Algorithms of the Mind. The Generative

Art of Drawing

Howard Riley, MA (Royal College of Art)

School of Art & Design, Swansea Institute of Higher Education,

Associate College of the University of Wales.

Abstract

Throughout the disciplines of art and design, interest in the possibilities of algorithmic methods for generating two- and three-dimensional visual forms grows apace. Evidence supporting this observation may be found in the increasingly diverse range of contributions to the Generative Art conferences.

Two research scenarios may be identified:

1 in which the generative process itself is the object of research,

2 in which the forms generated are the objects of research.

The question of what criteria may be appropriate to the evaluation of such research is addressed in this paper. Lincoln and Guba’s term “criteria of authenticity” is elaborated in a case study based on the author’s research into teaching drawing to fine are undergraduates.

Although the drawings produced are not computer-generated, it is argued that the concept of ‘algorithm’ as a set of rules for the generating of visual representations may be usefully applied to the mental ontological constructions, or ‘mind-set’, or the student. Such mind-sets affect the ways that drawings are constructed.

It is suggested that a teaching method which enables students to recognise their mental algorithms as cultural constructions, may also empower them to reconstruct those algorithms in order to generate visual representations previously unimagined.

Paradigms of research and criteria of assessment

Perhaps one of the most contentious issues currently exercising the community of researchers, supervisors and examiners in art and design is the nature of research within those fields.

Bruce Archer [1] categorised several types of research activity in the scientific tradition which, he maintains, are generally recognised and widely accepted. It may be useful to reiterate them here.

1. Fundamental research. Systematic inquiry directed towards the acquisition of new knowledge, without any particular useful application in view.

2. Strategic research. Systematic inquiry designed to fill gaps in fundamental research and/or to narrow the gap between fundamental research and possible useful applications.

3. Applied research. Systematic inquiry directed towards the acquisition, conversion or extension of knowledge for use in particular applications.

4. Action research. Systematic investigation through practical action calculated to devise or test new information, ideas, forms or procedures and to produce communicable knowledge.

5. Option research. Systematic inquiry directed towards the acquisition of information calculated to provide grounds for decision or action.

Archer observed that “the greatest volume of research in the Science tradition is categoriseable as Applied Research”. [2]

With these scientific paradigms established, he went on to discuss research in the Humanities tradition, and in particular, the arts. Research in the arts, he argued, consists in “finding new thing to know, or of identifying new ways of knowing them, or in refuting previous commentary on existing material”. [3]

Arguably, the fundamental difference between science and art, in general terms of their research attitudes, is that science is motivated to explain the world quantitatively whereas arts research is motivated to evaluate qualitatively. Of course, this stark distinction may become blurred in practice.

Archer maintained that science has become less reductionist in its attitudes and the humanities more empirical. He suggested this may be due to their mutual use of databases and information technology.

What is certain is the evidence of a current concern about whether arts practice may be deemed legitimate research. The present Rector of the Royal College of Art, Christopher Frayling, [4] was one of the first to articulate the circumstances under which artistic practice may be regarded as research.

He identified three specific trends within art and design research: research into art and design; research through art and design; and research for art and design. Research into art and design may include historical, theoretical, critical or aesthetic research. The methodologies for this category are firmly established in disciplines such as sociology, anthropology, philosophy, and are commonly applied to research in art and design history. Research through art and design, involves studio project work. This may be understood in terms of Archer’s category applied research, in which a systematic inquiry results in the acquisition or extension of knowledge for use in particular applications. Methodological precedents may be found in the disciplines of engineering and material science.

Frayling pointed out that methodological problems arise in research for art and design. Such research culminates in some form of artefact, and may be likened to Archer’s category of action research.

Few methodological models existed for this type of research at the time of his writing. However, recent collaborative work between Alex Seago, who directed the Research Methods programme at the Royal College of Art between 1991 and 1995, and Anthony Dunne, has begun to address this problem [5, 6]

An important question may be raised here: should researchers in departments, schools or faculties of art within the institutions of higher education adopt the research methodologies developed in their neighbouring disciplines, or should they devise alternative methodologies and criteria for assessing the quality of their research which reflect the distinctive differences in the nature of art?

This Section discusses quantitative methodologies and the four criteria by which their results are assessed: internal validity, or the degree to which findings correctly model the subject under study; external validity, or the degree to which findings may be generalised in other research settings; reliability, or the extent to which findings may be replicated; and objectivity, or the extent to which findings are free from any bias.

The implications involved in not adopting such criteria become apparent when it is realised that they are central to the established research culture of the universities responsible for validating research. In the face of this situation, one which Seago [7] has rather bellicosely dubbed “methodological intimidation”, research carried out in departments of art may be in danger of losing the quality of innovative iconoclasm which characterised the best of art school culture.

In an attempt to address this dilemma various paradigms of qualitative research are also discussed, and alternative sets of criteria for evaluating such research are considered.

All paradigms of research may be defined as constructions of belief systems involving ontological, epistemological and methodological assumptions.

Ontological assumptions deal with the form and nature of reality adopted; epistemological assumptions deal with the relationship between the researcher – the would-be knower – and what can be known; methodological assumptions deal with how the researcher actually approaches the research. All of these factors are tabled in Figure 1.

PARADIGMS OF RESEARCH

Positivism

Post-positivism

Critical theory

Constructionism

Ontology

Naïve realism.

Reality as an absolute understanding

Critical realism.

Reality only imperfectly understandable

Historical realism.

Reality shaped by social, political, economic values

Relativism.

Realities constructed specifically under local conditions.

Epistemology

Dualist/

Objectivist.

Findings deemed true

Modified dualist/

objectivist.

Findings deemed probably true.

Transactional/

subjectivist.

Value-mediated findings

Transactional/

Subjectivist.

Findings socially constructed

Methodology

Experimental/

manipulative.

Verification of hypotheses.

Quantitative methods.

Modified experimental. Falsification of hypotheses. May include some qualitative methods.

Dialogic/

Dialectical

Hermeneutical/

Dialectical

Figure (1) Paradigms of research

Qualitative research such as that demonstrated in this paper implies an emphasis on the study of processes and meanings that are not measured in terms of quantity. Qualitative research stresses the socially constructed nature of reality. It acknowledges the relationship that exists between the researcher and what is studied, and the situational constraints that shape inquiry.

The answers that qualitative research seeks are concerned with how social experience is made meaningful. This is in contrast to quantitative studies which emphasise the measurement of relationships between variables, not processes. In addition, quantitative research assumes the objectivity of the researcher within a value-free framework.

The traditional, positivist paradigm of research argued for four criteria with which to judge the worthiness of research. These were to be applied to any disciplined inquiry, whether qualitative or quantitative in nature. To recap, they were internal validity, the degree to which findings correctly map the phenomenon in question; external validity, the degree to which findings can be generalised to other settings; reliability, the extent to which findings may be replicated by another inquirer; and objectivity, the extent to which findings are free from bias.

A second paradigm, which may be called post-positivist, argues that a set of criteria unique to qualitative research needs to be developed. This is because it represents an alternative paradigm to quantitative research. Martyn Hammersley [8] suggested post-positivist criteria, amongst which were the following:

Assessing research in terms of its ability:

1. to generate generic/formal theory

2. to be empirically grounded (and scientifically credible)

3. to produce findings that can be generalised or transferred to other settings

4. to be internally reflexive in terms of taking account of the effects of the researcher and the research strategy on the findings that have been produced

A third paradigm of research activity, a postmodernist one, argues that “the character of qualitative research implies that there can be no criteria for judging its products.” [9]

Advocates of a fourth, post-structuralist paradigm, argue that a new set of criteria, not associated with positivist and post-positivist traditions, needs to be constructed. Post-modernist and post-structuralist paradigms may be combined in various proportions under the generalised label of a paradigm of critical theory. This term is one that Jürgens Habermas [10] used in his typology of approaches to research:

1. The empirical-analytic sciences, comprising natural science but also including attempts to apply natural science methods to the study of human behaviour.

2. The historical-hermeneutical sciences, consisting of the discipline of history and those parts of social science that are guided by an interpretative orientation.

3. Critical theory is exemplified in the work of Marx and the Frankfurt School. It is based on the assumption that by providing an analysis of a social system, any oppressive ideologies may be revealed, and members of such oppressed groups may thus be enlightened.

Egon Guba and Yvonna Lincoln [11] favour a paradigm called “constructivism.” In order to avoid possible confusion with the Russian art and design movement of the same name, this term has been replaced in this paper by a widely accepted alternative constructionism.

Two sets of criteria for judging the quality of research within a constructionist paradigm have been proposed. Firstly, the four proposed by Guba [12] and Lincoln & Guba [13] which parallel the four positivist criteria: They are the four so-called trustworthy criteria of credibility, similar to the positivist criterion of internal validity; transferability, similar to the positivist criterion of external validity; dependability, paralleling reliability; and confirmability, paralleling objectivity.

Secondly, the set of five called by Guba & Lincoln [14] the criteria of authenticity: fairness, that is, a demonstrable openness between researcher and subjects; ontological authenticity, or an indication of expansion in the range of personal ontological constructions; educative authenticity, or an indication of improved understanding of the ontological constructions of others; catalytic authenticity, an indication of the degree to which the individual or group has been stimulated to action; and lastly tactical authenticity, an indicator of how the individual or group has been empowered to act beyond the confines of the research parameters. These five will be elaborated shortly, when it will be argued that they appear to be particularly relevant and appropriate for the assessment of changes in attitudes of students exposed to a new teaching programme.

The paradigm of research adopted for the research described in this paper is a constructionist one, with a relativist ontology, which accepts that realities are socially constructed under specific local conditions. Although they may be shared across groups of individuals or even whole cultures, those constructions are deemed to be not more true or less true than one another, but more or less informed and sophisticated. Constructions of reality are deemed to be alterable. It is this ontological position that differentiates constructionism from other paradigms.

The adopted paradigm’s epistemology may be defined as subjectivist, in the sense that the researcher has been interactively linked to the subject under investigation.

Having assumed the above ontological and epistemological positions, where the variable nature of social constructions may be elicited through interaction between researcher and (in this case) students, a methodology based on hermeneutics and dialectics was considered suitable. Varying social constructions, made visible in the form of Drawings, are discussed and interpreted using the methodological tool of systemic-functional semiotics illustrated in Figure 2.

LEVELS OF		FUNCTIONS OF DRAWING
ENGAGEMENT		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 · Size and format · 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 · Interplay between objects, poses, events
Sub-divisions of the Drawing’s surface		· Secondary geometry · 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	· Primary geometry · Actions, poses, events, objects · Awareness of distal and proximal perceptual values
Combinations of drawn marks		· Relative size of marks · Relative orientation of marks · Relative position of marks · Colour, tone and texture contrast – bouindaries · Pattern · Rhythm · False attachments	· Deep/shallow range of depth illusion · Foreground/Background range of positioning · Stability/Instability · Scale · Heavy/light	· Distance between surfaces · Edges: occlusion of one surface ny another · Direction · Transparency/Opacity of surfaces · Atmospheric conditions · Quality of light · Time of day · Awareness of haptic perceptual values · Weight
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	· Psychological 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 4.32

The final objective of the research is to demonstrate how the proposed teaching programme laid out in Section 5 may expand students’ awareness of cross-cultural visual constructions, and their capabilities of producing more varied, more informed constructions in the form of Drawings. To this end, the criteria of authenticity proposed by Guba and Lincoln are adopted.

The authenticity criteria for assessing research within a constructionist paradigm.

Fairness refers to the degree of integrity with which different points of view and constructions of reality along with their underlying ideological values are elicited and recognised as valid throughout the evaluation process.

In the specific context of the research described in this paper, all information was elicited with the complete agreement and non-coerced participation of the student groups. All stages of the process of gathering data about student views were conducted in full view of the student groups. All stages of the research were explained to students, and all data were accessible to students at all times.

Ontological authenticity refers to the extent to which an individual’s own internal, emic constructions are expanded, matured, and elaborated to a more sophisticated level of use.

Ontological authenticity is “improvement in the individual’s (or group’s) conscious experiencing of the world”. [15] Guba & Lincoln [16] identify two techniques for demonstrating ontological authenticity. Both are applied in this research.

1. Testimony of participating students. When students can attest to the fact that they recognise a broader range of approaches to drawing as being valid for describing a broader range of responses to a broader range of constructions of reality, then that is deemed to be evidence of ontological authenticity. When their own Drawings can be shown to illustrate such recognition, that too is regarded as material evidence.

2. A questionnaire in the form of a Likert Set completed by student groups before and after the delivery of the new teaching programme will be collated and analysed so as to reveal the changes in the student group attitudes to, and understanding of, ontological constructions.

Educative authenticity refers to the extent to which an individual’s understanding of and appreciation for the constructions of others outside their own group are enhanced.

It is not enough that the actors in some contexts achieve, individually, more sophisticated or mature constructions, or those that are more ontologically authentic. It is also essential that they come to appreciate (apprehend, discern, understand) – not necessarily like or agree with – the constructions that are made by others and to understand how those constructions are rooted in the different values systems of those others. [17]

Two techniques have been identified by Guba & Lincoln [18] for establishing that educative authenticity has been achieved. Both are applied in this research:

1. Testimony of participating students. When students can attest to the fact that they understand the constructions of others different from themselves, then that is deemed to be evidence of educative authenticity. In this particular context, students’ Drawings may well provide material evidence of educative authenticity.

2. Questionnaires in the form of Likert sets completed by student groups will be used before and after the delivery of the new teaching programme. These are collated and analysed to reveal any changes in the student groups’ understanding and appreciation of the constructions of others.

Catalytic authenticity. Guba & Lincoln [18] define this criterion as “the extent to which action is stimulated and facilitated by the evaluation process”. In this particular research context, the students’ Drawings will be shown as evidence of such action.

Tactical authenticity refers to the degree to which research participants are empowered to act outside the confines of the new teaching programme itself. Tactical authenticity may be demonstrated by evidence of the student’s own expanded recognition and understanding of personal constructions and the constructions of others appearing in work produced outside the confines of the new teaching programme itself.

Evaluation of students’ Drawings produced in and around the new teaching programme

The purpose of evaluating students’ Drawings is:

1. to demonstrate the efficacy of the new teaching programme in empowering students to produce work which indicates an increased awareness of the range of their ontological constructs, and those of others. Such indications are offered as evidence of the ontological, educative, and catalytical authenticity of the research project.

2. to demonstrate the efficacy of the new teaching programme in empowering students to discover new directions of visual research, and to sustain their visual inquisitiveness and capacity for production of new work over a period of time following the delivery of the new teaching programme. Such production is offered as evidence of the catalytic and tactical authenticity of the research project.

3. to demonstrate the efficacy of the systemic-functional semiotic model of drawing (Figure 2) as a means of devising exercises designed to focus attention upon specific drawing issues, and as a means of evaluating Drawings.

Drawings from the ‘Visual Studies Workshop’

In their first life-class, the majority of students drew an outline of the figure. Very few, if any, marks were made outside this figure-shape. Generally, tone was added within the figure shape after its completion, and was referred to as ‘shading’.

With the Chart as reference, exercises were devised at the level of engagement of Combinations of drawn marks in order to increase student awareness of the greater possibilities of line, how it may represent visual phenomena, and how the primary geometry of the figure in space may be transformed to Drawing through an expanded range of combinations of drawn marks.

Students were encouraged to replace line with a concept of contrast-boundary. The terms edge and occlusion of surfaces were discussed.

Figure 3 illustrates the first indication of this expanded awareness. Edges in the primary geometry are beginning to be treated as boundaries between contrasting tones in the secondary geometry of the Drawing, particularly at the shoulders, the right knee and left wrist.

Figure 4 illustrates a full awareness of how tonal contrast may appear to fluctuate along an edge; dark figure/light background: light figure/dark background.

At the level of engagement Sub-divisions of the Drawing’s surface, exercises were devised to explore the primary geometry of the model’s pose in terms of Gestalt relationships between axes and shapes of tone may afford the viewer eye-paths and focal points, a sense of depth and scale, and a sense of stability or dynamism.

Evidence of students’ increased awareness of how these early exercises may be combined to produce Drawings which engage the viewer is offered in Figures 5 and 6. These drawings allow meanings to be made about the position of the figure in space, its mass, the distance between surfaces, the quality and direction of the light, the balance and stability of the pose.

In contrast, Figure 7 provides evidence of an awareness that the figure in space may be construed simply as a pattern of salient edges. No information about mass or illumination, but an opportunity to focus upon the proximal values, the linear pattern of the scene. An ability to construe line as something other than outline is evidence of the student’s expanding ontological constructions.

Drawings from the ‘Plantasia’ project

The Plantasia project offered students an opportunity to increase their awareness of ontological constructs to do with ways of seeing. Three levels of perception were introduced:

1. the haptic level, or the noticing of textural variation and detail in the scene.

2. the distal level, or the noticing of information about spatial depth in the scene.

3. the proximal level, referring to the noticing of pattern across the visual field.

These three levels of visual information had been mentioned throughout the previous Visual Studies Workshop, so that students were familiar with the terms. However, during the Plantasia project these levels were discussed as potential means of organising visual information in compositions that may both communicate the experience of seeing and position the viewer in terms of attitude and mood. The three functions of drawing identified in Figure 2 were introduced in a talk illustrated with slides.

Figure 8 illustrates two stages in a sequence of studies which draw attention to the proximal values within the observed subject-matter of cacti, as well as indicating their textural contrast between smooth and spikey. The top drawing sets up a reversible figure, in which the viewer’s reading of depth is teased by the S-shaped contrast-boundary separating light from dark, and also by the relative size of marks representing the bases of the spikes. Figures 9 and 10 illustrate two of a series of finished large-scale drawings in which the viewer is drawn into the frame by a series of eye-paths which run along the edges or spines of leaves, thus drawing attention to their differences. In particular, the viewer is invited to dwell on the textural smoothness and sharpness of edge, qualities which result from the student’s engagement at the level of drawn mark, and experimentation with various combinations of paper texture and drawing medium. Here is evidence of the student’s increasing ability to communicate the effects of light upon material surfaces. Such ability, may be developed from a greater awareness of the three levels of perception and the three functions of communication.

Figure 11 affords the viewer an opportunity to contemplate all three levels of perceptual information in one Drawing. At the level of engagement of A drawn mark, the bottom third of the Drawing provides evidence of the variety of textures present in the subject-matter, and of how those textural qualities appear (or rather disappear) as viewing-distance increases. Further information about spatial depth in the scene is available at the level of engagement Combination of drawn marks. For example, depth is indicated by the use of contrast boundaries representing the play of light at occluding edges within the scene. Particularly useful as a means of indicating spatial depth is the gradual reduction of contrast from foreground (i.e. the bottom third of the Drawing) to background (i.e. the top third of the Drawing). A reduction in sharpness of contrast boundaries from foreground to background would have further emphasised the distal values of the scene.

However, the consistency of sharpness of contrast-boundaries does serve a purpose. The student’s experience of the proximal values, or the overall patterns within the scene, is shared when the viewer engages with the Drawing at the level of Sub-divisions of the Drawing’s surface.

Pattern is produced through the repetition of proportional relationships: The similarity of size and shape of the leaf fronds; the similarity in sharpness of the contrast-boundaries, generating a rhythmic, curved eye-path across the Drawing’s surface; and the repetition of the light/dark alternation between frond-shape and background space all contribute to the communication of pattern.

Figure 12 is presented as evidence of the catalytic and tactical authenticity of the research project. This Drawing is generated from a series of studies carried out during the Plantasia project. It displays a high level of intelligence of seeing, affording the viewer ample information about textural qualities of the various plants represented, as well as a strong illusion of depth.

The Golden Section proportion of the vertical and horizontal axes which sub-divide the Drawing’s surface, and the smoothness of the eye-line from the focal point of the intersection of those axes, the Bird of Paradise flower at left foreground, though to the complexity of forms at night background, may be read by the viewer as metaphor for the complex harmonies to be found in the structures of natural forms.

Drawings from the ‘Seeing and Believing’ project

The Seeing and Believing project afforded students an opportunity to explore the essences of reality, those ontological constructions of space-time relationships. A variety of realisms was discussed, and the ways in which those realities have been expressed through the drawing conventions of different cultures in different periods were studied. Students were encouraged either to analyse and if necessary adapt an existing convention from the range, or invent from first-principles their own means of visually representing a belief system to do with the space-time relationship.

A world in which forces are codified and made visible is displayed in Figure 13. At the level of engagement The Drawing as displayed in context, a framing device has been invented, with a fragility susceptible to the slightest force of air movement. Here, the Drawing (i.e. the combination of twenty eight parts) moves in response to the viewer’s movement, emphasising the experience of interplay between viewer and viewed. At the level of engagement Sub-divisions of the Drawing’s Surface, the twenty eight sub-sections are arranged in a regular grid which flutters in response to air movement. In this way the viewer is confronted with a work that is both dynamic and static, both calm and excited, both balanced and unbalanced. At the level of engagement A drawn mark, each of the twenty eight components bears a mark, visible indications of a variety of forces which were applied to the paper: compression, tension, torsion and shear. Here is evidence of the student’s ability to move away from conventional representations of the visible world, towards a fresh representation of the forces which form the visible world. Here too is evidence of the efficacy of the new teaching programme in empowering a student to discover new directions of visual research. It is presented here in support of the ontological, educative and catalytic authenticity of the research project.

In contrast to the fragility of the work illustrated in Figure 13 is the robust solidity of a large-scale (six feet square) heavy gauge drawing paper completely rendered with graphite stick. (Figure 14). Engaging with this work at the level of A drawn mark, each hand-made scribble of the graphite is standardised in terms of size and orientation, producing a grain structure across the surface. The rough surface texture of the paper is compressed by each mark to produce a polished sheen of graphite. The viewer is able to interact visually with this surface, since any movement of viewing position sets off a shimmer of surface reflection and illusions of spatial depth.

Upon this shimmering, deep surface, four totemic columns have been stamped from a wooden plank routed with patterns of linear marks.

The printing ink mixed with sand produces a completely matt finish in stark contrast to the graphite’s sheen, with the result that the irregular patterns of linear marks appear to dance upon the matt surface.

The liveliness of the light, small-scale irregular contrasts with the large-scale, heavy, regular rhythm of the four columns spaced evenly across the whole Drawing. Engaging with the Drawing as a whole, the viewer may discern another contrast, that between the intimacy of each hand-cut mark and the (relative) monumentality of scale of the overall work. This Drawing on display becomes a very public statement about a developing private code. A code which may not be fully systematised, but which recognises its need to articulate oppositions and one which invites viewers to ponder upon the arbitrariness of their own cultural conventions.

Drawings from the ‘Geometries of Vision’ project.

The Geometries of Vision project afforded students the opportunity to relate the concepts of primary geometry and secondary geometry to those of viewer- and object-centred representations through their drawing practice.

Figure 15 illustrates student inquiry into the assumption implicit in perspective projection, that of the fixed, single point of viewing. Here is an attempt to break out from such ontological constraints, and to invent a way of representing the information in the light received at both eyes. Focusing upon the wooden framework with each eye in turn, but paying attention to the primary geometry of the scene, the student shares the experience of both eyes in the one Drawing. The primary geometry of the scene is transformed into a secondary geometry rarely explored.

The Drawing illustrated in Figure 16 evolved from the student’s study of projective geometry systems in common usage. An awareness that all of those assumed a flat plane of projection stimulated inquiry into the possibility of projecting onto a non-flat plane. Discussion around the notion of a ‘cone of vision’ developed into the idea of inventing a system for geometrically projecting what was noticed in the cone of vision onto a cone of projection. A paper cone was duly constructed and arranged at eye level, apex pointing to eye. With one eye closed, so as to flatten the cone perceptually, the student proceeded to mark the cone at appropriate distances from the eye, the marks representing the salient scene primitives (corners and edges). When the paper cone (or pyramid, to be precise) was laid out as a surface development, an original projection system was revealed. Here is evidence of the ontological and educative authenticity of the research project.

Figures 17 and 18 illustrate two students’ efforts to explore the inter-relationships between primary geometry, secondary geometry, and viewer-centred and object-centred representations. At the level of engagement of Sub-divisions of the Drawing’s surface, under the column headed Compositional function, Figure 17 attempts to employ a secondary geometry constructed from the combination of a viewer-centred representation (that of the figure itself) and several views of the wooden frame which made up the subject-matter. Such multiple views of a single object have the effect of increasing our information of the object as if we were able to move forwards around it. Such object-centred representations combined with a viewer-centred representation of the figure produces a Drawing in which the viewer’s position is ambiguous.

Figure 18 attempts a further complication. Here the figure itself is represented as mirrored, and the wooden frame appears in front of the figure and behind the figure simultaneously, as well as forming the geometry of the space within which the figure exists. The effect upon the viewer is that of a shattered image, dynamic and excited. This exercise stimulated the student to further explore the possibilities of combining viewer- and object-centred representations in a Drawing.

The series of Drawings, Figure 19, a, b, c and d illustrates a systematic approach to the exploration of a possible transition from a viewer-centred representation to an object-centred one. Figure 19 was drawn from a (relatively) fixed position and indicates the student’s grasp of the transformation process from primary geometry to a viewer-centred secondary geometry. As the series progresses (19 a, b, c & d) lines and contrast-boundaries between tones representing the salient edges in the scene become interlocked, producing a complex web of compositional axes. This pictorial device enables the viewer to see relationships between those edges defining the space which are not available from a fixed viewing position. As more information about spatial relationships is added, less is revealed of the viewer-centred representation of the figure within the space. Finally, in Figure 19d, the figure is transformed through geometry into pure organic form.

The research is ongoing. Critical comment is welcome.

References

1.	Archer, B. 1995	The nature of research. Co-design 3 6-13.
2.	ibid. p6
3.	ibid. p9
4.	Frayling, C. 1994	Research in art and design. RCA research papers 1(1), Royal College of Art, London.
5.	Seago, A. & Dunne, A. 1999	New methodologies in art and design research: The object as discourse Design issues 15(2) 11-17
6.	Seago. A. 1995	Research methods for MPhil and PhD students in art and design: Contrasts and conflicts. RCA research papers 1(3), Royal College of Art, London.
7.	Seago & Dunne 1999 p12
8.	Hammersley, M. 1992	What’s wrong with ethnography? In Methodological explorations, Routledge, London.
9.	ibid. p58
10.	Habermas, J. 1987	Knowledge and human interest, Polity, London.
11.	Guba, E. G. & Lincoln. Y. S. 1994	Competing paradigms in qualitative research. In Denzin, N. K. & Lincoln, Y. S. (eds) Handbook of qualitative research, Sage, Thousand Oaks, CA.
12.	Guba, E. G. 1981	Criteria for assessing the trustworthiness of naturalistic inquiries. Educational communication and technology journal 29 75092
13.	Lincoln, Y. S., & Guba, E. G. 1985	Naturalistic inquiry, Sage, Beverley Hills, CA.
14.	Guba, E. G. & Lincoln, Y. S. 1989	Fourth generation evaluation, Sage, Newbury Park, CA.
15.	Lincoln, Y. S. & Guba, E. G. 1986	But is it rigorous? Trustworthiness and authenticity in naturalistic evaluation. In Williams, D. D. (ed.) Naturalistic evaluation, Jossey-Bass, San Francisco, CA.
16.	Guba. E. G. & Lincoln. Y. S. 1989 p248
17.	Lincoln, Y. S. & Guba, E. G. 1986 p81
18.	Guba, E. G. & Lincoln, Y. S. 1989 p249