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A Dynamic Ensemble for Second Language Research: Putting Complexity Theory Into Practice

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Abstract

In this article, we introduce a template of methodological considerations, termed “the dynamic ensemble,” for scholars doing or evaluating empirical second language development (SLD) research within a complexity/dynamic systems theory (CDST) framework. Given that CDST principles have yielded significant insight into SLD and have become central to the concerns of applied linguists in many domains, we propose the need for a practical blueprint to ensure compatibility between its theoretical tenets and empirical SLD research designs. Building on “complexity thought modeling” (Larsen–Freeman & Cameron, 2008), we present a practical catalog of 9 considerations intended to inform research design at multiple stages. We contextualize the 9 considerations of the dynamic ensemble by discussing how these have been framed and addressed within one previous CDST study. Finally, we address the issue of what practical implementation of this dynamic ensemble would entail and introduce several case-based methods for building off of the considerations in our dynamic ensemble. We hope that this user guide can help orient researchers interested in working within a complexity framework and spur continued methodological discussion in the field.
A Dynamic Ensemble for Second
Language Research: Putting
Complexity Theory Into Practice
PHIL HIVER
International Graduate School of English
17 Yangjae-daero 81-gil
Gangdong-gu
Seoul 05408
South Korea
Email: philiphiver@igse.ac.kr
ALI H. AL-HOORIE
University of Nottingham
School of English
University Park
Nottingham NG7 2RD
United Kingdom
Jubail Industrial College
The English Language Institute
Jubail Industrial City, 31961
P.O. Box 10099
Kingdom of Saudi Arabia
Email: hoorie_a@jic.edu.sa
In this article, we introduce a template of methodological considerations, termed “the dynamic ensem-
ble,” for scholars doing or evaluating empirical second language development (SLD) research within a
complexity/dynamic systems theory (CDST) framework. Given that CDST principles have yielded signif-
icant insight into SLD and have become central to the concerns of applied linguists in many domains,
we propose the need for a practical blueprint to ensure compatibility between its theoretical tenets
and empirical SLD research designs. Building on “complexity thought modeling” (Larsen–Freeman &
Cameron, 2008a), we present a practical catalog of 9 considerations intended to inform research design
at multiple stages. We contextualize the 9 considerations of the dynamic ensemble by discussing how
these have been framed and addressed within one previous CDST study. Finally, we address the issue of
what practical implementation of this dynamic ensemble would entail and introduce several case-based
methods for building off of the considerations in our dynamic ensemble. We hope that this user guide
will help orient researchers interested in working within a complexity framework and spur continued
methodological discussion in the eld.
Keywords: complexity theory; dynamic ensemble; methodology; research design; transdisciplinarity
NEARLY TWO DECADES HAVE PASSED SINCE
Larsen–Freeman (1997) rst proposed that ap-
plied linguistics issues could prot by being
viewed explicitly in complexity terms, and while
complexity theory1(CDST) may not be the dom-
inant paradigm in second language research,
The Modern Language Journal, 100, 4, (2016)
DOI: 10.1111/modl.12347
0026-7902/16/741–756 $1.50/0
C2016 The Modern Language Journal
it has gained considerable currency since then
(Larsen–Freeman, 2017). More importantly, how-
ever, complexity has persisted not only because
it is a useful metaphor, but because it is an em-
pirical reality (Morin, 2008), and one that has
yielded signicant insight into second language
development (SLD). Since Larsen–Freeman and
Cameron (2008a) rst offered a novel perspec-
tive on long-standing questions to which tradi-
tional paradigms failed to offer satisfying answers,
CDST has virtually exploded into domains as di-
verse as English as a lingua franca (Baird, Baker,
742 The Modern Language Journal 100 (2016)
& Kitazawa, 2014), sociolinguistics (Blommaert,
2014), multilingualism (de Bot, 2012; Jessner,
2008), educational linguistics (Hult, 2010), sec-
ond language (L2) pedagogy (Mercer, 2013), and
conversation analysis (Seedhouse, 2010). The fact
that understandings from complexity now appear
central to the concerns of most applied linguists
signals that CDST is here to stay.
Applied linguistics is an applied social science
and therefore any proposal to borrow CDST as a
framework for research must have unapologetic
practical utility. However, apart from literally a
handful of exceptions (e.g., Byrne & Ragin, 2009;
Dörnyei, 2014; Verspoor, de Bot, & Lowie, 2011),
scholarly works connecting CDST to social inquiry
stop short of the level of practical application
that would allow scholars to ensure compatibility
between empirical research designs and the the-
oretical tenets of complexity. In the current arti-
cle we address this issue head-on by formulating
an explicit operational user guide to the CDST
considerations necessary both for L2 researchers
designing a study and for consumers of research
evaluating these studies. All research represents
a story of sorts, and most traditional L2 research
reports contain features corresponding with well-
dened conventions—what we might call the
“story grammar” of research—that help in under-
standing the structure and purpose of that re-
search. Missing from the discussion of CDST in
SLD is a focus on the methodological choices
scholars must make. In a sense, then, our eld
is still developing the story grammar for talking
about complexity research, a task we agree is es-
sential for CDST to live up to its full potential
for SLD research (MacIntyre, Dörnyei, & Henry,
2015). Thus, our primary goal in this article is to
build a preliminary template of CDST considera-
tions that are important in research design, and to
make these issues from CDST as transparent and
pragmatic as possible.
We do not provide an exhaustive treatment
of the ideas or terms underlying CDST as we
feel that existing overviews published in our eld
have much to recommend them (e.g., Dörnyei,
MacIntyre, & Henry, 2015; Larsen–Freeman &
Cameron, 2008a, 2008b; van Geert, 2008). In-
stead, our overarching aim in this article is to out-
line a blueprint of methodological propositions
that will allow researchers to incorporate core in-
sights from CDST. To this end we present an initial
map of the considerations for scholars who are do-
ing, or considering doing, complexity-informed
empirical research. As a preliminary step, let us
scope outward to highlight the CDST ethos with
regard to SLD research.
THE CONTRIBUTION OF COMPLEXITY TO
APPLIED LINGUISTICS
Scholars examining CDST’s contribution to
knowledge-making in other disciplines have un-
derscored its function as a frame of reference
(Byrne, 2011), a conceptual toolbox (Walby,
2007), a habit of thought (Kuhn, 2008), a trans-
disciplinary discourse (Klein, 2004), even a world-
view (Cilliers, 2005). Most also emphasize that
complexity has yet to be articulated in such a way
that it could be termed a theory per se (Overton,
2007). Accordingly, our usage corresponds with
what Larsen–Freeman (2013, 2015b) has termed
ameta-theory—a set of coherent principles of real-
ity (i.e., ontological ideas) and principles of know-
ing (i.e., epistemological ideas) that, for applied
linguists, underpin and contextualize object the-
ories (i.e., of language and language develop-
ment) consistent with these principles (de Bot
et al., 2013). The complexity meta-theory groups
together a set of well-known relational principles
(Overton, 2013), namely that certain phenom-
ena involve multiple parts interacting together
through dynamic, nonlinear processes that lead
to striking emergent patterns over time. As a meta-
theory, CDST represents a set of powerful intel-
lectual tools and concepts “capable of informing
all theories” (Morin, 1992, p. 371). These con-
ceptual tools serve as a rigorous aid to think-
ing and theorizing, as well as conducting and
evaluating research about the human and social
world.
The contemporary reorientation toward using
complex-systemic understandings as the founda-
tion for human and social inquiry suggests that
CDST is now a part of mainstream intellectual
culture (Norman, 2011). In retrospect, however,
the earliest explicit attempts to form connections
between phenomena of interest to applied lin-
guists and the theoretical principles of complex-
ity (e.g., Ellis, 1998; Larsen–Freeman, 1997) were
a radical departure from what was, at the time,
the norm—though some of that sentiment had
already begun to emerge in the work of other
scholars who did not explicitly associate them-
selves with CDST (e.g., Dörnyei & Malderez, 1997;
MacWhinney, 1998; Meara, 1997; van Lier, 1988).
Nearly two decades on, the current level of up-
take of CDST principles suggests the existence
of a coherent new normal that has begun to
spread dynamically throughout mainstream ap-
plied linguistics (Larsen–Freeman, 2012a, 2015a,
2015b). Clearly, no individual framework is the
singular solution to the challenges of understand-
ing the complexities of SLD (Ortega, 2012; The
Phil Hiver and Ali H. Al-Hoorie 743
Douglas Fir Group, 2016). However, too often ap-
plied linguists let their paradigms dene prob-
lems (Hulstijn et al., 2014). Nevertheless, by
emphasizing dynamic change, interconnected-
ness, and multicausality, and by discouraging
determinism, reductionism, and precise (rather
than probabilistic) prediction, this new complex-
ity agenda has provided a more useful perspec-
tive for looking at existing problems and opened
the door to reconguring the eld’s program of
knowledge and making better sense of SLD phe-
nomena (Larsen–Freeman, 2015a).
As with other theoretical frameworks (e.g., crit-
ical or sociocultural theories), complexity has
not offered ready-made research templates, nor
should it be expected to. The real and more excit-
ing contribution the complexity perspective has
made is not purely in the realm of methods of in-
strumentation and analysis, but instead in onto-
logical and epistemological considerations of how
we think about the world, considerations that are
linked with the issue of how we engage in scien-
tic inquiry (Ellis & Larsen–Freeman, 2006; Or-
tega, 2013). The inescapable fact is that many
researchers have recognized that CDST princi-
ples are indispensable for consolidating exist-
ing understanding and providing new empirical
answers to long-standing questions—even in do-
mains that did not interface with complexity
in their original conceptualization or empirical
validation. Examples in which CDST has be-
come an integral part of empirical research in-
clude L2 anxiety (Gregersen, MacIntyre, & Meza,
2014), learner language (Larsen–Freeman, 2006,
2010; Lowie & Verspoor, 2015), lexical develop-
ment (Ellis & Larsen–Freeman, 2009; Verspoor,
Lowie, & van Dijk, 2008), L2 motivation (Dörnyei
et al., 2015), L2 writing (Baba & Nitta, 2014; Ver-
spoor, Schmid, & Xu, 2012), self-concept (Henry,
2015; Mercer, 2014), and willingness to communi-
cate (MacIntyre & Legatto, 2011). This evidence
indicates that acceptance of CDST principles is
beginning to reach a critical mass in our eld.
THE DYNAMIC ENSEMBLE
Our main objective in this article is to pro-
vide practical suggestions for how empirical
L2 research designs can incorporate conceptual
tools from CDST. To this end, we have con-
structed a blueprint termed the dynamic ensemble
(Table 1). This dynamic ensemble functions as a
practical catalog of complexity considerations, all
of which should inform the planning and design
of SLD research. It builds on “complexity thought
modeling” (Larsen–Freeman & Cameron, 2008a,
p. 41)—originally introduced as an approach
to exploring a research question from a CDST
perspective—and is compatible with various exist-
ing methods as we explain in detail below. What
we propose is a systematic expansion of it, and we
imagine this as a user guide with questions that
can be consulted at multiple junctures in the re-
search process to inform the choice of research
problems, development of hypotheses, sampling
of participants, types of data collected, and analy-
sis and interpretation.
A growing number of empirical studies using a
CDST perspective can be found. From them we
have selected one study (Spoelman & Verspoor,
2010) that effectively illustrates many of the con-
siderations we raise. While we acknowledge that
multiple sources exist to exemplify these consid-
erations, using different studies for each of the
points would be burdensome for readers as it
would require a high level of familiarity with each
study. Thus, we have chosen to embed the dis-
cussion of this single article within our text, us-
ing it to contextualize the nine considerations
of the dynamic ensemble. We introduce consid-
erations from our blueprint before explaining
how they have been addressed by Spoelman and
Verspoor, then also recommend some further im-
provements in light of our considerations. Certain
considerations may be more prominent than oth-
ers simply because their study was not designed
to align systematically with the dynamic ensem-
ble. We should note that by choosing this one
study, we are not elevating it to model status.
Rather, Spoelman and Verspoor’s study provides
a richness of evidence framed from a CDST per-
spective that facilitates consideration of a num-
ber of the aspects we wish to highlight—as well
as their interrelationships. We begin here with a
brief summary of this article.
In their study, Spoelman and Verspoor (2010)
investigated the development of accuracy rates
and complexity measures in the learner lan-
guage of a Dutch adult learner of Finnish. Us-
ing data (i.e., 54 writing samples) produced over
the course of 3 years, these researchers analyzed
the learner’s language around (a) distinct sources
of complexity, for which developmental patterns
were investigated at the word, noun-phrase (NP),
and sentence levels; and (b) overall accuracy, for
which they calculated the development of case er-
ror rates relative to the overall number of cases
used (the Finnish case system comprises 15 cases).
They examined the variability in the learner’s lan-
guage by rst plotting the accuracy and complex-
ity score range for each measurement occasion
(i.e., 1 to 54) in a moving min–max graph plot;
744 The Modern Language Journal 100 (2016)
TABLE 1
The Dynamic Ensemble
Operational
Considerations
Systems What is the complex system under investigation?
What gives this case phenomenological validity?
Who are the agents in the system?
Level of Granularity On what timescale(s) will the system outcome(s) or
behavior(s) be examined?
What type(s) and what level(s) of data are required to study
the system?
Contextual
Considerations
Context What are the contextual factors that are part of the
environmental frame of reference for the system, its
dynamic actions, and its patterned outcomes?
How are these contextual factors formalized into system
parameters that inuence behavior?
How does the system adapt to the context it is embedded in,
and vice versa?
Systemic Networks To which other systems (i.e., nodes) does this system link?
What is the nature of these networked relationships?
What processes ensue in coordination with other systems?
When and how should these links be highlighted explicitly
and investigated?
Macro-System
Considerations
Dynamic Processes What general principles of change exist for this system?
What specic mechanisms of change are present in the
system?
What trajectory has the system followed, and how did it get to
where it is?
What causal signature dynamics (e.g., self-organization)
produced the system outcomes, and why?
Emergent Outcomes What salient dynamic outcome congurations (i.e., attractor
states) emerge for this system, and why?
What are the characteristics of these patterns of stability for
the system in the state landscape?
What variability exists around these patterns of stability?
Micro-Structure
Considerations
Components What are the parts that make up the system under
investigation?
Which are the most prominent components of the system in a
given process of change, or for an emergent outcome, and
why?
Interactions What types of relationships exist between system components,
and what are their characteristics?
How do these exchanges manifest and affect system behavior?
How do these relationships change over time?
Parameters What are the constraints and specications that mediate the
changes and interactions possible within a system, and how
do they determine the system’s behavior?
What are the critical dimensions or values of a system (e.g.,
the motors of change) which, when they uctuate, may
result in a change in outcome?
then they calculated raw and detrended correla-
tions between variables to compare the statistical
similarity of the time-series measurements; nally,
they tested for the probability of interaction be-
tween these variables using Monte Carlo simula-
tion. Their data demonstrated that the nonlinear
variability seen in learner language provides valu-
able insight into L2 developmental phenomena,
highlighting that the interaction within a linguis-
tic domain (e.g., between word, NP, and sentence-
level complexity) illustrates how developmental
systems are often in competition for resources.
Phil Hiver and Ali H. Al-Hoorie 745
Operational Considerations
Systems. In the complex social world that is our
research stage, what do we take as the basic unit
of analysis? A unit that reects this complex re-
ality is a complex system.2We agre e that “t here
is nothing metaphysical about complex systems”
(Cilliers, 2000, p. 31), and we propose that the
most tractable approach would be to restrict the
term system to something that has phenomeno-
logical validity or concrete existence. Although
they are less denitive about this than with regard
to other considerations, Spoelman and Verspoor
(2010) do provide some indication that the sys-
tem under investigation is their learner’s writing
development in L2 Finnish, which is phenomeno-
logically valid in light of the learner minoring in
Finnish for 3 years and having to produce writ-
ten homework assignments on academic topics
throughout this period of study. This view, that sys-
tems are real entities that reect the operation of
actual causal mechanisms, is consistent with the
notion in social complexity of a case as a complex
system (Ragin & Becker, 1992; Uprichard, 2013).
Casing is the act of specifying the phenomenolog-
ical boundaries of a unit of analysis for investiga-
tion, although boundary does not imply closure.
In light of the growing consensus that the
learning process cannot be separated from the
learner (Larsen–Freeman, 2012a), we would
suggest that in the human and social domains a
necessary additional dimension of a system is an
agent (de Bot et al., 2013). Distinct from broader
meanings in CDST, by agent here we mean people,
or collections of people, capable of exercising
independent choices or intentional actions that
contribute causally to any behavior of the system
(Al–Hoorie, 2015). In their study, Spoelman and
Verspoor (2010) position their learner, a young
adult native speaker of Dutch with no previous
knowledge of the Finnish language, as the agent
of the system. Apart from an individual, any of
the following could also be cased as a complex
system: a group, a social movement, a language
classroom, a community of professionals, or an
institution. The individuals participating in each
of these systems are the agents, with the smallest
system possible having only a single agent.
To extend existing denitions (de Bot &
Larsen–Freeman, 2011, p. 9; Larsen–Freeman &
Cameron, 2008a, pp. 36–38) with these criteria,
for SLD research purposes a complex system
(a) has concrete phenomenological validity, (b)
is composed of multiple connected and inter-
acting parts, including an agent (or agents),
(c) is open to adaptive feedback and dynamic,
nonlinear change in behavior, (d) is part of the
context that is part of it, and (e) exhibits emer-
gent outcomes. Spoelman and Verspoor’s (2010)
choice of a system, indeed, satises these criteria.
Caution must be exercised, however, not to take
for granted that the unit under investigation is
a complex system (Larsen–Freeman & Cameron,
2008b); it may actually be a simple or closed sys-
tem, or not a system at all. Viewed from our
current denition, therefore, constellations (e.g.,
goals, interest) and abstract phenomena (e.g.,
L2 prociency, L2 motivation) differ from sys-
tems because they do not produce an outcome
by themselves, and must rst be located within an
agent who experiences and acts on them.
Level of Granularity. In designing a study,
deliberately deciding what to investigate as a
complex system, and the timescale(s) (i.e., the
temporal window or duration at which a process
is to be studied) and level(s) (e.g., a whole-system
level, a micro-components level) at which to
investigate and analyze that system will impact
the type of questions appropriate for exploration,
the types of evidence that can be collected, and
ultimately the theoretical and empirical advances
made (Eve, Horsfall, & Lee, 1997). In Spoelman
and Verspoor’s (2010) study, for example, the
timescale on which SLD is examined spans a
period of 3 years, with samples of learner lan-
guage data collected at 54 intervals from written
homework tasks. This type of data, collected
longitudinally and analyzed in a multivariate
and dynamic way, allowed the authors to ex-
plore intra-individual developmental patterns
in the learner’s accuracy and complexity. The
higher the dimensionality of a system (e.g.,
the universe) the more data is necessary for a
valid representation of it, and because system
changes and stabilities occur continuously across
time and levels of activity, this sort of modeling
would approach the complex reality of the system
proper (Byrne, 2011). The goal in CDST research
will rarely be to represent the entire complex
system in question. However, settling on precise
levels of detail in data collection and analysis, as
Spoelman and Verspoor (2010) do, for instance,
in limiting their analysis to three related mea-
sures of complexity (i.e., at the word, NP, and
sentence level), can contribute to understanding
complex phenomena without knowing the entire
hierarchy of nested levels and timescales.
One strategy for settling on the appropriate
level of granularity, recommended by Lemke
(2000) and de Bot (2015), is to investigate dy-
namic phenomena at a timescale of primary
746 The Modern Language Journal 100 (2016)
interest along with two adjacent timescales and
generating complementary data at these corre-
sponding timescales. Another pragmatic strategy
for telescoping the analytical focus or perspec-
tive breadth of a study is through simultaneously
exploring only the most conspicuous segments,
aspects, or interactions of a system (e.g., complex-
ivists studying history may deal with either whole
epochs, individual biographies, or historic events;
Kiel & Elliot, 1996). The goal here is to system-
atically produce coarser or more nely grained
research designs as appropriate, rather than
partitioning a system purely for the sake of con-
venience. Greater clarity and precision in choos-
ing an appropriate level of granularity often nar-
rows the focus of attention, producing relatively
arbitrary boundaries in data collection and anal-
ysis (Ulrich, 2001). In their study, Spoelman
and Verspoor (2010) acknowledge that SLD can
take many shapes, given that complexity and
accuracy both manifest themselves in multiple
domains of language and implicate various un-
derlying linguistic, cognitive, and psycholinguis-
tic correlates. Thus, in pragmatically deciding
the level of granularity to adopt in a study, re-
searchers will rarely be able to claim comprehen-
siveness of all the considerations that bear on a
phenomenon (Cilliers, 2001). Nevertheless, when
applied judiciously and offset by critical trans-
parency, these strategies present the opportunity
to produce structural denition in data and still
capture the complex causal dynamics of a system
without idealizing away its essential aspects.
Contextual Considerations
Context. Grounding a system in a context is
crucial to understanding its behavior and out-
comes, as context is an integral part of any
system under investigation (Ushioda, 2015). Con-
text encompasses the background situational fea-
tures in place before interactions occur among
system components, which can either limit or fa-
cilitate certain outcomes. These conditions will in-
clude features that are directly observable (i.e.,
that can be recorded or measured) or that are
otherwise empirically relevant (i.e., salient in the
dataset) to the makeup and location of the sys-
tem, and which co-adapt with it. Spoelman and
Verspoor (2010) highlight surface-level contex-
tual aspects of the system: The agent of the sys-
tem was an undergraduate theoretical linguistics
major learning Finnish at a Dutch university over
a period of 3 years. Finnish happens to have
one of the more elaborate case systems. Their
study deliberately examined this learner’s SLD at
the earliest stages of prociency, and the written
homework task conditions involved available ref-
erence materials and no time pressure. Thus, con-
text rst functions as a way of bracketing the sys-
tem within an environment and giving ecologi-
cal coherence to that system, its actions, and its
states (Byrne & Ragin, 2009). However, outcomes
and change not only emerge in context, they are
also mediated and adapted by contextual factors
(Radford, 2008). Spoelman and Verspoor (2010)
do not elaborate on how the contextual factors
they highlight might mediate, inuence, or adapt
to dynamic mechanisms of change in the learner’s
SLD.
As we have mentioned, a system is insepara-
ble from the context that is part of it (Mercer,
2016); unlike with closed systems, contextual
factors are a major determinant of complex
system behavior and outcomes, which may be
“formalized into the system parameters” (Larsen–
Freeman & Cameron, 2008a, p. 68). The notion
that dynamic mechanisms of change, in interac-
tion with the context, produce a causal force by
which outcomes appear, is not new in our eld
(de Bot et al., 2013), and intensely concentrat-
ing attention on dynamic mechanisms for change
and stability should not lead researchers to treat
context as an optional add-on for explaining sys-
tem development. Just as knowledge often cannot
be made sense of fully if it remains separate from
a wider schematic context, these system dynam-
ics are only made meaningfully coherent when
framed in a social setting (Vallacher, van Geert,
& Nowak, 2015). It follows, of course, that a re-
searcher should aim to obtain intimate knowl-
edge of the system and its context. One of the key
elements of CDST research is to determine “the
range of transferable application of any proces-
sual and causal knowledge” (Byrne, 2011, p. 155),
and because context is a key causal factor for any
dynamic change in a system, this is best done by
referencing the context in which the system un-
der investigation is embedded.
Systemic Networks. If systems are the basic
structural building blocks of the complex social
world and context is pragmatically constrained to
include the social, cognitive, and psychological
aspects that form the immediate environment of
a system’s ecology, then a network is the architec-
tural superstructure in which these systems are
embedded (Kadushin, 2012). This multi-node
hub is composed of interconnected systems,
their relationships, and processes which together
form the foundational web of the complex social
world. It may help to think of this web as a CDST
Phil Hiver and Ali H. Al-Hoorie 747
equivalent to a nomological net, which functions
as a specication of the phenomenological con-
cepts or theoretical constructs of interest in a
study, their observable manifestations, and the
linkages between them. While they do set out to
examine complexity and accuracy organically and
longitudinally, with their main focus on dynamic
variability, Spoelman and Verspoor (2010) do not
comment in detail on the networked relation-
ship between systems. Among other networked
systems, these scholars could have considered
the ways in which the L2 learner’s Finnish writ-
ing development linked and coordinated with
aspects of her underlying knowledge base and
its cognitive representation, with the ongoing L2
classroom instruction she was receiving, with her
formation of a multilingual identity, or with her
ongoing academic performance in linguistics
(her major). Because any single system will be
just one of many nodes embedded within this
dynamic network of interwoven systems, progres-
sively unraveling which systems are networked
and the precise dimensions in which they recip-
rocate will often form a sophisticated agenda for
a given strand of CDST research.
Considering interconnectedness also relates
to the conceptual abstractions opened up by the
analysis of systems. Here, we acknowledge the
possibility for systems to be conceptualized as
theoretical, as some studies have done (Henry,
2015). However, our own experience illustrates
that relying on conceptual and abstract distinc-
tions to construe a complex reality is problematic
for practical reasons. Time and again, editors and
reviewers have asked what we are framing as the
system under investigation, and how we propose
to resolve the issues of boundary specication
or agency. On the other hand, regarding our
proposal for an agentic, phenomenologically real
conception of systems, we are not suggesting that
cases be treated as contiguous or networked sys-
tems simply because they were sampled together.
A relevant set of cases can only be thought of
as adjacent or networked if those systems are
bounded together in some phenomenologically
real way (Carolan, 2014). Interconnectedness,
with each system taking all other systems as its
global environment, is an important message of
CDST research; nevertheless, this consideration
should still be tempered by prudence with regard
to how wide a net is cast and how deep within the
network structure researchers go (Mercer, 2015).
On reection, it is Spoelman and Verspoor’s
(2010) choice of granularity level—which was
an appropriate timescale and level of data—that
imposes some limits on their ability to contem-
plate and illustrate networks between their system
and others. Despite this seeming trade-off, we
would suggest that networks should be consid-
ered throughout research design, data analysis,
and interpretation of results.
Macro-System Considerations
We have suggested that in SLD research cases
are the methodological equivalent of complex
systems, and it is through choices of research
questions and data collection procedures that
researchers can focus more closely on systems’
dynamic processes of change or on emergent
outcomes. Although in this blueprint the system
dimensions of becoming (i.e., dynamic change)
and being (i.e., emergent outcomes) can be seen
as two sides of the same coin, we must also empha-
size that L2 research to date has had a more con-
ventional product or outcome focus. A particular
added value of research from a CDST perspective
comes from investigating how the process of SLD
evolves over time.
Dynamic Processes. The pivotal characteristic
of complex systems is that of dynamic change and
adaptation, which may be gradual or dramatic.
Whereas emergent outcomes (see subsequent
discussion) account for what a system is doing
now and the state in which it has stabilized, adap-
tive change provides a temporal narrative for the
process of how and why the system got here and
where it may be going. Through moving window
graphs, for instance, Spoelman and Verspoor
(2010) provide an intuitive visual representation
of the shape of the system’s growth as a nonlinear
learning curve “lled with peaks and regressions,
progress and backsliding” (p. 535). As they expe-
rience change, systems attempt to take advantage
of it by adaptively restructuring the working
parts and connections—using positive feedback
to amplify change, or negative feedback that
dampens it (Holland, 2012). Adaptations that
result in a system spontaneously, but purposefully,
varying its internal structure or its higher-order
function is evidence of self-organized change
(i.e., not explicitly engineered). Self-organization
can, thus, be seen as a robust general process
that leads to emergent outcomes (Gaustello &
Liebovitch, 2009).
While dynamic change is constant, careful
tracing of a system’s self-organization offers one
solution to ngerprinting the moving target that
the signature dynamics represent. For exam-
ple, Spoelman and Verspoor (2010) provided
longitudinal evidence that self-organization in
748 The Modern Language Journal 100 (2016)
complexity and accuracy progressed in discontin-
uous developmental jumps (i.e., stage transitions)
combined with instances of isolated stepwise
growth. Tracing the modes of change that a
system undergoes is one way of testing causal
inferences about trajectories of change (Bennett
& Checkel, 2015). Specic mechanisms of change
produce a particular time signal (i.e., pattern or
trajectory of change over time) in the system,
which is essential for understanding the causal
complexities of system development or change.
Spoelman and Verspoor’s (2010) results, for
instance, indicate that variability in the vicinity of
a developmental jump for accuracy was highest in
the earliest stages, and that the three types of com-
plexity (i.e., word, NP, sentence-level) interacted
and competed for resources until the 46th text.
Each and every system has a history that plays a
critical role in its trajectory of development, its dy-
namics, and its process of becoming (Prigogine,
1980). Just as the emergent states for a system are
not unlimited, the trajectories to those outcomes
are more or less nite, although the dynamic
behavior may include rich variations or facets that
are diachronically asymmetrical (Elman, 2003).
Emergent Outcomes. Within a CDST frame of
reference, the outcomes of interest to SLD schol-
ars are no longer those found in studies taking a
standard product approach and asking questions
such as “Does planning time predict an increase
in CAF measures on a task?” or “Are L2 learn-
ers’ attentional resources correlated with their
processing speed?” Instead, CDST is concerned
with emergent outcomes, tied to the notion of
attractor states, which represent pockets of dy-
namic equilibrium that a system stabilizes into
(Hiver, 2015a), and their existence explains why
the complexity inherent in emergence results in
some stability. Spoelman and Verspoor’s (2010)
ndings illustrate this particularly well: From the
28th written text onward, acquisition of 12 of
the 15 Finnish cases settled, indicating system sta-
bilization; toward the end of the data sample,
the distribution of complexity types (i.e., word,
NP, sentence-level), by remaining “within a steady
bandwidth” (p. 547) and minimizing their compe-
tition, also showed evidence of stabilizing into an
attractor state. It may seem counterintuitive that
emergent outcomes at the system level have no
direct counterpart at the lower component level
(Holland, 2012). However, the fact that higher-
order patterns of dynamic equilibrium for a sys-
tem are emergent allows for a more accurate and
parsimonious explanation than is possible by ag-
gregating the individual components and their in-
teractions (Jörg, 2011).
To reiterate an earlier point, the number of
novel emergent outcomes observable in the so-
cial world is nite (De Wolf & Holvoet, 2005).
A board game provides one illustrative analogy
of this. The state of a game at any given time is
the placement of pieces on the board, and game-
play consists of moving pieces around the board
from conguration to conguration based on the
rules of the game. Similarly, the state space is the
Xlandscape (Xsignifying the phenomenon un-
der study such as L2 development) on which all
emergent outcomes or states for a system phe-
nomenon can be found. By pinpointing other oc-
casions of emergent outcomes in their data—the
11th text for accuracy, the 12th and 42nd texts for
sentence and NP complexity respectively, and the
23rd text for the relationship between accuracy
and complexity—Spoelman and Verspoor (2010)
capture snapshots of system equilibrium in the
development landscape. One method, retrodictive
qualitative modeling (e.g., Dörnyei, 2014), exploits
this notion of a possibility landscape by identifying
salient outcome patterns, and investigating the
unique signature dynamics (i.e., the robust causal
mechanisms of the “gameplay” within a system)
that preceded those outcomes. Only a nite num-
ber of possible attractor states exist for a given
system, and while the law of unintended con-
sequences may still apply, identifying these may
reduce much of the unpredictability of complex
systems’ functioning and allow researchers to
make informed choices about how to interact with
respective outcomes (Vallacher et al., 2015).
Micro-Structure Considerations
Components. The task of describing and ex-
plaining system behavior must take into account
the makeup of that complex system. This presents
a dilemma, as the convention may be to posi-
tion variables as the basic unit of analysis, and
attempt causal-analytic explanations from these.
Social complexivists have raised concerns regard-
ing this type of design, proposing that because
the social world is not composed of variables,
they do not merit being reied as the entire ob-
ject of research (Byrne & Callaghan, 2014; Ragin,
1997). Spoelman and Verspoor (2010) are very
deliberate in their multidimensional conceptual-
ization of complexity and accuracy, and they ac-
knowledge that their primary perspective of SLD
is one that is integrative and more ecologically
valid. This reects reality: Most phenomena in the
social realm are multi-determined and dynamic.
Because no single input or force governs the de-
velopment and behavior of a system, change in
Phil Hiver and Ali H. Al-Hoorie 749
system behavior is not the net causal effect of
a variable’s force on a system (Larsen–Freeman,
2015b). Given the integral nature of the con-
siderations in this dynamic ensemble, we would
suggest that isolating individual components for
examination—regardless of the level of sophis-
tication applied to their analysis—cannot give a
true measure of their inuence.
One approach to dealing with system compo-
nents is to acknowledge that variables constitute
partial attributes of a system—the real integral
unit in the social world (Byrne & Uprichard,
2012)—and that variables may in fact be more
complex and dynamic than our measures por-
tray them to be (Michell, 2008). This perspective
would also require researchers to consider con-
text and networks (see our previous comments).
Then, working from the outside in, researchers
would begin by casing the systems in context that
do make up the real world and scrutinizing their
emergent outcomes and dynamic behavior and
only then move to the component or variable
level. This is precisely what Spoelman and Ver-
spoor (2010) accomplish prior to narrowing their
focus to the developmental function of within-
subject variability. Complexity inquiry rules out
the possibility of adequately understanding a com-
plex system and its behavior by examining only
one level or manifestation of it. Thus, rather than
seeing the whole system and its parts as being
in tension, frequent “level jumping” (Davis &
Sumara, 2006, p. 26) in data collection and anal-
ysis may be necessary in SLD research.
Interactions. System outcomes are not the re-
sult of sums of components, but of dynamic inter-
actions. No matter how many components are in
a system, if there is no potential for components
to interact, there is no complexity (Vallacher
et al., 2015). Ideas from game theory (Gintis,
2009) and nonlinear pedagogy (Chow et al.,
2016) provide a way for SLD researchers to
explore these internal dynamics from the per-
spective of their manifestations and their latent
characteristics. The manifestation of interaction is
the specic observable behavior between the com-
ponents themselves, between multiple systems,
and with the environment. The latent character-
istics give interactions their causal and functional
coherence, and include the aim, purpose or in-
tention of the interaction; its directionality, inten-
sity, frequency, and duration; its utility, and the
rewards or costs that accrue from it.
Spoelman and Verspoor (2010) characterize
the interactions within their participant’s learner
language (i.e., between accuracy and complexity,
and between types of complexity) as simultane-
ously drawing on supportive and competitive re-
lationships leading them to describe these com-
ponents as “connected growers” (p. 548). This
manifested, for example, in the form of overall
signicant competition between word and sen-
tence complexity, but not between NP and word
complexity. Interactions between components of
a system and with the environment are indeed a
system’s lifeblood as, without these relationships,
systems would be unable to develop or behave
dynamically, but to throw even more excitement
into the mix, these interactions are themselves dy-
namic. Spoelman and Verspoor (2010) illustrate
the existence of changing system interactions that
are distributed across varying strengths at differ-
ent periods of development. At the very early
stages, for instance, accuracy and complexity ap-
peared to compete for attentional resources, be-
fore tapering off for a longer period, followed by
several more iterations of this up–down pattern.
Because system change is contingent in large part
on these interactions, they are essential to under-
standing a system’s self-organized processes and
emergent outcomes (Overton, 2013). However,
SLD researchers examining the characteristics of
interactions, their manifestations, and how they
change must remain tacitly aware that these are
not singular explanatory causal mechanisms.
Parameters. Parameters reveal yet another
layer of the multidimensional conceptualization
of causality necessary in CDST research. Each
serves a complementary purpose. Order parameters
(also known as constraint parameters) are the
various contextual constraints and specications
that determine the changes and interactions pos-
sible within a system (Haken, 1997). Spoelman
and Verspoor (2010) portray SLD as a resource-
dependent process in which these resources (e.g.,
attention, aptitude, frequency of input) are inher-
ently limited. The order parameter they allude to
here is that the developmental load a system can
sustain is restricted by these limited resources.
Part of the reason why the complex dynamic
social world does not exhibit innite permuta-
tions is because order parameters reduce the
degrees of freedom within which components
are able to interact (Gaustello & Liebovitch,
2009). These guidelines for interaction among a
system’s elements function as operating rules for
interpreting system behavior. Once these rules
are known, it becomes possible to make more
robust observations and potentially inuence
movement toward a desired outcome (Morrison,
2012).
750 The Modern Language Journal 100 (2016)
Control parameters (also known as driving param-
eters), on the other hand, are critical dimensions
or values of a system (e.g., temperature, interest
rates, stress, taxes) which, when they uctuate,
may result in a change in outcome (Haken, 2009).
Control parameters are particularly useful for in-
tentionally inducing change in a system, and there
may be large sets of control parameters present
for any complex system in SLD, each operating
on different scales. On this point, little is said in
Spoelman & Verspoor (2010), but it is not hard to
imagine the notion of competition as one key con-
trol parameter in the system. Determining which
control parameters a system is particularly sensi-
tive to is a key task of CDST research as it may be
the most productive way of nding the “motors
of change” (Larsen–Freeman & Cameron, 2008a,
p. 70) for intervention. Research may indicate, for
instance, that a conuence of personal relevance,
task requirements, and motivation act as control
parameters for L2 task performance. In this way,
system intervention may entail setting the condi-
tions and shaping the path of emergent outcomes
from a good enough design of the pertinent con-
trol parameters (Byrne & Uprichard, 2012).
PUTTING COMPLEXITY INTO PRACTICE
CDST research is, perhaps, at too early a stage
in applied linguistics for us to conduct a state-of-
the art review of available methods. Nevertheless,
one ongoing purpose of CDST research will be to
develop a methodological repertoire adequate to
the social phenomena we are concerned with in
applied linguistics. Taking our cues from other so-
cial and human disciplines, where a wide range of
methods for complexity research are already in
use, here we address the issue of what practical
implementation of the dynamic ensemble would
entail.
First and foremost, because it is a meta-theory,
CDST does not dictate the use of unique methods
of data elicitation and analysis, nor does it exclude
existing research methods so long as they are
fundamentally compatible with the principles of
complexity (Byrne, 2011). CDST is grounded in
the phenomenological reality of the social world
and calls for approaches that emerge from the
needs of inquiry (Morin, 2008), which we be-
lieve complements the recent pivot toward a more
transdisciplinary, problem-focused orientation to
research methodology (King & Mackey, 2016).
CDST has undeniable methodological implica-
tions regarding, for instance, what may count as a
more valid representation of causal mechanisms.
On the grounds of incompatibility, this may rule
out certain techniques (e.g., pre/posttest designs,
linear analyses) as they do not shed adequate
light on the dynamic processes CDST research is
interested in. In a sense, however, there are no
such things as “methods of complexity” because
CDST encourages innovation and diversication
in understanding complex social phenomena
(Manson, 2001). The pragmatism central to com-
plexity research dictates that, instead of search-
ing for problems to which to apply our tools,
we should be looking for tools suitable for solv-
ing the problems we come up against—with the
added caveat that fundamental criteria of sound
research practices still hold (see e.g., Banaji &
Crowder, 1989). There is no shortage of suit-
able research methods for CDST (e.g., narrative
methods, multilevel modeling procedures, event
history analysis, grounded theory, Bayesian anal-
ysis, cluster analytical methods, the experience
sampling method, nonlinear time-series analysis).
We would suggest, therefore, that CDST research
might gain greater traction in applied linguis-
tics if scholars recognized that CDST encourages
repurposing existing methodological toolkits—
both qualitative and quantitative—to ensure they
are congruent with the complexity framework
(van Geert, 2008).
While a book-length treatment would be nec-
essary to provide adequate detail about potential
methods for SLD research, below we briey
introduce ve case-based methods—widely used
in the social sciences—which are some of the
most accessible designs for building off of the
nine considerations in our dynamic ensemble for
research. We also suggest questions about SLD
which could be addressed empirically using each
method. These methods incorporate the CDST
logic of causal explanation, generalization, and
hypothesis conrmation in which system out-
comes are the contingent products of multiple
complex adaptive mechanisms and causal analysis
must explain why the course of development ulti-
mately led to the outcome in question rather than
to alternative ones (Morrison, 2012). The fact
that our complex social world presents a set of
phenomenological outcomes and self-organized
processes, which are found in recurring instances
and guises, has real signicance for this project
(De Wolf & Holvoet, 2005).
Qualitative Comparative Analysis
Qualitative comparative analysis (QCA) is a
set-theoretic method appropriate for either the-
ory building or theory testing (Rihoux & Lobe,
2009). Better suited to the macro or meso level of
Phil Hiver and Ali H. Al-Hoorie 751
granularity, QCA ts well into a multi-method de-
sign: Data is often both qualitative and quantita-
tive, and the analysis proper is designed to arrive
at a complex model of an emergent outcome be-
ing investigated. Similar to retrodictive qualitative
modeling, QCA begins with the selection of one
or more cases (i.e., complex systems) and de-
nition of a particular outcome of interest before
investigating the causal conditions that led those
systems to that emergent outcome (Ragin, 2014).
Contextual factors are central to QCA and are
coded as fuzzy or crisp variables, as are the system
components, interactions, and parameters which
empirically factor in to the outcome of interest.
However, with its focus on a relevant outcome for
particular systems and a complex causal explana-
tion of that outcome, QCA foregrounds emergent
states and says little about systemic networks. QCA
might be used to explore how dynamic learner
factors interact with contextual factors and con-
tribute to various outcomes and stages in the pro-
cess of individual L2 development, and to uncover
how cognitive and affective processes which un-
fold over the long term inuence decisions and
actions by L2 users on shorter timescales. Rihoux
and Lobe (2009) provide an intuitive overview of
QCA’s purposes and procedures, and we know of
at least one study in our eld that has used QCA
(Hiver, 2015b).
Process-Tracing
Process-tracing is a within-case (i.e., single
system) method used to explain complex causal
mechanisms at a micro level of granularity. By
analyzing “evidence on processes, sequences,
and conjunctures of events” (Bennett & Checkel,
2015, p. 7), termed diagnostic evidence, process-
tracing attempts to identify how and why an
intervening causal chain led to an emergent out-
come. A versatile method, process-tracing may
be quantitative, quasi-quantitative, or entirely
qualitative in design. This method has parallels
in historiography, and unlike QCA—which also
models emergent outcomes—process-tracing
relies on microscopic tracing of a dynamic tra-
jectory and examines evidence for competing
explanations through a sequence of inferential
tests. Process-tracing can progress (a) backward
into the system’s context and history, (b) forward
into the dynamic mechanisms of change, (c) up-
ward into the network of systems that anchor and
interact with the system being examined, and (d)
downward into the system’s components, interac-
tions, and parameters to explain complex causal
processes for a given outcome (Beach & Peder-
sen, 2013). Within instructed L2 settings, process
tracing might be used to analyze how learning
events involving teachers and learners add up to
coherent wholes of activity over periods ranging
from minutes and hours to days and months,
and to trace how multilingual learners construct
a sense of identity through learning and use of
their additional languages. In the introduction to
their edited volume, Bennett and Checkel (2015)
provide a comprehensive list of techniques and
best practices in process tracing; however, we are
not aware of any study in the L2 eld that has
applied this method.
Concept Mapping
Concept mapping is a theoretically grounded
diagrammatic method used for complex-systemic
problem solving, that is, investigating a system’s
emergent states and dynamic processes of change,
and in turn doing something about them. Using
thematic clusters, concept mapping produces a
spatio-temporal representation of a system and
the structural links between clusters. It thus draws
on Kurt Lewin’s often-cited maxim that “there
is nothing so practical as a good theory” (Kane
& Trochim, 2007), and is particularly suited for
building large-scale, concrete models of systems.
More often qualitative than not, concept map-
ping is rmly focused on the system level of com-
plex phenomena. Though its primary objective
is to serve as the basis for action, it incorporates
fewer considerations from context or systemic
networks than other methods discussed here.
With an aggregate visual diagram of a system and
its mechanisms as the point of departure, concept
mapping aims to strategically implement innova-
tions that optimize system functioning in order
to solve real-world problems (Moon et al., 2011).
Given the nonlinear relationship between instruc-
tion and L2 learning, concept mapping might
be used to examine the precise roles that adap-
tive behaviors in L2 task performance play in the
self-organized development of a learner’s com-
plexity, accuracy, and uency, and to study the
motors of change in developing dynamic, uid,
and socially situated language competences. In
their accessible guide, Kane and Trochim (2007)
demonstrate the uses of concept mapping which
range from organizing work ows and solving
problems, to developing models of processes and
synthesizing knowledge. We are unaware of any
study in the SLD eld designed using concept
mapping.
752 The Modern Language Journal 100 (2016)
Social Network Methods
Social network methods, similar to concept
mapping, use visual matrices (e.g., information
maps, sociograms) and add their own sophisti-
cated computational analyses that draw on graph
theory. These methods are equally well-suited to
exploratory research designs or to hypothesis test-
ing (Kadushin, 2012). Unlike concept mapping,
however, social network methods shift their focus
more broadly to modeling and analyzing the envi-
ronment (i.e., systemic networks) that systems ex-
ist in and the relational patterns and implications
this interwoven network has on systems (Mercer,
2015). Although social network methods’ primary
emphasis is on the graphic architecture of the
systemic networks, multiple levels of analysis are
possible, and these methods do place importance
on what this structure can reveal about the be-
havior and functioning of the systems within it
(Carolan, 2014). For these reasons, systemic
networks can also be used to model dynamic
processes and to shed light on the micro level
considerations we have included in our dynamic
ensemble. We know of at least one recent study
in our eld (i.e., Gallagher & Robins, 2015) em-
ploying these methods. Social network methods
might also be used to examine broad questions
of how the changing priorities, populations, and
problems of L2 contexts inuence the larger edu-
cational system’s agendas, policies, and practices.
Agent-Based Modeling
Agent-based modeling is a method for build-
ing, from the ground up, working models of com-
plex systems and for simulating their dynamic
processes and emergent outcomes (Castellani &
Hafferty, 2009). This type of modeling is com-
monly used to investigate the empirically opti-
mal solutions to system behavior and outcomes,
especially when actual manipulation of a system
or its agents for this purpose presents practical
challenges (e.g., due to issues of access or scale).
Agent-based modeling is a process often used for
solution nding in complex scenarios. Among
other steps, it involves formulating a model that
is a transformation of an empirical situation,
specifying quantitative values and indicators that
connect a model and the target system (i.e., pa-
rameterization), then assessing, calibrating and
scaling a model based on data collection (e.g.,
using observations, surveys, interviews, or other
data elicitation tasks). By combining heteroge-
neous sources and levels of data, its priority is
on discovering ways to represent the interacting
components and experimentally display the emer-
gent properties and dynamic reactions of systems
(Siegfried, 2014). Agent-based modeling might
be used to study how delayed effects and in-
stances of regression contribute to an L2 learner’s
trajectory of development, and to model how
conceptual information is transformed, ltered,
re-organized, and added to throughout the L2
development process. In their review, Macy and
Willer (2002) provide a clear introduction of the
assumptions and principles of model design. To
our knowledge no L2 research has yet used this
method.
SUMMARY AND CONCLUSIONS
In this article, we began by highlighting the
need for a more explicit consideration of how
the theoretical framework of complexity can be
adopted in L2 empirical research designs. We
outlined the conceptual tools of complexity in
order to clear up some of the apprehensions
surrounding CDST research. The central pur-
pose of this article was to present a blueprint
of consensus-forming considerations for empiri-
cal CDST research—a model we termed the dy-
namic ensemble. Rather than an intimidating list
of desiderata our proposed categorization should
be seen as just one of many possible ways to struc-
ture the eld. Using an exemplary study we have
illustrated the ways in which these nine consider-
ations might inform empirical research in prac-
tice. We ended this article by considering what
practical implementation of the dynamic ensem-
ble would entail, and introduced several accessi-
ble research methods for building off of the nine
considerations in this template.
Using this dynamic ensemble, the core ob-
jectives of CDST research in applied linguistics
are to (a) represent and understand specic
complex systems at various scales of description,
(b) identify and understand the dynamic patterns
of change, emergent system outcomes, and be-
havior in the environment, (c) trace, understand,
and, where possible, model the complex mecha-
nisms and processes by which these patterns arise,
and (d) capture, understand, and apply the rele-
vant parameters for inuencing the behavior of
the systems. Perhaps thus far, CDST has not easily
lent itself to telling compelling research stories,
but many SLD scholars will undoubtedly recog-
nize its untapped potential to provide more accu-
rate answers and solutions. Because there are only
a certain number of patterns that one will see or
come up against, we rmly believe that the varied
complex dynamic phenomena observable in the
Phil Hiver and Ali H. Al-Hoorie 753
social and human world are well within the reach
of scientic inquiry. There may in fact be research
stories about SLD that can only be told properly
using complexity. If current levels of engagement
with CDST in L2 research are any indication, com-
plexity will continue to grow as a signicant force
in the eld for some time to come. We are cer-
tain that the best research and the most insightful
ndings in SLD are still ahead of us, and welcome
greater engagement with CDST as we attempt to
move research to a new level of complexity, rigor,
and usefulness.
NOTES
1Contemporary branches of the three parent elds
general systems theory, cybernetics, and dynamic(al) sys-
tems theory are subsumed under the umbrella term com-
plexity theory (alternatively complexity science). However, as
one reviewer recommended, SLD scholars have increas-
ingly adopted the abbreviation “CDST” to maximize the
inclusivity of mutually intelligible and complementary
foci (e.g., emergentism, dynamic systems theory, chaos
theory).
2We adopt this term because complex systems are by
denition dynamic, whereas dynamic systems are not
inherently complex. The term complex dynamic system,
technically, is redundant. Complex adaptive systems, on the
other hand, are the particular class of complex systems
that learn adaptively.
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