Discourse: Patterns of Complex Adaptation
Complexity, Society, and Liberty

? Copyright 1996. Chaos Limited. All rights reserved.

Glenda H. Eoyang
Chaos Limited
50 East Golden Lake Road
Circle Pines, MN 55014

Brenda Fiala Stewart
University of Minnesota
5244 Beaver Street
White Bear Lake, MN 55110-6539


This paper attempts to contribute to an understanding of the dynamics of conversation in a learning community as a special case of complex adaptive systems. The transcript of a conversation is coded according to categories drawn from complex adaptive systems. The time series of the conversation is analyzed for patterns of participation by various speakers and patterns of sequence of types of comments (self-similarity, difference, and self-organization). Best-fit linear time series models are estimated and correlated to the experiences of speakers in the conversation. A phase-space diagram of the participants' contributions is generated and analyzed.


The authors would like to thank Dr. Leslie Patterson of The University of Houston and Jeannine Hirtle for their participation in this study which provided its impetus, content, context, and meaning; and to Dr. Kevin Dooley of The University of Minnesota for his support in the analysis and presentation of the data.

The Problem

In The Quark and the Jaguar, Gell-Mann describes the objective of the sciences of complexity.

"Research on the science of simplicity and complexity . . . naturally includes teasing out the meaning of the simple and the complex, but also the similarities and differences among complex adaptive systems functioning in such diverse processes as the origin of life on Earth, biological evolution, the behavior of organisms in ecological systems, the operation of the mammalian immune system, learning and thinking in animals (including human beings), the evolution of human societies, the behavior of investors in financial markets, and the use of computer software and/or hardware designed to evolve strategies or to make predictions based on past observations" (Gell-Mann, 1994).

In March of 1995 a group of three researchers came together for four days to think about the ways in which learning communities (of human beings) function as complex adaptive systems. Dr. Leslie Patterson was a professor in a university literacy education department. Glenda Eoyang was a management consultant specializing in the implications and applications of complexity in organizational development. Jeannine Hirtle was a high school English teacher, working on a doctorate in literacy education. The three had come together to finalize a presentation for a national teachers' conference. The presentation was to investigate ways to apply the principles of complexity to cooperative learning in literacy classrooms.

Several factors affected the dynamics of this particular conversation. The group had worked and talked together for three days prior to the segment of the conversation that is to be analyzed in this study. In many ways their schema had already overcome many fundamental differentiations, and some agreement among group members had been achieved. During this conversation, the group was developing a plan for their presentation, so an authentic task and determinate schedule may have helped shape the dynamics of the conversation. The speakers were familiar with each other and had multiple additional relationships beyond those of fellow researchers and presenters. Common theoretical grounding and assumptions about the subject matter had drawn these persons together in the endeavor to understand community and individual learning. All discussants were women. Many of these factors would increase the expectation that self-similarity would predominate over differentiation in the data (Tannen, 1989).

During the four days of work, the group began to see themselves as a cooperative learning community. Periodically they reflected on the dynamics of their own individual and group processes. Repeatedly they noticed the same pattern. A question would be asked. Conversation would move slowly with additional questions and responses. New contexts, definitions, and perspectives would be added. The conversation would accelerate with the addition of new and interesting ideas. The talk would reach a crescendo, an integrating concept would be stated, the group would laugh, and the energy would drop. After a few moments of silence, the cycle would begin again. This cyclical pattern was so pervasive, that the group began to wonder aloud if some deep pattern underlay their discourse. What was the dynamical pattern that was driving or being driven by their discourse?

The group decided to investigate this question. This paper describes the process and findings of part of that analysis. Though the analysis includes the use of some quantitative tools, it is essentially a qualitative analysis to gain an understanding of the dynamic of discourse in a learning community. The artifacts to be analyzed include:
Reflections of the interlocutors recorded within a month of the taping. Transcript of the tape. Qualitative analysis performed by one of the interlocutors upon review of the transcript one year following the original conversation.


Within the month following the conversation described here, each of the interlocutors recorded her reflections on the conversations that took place over the four days. The reflections included the entire conversation, not just the part that was taped and analyzed. The reflections describe the dynamic process experienced in the conversation.

Speaker one described the following:

"Our beginning conversation was like popcorn--individual statements of insight arose from one then another. The movement was almost random with an idea from here and an idea from there. All of us gave open support to all ideas, whether we understood them at that point or not. These random pops and sparks served as a prelude to our more methodical investigations. . . . The pattern of discourse was so clear that it is almost a physical presence. The question came first, always. Anyone could ask it. The context could be similar or different from the last we encountered."

Speaker two described the following:

" . . . When I think about those few days I think about a kaleidoscope of shifting perspectives and themes colored by the synergy that was formed by this community of thinking, talking, listening, and reflecting women. As we worked to understand the ways of knowing through the lens of complexity theory, an array of images came into focus. . . . What words uttered at any point in time influence thoughts, which influence actions or language, which feeds back into the system? . . . How do the couplings between and among learners, learners and facilitators, learners and resources, learners and texts, learners and instruments of technology affect thoughts, knowledge, and action? . . . "

And, speaker three:

" . . . We circled through our questions, explored connections and previous understandings. We told stories and made new connections. Our conversations seemed to happen in waves, in pulsation, in cycles. . . . We would come together around a question, explore connections among different perspectives, tell stories, point out connections from different disciplines, and then the energy, the questions, the confusion, and the excitement would build and build and build until someone would make a point, a discovery, which seemed to resolve the issue. For a time."

All three speakers talk about a dynamic pattern in the experience of the conversation. The pattern is recognizable as it emerges from the talk, but it is never the same twice, and it is never finished. Each interaction is context-rich in terms of individual meanings, group meanings, personal relationships, and recognition of place and time. Each brought her unique characteristics, needs, history, and information into the conversation. Each took away a deeper understanding of the content of the conversation. Each was transformed in some way.

The process of discourse among individuals is an excellent context in which to study the complex adaptive systems of learning and thinking. In discourse, evidence of individuals' schema and changes in those schema can be captured and analyzed (Dooley, 1996). Complex interdependencies among individual schema can be revealed, and emerging schema of the group can be identified and followed over time. All of the reflections of the interlocutors indicate this process of developing individual and group schema.

The qualitative ways in which discourse is similar to other complex adaptive systems are easily identified. Metaphors such as sensitive dependence on initial conditions, boundary conditions, phase transitions, far-from-equilibrium systems, agents, self-organization, and fractal boundaries are relatively easy to find in the process of discourse (Eoyang, 1994; Eoyang, 1994). The question we are interested in addressing in this paper is, what analytical methods can be used to "tease out the meaning of the similarities and differences" inherent in human discourse?

Discourse includes multiple levels of self-organization. First, interaction among neural clusters in the individual brains of the interlocutors indicates self-organization. Second, behaviors such as "perceiving, intending, acting, learning, and remembering arise a metastable spatiotemporal patterns" (Kelso, 1995, page 257). Finally, individuals interact in the conversation to generate common schema and patterns of behavior.

Many methods have been used previously to analyze patterns and transformation in discourse (Greeley, 1994; Tannen, 1989). The purpose of this study is to use the dynamics of complex adaptive systems to examine one particular instance of discourse and to seek an understanding of the dynamics that arose on both the individual and group scales.

The Transcript

The data was collected during a forty-five minute discourse among three interlocutors. The conversation was taped, and a transcript was prepared. The transcript was coded, using categories derived from the behaviors of complex adaptive systems. Based on the coding, the transcript data was evaluated using a variety of tools.

These data formed the foundation of the analysis described below. The data analysis includes an analysis of the coding process, time series analysis of the data, phase space analysis of the data, and evaluation of the reflective essays prepared by the interlocutors.

The purpose of the data analysis was to identify patterns of behavior that might indicate characteristics of the dynamics of the conversation. Analysis of the data included four stages. We began with a coding process to identify the basic units of measure from which a possible pattern might emerge. Second, we performed a variety of time series analyses on the data to identify gross temporal patterns and to determine a potential fit with a linear model. We used phase space analysis to characterize the attractor(s) of the system.


The first task in coding was to determine the basic unit of analysis. We decided to consider each person's individual statement or contribution as one unit. Several factors influenced this decision. The transcript did not include long monologue-type speeches, but short ones. Our concern was with the inter-personal development of schema in the learning community, as opposed to intra-personal schema development that might be approached from the perspective of cognitive sciences and decomposition of a single contribution to the conversation. During early trial coding, we found little evidence of multiple purpose statements in the conversation--each statement had a single focus and intent.

Developing a coding scheme was an interactive process. We began the analysis as a group, including all three interlocutors. After reviewing the entire transcript, we tried a variety of coding schemes familiar to us from linguistic, educational, and communications methodologies.

We were not able to generate a coding scheme based on these approaches that 1) included a workable number (fewer than 7) of categories 2) would work consistently across the entire discourse or 3) reflected the rich contexts that we remembered from the experience of the discourse. After several false starts and dead ends, we began to think about using categories drawn from complex adaptive systems characteristics. We generated a list of characteristic behaviors in complex adaptive systems (Eoyang and Holladay, 1996). After a brief test of these categories, we concluded that they would meet our criteria for number of categories, sensitivity to context, and applicability across the entire transcript. Sample of the coded transcript appears in Appendix A. The original categories included:
Blank--inaudible response Differentiation--identifies a distinction between two ideas Self-organization--indicates a creation of a new idea by establishing a relationship between or among among preceding concepts Scaling--acknowledges a self-similarity of one idea with another idea Attractor--determines an overarching idea that constrains other ideas Feedback--connects current idea with previous idea(s) or concept(s) Self-similarity--identifies a similarity between two ideas Boundaries--describes a pattern of differentiations

or differentiation between the discussants and others outside of the group. Issues of scale and context overwhelm systematic analysis of aspects of the conversation other than the content of the ideas. For this reason, we will focus in this paper on the analysis of dynamics of the content of the statements in terms of their ideas and concepts.

After all interlocutors accepted the categories and their definitions, the transcript was coded by two raters--one a member of the original conversation and the other not. We found significant problems with interrater reliability. Sixty percent of the statements were coded differently by the two raters. Referring back to the content of the conversation, we recognized the following reasons for the lack of reliability. Context of the conversation and preceding interactions caused the person who participated in the original conversation to classify statements differently than the person who was not a participant. We are currently pursuing issues of interrater reliability among persons not involved in the conversation as well as among the interlocutors. In addition to involvement of the rater in the original conversation, the variable that had the greatest effect on reliability appeared to be length of comment being rated. Shorter items were more ambiguous, with single-word responses being most difficult to rate reliably. Finally, we found issues with reliability based on ambiguity between pairs of the categories. Ambiguity between self-similarity and scaling; boundaries and differentiation; positive feedback and self-similarity; negative feedback and differentiation; and self-organization and attractors confounded the rating process. We combined these pairs of categories and reduced the number of categories to three (self-similarity, difference, and self-organization). Through this change, we reduced the percentage of interrater differences to 30 percent.

We resolved the remaining issues by converting statements rated by either rater as self-organization to self-organization and statements rated by either rater as difference to difference. These transformations provided a list of consistent ratings for analysis.

This indicates that differentiation statements predominated for the first speaker, while self-similarity statements predominated for the other two speakers. For all speakers, self-organization statements were least frequent.

The same categories provided the following distribution by speaker of each type of statement.

This indicates that the larger number of statements by speaker one was primarily due to her increased number of difference statements over the other two speakers. It also shows that all three speakers contribute approximately equivalent numbers of self-similarity statements.

This analysis provides some clues about the overall participation of speakers and the uses of each type of statement throughout the discourse. However, time series analysis will be necessary to capture information about the dynamical development of the discourse.

Time Series Analysis

The next step in the analysis was to decompose the conversation by type of comment and by speaker and to analyze the time series dynamics of these components. We will look first at the time series across the conversation of all participants and all statement types.

Figure 1 shows the time distribution by speaker across the sequence of the conversation. Speakers one, two, and three are represented by their numbers along the Y axis. Zero (0) indicates an unintelligible statement or one in which all three interlocutors are talking at the same time. This figure shows that all speakers experienced periods of silence. Speaker three shows patches of silence early, mid-way, and toward the end of the dialogue. Speaker two increases her periods of silence beginning half-way through the dialogue. Speaker one has one discernible period of silence early, then very short periods equally distributed throughout the remaining time.

The cluster of three zeros between 105 and 140 indicate some deviation. Referring to the transcript, we find statements 113 and 118 to be unintelligible because of laughter. In statement 115, all three speak at the same time to say, "Our whole became more than the sum of the parts." This is a shared restatement of an insight about the process of the discourse as a whole. It served to reaffirm and consolidate the perspectives of the group.

Figure 2 shows the distribution of statement type over the entire discourse time. Zero (0) on this chart indicates an unintelligible statement. One (1) indicates a statement of self-similarity. Two (2) indicates differentiation. Three (3) indicates self-organization.

The figure indicates that self-similarity predominates at the beginning of the conversation and again between statements 105 and 140, disappearing almost entirely during the last segment of the conversation. This is a finding we would expect from prior research (Eoyang and Holladay, 1996) and from the reflections of the speakers. They frequently described beginning at a point where all agreed and watching the difference emerge through the conversation.

Difference statements are distributed throughout, though they are not as frequent before statement 35 or between statements 100 and 120. Emerging difference in the conversation would explain the relative lack of difference statements early. The decrease of difference statements between 100 and 120 may be due to the growing move toward a consistent series of self-organization statements during that period and the common statement at 115 described above.

Through the first half of the conversation, self-organization statements are scattered sparingly. After statement 105, the self-organizations are fairly constant, reaching a peak shortly after statement 140.

Looking at all three types together, a pattern emerges between statements 120 and 140. A cluster of self-similarity is followed by a differentiation cluster, which is followed by a self-organization cluster. Referring to the transcript, we see that this sequence of statements is, again, building up to a climax for the speakers.

139: That it is the transaction between the grounded [fields of constructivist education and complexity]--
140: (Laughing) It's just that every time I come to a stopping place I think it's a period and it's just a comma.
141: --don't just validate the other, but enrich each other.

The differentiation statements following these self-organizations serve to clarify and make them more specific.

This analysis shows how the sequencing of speakers and of the types of comments contribute to the perception of development and evolution during the conversation. Our next task was to attempt to fit a linear time series model to the data.

Linear Time Series Model

Our intention was to fit the series of sequence numbers describing the conversation to a linear model. Because the sequence numbers for the entire conversation would provide no information about the dynamics of the system, we adjusted the data to allow for a meaningful time series model. First, we extracted the difference statements from the overall conversation. This allowed us to determine variable differences between the statements. We chose to analyze the difference statements because they were numerous throughout the conversation and seemed to mark critical shifts in the content and dynamics of the conversation as marked in the transcript.

The series related to difference statements would provide the amount of time (in terms of intervening numbers) between statements of differentiation. The absolute time between statements was not correlated to the perceptions of speakers as reflected in their written or spoken descriptions of their experiences, so this did not seem to be an appropriate series to model. Rather, the interlocutors spoke of increasing and decreasing impetus in the conversation based on variations in speed. This characteristic would correspond to a second difference in the data. Based on this understanding, we took the second difference and completed a Hannan Rissanen Estimate to identify three best fit models for the conversation as a whole and for each of the speakers individually.

Figure 3 shows the time plot of the second-differenced data for difference statements throughout the entire conversation. Peaks in the first five comments and around 44 indicate that the beginning and approximate middle of the conversation were times when the differences in time between differentiation statements varied most. The 44th difference statement corresponds to statement number 127 in the overall conversation. This period of variable acceleration corresponds to the beginning of the sequence leading to the climax points of the conversation at statement 140. During the rest of the conversation, the acceleration of difference statements tends to vary regularly around zero (0).

The autocorrelations and partial autocorrelations in figures 4 and 5 indicate a very low order AR system with a higher order MA component. The Hannan Rissanen Estimate confirms this by suggesting best fit models as MA(1), MA(2), or MA(3).

This would indicate that the system is driven by noise, rather than by close correlation between xt and xt-1. In terms of the speakers' perceptions of the conversation, this would mean that the previous change in rate of difference statements would have little effect on the future change in rates of difference statements. On the other hand, factors extraneous to the measured series would drive the change in the rates. These factors might include the attention spans of speakers, focus on textual references, memory of relevant personal experiences, interpersonal or psychological needs, distracters that are irrelevant to the conversation. Any of these factors might cause one speaker or another to introduce differentiation statements more or less frequently into the conversation. A high MA system would contribute to the speaker's perception that "Our beginning conversation was like popcorn--individual statements of insight arose from one then another."

The frequency plot in Figure 6 appears to peak at approximately 2.5 pi, indicating a period of approximately 2.5 statements. This is consistent with the apparent period demonstrated in Figure 3.

We followed the same procedure to analyze the acceleration of difference statements made by each participant individually. Outcomes from that analysis appear in Figures 7 through Figure 9.

Figures 7a through 7d show data for speaker one. Figure 7a shows the time series for second differenced data from the sequence of differentiation statements for speaker one. Again, the autocorrelation indicates lower AR parameter than the MA parameter for the model. In fact, the Hannan Rissanen Estimate indicates that MA(2), ARMA(1,2), or MA(3) would be best fits. A period of 2.5 statements is indicated by the frequency plot in 7d. Again, the change in rates of the difference statements for this speaker appear to be driven by "noise." This speaker might be thought of as the source of variety, bringing new data and personal reflections into the conversation frequently.

Figure 8a shows the time series for speaker two. Her series shows more autocorrelation than speaker one. The best fit estimates were MA(1), ARMA(1,2), and ARMA(2,1). The frequency plot in 8b indicates a slightly longer period at 2.8 statements. This speaker might be considered to be the student, balancing her own learning and growth with the development of the rest of the conversation.

Figure 9a shows the time series for speaker three. This indicates a great deal of variation in the middle of the conversation and less variation at the beginning and end. The autocorrelation and partial autocorrelations indicate a much higher AR parameter than either of the other speakers. The best fit model estimates are ARMA(3,1), ARMA(3,2), and MA(1). Her data also includes a period that is the longest of the three at 4 statements per period. This speaker might play the function of the teacher, focusing on continuity and reflecting the pace of the conversation as a whole.

Phase Space Analysis

In addition to the time series analysis, we performed a phase space analysis of the data to compare the participation of each of the interlocutors to the dynamics of the whole group. Again, we focused on the difference statements in the conversation, for this analysis, however, we took only the statements that were rated as difference statements by both raters. We took the sequence numbers for difference statements made by anyone, found the second difference, and plotted that difference against the same data for each of the individual interlocutors. These phase portraits appear in Figures 10 through 12.

For speaker one, the amplitude of the plot indicates that this speaker was fairly consistent throughout the conversation in the pacing of her difference comments. Within this general shape, the phase space plot shows a cluster of points around the vertical axis and in the upper, left quadrant. This indicates that this speaker tended to move counter to the conversational flow. When the group speeded up, she slowed down and when the group slowed down, her difference statements speeded up. In only two statements, approximately half-way through the conversation, did she match the pace of the conversation. This finding is consistent with the time series modeling analysis of this speaker as the source of variety.

For speaker two, the plot indicates a fairly clear two-cycle system. Variations from the two cycle paths are seen in the first and last pairs of statements. Otherwise, the plot shows a tendency to visit quadrant 1 (decreasing acceleration when the group decelerated) and quadrant 4 (speeding up when the group slowed down) alternately with a wide variation in times between difference statements. This would indicate that the autocorrelation in her time series plot was a slightly negative one. She worked against the changing dynamic of the group.

For speaker three, the plot also shows a strong two-cycle system with high amplitudes showing wide variation in timing of difference statements. This plot, however, shows the speaker moving with the conversational pace--speeding up her difference statements as the overall pace increased and slowing as the conversation slowed. Like the time series analysis, this phase portrait indicates a stronger correlation over time between speaker 3 and the group as a whole.

These three distinct phase space diagrams indicate different dynamics of each speaker when compared with the whole. Each seems to play a different role in the dynamics of the conversation. Speaker one balanced the conversation. Speaker two countered the pace of the conversation, and speaker three amplified the existing pace of the conversation.

Questions for Further Study

This study has been preliminary and exploratory in nature. Many issues and questions remain for future study.

The difficulties we experienced with interrater reliability need further research. Differences between raters who participated and those who did not participate in the original conversation should be investigated to distinguish between disagreements based on understanding immediate context and other confounding variables. The coding categories should be clarified and standardized to minimize problems of reliability related to the translation from qualitative representation of data to a quantitative representation.

The sample of discourse included in this study is far simpler than many because it included such a small number of participants who shared many common perspectives and interests. Similar studies should be completed with larger and more diverse groups of interlocutors.

The phase space and time series dynamics of this particular study should be cross-referenced more extensively with the content of the conversation to determine how shifts in the dynamics correlate to shifts in content or intention in the context-rich textual data. Such analysis will determine what kinds of shifts trigger movements among statements of self-similarity, difference, and self-organization.

Finally, the characteristic patterns of individuals in conversation should be investigated further to determine whether these patterns represent personality preferences, conversational roles, or some other determining factors of group conversation.


Three learners and teachers came together in conversation. Each brought with her a wealth of experience and theory and many questions about the dynamics of a learning community. The context of self-similarity gave the group coherence through common language, goals, and tasks. The context of difference allowed each to inform the schema of the others. Their interactions generated self-organization of new individual and group schema.

This process was experienced and observed by the participating individuals. Each developed an experiential understanding of the phenomenon. By applying a variety of qualitative and quantitative sign systems, we have sought to think and talk about the experience. Our objective is to gain a more thorough understanding of the dynamics of interaction in group learning.