3.1 Introduction
The performance-studies paradigm outlined in Chapter 2 precedes the case studies (Chapters 5 and 6) and analyses (Chapter 7) that form the bulk of this study’s findings; this chapter explores two bodies of theory which, by contrast, emerged alongside and after those findings. As practice- research progressed, Complexity Thinking and embodiment theory arose as fields that could usefully enrich inductive findings. Since they are themselves largely to do with practice – in fact, they are often presented in the context of practice-research – they can engage in discourse with singers’ responses in the case studies of Chapters 5 and 6. What arises from this ‘conversation’ is an understanding of the performance of choral aleatorism that is at once immanent to the experience of singers as investigated below and open to comparison with other phenomena that may be described as Complex and embodied. This chapter lays out important tenets of Complexity Thinking and notions of embodiment, which all serve to point towards practical considerations.
3.2 Complexity Thinking
The generally constructivist bent of this project is carried into practice with the help of Complexity Thinking: a field of thought and study that helps reconcile the different levels on which constructions occur (recalling the main streams of constructivism represented by Piaget and Vygotsky, discussed previously in the Introduction 1.4), and which can help steer findings towards practical outcomes. In essence, Complexity Thinking deals with the unpredictable outcomes of a system born of the interaction of its component parts. Its incarnation in educationalist writing accords with my inductive orientation by enfolding previous studies of practice and group behaviour (most often in the classroom or school) into this new understanding of the unpredictable
outcomes of choral aleatorism. It also offers a useful framework in that it seeks to elucidate performer agency – the parts within a system – without presupposing the nature of that agency’s enactment or outcome.
It is worth tracking in detail how Complexity Thinking may answer questions that the constructivist view cannot. Mordechai Gordon faults education-orientated constructivism for overlooking the fact that ‘knowledge construction involves an integration of individual cognition processes and social processes’.1 The constructive acts of individuals within an ensemble, and of that ensemble as a whole, are clearly mutually effective. Brent Davis and Dennis Sumara offer a fuller objection to constructivist-based activity than Gordon’s, writing that ‘these perspectives were never intended as sources of practical advice’;2 they are merely descriptive. Piaget- and Vygotsky-inspired notions of knowledge-construction can only ‘operate more as critiques of any deliberate, institutionalised attempt to affect individual knowing or collective knowledge’.3 When teachers – or conductors – attempt to enact constructivist learning, they typically only reinforce behaviourist or cognitivist training.4 The conditioning of performers’ behaviour (behaviourism) and the systemisation of pedagogy (cognitivism) are inevitable, even valuable, aspects of musical training – yet the view held here is that music-making also involves construction. Two objectives emerge in promoting a practice that facilitates and even expands the constructions already occurring in aleatorism, then: first, bringing singers’ constructions into conversation with helpful additional discourses that might begin to render them into practice; and second, orientating such practice towards the simultaneously individual and grouped nature of aleatory construction.
1 Mordechai Gordon, ‘Toward a Pragmatic Discourse on Constructivism: Reflections on Lessons from Practice’,
Educational Studies, 45 (2009), 48.
2 Davis and Sumara, ‘Constructivist Discourses’, 417. 3 Davis and Sumara, ‘Constructivist Discourses’, 418. 4 Davis and Sumara, ‘Constructivist Discourses’, 418.
Gordon offers John Dewey’s idea of pragmatic constructivism to encourage constructions practically. He cites Dewey’s belief that ‘genuine knowledge comes neither by thinking about something abstractly nor by acting uncritically, but rather by integrating thinking and doing, by getting the mind to reflect on the act’.5 Knowledge, then, can be constructed through critically engaged rehearsal. This notion might vindicate the involvement of singers in the research process and encourage a certain rehearsal tactic, but still falls short of a complete, useable paradigm. Davis and Sumara therefore recommend Complexity for its ‘emphasis on the pragmatics of effecting transformations in complex situations’.6 Not only does Complexity Thinking reconcile individual and social knowledge-construction,7 it also provides a realm of discourse in which one might proactively ‘incorporate constructivist insights into educational discourses’.8 Concepts from Complexity Science may be usefully co-opted to this end without pretending to any comprehensive presentation of a vast field. The adoption of specific, circumscribed ideas is limited by the scope of this project and by a cautious need not to apply this thinking to aspects of the choral situation which are not truly complex.
Built on the work of physical chemist Ilya Prigogine (1917–2003), Complexity Science derives from the idea that phenomena emerge out of the interactions of agents in a way that cannot be deterministically predicted.9 It is usefully adapted to educationalist research,10 and it holds comparable appeal for understanding group musical practice, especially when a work is as actively constructed as in aleatorism. It can act as an opening into understanding the constructions
5 Gordon, ‘Toward a Pragmatic Discourses’, 49. 6 Davis and Sumara, ‘Constructivist Discourses’, 424–5. 7 Davis and Sumara, ‘Constructivist Discourses’, 426–7. 8 Davis and Sumara, ‘Constructivist Discourses’, 427.
9 Complexity contrasts from ‘hyper-complication’, or high levels of mechanistic – and therefore still predictable –
complication. Michel Alhadeff-Jones, ‘Three Generations of Complexity Theories: Nuances and Ambiguities’, in Mark Mason (ed.), Complexity Theory and the Philosophy of Education (Chichester: John Wiley and Sons, 2008), 73.
occurring during aleatorism, rather than as a deductive descriptor. Indeed, Lesley Kuhn prefers the term ‘Complexity Thinking’ to ‘Complexity Theory’ and considers it a ‘style of thinking or a paradigmatic approach’11 rather than a testable assertion. It is for this reason that I use her preferred designation. As a ‘theory’, it runs the risk of imposing the kind of metanarrative that might run afoul of aleatorism’s general sense of postmodern plurality;12 it is more helpfully enlisted as an orientation that ‘does not rise over, but arises among other discourses’.13 It therefore supports the inductive mode used here as it affords tools to guide thinking rather than ‘imposing verdicts’.14
Complex systems are not mechanised – not borne of the stable responses of their agents. They are described as indeterminate and resemble more closely clouds than ‘finite and predictable’ clocks.15 They exist in a state of imbalance, which yields change and adaptability; the inherent self-organisation of the system, born of spontaneous interactions of ‘autonomous agents’, is what brings change.16 This change is considered ‘emergent’, 17 meaning that its source is ‘within’ the system and it derives from that system’s self-organised behaviour. Thus far, the performance of indeterminacy might reasonably be so described.
Less intuitively obvious is the connection between aleatorism and the ‘autocatalytic’ nature of emergent change.18 ‘Autocatalytic’ describes a system which is self-defining or driven by the interaction of its parts. Change within that system emerges from such interactions as the emergent
11 Lesley Kuhn, ‘Complexity and Educational Research: A Critical Reflection’, in Mark Mason (ed.), Complexity
Theory and the Philosophy of Education (Chichester: John Wiley and Sons, 2008), 170.
12 Davis and Sumara, Complexity and Education, 7 and 35.
13 Davis and Sumara, Complexity and Education, 8. I will not confront here Davis and Sumara’s problematising of
‘intersubjectivity’ in favour of ‘interobjectivity’, which seems to me to miss intersubjectivity’s notion that even if reality is subjectively constructed, it can still qualify as ‘a grander, more-than-human’ context, and which does not provide a thorough epistemic answer to the experience of reality.
14 Kuhn, ‘Complexity and Educational Research’, 173, citing Morin (from 2001), 25.
15 Mike Radford, ‘Complexity and Truth in Educational Research’, in Mark Mason (ed.), Complexity Theory and the
Philosophy of Education (Chichester: John Wiley and Sons, 2008), 143–4.
16 Davis and Sumara, Complexity and Education, xi. 17 Davis and Sumara, Complexity and Education, xi.
function of autocatalysis. In a situation with clear leaders (such as a conductor) and authors (such as a composer) this autocatalytic emergence is arguably less palpable. Yet autocatalysis might still occur within the ensemble as a whole, especially between singers. Autocatalytic scenarios are those in which there is a self-defining system which is nevertheless not systematised. They capitalise on ‘collective intelligence’, but avoid the dangers of ‘mob mentality’ by eschewing the hegemony of consensus.19 The actions of agents both mutually influence each other20 and feed into group behaviour which itself influences individuals’ behaviour21 – reciprocity operating on multiple levels. In a choral setting, leadership is both imposed (by the conductor, for instance) and emergent. Singers in a choir have agency in creating autocatalytic change. But, for Davis and Sumara, true learning emerges at multiple levels which might interact in a Complex way.22 Citing Vygotsky, they consider the site of learning is ‘the individual-and-environment as [a] dynamic unity’.23 The conclusion that even authority is just one layer of a larger complex system of learning is no less cogent for seeming facile; the emergent nature of power and leadership binds it to the complex interactions within a system. Just as it deals with authority, Complexity pertains to authorship. Its attention to the site of creative drive in performance reveals the importance of shared complicity: ‘[J]ust as learning is distributed, so is authorship’.24 In an autocatalytic situation of choral performance, both leadership and creativity are impelled from multiple levels.
Shared creativity – authorship, in a deliberate sense – in aleatorism is usefully addressed in several particulars of Complexity Thinking. Those particulars are: (i) emergence, the idea that phenomena emerge non-deterministically ‘from interactions within and among self-organising and
19 Davis and Sumara, Complexity and Education, 84. 20 Davis and Sumara, Complexity and Education, 11.
21 Cohen, Manion, and Morrison, Research Methods in Education, 28. 22 Davis and Sumara, Complexity and Education, 85.
23 Davis and Sumara, Complexity and Education, 119. 24 Davis and Sumara, Complexity and Education 145.
adaptive systems’;25 (ii) the importance of proximity and agency to those interactions; and (iii) the nested situation of complex systems within complex systems.
i. Emergence
Emergent outcomes cannot be predicted.26 Complexity Thinking, along with its cousin chaos theory, argues
against the linear, deterministic, patterned, universalisable, stable, atomised, modernistic, objective, mechanist, controlled, closed systems of law-like behaviour which may be operating in the laboratory but which do not operate in the social world of education […].27
Conductors’ impositions upon singers, for instance, are disrupted by the disorder of aleatorism. Michel Alhadeff-Jones writes that the components of a complex situation are ordered, in that they are closely linked and follow an internal logic, but disordered because they ‘evolve and vary according to some forms of inequality, agitation, turbulence, chance encounter, rupture, catastrophe, fluctuation, instability, disequilibrium, diffusion, dispersion, etc.’.28 Yet the performance of aleatorism is concerned with permitting patterns, just as studies (including this one) are concerned with discerning those patterns.29 A pattern might gain enough momentum
25 James Horn, ‘Human Research and Complexity Theory,’ in Mark Mason (ed.), Complexity Theory and the
Philosophy of Education (Chichester: John Wiley and Sons, 2008), 125, citing Barlow and Waldrop (from 1994); Richardson (from 2005).
26 Lindsay Hetherington, ‘Complexity Thinking and Methodology: The Potential of ‘Complex Case Study’ for
Educational Research’, Complicity: An International Journal of Complexity and Education, 10.1/2 (2013), 71–85 <https://ejournals.library.ualberta.ca/index.php/complicity/article/view/20401/15672 > [accessed 28 Jan 2016], 73.
27 Cohen, Manion, and Morrison, Research Methods in Education, 29
28 Michel Alhadeff-Jones, ‘Complexity, Methodology and Method: Crafting a Critical Process of Research’,
Complicity: An International Journal of Complexity and Education, 10.1/2 (2012), 19–44 <https://ejournals.library.ualberta.ca/index.php/complicity/article/view/20398/15669> [accessed 28 Jan 2016], 29.
among agents to become ‘locked in’, but this eventuality cannot be predicted.30 Therefore, a conductor’s impositions can only ever be catalytic perturbations – but even those cannot be said to determine their own outcomes.31 Outcomes and patterns are the products of interactions within the system.
ii. Proximity
Those interactions are most fruitful when part of a network of ‘short-range relationships’, in which information is ‘exchanged among close neighbours’.32 Feedback occurs between these neighbours; positive feedback ‘brings increasing returns’ and ‘amplifies small changes’.33 Given the reciprocal nature of interaction in complex systems, a choir can feasibly create a positive feedback loop whereby emergent musical patterns gain momentum. These connections occur at all levels and are contingent on commonalities among members beyond physical proximity.34 Connectedness in a choral situation might take place between those of similar voice parts, perceptually bound by the acoustics of tessitura and timbre, or those whom the score assigns similar processes at similar times.
Proximity, in its various forms, might be mapped. Davis and Sumara summarise varieties of ‘network architectures’ of complex systems according to how information is transmitted through ‘neighbour interactions’.35 Different architectures have different levels of centralisation: high centralisation shares information slowly, via a central hub, whereas denser webs with a mixture of strong and weak connections between neighbours allow for richer, if still not especially
30 Mark Mason, ‘Complexity Theory and the Philosophy of Education’, in Mark Mason (ed.), Complexity Theory and
the Philosophy of Education (Chichester: John Wiley and Sons, 2008), 2.
31 Davis and Sumara, Complexity and Education, 99–100. 32 Davis and Sumara, Complexity and Education, xi.
33 Cohen, Manion, and Morrison, Research Methods in Education, 29. 34 Cohen, Manion, and Morrison, Research Methods in Education, 29. 35 Davis and Sumara, Complexity and Education, 142.
rapid, information transmittal.36 Additional weak links – between singers, or between a singer’s individual process and collective acts of construction – can imbue the system with strength from redundancy.37 This richness is reinforced further by internal diversity and specialisation:38 ‘Specialisation entails a balancing of individual obsession and collective necessity – that is, a balancing of internal diversity and internal redundancy’.39
iii. Nesting
Connections and reciprocity also occur between multiple strata in ‘nested structures’, where ‘complex unities are often composed of and often comprise other unities that might be properly identified as complex’.40 In essence, a complex system might contain, and be contained by, other complex systems, with which it interacts. Complex systems are closed, contained systems, but they openly and ‘continuously exchange matter and energy with their surroundings’.41 Understanding how these interactions occur, and how nested systems generally impact and bound each other, is fundamental to understanding complex systems,42 including how performers’ individual processes enfold themselves into the ensemble’s process of performing an aleatory piece, or into a larger situational or historical context.
36 Davis and Sumara, Complexity and Education, 52.
37 Davis and Sumara, Complexity and Education, 52. They also deal with ‘self-similar’ fractals, in which relationship
patterns on all levels are similar, according to a fractal pattern. This idea, though interesting on a larger scale, does not readily apply to choral rehearsals (43–4, 51–2).
38 Davis and Sumara, Complexity and Education, 137–8. 39 Davis and Sumara, Complexity and Education, 140. 40 Davis and Sumara, Complexity and Education, xi. 41 Davis and Sumara, Complexity and Education, xi.
42 Jay L. Lemke and Nora H. Sabelli, ‘Complex Systems and Educational Change: Towards a New Research Agenda’,
in Mark Mason (ed.), Complexity Theory and the Philosophy of Education (Chichester: John Wiley and Sons, 2008), 115. Also Davis and Sumara, Complexity and Education, xi.
It is worth discussing briefly the ways in which Complexity Thinking may enrich or condition the methodology of this iterative study. (Notably, iterative study is valued in Complexity Thinking.43) Just as Complexity Thinking suggests that changes must be brought about on numerous levels, it also corroborates the need for a holistic, multi-level study of phenomena.44 As such, it ‘suggests the need for case study methodology, narratives, action research and participatory forms of research, premised in many ways on interactionist, qualitative accounts’.45 The field’s suggestion that the ‘whole’ situation of aleatory performance should be studied is practically impossible and ignores the (presumably Complexity-compliant) problematisation of trying to delineate a discrete ‘whole’. But, even beyond the reasonable multi-methodological implications of the above suggestions, Complexity Thinking advocates an expanded pool of participants in aleatorism, as well as a thorough investigation of ‘multiple causality, multiple perspectives and multiple effects’.46
Complex situations arguably require equally complex representations, resulting in a ‘need to observe complex human systems as comprised of fully embodied interactive agents’.47 Given the convoluted, nested nature of a choir within its context and history, this admonition would require an absurd and impossible research artefact. However, another line of Complexity Thinking acknowledges that only local solutions may be possible,48 suggesting a more contained research response. Moreover, it recognises that ‘what is measured is already history’; variables are not fixed, and conclusions can only contribute to a stream of evolving discourse.49 Contrasting with
43 Lemke and Sabelli, ‘Complex Systems and Educational Change’, 119. 44 Cohen, Manion, and Morrison, Research Methods in Education, 29. 45 Cohen, Manion, and Morrison, Research Methods in Education, 30. 46 Cohen, Manion, and Morrison, Research Methods in Education, 30. 47 Horn, ‘Human Research and Complexity Theory,’ 134.
48 David Byrne, ‘Thoughts on a Pedagogy of Complexity’, Complicity: An International Journal of Complexity and
Education, 11.2 (2014), 40–50, <https://ejournals.library.ualberta.ca/index.php/complicity/article/ viewFile/22963/17094> [accessed 28 Jan 2016], 42.
‘hyper-complication’, Complexity implies ‘the impossibility of defining the list of potential states of a system, or the list of contributing factors’.50 And the mere act of studying can be part of a process ‘whereby boundary judgments and contestations continually occur’.51 Therefore, even given an expanded pool of participants, Complexity Thinking is important in that it emphasises that these case studies are necessarily limited and can only offer contingent and limited findings, which may nevertheless drive further findings.
3.3 Embodiment and Complexity Thinking
It is worth recalling that a driving interest behind this study is the powerfully embodied nature of singing. It will become apparent in Chapters 5 and 6 that the nature of choral aleatory performance also has an important embodied dimension, in addition to having characteristics of a complex system. I therefore draw on the work of several writers who have confronted embodiment in such a way as helps to frame improvisatory singing as a Complex act.
In placing this act in the body, I suggest it is helpful first to review the historical dichotomisation of mind and body – the essence of Cartesian dualism. The theatre-maker Gavin Thatcher and I have argued elsewhere that the voice is subject to this segregation: ‘the expressing body (vocal technique, stagecraft) is separated from the expressive soul (interpretative instinct, entrained musical/dramatic exegesis)’.52 Singing, especially when considered from a technical perspective, is a means of putting the body at the service of the rational soul – the mind residing within, and directing, a subordinate body.53 David Borgo reconciles this dichotomisation by
50 Alhadeff-Jones, ‘Three Generations of Complexity Theories’, 72. 51 Kuhn, ‘Complexity and Educational Research’, 176.
52 Gavin Thatcher and Daniel Galbreath, ‘Essai: The Singing Body: Towards a Unified Training of Voice, Body, and
Mind’, Theatre, Dance and Performance Training, 8.3 (2017) <https://doi.org/10.1080/19443927.2017. 1370268> [accessed 19 January 2018], 360.
outlining how cybernetics, a complexity-adjacent field, has been drawn into understandings of improvisation,
either by exploring the interrelationship between mind and body or by theorising the interpersonal and intersubjective dynamics of performance. However, after one comes to the realisation that the mind is in the body and the body is in the mind (or, more precisely, that our conceptual, sensory, and motor capacities are intertwined and have coevolved), and that the mind extends beyond skin and skull into the social, cultural, physical, and technological environments that influence human experience, it can be unclear where to go next.54
His suggestion as to ‘where to go next’ recalls the Complexity idea of nesting: in his cybernetics- based framework, systems (here, improvisers) are closed and self-determining (autonomous) only inasmuch as they are open to their context, or the systems in which they are nested (ensemble,