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  • Drawing and culturally-conditioned perception: Howard Riley

  • Abstract
    The paper begins with a brief explanation of David Marr's computational theory of visual perception, and his key terms. Marr argued that vision consists in the algorithmic transformation of retinal images so as to produce output of viewer-centred and object-centred representations >from an input at the retinae. Those two kinds of output, the viewer-centred and the object-centred representations, enable us to negotiate the physical world.

    The paper goes on to suggest that the activity of Drawing is comparable as a process of transformation: a picture is a transformation from either viewer-centred, or object-centred descriptions, or a combination of both types of mental representation, to a two-dimensional drawn representation. These pictures may be described as resulting from algorithmic transformations since picture-making utilises specific geometric procedures for transforming input (our perceptions) into output (our drawings).

    However, a key point is made about such algorithms: they are culturally-determined. They may be defined in terms of the procedure of selecting and combining choices from the matrix of semiotic systems available within a particular social context. These systems are presented in the paper as a Chart, and are further correlated with the social functions of a communication system such as Drawing. Thus, the paper proposes a systemic-functional semiotics of Drawing, within which algorithms operate to realise specific cultural values in material form.

    Introduction
    David Marr's computational theory of vision Along with all other major theorists, except James Gibson (1979), David Marr (1982) assumed that vision is the result of some kind of processing - interpretation or construction - of the incomplete data provided by the retinal image.

    The revolution in information technology throughout the 1960's and 1970's inspired Marr to develop a new model for explaining what happens between the retinal stimulus and our response. A model based on the hypothesis that retinal images could be processed by the human visual perception system in ways analogous to the processing of input by a computer: Vision is a process that produces from images of the external world a description that is useful to the viewer and not cluttered by irrelevant information.
    Marr & Nishihara (1978 : 269)

    Marr's computational model is an attempt to explain vision in terms of input to the physiological system - the patterns of light falling on the surface of the retina - and output, the information about surfaces, objects and events in the environment which any animate organism requires in order to survive. He shares a great deal with Gibson - for example, both agree that incident light reflected from surfaces and edges of the environment is re-structured as an array of differing light intensities. But Marr's theory considers the input to be the retinal image, not an array of light. He described visual processing as the means of producing a description of the environment by the construction of a range of representations from the values of light intensity falling upon the retina. Representation here refers not to retinal or mental images but to "a formal system for making explicit certain entities or types of information, together with a specification of how the system does this". (Marr 1982 : 20) This is perhaps more familiar to artists than it sounds. Any conventional semiotic code is a formal system which has rules for selecting and combining signs from within it in order to describe their referents. For example, the formal system of geometric projection known as artificial perspective is a code with rules which dictate the 2-D geometrical relationships between lines and points of convergence in order to describe the 3-D spatial relationships of an environment from a single, static point of observation.

    The first stage of representation Marr described as the raw primal sketch, in which information about edges and textures of surfaces in the world is present. The raw primal sketch represents the various light intensities in the retinal images. These are subject to the orientation and disposition of surfaces in the world; the reflectance properties of those surfaces; the illumination of the scene; and of course the observer's viewpoint. All these factors influence the retinal light intensities, and the purpose of this earliest stage of visual processing is to separate out which factors cause which intensities.

    The full primal sketch describes many of the shapes and textures within the retinal image, but this is only part of the first phase of visual processing. The main objective is to describe surfaces relative to the viewer. Marr identified the end-product of early visual processing as a 21/2D sketch, a viewer-centred representation, which is obtained by an analysis of depth, motion and shading, as well as the primitive structures in the primary sketch.

    The 21/2D sketch, describes the layout of surfaces in the world from a particular point of view which of course is a pre-requisite for effective locomotion, and hence survival.
    An equally essential requirement of vision is the recognition of objects and other structures within the perceived environment. In order to recognise what object a particular processed shape corresponds to, a third level of representation was theorised by Marr, one centred on the object, not the viewer. This third level was identified as a 3D model representation. The purpose of vision is to provide information about the world - a description of what is there - from the information in the retinal images. Marr (1982 : 36) proposed that since this is "almost certainly impossible in only one step", we require "a sequence of representations", starting with descriptions that may be accessed from the retinal images and that act as prompts to subsequent representations of the objective world. Marr's sequence of representation is illustrated below adapted from Marr (1982 : 37 Table 1-1).


    1. Levels of representation (Marr 1982 : 37)


    Level of Representation Purpose Primitives
    Retinal images Represents light intensities Intensity values at each point in the retinal image
    Primal sketch Clarifies the geometrical organisation of retinal light intensities Zero-crossings, blobs, Terminations and discontinuities,
    Edge segments,
    Virtual lines, Groups, Boundaries, Curvilinear organisation
    2 1/2-D sketch Clar ifies the angle and depth of visible surfaces in a viewer-centred co-ordinate system Orientation of surface,
    Distance from viewer,
    Discontinuities in those two primitives

    3-D model representation

    Describes forms and their organisation in space in an object-centred co-ordinate system. This representation uses a modular, hierarchical scheme utilising volumetric primitives and surface primitives 3-D models arranged hierarchically, each one based on a spatial configuration of a few axes, to which volumetric or surface primitives are attached

     

    Algorithms
    Compatible with a computational theory, Marr proposed algorithms, specified procedures for transforming input into output. He argued that the algorithms he demonstrated on computer systems are actually implemented by the physiological structures of neurons involved in the human visual system. His theory has therefore had repercussions within the disciplines of biology and physiology.


    Marr and Hildreth (1980) devised an edge-finding algorithm consisting of a series of mathematical operations performed on a computerised image. This, they argued, was analogous to the way that the human visual system operates at the representational level of the primal sketch.
    A visible edge in the world may be specified as where a material surface either a) changes direction along a straight, curved, or ragged contour, or b) occludes another surface or the sky.
    These conditions are specified on the retina as the boundary formed when an area of a certain light intensity is adjacent to an area of different intensity. A specific procedure for recognising such an edge could begin by identifying changes, or gradients of light intensity in the retinal image. Of course such gradients may be steep (at sharp edges) or shallow (at blurred or ragged edges). Any change in value of light intensity across a small masked area of the image would therefore indicate an edge. The field of a simple cell in the visual cortex is such a masked area. (Bruce & Green 1985 : 73) Marr claimed that many such cells, each capable of locating specific gradients of steepness, could identify the full range of contrast boundaries, and therefore edges, within a retinal image. But the primal sketch is still only a description of the retinal image, rather than of the world. The materials of the world we see, surfaces and media such as air and water, extend over distance; some surfaces occlude others, and of course the patterns of light reflected from and through them are never static upon the retina: The world moves, as do we, and we constantly need to know where we are in relation to the world. Marr and Poggio (1976, 1979) offered two algorithms demonstrating procedures by which a viewer's position may be located with respect to the distance and disposition of surrounding surfaces. The extraction of such stereoscopic information from the input of the play of light upon the retinae is crucial to the formation of a 21/2-D sketch. Marr and Poggio (1976 : 284) suggested two rules for how the primitive descriptions obtained from the left and right eyes may be combined to produce stereoscopic vision:
    Rule 1. Uniqueness Each item from each retinal image may be assigned at most one disparity value. This condition assumes that an item corresponds to something in the visual world that has a unique physical position.
    Rule 2. Continuity Disparity between retinal images varies smoothly almost everywhere. Marr and Poggio utilise the Gestalt principle of continuity based upon the cohesiveness of matter to formulate rule 2: Only a small fraction of the area of a retinal image is composed of boundaries that are discontinuous in depth.
    Since each eye receives a different array of light, an algorithm designed to represent a 21/2-D sketch must be capable of co-ordinating these disparities. Marr & Poggio (1976 : 284) constructed an explicit representation of the two rules, and derived a co-operative algorithm which specified how a representation of the two retinal images may be transformed into stereoscopic vision. Random-dot stereograms were used as input for the testing of the algorithm: When we view a random-dot stereogram, we probably compute a description couched in terms of edges rather than squares, whereas the inputs to our algorithm are the positions of the white squares. Marr and Poggio (1976 : 285)

    Figure 2 below (from Marr & Poggio 1976 : 286) shows an example in which the algorithm successfully allows disparity values to be assigned to elements in each image. The shapes in the right-hand column are the computed resolutions of the paired inputs at the left.

    In order to verify the resolutions, the reader should focus the eyes on a plane beyond the page so that the pair of random-dot stereograms fuse together. It is then possible to view all four pairs at once. We have seen how the 2¸-D sketch theorises a viewer-centred perception of >the world, so that we may be aware of our position relative to the surfaces within our environment. But how do we differentiate between surfaces which form three-dimensional objects, and those which form the landscape? Marr and Keith Nishihara (1978) proposed a solution for this problem based upon an object-centred description in which the object is described within a frame of reference based on the 3-D form of the object itself. The resulting representation of the object may be assessed in three ways: the co-ordinate system of the representation; its primitives, Marr's term for the primary elements of 3-D form information such as edges, boundaries, textures; and how such information contained in the representation is organised.

    2. Random-dot stereograms (Marr & Poggio 1976 : 286)

    An object-centred co-ordinate system is one independent of the viewer's position. A single description of an object's spatial structure, for example based on the object's natural axes of length, rotation, or symmetry, could then render the object recognisable from any viewing point. Sets of descriptive elements, the primitives of the representation, are best organised in a modular way, as illustrated in Figure 3 (Marr & Nishihara 1978 : 278). Marr and Nishihara discussed the process from representation to object recognition, and in particular the importance of being able to relate object-centred information to viewer-centred information by means of a process of transformation (Marr & Nishihara, 1978 : 285). Marr (1982 : 25) summarised the different levels at which an information-processing device must be understood in the following table Figure 4 Computational theory Representation and Algorithm Hardware Implementation What is the goal of the computation, why is it appropriate, and what is the logic of the strategy by which it can be carried out? How can this computational theory be implemented? In particular, what is the representation for the input and the output, and what is the algorithm for the transformation? How can the representation and the algorithm be realised physically?

     

     

     

     

    3. The organisation of shape information in a 3-D model description (Marr & Nishihara 1978 : 278)


    Computational theory Representation and Algorithm Hardware implementation
    What is the goal of the computation, why is it appropriate, and what is the logic of the strategy by which it can be carried out? How can this computational theory be implemented? In particular, what is the representation for the input and the output, and what is the algorithm for thr transformation? How can the representation and the algorithm be realised physically?

    4. Information-processing device

    Figure 4 David Marr emerges as the leading advocate for an indirect theory of vision, one in which perception is argued to be the result of processing the retinal image. James J Gibson argued for a direct theory in which information about the world is picked up directly from the structured array of light arriving at the eyes, and acted upon by our physiological systems.
    Both agree that the pre-requisite for vision can be described in terms of the structure of light:

    Gibson's important contribution was to take the debate away from the philosophical consideration of sense-data and the affective qualities of sensation and to note instead that the important thing about the senses is that they are channels for perception of the real world outside, or, in the case of vision, of the visual surfaces. He therefore asks the critically important question. How does one obtain constant perceptions in everyday life on the basis of continually changing sensations? This is exactly the right question, showing that Gibson correctly regarded the problem of perception as that of recovering from sensory information 'valid properties of the external world'. Marr (1982 : 29)

    The two theories differ over their explanations of how our physiological apparatus deals with the incoming light. Gibson claimed we resonate directly in response to the ecologically-structured information contained within the arrays of light arriving at our eyes. Some invariant aspects of the structured arrays specify lower-order information about surfaces - their distance and slant for example. Other invariants, yet to be defined, are supposed to specify higher-order information about objects and what they may afford us. There is therefore no requirement in Gibson's theory for an intermediate level of information-processing. The reception of affordance information leads automatically to active response. The theory does not address how resonance is accounted for physiologically. Marr's theory proposes three levels at which perception needs to be explained; the ecological, and the physiological, with a level of mediation in between, an algorithmic level, in Marr's term, which organises the ecologically-conditioned information arriving at the eyes in a way suitable for representation by the physiological system. In Marr's opinion, the omission of such a level of mediation - information-processing - invalidates Gibson's theory of direct perception:

    Gibson's....fatal shortcoming...results from a failure to realise two things. First, the detection of physical invariants, like image surfaces, is exactly and precisely an information-processing problem. And secondly, he vastly underrated the sheer difficulty of such detection. (Marr 1982 : 30)

    Detecting physical invariants may be difficult, but we are able to do it. Marr's difficulty may be in demonstrating computationally how it is done. Marr's important distinction between a viewer-centred representation of a scene and an object-centred representation allows interesting insights into the ways people have developed systems of geometry in order to make visual records of these various perceptions.

     

    David Marr's computational theory of vision related to Drawing
    In the Introduction some of the terminology of machine vision research which Marr (1982) utilised and developed was defined and discussed. Here it will be necessary to introduce some other terms from that discipline in order to specify the differences in discussion of the visual world, or scene, and two-dimensional material representations of it, pictures. The simplest elements making up the material world, scene primitives such as edges, boundaries, corners, texture units and surface segments, are transformed through drawing into picture primitives such as lines, line-junctions, points and regions (Willats 1997 : 290) Marr argued that vision consists in the algorithmic transformation of the retinal images so as to produce viewer-centred internal representations and ultimately object-centred internal representations which enable us to negotiate the physical world. Using such terminology, Drawing itself may be considered as a process of transformation; from those object-centred, internal 3-D model descriptions of a scene, to a two-dimensional external representation, or picture. A picture too may be either viewer - or object-centred, depending on the algorithm which specifies its particular system of geometric projection. Some of these algorithms may describe the way light is transmitted through space - for example, the algorithm that specifies an artificial perspective projection. Some of them most certainly do not - transformation rules that specify the reversal of optical rules are evident in Drawings - for example, reverse perspective, or pictures based on topological transformations. One purpose of such pictures is to communicate the experiences of seeing, and actually, drawing may enable contemplation of the very process of transformation from viewer-centred to object-centred representations. Apart from informing the activity of drawing itself, Marr's methodology adapted to the study of children's drawings has been able to provide insights into how they develop through a series of stages identified with children's developing awareness of themselves and their relationship with the world of objects and events.

    John Willats' adaptation of Marr's theory
    Willats (1987, 1995, 1997) has been able to forward a consistent theory of children's drawing development by treating them as "information-processing devices for producing pictures". (Willats 1995 : 28) He proposes that the ways people convey their experiences of the world through Drawings may be described in terms of two systems that afford the Drawer access to compositional choices: the drawing system, and the denotation system. Although Willats does not refer to Halliday (1985) or O'Toole (1994) and makes no reference to systemic-functional semiotics in his writings, his intention appears remarkably similar: "...

    I shall try to show that analysing pictures in terms of these two representational systems (the drawing system and the denotation system) can be useful:·.I shall argue that differences in the representational systems found in different periods and cultures, and the changes that have taken place in these representational systems during the course of art history and that take place during the course of children's drawing development, are mainly determined by the different functions that representational systems are called on to serve". Willats (1997 : 1-2)

    Willats' proposal is derived from Marr's and Nishihara's work on what they called the representation of "three-dimensional shapes" or form. They identified three aspects of a representation's design:

    "(i) the representation's co-ordinate system (ii) its primitives, which are the primary units of shape information used in the representation, and (iii) the organisation the representation imposes on the information in its descriptions". Marr & Nishihara (1978 : 269)

    Viewer - and object-centred co-ordinate systems used in drawing, and Willats' contributions to their classification may be described by the term Drawing conventions. Their function is to transform three-dimensional spatial relationships in the scene into two-dimensional geometrical relationships on the picture surface. The function of Willats' denotation systems, however, is to transform scene primitives into picture primitives. The distinction between the geometric relationships on the picture-plane and what they denote is crucial, since the two are easily conflated. For example, in our everyday usage of language, lines on a Drawing surface are referred to as edge of objects; depicted two-dimensional shapes are described as three-dimensional forms; two-dimensional patterns are spoken of as three-dimensional texture. Gibson identified this problem when he wrote of the duality of seeing; the perception of the spatial world of undulating surfaces, edges, colour and texture as opposed to the perception of the world of signification, which of course includes drawings.

    Denotation systems, scene primitives and picture primitives Scene primitives are such things as edges, corners, surfaces or 'generalised cones'. Marr (1977 : 442-3) defined a generalised cone as "the surface swept out by moving a cross-section of fixed shape but smoothly-varying size, along an axis". Willats prefers the term extendedness in one, two and three directions to describe such volumes. Scene primitives may be zero-, one-, two-, or three-dimensional. A zero-dimensional scene primitive may be a corner-point of an object. An edge may be a one-dimensional primitive, a surface may be a two-dimensional primitive, and a volume or generalised cone may be a three-dimensional primitive. The activity of drawing transforms these scene primitives into picture primitives, and Willats (1997 : 93) classifies denotation systems as being based upon such picture primitives, as points, lines or regions. Picture primitives may be zero-, one-, or two-dimensional. A zero-dimensional picture primitive representing a corner, may be the point of a junction between two lines. A one-dimensional picture primitive representing an edge, may a line. Two-dimensional picture primitives, representing surfaces, are regions, or faces. (A region in a Drawing is Willats' term for the projected shape of a three-dimensional object in a viewer-centred drawing system; a projected shape of an object in an object-centred drawing system he terms a face) Such a concise terminology deriving from Marr's approach and differentiating between viewer - and object-centred Drawings, scene and picture primitives, has allowed Willats to offer critiques of other theories of children's drawing development, and to propose an alternative.

    Marr, Willats, and children's drawing The most generally accepted explanation of children's drawing development until Willats' was that young children draw what they know, and older children draw what they see. This argument, put forward as early as A. B. Clark (1897) was developed by G. H. Luquet (1913, 1927) into a theory of intellectual realism versus visual realism. The change from intellectual to visual realism is deemed to occur between the ages of seven and nine years. Willats (1997 : 288) has suggested that the distinction between intellectual and visual realism may be interpreted as that between object-centred and viewer-centred internal descriptions as theorised by Marr. Jean Piaget and B. Inhelder (1956) inherited Luquet's theory, but added their insight about the child's development of space conception based upon invariant geometry, in which certain spatial relations remain invariant over transformations from one co-ordinate system to another. The classes of invariant geometry form a hierarchy in which each one is a special case of the one before (above) it:


    Stage 1 Topology
    Stage 2 Projective geometry (perspective)
    Stage 3 Affine geometry (oblique projections)
    Stage 4 Metric geometry (orthographic projections)


    The number of invariant features increases from stage 1 to stage 4, so that features remaining invariant under transformation in Metric geometry include: size, shape, angle relationships, straightness, parallelism, length, ratio of length, area, and others. Piaget and Inhelder suggested that progression from stage 1 to 4 could account for the child's development of a conception of space, and therefore the development of drawing ability. However, Willats (1977) showed that in practice the developmental sequence was the reverse: Children aged between 5 and 17 were asked to draw a table with various objects on it from a fixed viewpoint.
    Figure 6 (from Willats 1997 : 11) illustrates typical results.


    6. Children's drawings of a table (Willats 1997 : 11)

    Figure 6 The Drawings and the children's ages were classified as follows:
    b No projection system (Topological); average age 7.4 years
    c Orthographic projection (Metric geometry); average age 9.7 years
    d Vertical oblique projection (Affine geometry); average age 11.9 years
    e Oblique projection (Affine geometry); average age 13.6 years
    f Na•ve perspective (Projective geometry); average age 14.3 years
    g Perspective (Projective geometry); average age 13.7 years


    This experiment demonstrated that there seems to be a clear sequence of development from orthographic, through oblique, to perspective drawing as the child grows older. In Marr's terminology, Willats' experiment shows that children begin drawing their surroundings using object-centred descriptions, and progress to viewer-centred descriptions. Willats' important contribution is to point out that the reason other theories of development of children's drawing seem to ignore the changes >from object-centred drawings to viewer-centred drawings is because they assume that both input and output are view-based regardless of age. The weakness of these arguments is that they do not recognise the possibilities of any algorithms that would allow the transformation of view-based input to object-centred drawings as output, and subsequently from object-centred drawings to viewer-centred drawings.
    Algorithms - the rules governing the transformations from one kind of drawing to another - are culture-specific, and indicate the Drawer's ideological positioning, as well as their mental positioning in relation to the scene depicted. Willats' insights are important to the teaching of drawing, since they allow the opportunity to explore how the variety of ways in which selections from the range of drawing systems and denotation systems may be combined to produce the cultural variety of drawing styles. This opportunity will be explored shortly, with discussion about how such selections and combinations operate semiotically to make visible the ideologies and belief-systems of the culture in which they are produced. Margaret Hagen (1986) presented an interesting conundrum when she argued firstly against any notion of a hierarchy of drawing styles (1986 : 271) "·.development in art does not take place historically or culturally, ·.no specifiable pattern or set of characteristics distinguishes earlier styles >from later ones", and then later (1986: 279-280) "In younger children, Orthogonality is commonplace;·In older children Affine and Projective systems also make an appearance·." In the first instance, her statement comes after, and in support of her argument that the way people draw is a function of their particular cultural experiences. Could it be that the process of development that both Hagen and Willats observed in the Drawings of children simply evidence of a growing awareness of their position as individuals within the culture? Such self-awareness may be indicated by the development from object-centred Drawings to viewer-centred Drawings. Only after children have achieved this state of awareness do their Drawings become subject to the wider demands of social conventions and cultural constraints, and the wider range of functions that Drawings are called upon to serve

    Marr and Gibson: common ground
    Hagen's work was heavily influenced by Gibsonian theory. Gibson's explanation of the development of children's drawing challenged the traditional argument that children first draw what they know and then develop to draw what they see, by pointing out that if the argument is to be couched in those terms, then they should be the other way around. Gibson attempted to by-pass that false antithesis of seeing versus knowing by claiming that children first draw those invariant features of objects that they notice first, and that their drawings alter as their awareness of what they notice expands. In doing so, Gibson appears to be explaining what in Marr's terms would be the transformation process from raw primary sketch through the 2¸-D sketch to a 3-D model description, and finally to pictures. It may be that as children's awareness of their positioning in the world develops along with hand-eye co-ordination, so does their ability to display their object-centred internal descriptions through the making of object-centred pictures, and later viewer-centred pictures. Marr's and Gibson's positions share common ground. For example, here are several principles laid down by Gibson (1950 : 6) that appear to be consistent with Marr's theory. The main principles follow from the hypothesis that there is no perception of space without the perception of a continuous background surface.


    1. The elementary impressions of a visual world are those of surface and edge.


    2. There is always some variable in stimulation which corresponds to a property of the physical environment (for example, the variable stimulus corresponding to 'surface' is probably a textured retinal image; stimulus for distance or depth over a continuous surface may be an increase or decrease in the density of the texture of the retinal image. The variable stimulus for 'edge' is probably the contrast boundary between two different light-intensities upon the surface of the retina).

    3. The stimulus-variable within the retinal image to which a property of the environment corresponds need only be a correlate of that property, not a copy of it (Gibson explains that solidarity and depth in reality cannot have any replica in the two-dimensional retinal image, but they may have correlates there).

    4. The inhomogeneities of the retinal image are analogous to the variables of physical energy and this means that the pattern of retinal image can be considered a stimulus.

    Such principles indicate a closer correlation between Gibson and Marr than is generally acknowledged, and it is these correlations that afford the opportunity to adapt both theorists within a wider model that relates perception theory and visual communication theory.

    The visual aesthetic process of production
    Consider the relationship between an individual piece of work and the state of the culture within which it is located: The individual piece may be expressed through identifiable conventions which may be taken to constitute the 'hallmark' of the period, or may challenge those conventions. It is to explore such relationship between individual expressions and cultural conventions that Raymond Williams (1968) invented the term "structure of feeling", A structure of feeling describes the ideological aesthetic construction through which we make sense of the unique within the generalities of a period's social conventions. The making visible of any idea requires an inception stage, in which social concepts and individual percepts are codified in material form. What I term the visual aesthetic process is an ordering of visual perceptual relations deemed appropriate by the producer for transforming into visible form some aspect of the socio-cultural values of the particular social and cultural context.
    (Seeing) (Knowing) (Producer) (Viewer)

    PERCEPTION

    Individual activity through which information about the world is taken up

    CONCEPTION

    The 'filtering' of perceptual information via social constructsC

    INCEPTION

    The encoding of concepts in material form

    RECEPTION

    Making sense of the work within a social contex

     

    Figure 7. The visual aesthetic production process

    At the inception stage, the semiotic requirements for visualising social ideology will determine the selection and combination of drawing elements:
    SELECT Elements of drawing:  
    COMBINE Combinations of elements produce:
      COMMUNICATE Combinations stand for physical and emotional experiences of the world:

    point
    line
    shape (2D)
    texture
    tone
    colour
    plane
     
    contrast
    proportion
    scale
    pattern
    rhythm
     
    spatial depth
    force
    direction
    movement
    volume, mass, weight
    balance
    symmetry
    structure
    form (3D)
    surface properties
    observer's position(s)/mood, attitude

    The combinations in the above chart are of course universal. They can be seen at work in all visual imagery in every culture. But how these combinations come to represent experiences of the world is very much culture-specific. What is noticed about distance-relations for example may be represented using proportion and scale encoded in a system of geometry deemed appropriate to that society's world-view: For example a society with no concept of egocentricity would have little need to develop an artificial perspective which represents distance relations from a static, one-eyed central viewpoint.

    The social semiotics of drawing
    In the materialist sense, Drawings are produced through the selection and combination of particular surfaces, drawing tools, and the marks resulting >from their interaction. But semiotically speaking both producers and viewers of Drawings take up positions, adopt attitudes, points of view which are influenced by their positions within their sets of social relations. Such an ideological positioning involves a definite way of using signs (a semiotic), and a structured sensibility (an aesthetic) both grounded in a particular system of social relations. How the producer selects and combines the compositional elements of the Drawing, and how the viewer relates to that Drawing are both functions of the social contexts in which the work is (re) produced. But to simply say that Drawings reflect social structure is too passive. Drawing not only expresses the social context but is part of a more complex dialectic in which Drawings actively symbolise the social system, thus producing as well as being produced by it. Variation in ways of drawing is the symbolic expression of variation in society. Drawing systems are produced within society, and help to produce social form in their turn. This dialectical relationship is what Michael Halliday (1978 : 183) discusses in the phrase "social semiotic".

    Varieties of drawing Of the two kinds of variation in language identified by Halliday (et.al. 1964), dialect expresses the diversity of social structure, and register expresses the diversity of social process. Whilst the meaning of dialect may be commonly understood, register may require further discussion. It refers to the fact that language usage varies according to the situation in which it is used. In terms of drawing, register would refer to the variation in selecting and combining visual elements according to the purpose for which the drawing was produced. The social system (the Culture) can be represented as a construction of meanings - as a semiotic system. And the meanings that constitute the social system are exchanged through the rich variety of semiotic codes developed by humans of which Drawing is one.
    From this social semiotic perspective, any social context may be understood as a temporary construct which may be mapped in terms of three variables which Halliday called field, tenor, and mode.

    Field of social process - what is going on at the time of production of the drawing.
    Tenor of social relationships - the type of drawing we produce varies according to the level of formality, of technicality, of need for clarity of communication, etc. It is the ROLE relationships - the drawer, the subject matter, the viewer and their inter-relationships - that affect the variations.
    Mode of symbolic interaction - in the sense that how we draw varies with our attitude: An attitude of objective observation may produce drawings in a realistic mode; emotional disturbance may be realised in an expressionist mode; absentmindedness in doodling mode. An attitude attuned to the necessity of clear communication may produce drawings in a highly conventional mode specified by British Standards or professional bodies.

    The functions of drawing Any code of communication has three main functions: to convey some aspect of our experience of the world; to both express our attitude, mood regarding our experience and to position the receiver in terms of mood and attitude; and thirdly to structure these two into a coherent, perceptible form. These first two functions may be labelled the experiential and the interpersonal. The third may be termed the compositional function.

    The parameters of social context; field, tenor, and mode are systematically related to the functions of the semiotic system. In fact, those meanings that constitute our understanding of any particular social situation are made visible through the selection and combination of elements within the semiotic system.
    Parameter of social context Function of drawing through which a social situation is realised
    Field (what is happening) Experiential function
    Tenor (who is taking part) Interpersonal function
    Mode (what part the semiotic code plays) Compositional function

    This is the basis of a model which may theorise how Drawings operate within a social context. Halliday (1973) elaborated upon this basis to provide a model which identified the systems of choices from which specific selections may be related to the functions of language in specific social contexts. Michael O'Toole (1990) was the first to demonstrate the power of Halliday's insights when they are applied to the analysis of painting. He offered a systemic-functional model of painting in which he substituted the labels Representational, Modal, and Compositional for Halliday's original terms Ideational, Interpersonal, and Textual describing the three functions of language. Later O'Toole (1994) demonstrated the versatility of Halliday's model by adapting it to theorise how sculpture and architecture may be made sense of within their social contexts. It is proposed that a systemic-functional model of the ways that Drawings may be produced and viewed would be immensely useful for studio discussion and drawing practice.

    A systemic-functional semiotic model for drawing

    Such a model is proposed in Figure 8 where the Experiential function of drawing relates to a drawing's ability to represent some aspect of our experience of reality; the Interpersonal function deals with how Drawings may exhibit the maker's attitude and may position the viewer in terms of attitude and mood. The Compositional function deals with the systems of selection of media, surfaces and marks that combine to make visible, to realise the other two functions in material form. The term levels of engagement refers to the hierarchical layering within which engagement with the Drawing is possible. The matrix of systems of choices emphasises the systemic nature of the model: these ranges of available choices do not simply allow meanings to be negotiated at any single functional level, but affect all functions as a whole. Social meanings to do with the Drawer's and viewer's experience within the field of the real world, and also the tenor of the relationship between Drawer and viewer are all realised simultaneously through the systems of Theme, Modality, Geometry, etc. Choices from these systems are realised as particular modes of drawing which are themselves realised as appropriate combinations of drawn marks upon a surface. In this chart, the varieties of geometries derived from the variety of ways of seeing, become some of the systems available to the Compositional function in order to realise - make visible - the Interpersonal and the Experimential functions. Also, Willats' denotation systems discussed earlier made up from selections and combinations of picture primitives, may be integrated within the systems of choices available. Combinations of selections from the available systems of compositional choices allow the Drawer to give visible material form to modulations of their physical, emotional and imaginative experiences of the world. Reciprocally, those combinations are modulated through and related to the viewer's own experiences of the world. Thus the proposed model may facilitate both a means of putting sense into Drawings, and making sense out of Drawings.

     

    LEVELS OF ENGAGEMENT . FUNCTIONS OF DRAWING

    COMPOSITIONAL . INTERPERSONAL . EXPERIENTIAL
    The Drawing as displayed in context MATRIX OF SYSTEMS OF CHOICES

    • Inter-textuality
    • Systems of Geometry: persp. orthographic, oblique, inverted persp., & topological
    • Primary or secondary geometries
    • Size and format of options, including framing devices
    • Location options
    • Systems of modality: Mood, attitude, positioning, viewer-centred, object-centred
    • Public/Private
    • Intimate/Monumental
    • Systems of theme: Physical, emotional, imaginative experiences. narrative, Historical genre
    • Realistic/Abstract á Interplay between objects, poses, events Sub-divisions of the Drawing's surface
    • Gestalt relationships: horizontal, vertical, diagonal axes
    • Proportional relationships
    • Tonal passages (aerial persp.)
    • Systems of gaze: Eye paths, focus points
    • Dynamic/Static
    • Calm/Excited
    • Balance/Unbalanced
    • Sub-themes:
    • Central/Supportive to narrative
    • Actions, poses, events, objects

    Combinations of drawn marks

    • Relative size of marks
    • Relative orientation of marks
    • Relative position of marks
    • Colour, tone and texture contrasts
    • Pattern
    • Rhythm
    • False attachments
    • Deep/shallow range of depth illusion
    • Foreground/Background range of positioning
    • Stability/Instability
    • Repetition
    • Scale
    • Distance between surfaces
    • Direction
    • Transparency/Opacity of surfaces
    • Atmospheric conditions
    • Quality of light
    • Time of day

    A drawn mark

    • Size relative to picture surface
    • Orientation relative to picture surface
    • Position relative to picture surface
    • Combination of surface texture and drawing medium
    • Picture-primitives
    • Phychological orientation
    • Range of textural meanings: wet/dry; hard/soft; matt/gloss
    • Denotation level of meaning
    • Spatial depth
    • Effects of gravity and other forces
    • Effects of light and water upon material surfaces
    • Scene primitives

    MATRIX OF SYSTEMS OF CHOICES

    Figure 8

     


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    Howard Riley MA (Royal College of Art)

    Faculty of Art and Design
    Swansea Institute of Higher Education Associate College of the University of Wales, UK

    Correspondence to:
    e-mail: howard.riley@sihe.ac.uk