim to show how the
     link between vectors and meaning can be established visually in painting. In the
     second part, we move on to explore the semantic significance of motion vectors,
     a concept which we adopt from Herbert Zettl.13 To assess its use in cinema we
     first define the filmic space in which vectors may articulate themselves visually.
     Having firmly grounded this spatial framework in film theory, we extend Zettl’s
     terminology to further distinguish between three types of motion vectors:
     primary motion vectors (elicited by motion of visual objects), secondary motion
     vectors (elicited by camera movement) and tertiary motion vectors (elicited by
     editing). We conclude by applying the proposed conceptual tools of this essay to
     three filmic case-studies in which the relation between narrative meaning and
     motion vectors is further discussed and illustrated.



20                                  Coëgnarts, The Meaning Potential of Motion Vectors
THE MEANING POTENTIAL OF VECTORS
  When people talk about force they usually refer to a physical or gravitational
manifestation of it. It is the literal sort that we all experience when our bodies
causally interact with objects and persons in our environment.14 Forces,
however, do not only manifest themselves in physical experience. We may
also observe them, as Arnheim pointed out, as ‘directed tensions’ in our acts
of perception.15 They constitute the ‘perceptual forces’ that are inherent in the
shapes, configurations, colors and locomotion that inhabit the visual world.
As Arnheim writes: ‘These dynamic properties, inherent in everything our
eyes perceive, are so fundamental’, Arnheim argues, ‘that we can say: Visual
perception consists in the experiencing of visual forces’.16 This applies to both
natural objects (e.g., the highly dynamic curve that we perceive in an ocean
wave) as well as works of art (e.g., a painting), but with this fundamental
difference that the former were never intended to be seen as embodying an
abstract pattern or configuration of forces. As Arnheim remarks: ‘They carry
visual form only impurely and approximately’.17 By contrast, works of visual
art are made for the exclusive purpose of being perceived, and therefore ‘the
artist endeavours to create the strongest, purest, most precise embodiment of
the meaning, that consciously or unconsciously, he intends to convey’.18 That
is, in works of art forces or visual dynamic fulfil an important semiotic function
as carriers of the meaning or theme of a work. The theme is the formal pattern
that indicates what the work is about. It turns the visual pattern into a semantic
statement on the human condition. This is also the original sense of the term
vector. Combining the Latin verb, vehere (to carry) with the agentive suffix -tor,
a vector literally means ‘carrier’. Vectors thus are the carriers of dynamics.
And since dynamics are the ‘very basis of expression’, and expression is the
manifestation of life, vectors become also the ‘carriers of meaning’.19
  To illustrate how the meaning of a work may be conveyed through a dynamic
configuration of vectors or directed forces, let us consider an excerpt from
Arnheim’s brilliant analysis of Giotto’s depiction of the Lamentation.20 This
fresco, as shown in fig. 1, depicts the subject matter of the story (death and
resurrection) through a formal interplay between the horizontal and the vertical.
As Arnheim writes: ‘The horizontal of death is indicated but left behind by the
body of Christ, which has been lifted and thus endowed with the dynamic quality
of oblique position’.21 Obliqueness thus fulfils a fundamental role in the creation
of directional tension (and hence meaning), something which Arnheim explicitly
states: ‘Oblique orientation is probably the most elementary and effective
means of obtaining directed tension’.22 Returning to the fresco, Arnheim draws
the viewer’s attention to the arms which ‘are made to deviate obliquely from the
body’. The author sees in this deviation ‘a motif of revival’ which then finds its
continuation in the vector of the diagonal ridge of the hill: ‘Just broad enough for
a man to walk upward, it leads through the entire picture, from the horizontal
of death to the verticals of the two upright men, the vertical edge of the picture


Cinéma & Cie vol. 22 no. 38 2022 · ISSN 2036-461X                                      21
Fig. 1:
Lamentation (The
Mourning of Christ) by
Giotto (c.1304 - c.1306)




                           frame, and the three. The tree takes over where the diagonal of the hill is about
                           to tend and turns the oblique climbing into straight rising’.23 It is only a brief
                           excerpt, but it vividly illustrates how graphical vectors play a significant role in
                           the shaping of visual meaning.
                             Throughout his career Arnheim analyzed many other examples, albeit almost
                           exclusively with an emphasis on the meaning potential of vectors in fixed
                           images such as photographs, sculptures and painting.24 There is, however, no
                           reason to assume that the vectors involved in motion do not play an equally
                           important role in the structuring of visual meaning. One merely has to look at
                           the experiments on so called ‘functional relations’, wherein one perceives such
                           high-level properties as animacy and causality in simple animated movies.25
                           Evidence can also be found in an increasing number of publications on the
                           subject of expression and cinematic movement.26 Moreover, Arnheim himself
                           includes the notion of ‘locomotion’ in his definition of directed tension.27 The
                           fundamental difference is that when actual motion is used, as in the dance,
                           the theater, and the film, ‘direction is already indicated by movement’.28 This
                           is also how Herbert Zettl defines a motion vector as ‘a vector created by an
                           object that is actually moving or seen as moving-on screen’.29 He considers
                           motion vectors generally to have a higher magnitude than index vectors, which
                           in turn have a higher magnitude than graphic vectors. The latter ‘is created
                           by a stationary element that guides our eyes in a certain albeit undefined
                           direction’ (e.g., horizontal and vertical lines) whereas an index vector is created
                           ‘by something that points undeniable in a specific direction’ (e.g., an arrow, or
                           people point or looking in a particular direction). Not all vectors are explicitly



22                                                        Coëgnarts, The Meaning Potential of Motion Vectors
supported by visual objects that are represented in the visual field (e.g., shape,
color, movement), what Arnheim, dubs ‘retinal presence’.30 For instance, the
index vector created by a figure’s glance, what Kress and van Leeuwen call an
‘eyeline vector’, is not.31 The magnitude of a vector then can be defined as ‘a
product of its relative strength, that is, its directional certainty and perceived
directional force’.32 It expresses what the scholar labels the ‘aesthetic energy’,
the energy that we perceive from aesthetic phenomena such as color, sound
and motion. A high-vector magnitude is strong, a low vector magnitude is
weak. Hence, because motion vectors always have a precise screen direction
(contrary to graphic vectors) and because they have a perceived object speed,
motion vectors are generally assumed to have a higher magnitude.
  Zettl’s definition of a motion vector, however, remains formal in the sense
that it provides no indication of the meaning potential of motion vectors.33 For
instance, he does not demonstrate, as Arnheim does with respect to graphical
and index vectors, how motion vectors can convey story content. In other words,
Zettl provides no semiotic definition. Moreover, his definition is strictly limited to
primary motion (motion of objects) and does not take into account the structural
importance of secondary motion (camera movement) and tertiary motion
(editing). In the next section of this paper we address this issue by providing a
tentative conceptual framework for analyzing motion vectors in cinema. Having
provided a toolkit for doing so, we are conceptually equipped to lay bare its
relation to the story content of three filmic cases.



MOTION VECTORS IN CINEMA
  Before examining the question of motion vectors in cinema, we first have
to define the space through and in which they may manifest themselves. A
distinction made by film theorist Noël Burch seems to be a good point to start.
In his classical book Theory of Film Practice, the author identifies two kinds of
space in a film: the space included in the frame, the on-screen space, and the
space included outside the frame, the off-screen space, which he further divides
into six segments.34 The first four of these areas are the most obvious ones, and
are determined by the four borders of the frame: the space left of the frame, the
space right of the frame, the space below the frame, and the space above the
frame. The fifth segment is a rather peculiar one as it cannot be defined with the
same degree of geometric accuracy. It refers to the off-screen space ‘behind the
camera’. Characters commonly reach this area by passing just to the right or
left of the camera. Finally, there is the sixth zone of space behind the set which a
character may reach by, for example, going out a door or going around a street
corner, or by ‘disappearing behind a pillar or behind another person […]. The
outer limit of this sixth segment of space is just beyond the horizon’.35
  We may continue to further define the on-screen space, as Zettl does,
by adapting the spatial coordinate system of the French philosopher René
Descartes which consists of three axes: the horizontal x-axis (screen width),


Cinéma & Cie vol. 22 no. 38 2022 · ISSN 2036-461X                                        23
                             the vertical y-axis (screen height) and the illusionary depth line or z-axis with
                             ‘stretches from the screen (camera lens) to the horizon’.36 Whereas the former
                             two axes have definite spatial limits, imposed by the boundary of the frame,
                             screen depth is ‘virtually infinite’.37 Zettl considers the z-axis aesthetically the
                             most flexible screen dimension for it allows for a staging or blocking in depth;
                             a technique which was famously applauded by the French film critic André
                             Bazin. However, as Wittusen has pointed out, Bazin’s interest lies not only in
                             the z-axis as the single possible articulation of depth.38 While making reference
                             to the films of Jean Renoir, he also attributes significance to another depth
                             dimension, which he coins ‘the lateral depth’. ‘In The Rules of the Game’, he
                             writes, ‘Renoir actually uses simultaneous action on the same plane more than
                             depth of field. This functions like a kind of lateral depth of field’.39 In other words,
                             the screen may suggest the presence of a field of depth which continues in the
                             off-screen space beyond the spatial limits of the x-axis and the y-axis. As Bazin
                             writes, ‘The rest of the scene, while effectively hidden, should not cease to exist.
                             The action is not bounded by the screen, but merely passes through it’.40 More
                             recently, Julian Hanich has adopted Bazin’s concept of lateral depth for his own
                             phenomenological analysis of complex mirror shots. Interestingly, he brings in
                             two additional concepts to the discussion of depth in film: the ‘anterior depth’
                             which he uses in a similar sense as Zettl’s z-axis dimension, and the ‘posterior
                             depth’, which he uses to signify the ‘depth’ of Burch’s sixth zone of off-screen
                             space, that is, the depth ‘behind and next to the camera’.41 Whereas the anterior
                             depth channels the viewer to look into the screen, the lateral and posterior
                             depth dimensions make us look beyond the image.
                               Taken together, these theoretical terms constitute a spatial framework,
                             which we may diagram as in fig. 2, and which allows us to further explore any
                             number of vectors and dynamic forces within the frame space including not
                             only graphical and index vectors, but also motion vectors which we will look




Fig. 2:
Diagramming the filmic
space on the basis of film
theory



24                                                            Coëgnarts, The Meaning Potential of Motion Vectors
into now. As stated above, Zettl originally used the term only to refer to the
movement of visual objects, what he elsewhere describes as ‘primary motion’.42
In this paper, however, we will expand the notion of motion vector to also
include Zettl’s two other categories of motion, namely ‘secondary motion’ (or
camera movement) and ‘tertiary motion’ (or editing). The latter further selects
the primary and secondary motion vectors of the individual shots to shape what
Karen Pearlman recently coined a ‘trajectory phrase’.43 In doing so, however, we
should be aware of the phenomenological differences that still exist between
the three types. As will become clear below, secondary and tertiary motion
vectors seem more elusive and less definable than primary motion vectors.



Primary Motion
  By primary motion we mean movement of visual objects (e.g., characters) in the
on-screen space. Since the movement trajectory in this space is always relative
to the ‘container’ of the frame in which the movement takes place, we may further
distinguish between four dynamic patterns of fixed-frame movement: ‘entry’, ‘exit’,
‘approaching’, and ‘distancing’.44 Entry is created by an object that enters the on-
screen space. The starting point from which the movement begins, is always
located in one of the six zones of off-screen space as defined by Burch. When that
same object leaves the screen space again, we speak of ‘exit’. In this case one of
the off-screen zones serves as the ending point of the moving object or trajectory.
An object may also exit the frame along the z-axis. In such a case the pattern of
exit is accompanied by a pattern of ‘approaching’. The visual object increases in
graphic mass as it comes closer towards the camera. By contrast, when an object
‘distances’ itself from the camera, the graphic mass will gradually decrease. As
Burch has argued, these patterns of ‘enters into’ and ‘exits from’ a frame are
crucial for delineating or ‘defining’ the spatial segments of off-screen space. By
this Burch means that ‘one or another of the spatial segments in question takes
shape in the viewer’s imagination every time an entrance or exit occurs into or out
of that segment’.45 This ‘shaping’ becomes especially vivid when a single primary
motion vector starts to interact with another primary motion vector. Zettl goes
further to delineate three such types of relationships that primary motion vectors
can have within a single shot (and as we shall see later, also across a series
of shots): ‘continuing’ (when two or more vectors point in the same direction),
‘converging’ (when they point to each other) and diverging (when they point away
from each other).46 The converging type can be nicely illustrated with a brief
example that Burch describes in his book and that occurs towards the beginning
of Jean Renoir’s Nana (1926). It involves a static shot (see fig. 3) in which the
paths of two men cross each other for a very brief moment. Young Georges has
just left Nana’s dressing room. Enchanted by her beauty he enters the frame left,
along the horizontal x-axis. At the same time, the other guy, Muffat, rushes toward
Nana’s dressing room by entering the frame from the right. Their motion vectors
cross like two arrows, without their even glancing at each other, and they exit on


Cinéma & Cie vol. 22 no. 38 2022 · ISSN 2036-461X                                      25
Fig. 3:                       opposite sides of the screen. As Burch observes: ‘The essential part of the action
Entries into and exits from   in this shot (the trajectories of the two men) takes place off screen, although in
the frame of Jean Renoir’s
                              such a brief span of time — the moment preceding and following each entrance
Nana (1926)
                              and each exit — that it borders on the instantaneous; this action simultaneously
                              defines the left and right segments of off-screen space’.47 In other words, primary
                              motion vectors play a significant role in further establishing Bazin’s concept of
                              ‘lateral depth of field’, as elucidated above.
                                 Primary motion vectors, however, should not be limited to the actual movement
                              of a visual object from one location to another. A primary motion vector may also
                              originate from a fixed position by a character that moves his eyes away from one
                              spatial zone to another (comparable to the tilting or panning of a camera). In
                              such a case the direction of the eyeline vector (as an instance of an index vector)
                              changes: the primary motion vector is not supported by the retinal presence of
                              a movement trajectory along one of the axes, but by the retinal presence of a
                              change of gaze. In a much cited example from Alfred Hithcock’s Notorious (1946)
                              there is a significant medium close-up in which Alicia (Ingrid Bergman) changes
                              the direction of her glance from one zone (containing the reflection of Sebastian’s
                              shadow on the bathroom door) to another (containing the keys on the desk) (see
                              fig. 4). Through this primary motion vector which makes us look beyond the image
                              into its lateral depth, the film already foretells the movement trajectories that will
                              unfold in the subsequent next shots, first of the camera getting closer, then of the
                              character itself.48




Fig. 4:
Primary motion change
of eyeline vector in
Alfred Hitchcock’s
Notorious (1946)



26                                                            Coëgnarts, The Meaning Potential of Motion Vectors
Secondary motion
   In cinema, however, we are not only dealing with motion vectors that have
their origins in the actual on-screen movement of objects. In addition, we may
also distinguish between motion vectors that emanate from the movement of
the camera (e.g. dolly, zoom, tracking shots, pan shots). Naturally we do not
see secondary motion vectors in the same way as we observe primary motion
vectors. We do not literally see the camera moving from the right to the left as
we see a character moving from the right to the left. What we do see is the on-
screen effect of the mobile camera, that is, the component changes in what the
camera records when its moves. For instance, it is well known that a camera
pan to the left makes it seem as if a static object onscreen moves to the right.49
   In contrast to primary motion vectors, secondary motion vectors usually do
not interact with other secondary motion vectors in one and the same screen
space unless the frame is a composite of multiple screens (e.g., split-screen).
What the viewer perceives is the dynamic effect of the mobile frame as elicited
by a single camera’s movement. But secondary motion vectors may engage
with primary motion vectors in various aesthetic ways. For instance, we speak
of motivated camera movements as when the secondary motion vector is in
tune or continuing with a primary motion vector. This occurs, for example,
when the camera follows a character from behind. In such a case, both camera
and character share the same direction. By contrast, when the secondary
motion vector detaches itself from the character, such as is often the case
in modernist cinema (e.g., the cinema of Antonioni), it becomes a ‘wandering
camera’.50 It reveals the presence of a filmic narrator distinct from any of the
characters. In this case, the independent movement of the camera (independent
of any character’s point of view) generates the spectators’ awareness of an
‘independent presence’, that of an omniscient narrator.51



Tertiary motion
  Once the primary and secondary vectors are created they can be further
shaped into a temporal sequence by means of sequence motion or what Zettl
terms ‘tertiary motion’. Through a change of shots (i.e., single runs of the
camera), we perceive ‘a progression, a visual development’.52 As Zettl points
out, ‘the important aspect of tertiary motion is not so much the vector field of
the individual shot but the moment of change — the relationship of vector fields
from shot to shot’.53 In her own research Karen Pearlman, who is an editor
herself, has termed this assemblage of movements appropriately ‘trajectory
phrasing’.54 Together with timing and pacing it is one of the tools at an editor’s
disposal for shaping time, energy and movement for the purpose of creating
cycles of tension and release. More specifically, trajectory phrasing ‘describes
the manipulation of energy in the creation of rhythm’.55 The word ‘trajectory’
means ‘the path described by a body moving under the action of given forces’.56


Cinéma & Cie vol. 22 no. 38 2022 · ISSN 2036-461X                                    27
     Trajectory phrasing then is joining together movement trajectories in different
     shots to shape the flow of energy (movements) between and through them.
     This is done by choices of takes and positioning of cuts. Using the vector
     terminology of this paper, we might well speak of ‘vector phrasing’ with the
     primary motion vectors and secondary motion vectors constituting a significant
     part of the raw material from which the editor produces affective rhythms, that
     is, patterned movement over time. This makes vectors at the level of tertiary
     motion to function more like an overflow effect, a higher-order accumulation or
     interplay of other vectors — comparable to what Eisenstein would label ‘tonal’
     and ‘over-tonal’ effects in montage. They become a good deal more indistinct
     and diffuse as a result of it. Depending on the intentions of the filmmaker, we
     may nevertheless distinguish between several styles of editing for putting
     these vectors together. In most cases of narrative cinema, the editor will keep
     the audience spatially oriented. For this purpose, the editor will adhere to a
     prescribed syntax of continuity editing.57 If for instance, a filmmaker shows a
     long shot of two people talking to each other (i.e., converging index vectors)
     and maintains these converging vectors in the subsequent separate close-ups
     of these people, there is still continuity across the converging vectors. Other
     filmmakers, however, will not strive for these subtle linkages, but for harsh
     collisions under Sergei Eisenstein’s dictum that ‘A smooth transition is an
     opportunity lost’. As Pearlman further writes, ‘a collision might be a cut that
     juxtaposes light and dark, close-up and wide shot, but also movement left to
     right with right to left, […] and so on’.58
        There is more to be said about vectors in cinema and of their possible
     relationships with each other and with other types of vectors (e.g., color
     vectors, sound vectors, musical vectors), but for now let us put some of the
     conceptual tools that we currently have into practice by exploring, as Arnheim
     and Kress and van Leeuwen did with respect to fixed images, the expressive
     and metaphorical potential of motion vectors in cinema.



     THREE CASE-STUDIES
       In the last section of this paper we briefly discuss three filmic cases for
     the purpose of showing how motion vectors contribute significantly to the
     conveyance of meaning in cinema. In doing so, we will first stress the importance
     of vectors in two existing film analyses from the literature. We conclude this
     section by providing a more elaborated case study of our own.



     Case study 1: Sanshiro Sugata (Akira Kurosawa, 1943)
       In his brilliant treatment of Akira Kurosawa’s cinema, Stephen Prince is keen
     to point out the importance of movement patterns in the conveyance of themes
     in the oeuvre of the Japanese director.59 He states among others that the director
     frequently organizes movement to produce dialectical relationships often



28                                  Coëgnarts, The Meaning Potential of Motion Vectors
in combination with the use of the telephoto lens. For instance, he describes
one brief moment of converging (primary) motion vectors from Yojimbo (1961)
in which the planes of movement are perpendicular to each other: the hero
(Toshiro Mifune) crosses the frame along the horizontal x axis, from left to
right in the foreground, while the villain advances from behind the setting (i.e.,
Burch’s sixth zone) towards the camera from the background (the z-axis), as the
telephoto lens produces the illusion that both primary motion vectors ‘are about
to crash into each other’.60 In other occasions, however, motion vectors serve a
more important narrative function by helping to situate characters according to
‘important psychological and social relations prevailing along them’, an interest
that according the author runs throughout Kurosawa’s oeuvre and reaches
its climax in Seven Samurai (1954).61 One vivid example that Prince analyses
appears already very early in the director’s career. It involves a scene near
the beginning of Sanshuro Sugata (1943) in which the young pupil Sanshiro
accompanies Momma and his mob to a late night ambush of the judo instructor
Shogoro Yano (Denjiro Okochi). Kurosawa’ formalizes Sanshiro’s relation to
Yano by introducing a lateral tracking shot and reduplicating its secondary
motion vector three times. Each time Yano defeats one of Momma’s men, the
motion vector ends by including Yano into the frame, while the film intercuts
between the two characters, ‘each framed in isolation, in contrast to Momma’s
group’.62 ‘Here we can see clearly’, as Prince argues, ‘Kurosawa’s injunction to
use form in a meaningful manner: Yano is to be Sanshiro’s teacher and spiritual
guide, and the bonds between them are set out in visual terms during this early
sequence, in which Sanshiro functions as an observer, learning a first lesson by
watching a master’.



Case study 2: Blade Runner (Ridley Scott, 1982)
  For our second example, let us consider a juxtaposition of images from Ridley
Scott’s Blade Runner (1982) that recently gave rise to an interesting discussion
among two cognitive film scholars: Tim J. Smith and Karen Pearlman whose
work we already cited above.63 The first shot, as shown in fig. 5, involves a
similar change of eyeline vectors that we already illustrated above with the
example of Notorious. It shows how the character of Deckard (Harrison Ford)
shifts his gaze from a horizontal x-axis index vector (pointing towards the
second off screen space where the character of Rachel is located) to a z-axis
index vector (pointing towards the sixth zone where an artificial owl is located).
In the next shot the actual owl is shown as it gestures an opposite movement:
the owl’s gaze shifts from right (a z-axis index vector) to left (horizontal x-axis
index vector). The film then cuts back to Deckard in a trajectory that exactly
copies the owl’s movement. Deckard now turns his head again from the owl in
the direction of Rachel in the fourth off-screen zone (left of the frame). Smith
considers this last cut to be ‘slightly off’, by which he means ‘that the owl’s
gaze shift will cue viewer attention in the opposite direction to the saccade


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Fig.5:                    required to shift back to Deckard’s face’.64 The owl looks over Deckard’s head
A trajectory phrase of
                          and guides your eyes to slip over Deckard’s head and then you slip them back.
eyeline motion vectors
in Ridley Scott’s Blade   ‘Such a mismatch’, he argues, ‘may result in a violation of a priori continuity’.65
Runner (1982)             In her own analysis of the same scene, however, Karen Pearlman, argues
                          that this mismatch is not a mistake. As she argues, ‘it offers a different kind of
                          editing, one that adds a visual rhythm, an embodied sense of alignment with
                          character’ and an element of what she reveals as ‘a significant subtext’.66 ‘Its
                          first creative purpose is to create a movement phrase. Like a dance phrase, a
                          movement phrase created by the juxtaposition of two gestures is a statement
                          of a rhythmic idea’.67 But more importantly, she also adds a semiotic purpose to
                          the movement phrase created by editing. As she writes: ‘By comparing the owl’s
                          behaviour with Deckard’s behaviour, the cut subtextually suggests that they
                          are alike’.68 She finds further evidence in the dialogue that immediately follows
                          the comparison. Earlier Rachel has asked Deckard if he likes their owl. When
                          Deckard moves his head away from the owl back to Rachel, he says ‘it’s artificial’
                          upon which Rachel responds ‘of course it is’. This is where the comparison
                          takes on a semantic dimension. As Pearlman argues, it suggests that ‘if they are
                          similar, the possibility Deckard is also artificial, something that (spoiler alert)
                          we learn only much later in the film may be true’.69 From the terminology of this
                          paper, we may further argue that this existential resemblance is pronounced
                          visually by a formal similarity that is articulated at the level of primary motion
                          eyeline vectors.70



30                                                       Coëgnarts, The Meaning Potential of Motion Vectors
Case study 3: The Untouchables (De Palma, 1987)
  Our last example considers a case study that shows how vectors play an import
role in the visual structuring of so called ‘flow-of-emotion scenarios’.71 A flow-of-
emotion scenario conceives emotions to be embedded in a causal chain of three
events: an emotion arousing event (the cause of event), an emotional state and a
behavioural response (the effect of emotion). Such narratives of mental causation
are not only ubiquitous in our ordinary lives, but also in films. To illustrate this,
let us consider the first segment of the famous ‘Odessa Steps’ inspired staircase
scene from Brian De Palma’s The Untouchables (1987). During the Prohibition-
era of the nineteen twenties, Chicagoan cop Elliott Ness (Kevin Costner) along
with his sharp-shooting partner George Stone (Andy Garcia) have arrived at the
city’s Union Station in order to arrest bookkeeper Walter Payne (Jack Kehoe),
the one man that could put Crime boss Al Capone in prison. As they wait for
his arrival, a suspenseful chain of mental causation starts to unfold which we
may analytically divide into a number of flow-of-emotion scenarios, the first of
which may be described as follows: Ness, at the top of the stairs, sees a young
mother appearing at the foot of the stairs, pushing a buggy while simultaneously
carrying two large suitcases (the emotion arousing event). Perception in turn
causes the first emotional state: Ness is nervously torn between helping the
woman carry her buggy up the marble steps, and maintaining his watch for
the accountant. The increase of emotional intensity results in a behavioural
response: Ness gives into his good nature, and rushes down the steps to help
the mother drag her buggy up the stairs (the effect of emotion).
  The first part of this flow-of-emotion scenario is visualised, as shown in fig. 6,
by extending the principle of index-vector target continuity: shots of Eliot Ness
looking off-screen alternate between POV shots of the woman and the baby
(located downstairs, Burch’s second zone of off screen space) and shots of the
station clock up the stairs. The emotional intensity increases as the clock almost
reaches the pivotal moment of 12 am. To express this the film makes use of the




                                                                                        Fig. 6:
                                                                                        Visually structuring the
                                                                                        flow-of-emotion scenario
                                                                                        in Brian De Palma’s The
                                                                                        Untouchables (1987)


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     dynamic pattern of enclosure, here elicited by tertiary motion rather than by
     secondary motion: as the clock nears the arrival time and emotional intensity
     increases, the clock inside Nett’s visual field increases in graphical substance.
     This visual progression in time can be seen as a cinematic manifestation of an
     embodied metaphor, which in the literature is known as the metaphor ‘increase
     in emotional intensity is increase of substance in a container’, a subtype of
     the more general metaphor ‘emotions are forces’.72 As the theory behind this
     metaphor goes, humans have a tendency to conceptualize the rising of a strong
     emotion (e.g., joy, anger, fear) inside a person’s body in terms of the increase of a
     substance inside a container. When there is very little substance in the container,
     the pressure is low and thus emotion is at low intensity (there is enough breathing
     space).73 By contrast, with an increase of the substance, the pressure becomes
     higher, and thus also the intensity of the emotion.74 The increase of pressure,
     here visualized through the increase of the clock’s graphical mass, further
     triggers a behavioral response. This is also what happens next. The eyeline
     vector, the directed force of Elliot’s gaze, soon changes into a motion vector as
     our hero now hastens himself to go downstairs and help the woman. This further
     prompts the camera to move: as Ned lowers himself to approach the lady (and
     the location of the camera), the camera tracks backwards so as to include the
     woman and the baby inside the frame (i.e., Ness’ ‘container’). Another way of
     capturing this would have been to start with a fixed shot of the woman followed
     by a motion vector of fixed-frame movement as Ned enters the shot from above.
     But the effect of this would have been less dynamic and meaningful as it is Ness
     who ‘brings’ the woman and the baby safe into his ‘personal container’, not the
     other way around.



     CONCLUSION
       The goal of this article was to draw attention to the meaning potential of motion
     vectors in cinema. To this aim we first provided a preliminary discussion of the
     concept of a vector in the visual arts by reviewing the pioneering work on visual
     dynamics by Rudolf Arnheim. This theorist has convincingly demonstrated
     and illustrated through various cases how vectors play an important role in
     the visual structuring of narrative meaning in fixed images. Subsequently, we
     extended the question of vectors not only to the domain of fixed images, but
     also to the domain of moving images by addressing the meaning potential
     of motion vectors. For this purpose, we first had to define the filmic space in
     which motion vectors may unfold themselves. Having done so we distinguished
     between three types of motion vectors: primary motion vectors, secondary
     motion vectors and tertiary motion vectors. Since the proof of the pudding is
     in the eating, we concluded this paper by illustrating the concepts proposed
     using three filmic case-studies. The insights offered in this paper will hopefully
     provide an impetus to further explore, in an interdisciplinary way, the role of
     motion vectors in the structuring of meaning in cinema.



32                                   Coëgnarts, The Meaning Potential of Motion Vectors
Notes
 1
     Barbara Tversky, Mind in Motion: How Action Shapes Thought (New York: Basic Books, 2019); Varela,
Francisco J., Evan Thompson and Eleanor Rosch, The Embodied Mind: Cognitive Science and Human
Experience (Cambridge: The MIT Press, 1991); Raymond W. Gibbs Jr., Embodiment and Cognitive Science
(Cambridge: Cambridge University Press, 2006); George Lakoff and Mark Johnson, Philosophy in the Flesh:
The Embodied Mind and its Challenge to Western Thought (New York: Basic Books, 1999).
  2
     The concept of an ‘image schema’ is central in two classic 1987 monographs: Lakoff, Women, Fire,
and Dangerous Things: What Categories Reveal About the Mind (Chicago: University of Chicago Press,
1987), and Johnson, The Body in the Mind: The Bodily Basis of Meaning, Imagination and Reason (Chicago:
University of Chicago Press, 1987).
  3
    Lakoff and Johnson, Metaphors We Live By (Chicago: University of Chicago Press, 1980).
  4
    Johnson, 42–48; see also Leonard Talmy, ‘Force Dynamics in Language and Cognition’, Cognitive Science,
12.1 (1988), 49–100.
  5
     Lakoff and Johnson, Metaphors We Live By, 184–185; María Sandra Peña Cervel, ‘Subsidiarity
Relationships Between Image-schemas: An Approach to the Force Schema’, Journal of English Studies, 1
(1999), 187–208.
  6
    For Johnson’s discussion of the force schema, see Johnson, 76–79.
  7
    Rudolf Arnheim, Visual Thinking (Berkeley and Los Angeles: University of California Press, 1969).
  8
     Arnheim, Art and Visual Perception: A Psychology of the Creative Eye (Berkeley and Los Angeles:
University of California Press, 1974); Rudolf Arnheim, ‘Perceptual Dynamics’, American Scientist, 76 (1988),
585–591; Arnheim, The Power of the Center (Berkeley and Los Angeles: The University of California Press,
1988).
  9
    Arnheim, ‘Perceptual Dynamics’, 590.
  10
     Arnheim, The Power of the Center, 229.
  11
     Ibidem, 226.
  12
      Gunther Kress and Theo Van Leeuwen, Reading Images: The Grammar of Visual Design (London:
Routledge, 2021); Morten Boeriis and Theo van Leeuwen, ‘Vectors’, in New Studies in Multimodality, ed. by
Ognian Seizov and Janina Wildfeuer (London: Bloomsbury, 2017), 15–36.
  13
     Herbert Zettl, Sight, Sound, Motion: Applied Media Aesthetics (Boston: Cengage Learning, 2017), 127–
131. As will become clear below, we will use the concept of a ‘motion vector’ in a wider sense than originally
proposed by Zettl.
  14
     Johnson, 43.
  15
     Arnheim, Art and Visual Perception, 416.
  16
     Ibidem, 412.
  17
     Arnheim, Visual Thinking, 270.
  18
     Ibidem, 270–271.
  19
     Arnheim, ‘Perceptual Dynamics’, 585.
  20
     Arnheim, Art and Visual Perception, 441–443.
  21
     Ibidem, 441.
  22
     Ibidem, 424.
  23
     Ibidem, 441.
  24
      It should be stressed, however, that Arnheim also wrote extensively about film, especially at the
beginning of his career. Notable in this regard is his landmark book Film as Art (Berkeley and Los Angeles:
University of California Press, 1957). However, since Arnheim never undertook any serious attempts to
update or revise his position, and since his later work mostly focuses on static art media, the implications
of vector dynamics for the study of meaning in film have been largely ignored in the literature.
  25
     Notable in this regard are two classic works in the field of perceptual psychology: Albert Michotte’s The
Perception of Causality (New York: Basic Books, 1963), which is also cited and discussed by Arnheim, Art
and Visual Perception, 388–395, and Fritz Heider and Marianne Simmel’s influential article on perceptual
animacy, entitled ‘An Experimental Study of Apparent Behavior’, The American Journal of Psychology, 57
(1944), 243–249.
  26
      See, among others, Christina Schmitt, Sarah Greifenstein and Hermann Kappelhoff, ‘Expressive



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Movement and Metaphoric Meaning Making in Audio-Visual Media’, Body-Language-Communication, vol.
2, ed. by Cornelia Müller, Alan Cienki, Ellen Fricke, Silva Ladewig, David McNeill and Jana Bressem (Berlin,
München and Boston: De Gruyter Mouton, 2014), 2092–2112; Jordan Schonig, The Shape of Motion: The
Cinema and the Aesthetics of Movement (Oxford: Oxford University Press, 2021); and Patrick Keating, The
Dynamic Frame: Camera Movement in Classical Hollywood (New York: Columbia University Press, 2019).
   27
      Arnheim, Art and Visual Perception, 416.
   28
      Ibidem, 28.
   29
      Zettl, 128. Notice that Zettl does not make reference to camera movement and editing in his definition
of a motion vector.
   30
      Arnheim, The Power of the Center, 228.
   31
      Kress and van Leeuwen, 72.
   32
      Zettl, 129.
   33
      See also the criticism of Boeriis and van Leeuwen, 16.
   34
      Noël Burch, Theory of Film Practice, trans. by Helen R. Lane (Princeton: Princeton University Press,
1981), 17.
   35
      Ibidem, 17. For a discussion, see also David Bordwell and Kristin Thompson, Film Art: An Introduction
(New York: McGraw-Hill, 2004), 258; Maarten Coëgnarts, Film as Embodied Art: Bodily Meaning in the Cinema
of Stanley Kubrick (Boston: Academic Studies Press, 2019), 75.
   36
      Zettl, 161–163; see also Michael Frierson, Film and Video Editing Theory: How Editing Creates Meaning
(New York: Routledge, 2018), 5.
   37
      Zettl, 162.
   38
       Cato Wittusen, ‘Varieties of Temporal Overlapping and Depth’, New Review of Film and Television
Studies, 12.2 (2014), 112–124 (118).
   39
      André Bazin, What is Cinema?, trans. by Timothy Barnard (Montreal: Caboose, 2009), 69.
   40
      Bazin, Jean Renoir, trans. by W. W. Halsey II and William H. Simon (New York: Da Capo Press, 1992), 89.
   41
      Julian Hanich, ‘Reflecting on Reflections: Cinema’s Complex Mirror Shots’, in Indefinite Visions: Cinema
and the Attractions of Uncertainty, ed. by Martine Beugnet (Edinburgh: Edinburgh University Press, 2017),
131–156 (141).
   42
      Zettl, 294.
   43
       For a discussion of the concept of ‘trajectory phrasing’, see Karen Pearlman, Cutting Rhythms:
Intuitive Film Editing (Amsterdam: Focal Press, 2016); Pearlman, ‘Editing and Cognition Beyond Continuity’,
Projections: The Journal for Movies and Mind, 11.2 (2017), 67–86; Pearlman, ‘On Rhythm in Film Editing’,
in The Palgrave Handbook of the Philosophy of Film and Motion Pictures, ed. by Noël Carroll, Laura T. Di
Summa and Shawn Loht (Cham: Palgrave Macmillan, 2019), 143–163.
   44
      Coëgnarts, Film as Embodied Art, 84–85.
   45
      Burch, 18.
   46
      Zettl, 129–130.
   47
      Burch, 19.
   48
       For a discussion of this scene, see also Pearlman, ‘Editing and Cognition’, 79; Vittorio Gallese and
Michele Guerra, ‘Embodying Movies: Embodied Simulation and Film Studies’, Cinema: Journal of Philosophy
and the Moving Image, 3 (2012), 183–210 (200–201); Coëgnarts, ‘Cinema and the Embodied Mind: Metaphor
and Simulation in Understanding Meaning in Films’, Palgrave Communications, 3.1 (2017): 1–15; and Mircea
Valeriu Deaca, ‘The Control Cycle: Cognitive Model in Biology, Film and Culture’, Ekphrasis. Images, Cinema,
Theory, Media, 20.2 (2018), 63–97 (88–89).
   49
      This apparently paradoxical phenomenon of the relativity of movement has been well described and
illustrated by perceptual psychologists. See e.g., Julian Hochberg and Virginia Brooks, ‘Perception of Motion
Pictures’, in Cognitive Ecology, ed. by Morton P. Friedman and Edward C. Carterette (San Diego: Academic
Press, 1996), 205–292 (237–240).
   50
      Seymour Chatman, Antonioni or, The Surface of the World (Berkeley: University of California Press,
1985). See also Kenneth Johnson, ‘The Point of View of the Wandering Camera’, Cinema Journal, 32.2
(1993), 46–56.
   51
      Ibidem, 49.
   52
      Zettl, 299.
   53
      Ibidem, 299.



34                                                         Coëgnarts, The Meaning Potential of Motion Vectors
 54
     Pearlman, Cutting Rhythms, 60.
 55
     Pearlman, ‘On Rhythm’, 155.
  56
     Ibidem, 155.
  57
     For a discussion of continuity principles in relation to vectors, see Zettl, 369–393.
  58
     Pearlman, Cutting Rhythms, 170.
  59
     Stephen Prince, The Warrior’s Camera: The Cinema of Akira Kurosawa (Princeton: Princeton University
Press, 1999).
  60
     Ibidem, 172–173.
  61
     Ibidem, 42.
  62
     Ibidem, 41.
  63
     Tim J. Smith, ‘The Attentional Theory of Cinematic Continuity’, Projections: The Journal for Movies and
Mind, 6.1 (2012), 1–27 (20); Pearlman, ‘Editing and Cognition’, 75.
  64
     Smith, 20.
  65
     Ibidem.
  66
     Pearlman, ‘Editing and Cognition’, 75.
  67
     Ibidem, 75.
  68
     Ibidem, 76.
  69
     Ibidem.
  70
     A similar interpretation may be given to the cutting of the red men’s bathroom in Stanley Kubrick’s The
Shining (1980). This is well addressed by Frierson, 22: ‘Kubrick cuts across the 180° line to create a visual
metaphor linking (Jack Nicholson) and Mr. Grady (Philip Stone) as socially isolated characters by flipping
their position from shot to shot)’. Here, we may speak of a flipping of eyeline vectors through editing or
rather the flipping of the participants from which these vectors emanate.
  71
     For a discussion, see Coëgnarts, Film as Embodied Art, 28.
  72
     Kövecses, 65–68; see also Coëgnarts, Film as Embodied Art, 63.
  73
     For a discussion of the container image schema, see Lakoff and Johnson, Philosophy in the Flesh, 31–32.
  74
     For a discussion of this metaphor in relation to the elevator scene from Francis Ford Coppola’s The
Conversation (1974), see Coëgnarts, ‘Analyzing Metaphor in Film: Some Conceptual Challenges’, in Current
Approaches to Metaphor Analysis in Discourse, ed. by Ignasi Navarro i Ferrando (Berlin: De Gruyter Mouton,
2019), 295–320 (314–316).




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