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Theoretic and Applied Chaos in Nursing

Volume 1 Number 1

Table of Contents

3 From the Editor

4 Author's Guide

5 An Auspicious Salutation

ARTICLES

7 Chaos Theory and Nursing Systems Research

Barbara A. Mark

15 Preliminary Evidence of Nonlinear Dynamics in Births to Adolescents in Texas, 1964 To 1990

Patti Hamilton, Bruce West, Mona Cherri, Jim Mackey, Paul Fisher

23 Complex Caring Dynamics: A Unifying Model of Nursing Inquiry

Marilyn A. Ray

33 The Process Method of Comprehensive Patient Evaluation Based on the Emerging Science of

Complex Dynamical Systems

Hector C. Sabelli, Linnea Carlson-Sabelli, Joseph Messer

45 Chaos Theory - Annotated Bibliography

Ann Smith, Jane Henderson, DeAnn Mitchell, Jan Nick, Jane Pollock, Donna Bachand, Carol Dickerman,

Deborah Flowers, Patti Hamilton

Manuscript Reviewers Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1

THEORETIC AND APPLIED CHAOS IN NURSING

Angela E. Vicenzi, RN; EdD

Associate Professor of Nursing

Southern Connecticut State University

EDITORIAL OFFICE

Theoretic and Applied Chaos in Nursing

Department of Nursing

Southern Connecticut State University

501 Crescent Street, New Haven, CT 06515

John Briggs, PhD

Western Connecticut State University

Denise F. Coppa, MS, RN-C

University of Rhode Island

Ross Gingrich, PhD

Southern Connecticut State University

Patti Hamilton, RN; PhD

Texas Woman's University

Tim Porter O'Grady, RN; EdD; FAAN

Tim Porter O'Grady, Inc.

Joseph Vitale, MS

Southern Connecticut State University

Bruce West, PhD

University of North Texas

THEORETIC AND APPLIED CHAOS IN NURSING, a peer reviewed journal, is published twice a year by the Editor. The first issue was supported by a grant from the Connecticut State University. Additional copies of the journal can be obtained form the editor at $10 per issue.

© Copyright 1994 by Angela E. Vicenzi, RN; EdD.

Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1 Vicenzi: From the Editor

From the Editor:

You are reading the inaugural issue of the journal Theoretic and Applied Chaos in Nursing. Consider it a primer in two senses of the word. It is a prim'er; a book giving the first principles of a subject and a pri'mer; a thing that primes, as a small explosive that sets off a main charge.

The scientific terms "chaos" and "fractal" are new to the paradigmatic lexicon; they were first used in the 1970s. It is to be expected that the originating disciplines of mathematics and physics have put their conceptual imprints on these two terms. But even within the physical sciences, there is a linguistic ambiguity in their description and meaning. This arises from the disparate frameworks from which the terms arose. Much like translating a passage from one language to another, sometimes the original meaning can be changed or lost. Hence the need for a primer, not only to transpose the concepts from their original sources but to develop the vocabulary, the grammar, the dialect of nursing within the language of Chaos theory.

These first efforts at translating Chaos need to be read tolerantly and carefully, a new paradigm is maturing here. New world-views aren't accepted immediately by a discipline. Rather, they are first greeted tentatively and may be comprehended in bits and pieces. Like a puzzle that needs to be solved, the concepts and propositions make sense, over time, to practitioners.

By necessity, this journal is for a general nursing scientist audience as there are few nurses who understand the language of chaotic nonlinear systems. But the journal will progress to a specialist publication as nursing science develops its theoretical and practice base. I believe that in the future, chaotic dynamics will be a nursing research spe cialty with its own community of scholars. However, to read this issue no technical knowledge is needed and each article can be read and understood independently of the others. To assist the interested reader, there is an annotated bibliography for use in deepening your comprehension of Chaos theory.

I am sure that Theoretic and Applied Chaos in Nursing will have a nonlinear impact on the thoughts and practice of nurse scientists. In some of you, the second meaning of primer will be set in motion; a spark of interest will be ignited that will have unpredict able results. The dialogue of Chaos within nursing science has begun, you are holding its first conversation. I hope you remain "strangely attracted" as the story emerges and is revealed by the trajectory of time.

Angela E. Vicenzi, RN; EdD

Editor

Author's Guide Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1

Call for Papers, Winter and Summer Issues

Author's Guide

Purpose of the Publication

The primary purpose of the publication Theoretic and Applied Chaos in Nursing is to contribute to the development of nursing as a transdisciplinary science. This will be achieved by promoting theory derivation from the natural sciences where the paradigm of chaos originated. Meteorology, human physiology and ecology have already transposed knowledge about chaos and found it useful in the development of their disciplines. There is reason to believe that transposition also holds promise for the discipline of nursing.

While the informal transmission of information within the nursing community has generated a core interest group, the establishment of a formal method of dissemination about the explanatory model of chaos will facilitate the further evolution of the concepts and theories associated with chaos and fractals.

Topics to be considered are: chaos theory derivations from the natural sciences and the social sciences, annotated bibliographies, research findings, applications of chaos theory to practice and the analyses of individual concepts within the paradigm of chaos. Also, examples of fractals in nursing and their implications for data analysis and pattern recognition.

Article Preparation.

Typed, double spaced, one inch margins on all sides. Number all pages on the upper right-hand side. Manuscripts should be limited to 20 - 25 pages. Include an abstract of 200 words or less.

The publication is peer-reviewed anonymously. Manuscripts should not contain identifying infor mation. Authors should provide their name(s) and affiliation(s) only on a cover sheet.

Illustrations and Tables

Authors should provide their own figures and drawings which should be black on white, and able to be photocopied. Typewritten lettering is accept able. The maximum size of illustrations is 6" x 6".

Authors must provide proof of permission to use copyrighted tables, figures or illustrations. Include the following information "Reprinted with permission from (author, Article, Date of publication, publisher)."

Writing Style

APA (American Psychological Association) style is used for text and reference lists.

Submission of Manuscripts

Authors should provide: 1. Three copies of the manuscript and abstract. 2. A separate page which identifies the author(s), their affiliation (s) and one author's mailing address and phone number.

The copies are submitted to:

Dr. Angela E. Vicenzi, Editor

Theoretic and Applied Chaos in Nursing

Department of Nursing

Southern Connecticut State University

501 Crescent Street, New Haven, CT 06515

Telephone:

(203) 397-4614 FAX: (203) 397-4154

The last date for submission of manuscripts:

For the Winter 1994 issue, July 30, 1994;

For the Summer 1995 issue, January 30, 1995

This publication is being supported, in part, by a University Research Grant from Connecticut State University.

Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1 Lorenz: An Auspicious Salutation

AN AUSPICIOUS SALUTATION

"Chaos" is an ancient word, but it has recently been appearing more and more often with a modern meaning. Instead of denoting a complete absence of systematic arrangement, as it originally did, it can now refer to processes that may be quite orderly, but appear on casual inspection to be disordered. This can happen because causes that are near enough alike to be virtually indistinguishable may in due time have vastly different effects.

When I first encountered what is now called "chaos," I thought of it as a characteristic of fluid motion, and called it "deterministic nonperiodic flow." It was quite a surprise when, a few years later, it began to show up in numerous other contextsthe social sciences and humanities as well as the physical sciences. Chaos in such diverse phenomena as the human heartbeat and the world economy is no longer a surprise. I was quite unprepared, however, when I learned a few months ago that chaos was playing an important role in nursing science.

I should not have been surprised. Nursing is certainly one of the most human of occupations, and, unlike much of what goes on today, it involves human kindness rather than aggressiveness. Wherever interaction among humans takes place, unnoticed or unanticipated minuscule events are likely to have big consequences; hence, chaos. It is therefore quite appropriate that a new journal in the field of nursing should be devoted to its chaotic aspects, and I extend my best wishes for success to Theoretic and Applied Chaos in Nursing.

Massachusetts Institute of Technology

Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1 Mark: Chaos Theory & Nursing Systems Research

CHAOS THEORY AND NURSING SYSTEMS RESEARCH

Virginia Commonwealth University, Richmond, Virginia

The open systems metaphor, with its assumption that organizations are equilibrium seeking systems, provides a limited perspective for understanding phenomena of interest to nursing systems researchers. Perhaps, organizations are better understood as dynamical and nonlinear rather than equilibrium-seeking. Chaos theory, or the theory of non-linear dynamical systems, challenges long held beliefs about the world in which we live. Chaos theory suggests that the apparent unpredictability that surrounds us is, in fact, only a piece of a larger, highly complex, and frequently unseen pattern (Priesemeyer, 1992). In physics, where the study of chaotic or dynamical systems has been underway for some time, the orthodox construction of classical Newtonian physics has been revised as deterministic explanations have been overturned by those that are stochastic and probabilistic. Despite being an explanatory model that embraces a holistic perspective, little has been published in the nursing literature about chaos theory and its potential contribution to developing a body of knowledge in the discipline.

The purpose of this article, then, is to examine the utility for nursing systems research of several ideas from the emerging science of chaos. First, three classic examples, the weather, a water wheel and a mathematical equation, are used to illustrate the general characteristics of chaotic systems. Then, four key concepts are discussed. An example of the application of chaos theory to nursing administration is then described. Finally, implications for the utilization of chaos theory in nursing systems research are discussed.

Global Weather, Water Wheels and a Mathematical Equation

Edward Lorenz was a research meteorologist at the Massachusetts Institute of Technology in the early 1960s. Computers then were huge and slow, but Lorenz was able to create a mathematical system of 12 equations that, while certainly oversimplifying weather, allowed him to construct models in an attempt to predict it. Weather was characterized by deterministic equations, numerical rules that expressed relationships between temperature and pressure, between pressure and wind speed, etc. At that time, science and measurement gave only passing acknowledgment to measurement error, assuming that trivial errors in measuring physical systems could be safely ignored. Computers operated on the same assumption: approximately accurate input yields approximately accurate output (Gleick, 1987, p. 15).

On a particular day in 1961, Lorenz wanted a cup of coffee, so he decided on a shortcut. Instead of starting at the beginning of a computer run, he started in the middle, by typing in the initial conditions defined by his weather system. After all, the same initial conditions should lead to the same end point. He left the lab, and when he returned, "he saw something unexpected, something that planted the seed for a new science" (Gleick, 1987, p. 16).

What Lorenz expected was that the run would duplicate itself just as had the last run. What he saw, however, was that this run, while it started out identical to the previous runs, quickly diverged, so that in the space of just a few "months" the weather pattern was completely different than his equations predicted. After attempting to determine the cause of the change, Lorenz finally discovered that while the computer stored six decimal places, Lorenz had typed in only three. The seemingly inconsequential difference in a starting value had an extraordinary and totally unpredicted effect. This sensitive dependence on initial conditions, where tiny differences in input yield enormous differences in output, is one of the hallmarks of chaotic systems. The idea is that trajectories that begin from "arbitrarily close" initial points will, over time, diverge exponentially (Robinson, 1982). Thus was born the term "butterfly effect," a term that encompasses the idea that a butterfly fluttering its wings in Singapore today can have an impact on next month's weather in New York City.

Lorenz was not content with discovering this kind of strange behavior in a system as obviously complex as the weather. He began to investigate whether other, simpler physical systems exhibited the same kind of chaotic behavior, turning his attention to the apparently simple behavior of a water wheel. In a water wheel, if the flow of water is slow, the top bucket never fills sufficiently to overcome the wheel's inertia: nothing happens the wheel does not move. But if the flow is faster, fast enough to overcome inertia, the water wheel turns, settling down into an even, steady rotation. If the flow of water is turned up, however, the rotation of the wheel can become chaotic because of nonlinearity in the system. Nonlinearity exists because the speed of the water wheel depends on the amount of water in the buckets, and the amount of water in the buckets depends on the speed of the water wheel. But speed of the wheel is not strictly proportional to the amount of water, nor is the amount of water directly proportional to the speed of the wheel. Speed and amount of water cannot be disentangled. During the time the buckets are under the water spigot, how much they fill depends on how fast the wheel is spinning. If the wheel spins fast, the buckets have little time to fill, and at high speeds, buckets can start back up before they have time to empty. Consequently, there are heavy buckets on the upside of the rotation and their weight tends to cause the spin of the water wheel, first to slow down, and then to reverse. Lorenz found that over long periods of time, the spin can reverse itself many times, never settling down and never repeating itself in a predictable pattern (Gleick, 1987).

An example from mathematics illustrates similar properties (Hofstadter, 1985). If a simple mathe matical function is repeatedly iterated, a constantly increasing number results. For example:

3x3 = 9

3x3x3 = 27

3x3x3x3 = 81, etc.

But in a nonmonotonic function, (one in which the impact of an independent variable does not have a constant effect on the dependent variable over all ranges of the independent variable) other results occur. The behavior of the logistic equation

Y = 4lX(1-X)

can be used to illustrate what happens. In this equation, X (varying from 0 to l) and the number 4 define the boundaries of the system. Lambda (l) is a constant, or stress parameter, (varying from 0 to l) that in essence "drives" the system. Now, select an initial value of X, say 0.04, and a constant (l) of 0.7, and iterate this equation; that is, use the first solution of Y as the starting value of X in the second iteration. The following series of numbers results:

.1075, .2686, .5500, .6930, .5957

.6743, .6149, .6630, .6256, .6558

These numbers get closer and closer to a single point, and after about twenty iterations, the equilibrium finally rests at about .643. Figure 1 is a graph, or what is called a one dimensional map of the calculated points. This illustrates what is called a stable attractor, that is, one that "attracts" all of the points that can be graphed consistent with the equation. The points clearly move toward a stable equilibrium.

The system can be "driven" harder by increasing the value of the constant (l) just slightly to 0.785, and then iterating the equation in the same way. Figure 2 illustrates what happens. Instead of achieving equilibrium on a single point, the points fluctuate continually between two values. In Figure 2, the attractor has become periodic, characterized by what is called "period two." At the 0.785 value of the constant, the single value of X splits into two oscillating values.

If the system is driven even more, setting the constant at 0.87, the two values of Y split again, into four oscillating values, and a "period two" becomes a "period four" attractor.

At some critical point, however, driving the system harder results in a continuous period doubling that eventually leads to chaos. The attractor then becomes a strange attractor because while it attracts all the values of Y (in this one dimensional system, all the points), over time the trajectory creates an aperiodic path on the attractor, never repeating itself. In Figure 4, there is no obvious discernible pattern the transition to chaos. Yet, within this chaotic system, there is order: the points never exceed certain values (the boundaries, or intrinsic order of the system), nor are they ever repeated. Figure 5 illustrates the same equation, iterated approximately 300 times.

Concepts and Their Definitions

From these examples, four key concepts can be identified: l) sensitive dependence on initial condi tions, 2) strange attractors, 3) bifurcations and the transition to chaos, and 4) dissipative systems.

Sensitive dependence on initial conditions can be explained as follows. A system that moves toward equilibrium will eventually reach a state that is determined by its boundary conditions, regardless of what its initial conditions were. In such a system, then, initial conditions are "forgot ten" at equilibrium. In a dynamical system, how ever, equilibrium is never reached. Consequently, trajectories that start from "arbitrarily close" points will diverge exponentially (Robinson, 1982). For example, when milk is stirred into hot coffee, two molecules that were initially close will, because of the chaotic whorls and vortices produced by the action of stirring, end up at unpredictably far distances from their original positions. The implica tions of the ability of chaotic systems to profoundly amplify microscopic "perturbations" are these: first, except in the very short run, it is impossible to predict the future, and, second, underlying seem ingly chaotic behavior lies order (Radzicki, 1990).

The comparison of Figure 6 with Figure 7 illustrates graphically this sensitive dependence on initial conditions. In Figure 6, the logistic equation was plotted with an initial value of 0.04. In Figure 7, the same logistic equation was again used, this time, however, with an initial value of 0.045. The differ ence of 0.005 in starting values, iterated 100 times, produces very different results.

This transition is universal in one-dimensional maps; that is, given any permitted value of the stress parameter (l) and a randomly chosen value for the initial condition (X), for sufficiently small stress, X tends to move toward a constant value, a periodic orbit with period one. At larger stress, there is a transition to period-two orbit. An infinite number of these "period doublings" will occur over successively smaller intervals of the stress parameter (lambda), terminating in an aperiodic orbit a strange attractor at a finite value of lambda (Wolf, 1983). In very simple terms, push a system beyond its capability to deal with stress and it becomes chaotic.

Strange attractors are somewhat more difficult to define, since like Freud's id, ego and superego, strange attractors are logical constructions that exist only in the mind. Nevertheless, physicists have developed computer models that can draw "pictures" of strange attractors. An attractor is a "set of points in the 'phase space' of a dynamical feedback system that defines its steady state motion" (Radzicki, 1990, p. 64).

An attractor can be a single point, a closed curve, or strange. A single point attractor was illustrated in Figure 1, and a closed curve attractor was illustrated in Figure 2. Closed curve attractors are associated with systems that fluctuate in a repetitive manner. Strange attractors are associated with systems characterized by non-repetitive fluctuations, in an information-generating and unpredictable manner (Radzicki, 1990, p. 65). That is two points that were initially "infinitesimally close" will diverge exponentially as the system moves through time.

Bifurcations and the transition to chaos. In general, a bifurcation indicates the transition from a steady state to a state characterized by periodicity. It also demarcates the transition from a state of ordered periodicity to a state of chaos. In Figure 2, a bifurcation exists at the place on the graph where the points begin to oscillate between two values. Chaotic systems typically illustrate a series of "period-doubling bifurcations" known as a "Feigenbaum cascade" (Feigenbaum, 1983). Figures 1 to 4 illustrate this period doubling phenomenon. In Figure 1, the system continues on to a steady state; Figure 2 is characterized by a 2T period-i.e., the plotted points oscillate between two values. In Figure 3, the system is characterized by a 4T period, i.e., the system needs four points to repeat itself. Finally, in Figures 4 and 5, the system is in chaos. In general, a bifurcation indicates an abrupt qualitative change in behavior. Figure 8 illustrates this transition to chaos. This figure incorporates the equations diagrammed in Figures 1 - 4.

When the system is pushed through its "thresh old level," the attractor that has defined the system's steady state becomes unstable and the system switches to a new attractor. Since the system is also characterized by sensitive dependence on initial conditions, the change to a new (strange) attractor exponentially increases the impact of system non-linearities. Thus, systems at far from equilibrium states are highly susceptible to even the slightest external perturbations.

Dissipative systems. Open systems are generally thought of as having a variety of characteristics: they are in open interaction with their environments, they have function and structure, and they differentiate and integrate based on these functions and structures. Systems are also homeostatic; that is, they have the ability to self-regulate and to maintain a steady state. In addition, systems are characterized by equifinality, in that there is more than one way to arrive at a desired end state. According to the laws of thermodynamics, all systems move toward a state of increasing entropy, defined as energy that cannot be turned into work. Such systems experience a "random arrangement of their elements, a dissolution of their differentiated structures, a state of maximum disorder" (Scott, 1992, p. 84). However, open systems can import energy from their external environments and experience negative entropy, or negentropy. This positive energy force opposes entropy, so the system avoids becoming trapped in a downward entropic spiral (Morgan, 1986).

According to the theory of self-organization (Prigogine, 1984), thermodynamically open, dissipa tive systems can be characterized as operating at equilibrium, operating near equilibrium, or operat ing far from equilibrium. The amount of negentropy the system is able to import determines the category to which the system belongs. For example, steady state systems are characterized by maximum total entropy, uniformity and disorganization. Near equilibrium systems are characterized by the ability to import some negentropy from their environments, but on balance and over time, entropy exceeds negentropy. These systems are attracted to an equilibrium condition, but are prevented from reaching it by some type of constraint. Therefore, they produce the maximum amount of entropy, uniformity and disorganization consistent with this constraint.

Finally, in systems in far-from-equilibrium conditions, total entropy production is negative; negentropy imported from the environment exceeds internally produced entropy. Systems in far-from -equilibrium conditions are not inclined toward equilibrium, maximum entropy, uniformity and disorganization, but rather "toward new structures characterized by increased levels of complexity, sophistication and variety" (Radzicki, 1990, p. 83). Systems operating in far-from-equilibrium conditions may evolve TO order FROM chaos. Dissipative, or self-organizing systems, then, are those that arise spontaneously out of conditions that look chaotic, but which, in fact, have a hidden order. These structures are called dissipative for two reasons. First, such a definition recognizes the constructive role of dissipative processes in their creation. Second, dissipative systems require more energy to maintain than the systems they replaced, because they incorporate adaptive structures profoundly different from those that had existed previously. Paradoxically, in dissipative systems, growth is found in disequilibrium, not in order and balance (Wheatley, 1992).

These four concepts, sensitive dependence on initial conditions, strange attractors, bifurcations and the transition to chaos, and dissipative systems are considered to describe the key characteristics of chaotic physical systems. While chaos theory represents an enormous breakthrough in the physical sciences, the question remains as to how it can be employed fruitfully for knowledge development in nursing administration.

Chaos and Nursing Administration

As an illustration of the ideas of chaos in nursing administration, consider the example of nursing turnover. Causal models of turnover typically investigate the relationship between a host of independent variables and nursing turnover as the dependent variable.

The variables most frequently examined are individual (i.e. age, marital status, years of experience, education); job-related (level of commitment, satisfaction, intent to leave); and organizational (supervisory support, nursing practice model, working conditions, pay). In addition, more recent research has incorporated the impact of macro level variables such as economic and labor market forces. The assumption is that an optimal level of nursing turnover exists, that organizational homeostasis is reached when this optimal level occurs, and that organizational actions and resources will be committed to achieve such an equilibrium. But what if an equilibrium level of nursing turnover does not exist, because turnover is a dynamical, not a homeostatic process-one that is governed by principles whose structure differs from the those nursing research has been using? What if the rate or level of turnover itself has a nonlinear impact on the individual, job-related, and organizational characteris tics that we have specified as part of our model? What if, like the Lorenzian water wheel, that impact produces non-random, but unpredictable period-doubling repercussions which result in unforeseeable swings in the level of turnover or which propel the system into chaos? Figure 8 illustrates graphically the results of the continued iteration of a mathematical equation. What happens if we, conceptually, iterate the effects of different levels of turnover in the organization? Can we produce results as different as those illustrated in the figures?

To make the example concrete, consider City Hospital, a 1,000 bed teaching hospital. Over a 12 month period, its nurse vacancy rate has tripled. The "random shock," that is the absolute unpredictability, of the unexpected increase in vacancies reverberates throughout the system with impacts ranging from increased personnel costs associated with hiring supplemental agency nurses to decreased patient satisfaction. Then, in this "far from equilibrium" system, another random shock is introduced City Hospital decides to dramatically increase nurse wage rates. If we think of this as a bifurcation point, the system faces two possible alternatives: nurses can respond to the salary in creases by returning to work, or not. If nurses do return to work in substantial enough numbers, the system may return to a previous steady state. Figure 1 might illustrate this phenomenon. Or, nurses may return to work, but only for a limited time. Turnover then begins to increase again. And again, the hospital responds by offering additional salary incentives. Once more, turnover returns to a baseline level. Figure 2 might illustrate this phenomenon. In both cases, however, the hospital's response is a superficial one, that essentially seeks to deny the complexity of the turbulent environmental field. In that sense, it is a response from which the organization learns nothing. If nurses do not return to work, however, City Hospital will close a considerable number of beds, vacancy rates will continue to climb, increasing dissatisfaction of patients will lead to a decrease in occupancy, and all these changes will result in general financial deterioration of the hospital-a critical bifurcation demarcating the transition to chaos.

Since chaos theory suggests that order exists in complexity, and that an organization's response is exquisitely dependent on its initial conditions, how might City Hospital approach this crisis in a constructive way? Borrowing from theories of thermodynamic dissipative systems, Gemmill and Smith (1985) suggest that dissipative organizations can arise out of chaotic conditions. Dissipative organizations have four characteristics: disequilibrium, symmetry-breaking, experimentation, and reformulation. In disequilibrium, which may be internally or externally produced, the organization is exposed to escalating levels of turbulence. Consequently, potentially useful solutions imported from the environment become less and less accessible. For City Hospital, internally produced disequilibrium is represented by the dramatic increase in nursing turnover. Symmetry-breaking occurs with the failure of tactics ordinarily employed by the organization in its attempt to regain a state of equilibrium; i.e., City Hospital's attempts to hire more nurses are ineffective. City Hospital retained old and no longer effective strategies for managing nursing turnover, resulting in an entropic (and failing) system.

Experimentation refers to the emergence of radically transformed structural arrangements or configurations that energize massive re-organization. For example, City Hospital, rather than continuing to focus on reducing turnover, may focus on iconoclastic work re-design, transforming relation ships with other disciplines, breaking down traditional service barriers and implementing radically new administrative technologies. Such an approach, one that does not include the prior superficial response of salary increases, may result in a much more stable nursing work force. Finally, reformulation involves the selection, out of the many attempted during a period of experimentation, a new configuration or organizing principle for the organization. Given that dissipative systems sow the seeds of their next bifurcation, one should not be surprised to find that such reformulations are temporary.

Implications for Nursing Systems Research

Changing our viewpoint to one which incorporates the ideas of dynamical and chaotic systems can generate novel research questions. If, for example, nursing turnover is considered a dynamical process, inquiry might focus on definition of the relevant stress parameters that should be identified in a dynamical model of turnover. For example, what organizational processes contribute to an increasing or decreasing rate of nursing turnover? Or, at what intensity of a given stress parameter do we find a continuing stable state or a first bifurcation? At what point does the system undergo a bifurcation into two different steady states, for example, a low and a high turnover state, as was illustrated in Figure 2? At what point does the system transform itself into either a chaotic or a dissipative one, capable of higher levels of integration and order? An equilibrium model of turnover may accurately predict turnover at certain levels of stress, but how effective will it be as the system moves further and further from equilibrium?

If one accepts the relevance of these ideas, the next consideration is how to be incorporate them into nursing systems research. There are several possibilities. The most important appears least complicated, yet is most difficult: take into account the time dependent nature of the theoretical model under consideration. Concepts representing organizational processes, such as turnover, performance, or job satisfaction, theoretically may be expected to change over time, yet all too frequently we approach their definitions and placements in a conceptual structure as if they were static. Non-recursive models may be useful to the extent that they require a clearer explication than other techniques of the relationships between variables and also permit incorporation of multiple feedback loops.

Methodologically, however, there are enormous challenges. Good research design mandates that time dependent phenomena be examined over time. Multivariate time series designs, ARIMA

Mark: Chaos Theory & Nursing Systems Research Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1

(autoregressive, integrated moving average) models, or the so-called Box-Jenkins models, permit the examination of both the initial and continuing impact of a random shock on selected measures. However, ARIMA models require multiple time intervals, large sample sizes, and massive quantities of data (Box & Jenkins, 1976; McCleary & Hay, 1980). Latent variable structural equation models may be useful in those instances where such quantities of data are unavailable, but latent variable models are also beset with their own problems.

Another methodological concern is the issue of generalizability. Under the assumption that an organization was equilibrium-seeking, universal "laws" were sought that, after meeting the constraints of randomization, could be generalized to other situations.

The need to understand dynamical systems holistically, almost phenomenologically, limits the extent to which learnings about one organization can be uncritically applied to other organizations. This calls into question the tenets of positivists. This discontinuity requires clear statements of the conditions under which the hypothesized relationships are expected to occur.

The challenges of introducing the ideas of dynamical, chaotic systems into theory building and nursing systems research are daunting. The depth and complexity of the methodological problems are enormous, and intimidating to all but the most experienced or daring researcher. So what contribution can there be if we are aware, even tangentially, of the science of chaos? The value lies in our questioning conventional assumptions and in ceasing our quest for universal, deterministic answers. This includes recognizing that when systems are operating in chaos, they are highly susceptible to magnification of the effects of even small changes. In turn, such amplifying effects can lead to unpredictable events. Chaos theory challenges the reductionistic assumption that management interventions will lead, inexorably, to a predicted and predictable future. Chaos theory requires substitution of the assumption of multiple, unpredictable futures. The contributions of chaos theory continue to unfold as we contemplate relationships previously unimagined, relationships that will imbue our theory and research with a broader perspective which in turn increases our comprehension of the complexity and richness underlying critical problems in nursing systems research.

References

Box, G.E.P. & Jenkins, G. (1976). Time series analysis: Forecasting and control. San Francisco: Jossey Bass.

Feigenbaum, J. (1983). Universal behavior in nonlinear systems. Physica. D, 7, 16-39.

Gemmill, G. & Smith, C. (1985). A dissipative structure model of organization transformation. Human Relations, 38, 751-756.

Gleick, J. (1987). Chaos: making a new science . New York: Penguin Books.

Hofstadter, D. (1985). Metamagical themas. New York: Basic Books.

McCleary, R. & Hay, R. (1980). Applied time series analysis for the social sciences. Beverly Hills: Sage.

Morgan, G (1986). Images of organization. Beverly Hills: Sage.

Priesmeyer, H.R. (1992). Organizations and Chaos. Westport, Conn: Quorum.

Prigogine, I. (1984). Order out of chaos. New York: Bantam Books.

Radzicki, M. (1990). Institutional dynamics, deterministic chaos and self-organizing systems. Journal of Economic Issues. 24, 57-102.

Robinson, A. (1982). Physicists try to find order in chaos. Science. 218, 554-556.

Scott, W.R. (1992). Organizations: Rational. Natural and Open Systems. Englewood-Cliffs, New Jersey. Prentice-Hall.

Wolf, A. (1983). Simplicity and universality in the transition to chaos. Nature. 305,182-183.

Wheatley, M. (1992). Leadership and the New Science. San Francisco: Berrett-Koehler.

Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1 Hamilton et al.: Preliminary Evidence of Nonlinear Dynamics in Births

Preliminary Evidence of Nonlinear Dynamics in Births to Adolescents in Texas,

1964 to 1990

Nonlinear dynamics is one of a number of emerging methodological and theoretical constructs which make up what is often called the science of complexity. The popular name for the "new" science is chaos theory. The chaos referred to in the theory is not a lack of organization or order but is instead a complex state in which apparent randomness of a system is really constrained by a type of order that is nonlinear. Nonlinearity is a condition in which the output of the system does not match the input i.e., small causes can have large effects. The aim of research using chaos theory is a richer description of the complexity of phenomena. Chaos theory lends itself to the exploration of multidimensional interactions within and among individuals, families and communities.

Traditional methods of analysis of such problems have been limited by their assumptions of an underlying linearity of causal processes. It is now being recognized that the irregularity so often observed in the behavior of complex systems or processes frequently can be traced to intrinsic nonlinearity or chaos. Because existence of such nonlinearities violates the linearity assumptions it necessitates the application of new methods of analysis. The methods used in this study are based on advanced mathematics, physics and analytic techniques which have been developed in the last decade for the purpose of understanding nonlinear systems.

Application of Chaos Theory to Nursing

Researchers from many disciplines have found chaos theory helpful in understanding complex phenomena. By employing the principles of chaos theory and the research methods appropriate for nonlinear analysis nurses can join with economists, educators, biologists, physicists, mathematicians and sociologists for collaborative investigations of complex human problems affecting health.

Few systems of interest to nurse researchers could truly be called linear. Whether researching physiologic responses of individuals or health problems of whole communities, nurses are faced with understanding apparently nonlinear systems in which very small inputs can result in disproportionately large outputs. In addition, research challenges nurses to describe and explain phenomena which seem to evolve very differently in apparently similar systems. In other words, we ask, "Why would a health care intervention for two essentially equivalent patients result in such different outcomes?" or "Why is a particular type of service effective in one community and ineffective in another when the two seem to be demographically indistinguishable?"

Purpose and Rationale of the Study

In this study, the new methods of nonlinear analysis were used for the purpose of identifying patterns in the daily occurrence of births to adolescent girls in Texas from 1964 to 1990. While the rise and fall of birth rates to adolescents over this period had been well documented, it was hypothesized that there are many more rich complexities of the data which, heretofore, had not been described.

Traditionally, research of adolescent births in a population over time has been conceptualized to answer research questions such as, "Which time intervals or periods are characterized by high frequencies of adolescent births?" or "Can a regression equation be derived which is predictive of future rates of adolescent births?" With nonlinear dynamical analyses these questions can be addressed but, in addition, a researcher can determine the overall patterns of change in adolescent births across time. Further analysis of the embedding dimensions of the overall pattern can yield the number of parameters at work determining the changes within the process over time. The goal of this type of analysis is richer description and deeper understanding, not prediction of specific events as in the case in more traditional research.

Rationale for Use of Nonlinear Dynamical Analysis Methods

Nonlinear dynamical analysis techniques were considered promising methods to employ due to the complexity of the pattern of adolescent births in Texas. This complexity was marked by ragged ups and downs in the process over time and by the constantly changing (nonstationary) background features of the population. The research team thought that the application of nonlinear analyses to the data might yield new insights for understanding adolescent births. If our analysis indicated that the phenomenon conformed to the behavior of a nonlinear or chaotic system then further nonlinear analyses would be conducted. This preliminary step was not aimed at explanation of factors contributing to adolescent births but, instead, was aimed at description of the change in this apparently complex phenomenon over time. The research was con ducted to answer the following questions:

1. What are the patterns of occurrence in births to adolescents in Texas from 1964 to 1990?

2. Is change in the phenomenon of adolescent births in Texas a nonlinear process?

Significance of the Problem

Attempts to discern patterns in adolescent pregnancy must contend with irregularity and nonlinearity. Rather than thinking of pattern as being regular, stable and predictable, knowledge of the "real" world necessitates we think of pattern instead as being a representation of the features of a complex phenomena changing over time; it is a description of the dynamics of an evolutionary process. Pattern in the science of complexity is associated with the intrinsic dynamics of a process which can be irregular, unstable and predictable only for a relatively short time interval.

Jones, et al., (1985) estimate that in the United States, 43% of all female adolescents and 63% of black adolescents will give birth before their 20th birthday. Births to adolescents are the result of individual decisions. However, individual decisions are influenced by complex interactions of factors which include characteristics of the young woman, her partner, her peers and her family as well as the social, political and economic influences of her community (Norr, 1991).

Relatively unequal distribution of income, lack of openness about sex, less sex education and limited distribution of contraception appear to account for a pattern of adolescent births different in the U.S. than in other developed countries (Jones, 1985). Norr (1991) asserts that there appear to be three patterns of adolescent pregnancy and birth within the U.S. The Southern states, Alaska and some Western states appear to reflect, "a continuation of a preindustrial pattern of early family formation. Higher rates of adolescent childbearing are associated with higher levels of religiosity, especially fundamentalism, social and sexual conservatism and a pattern of early marriage and low education..." (p. 180). In the Northeast, the Midwest and California, the pattern is more European. There are relatively liberal attitudes toward sexuality, higher rates of sexual activity, more unintended pregnancy, often due to lack of contraception (not choice), and there is a more frequent use of abortion. A third pattern of adolescent childbearing may be, "a response to community disorganization and the inability to control youth activities plus a lack of perceived opportunities that would reward delayed childbearing" (p. 180). This pattern is not geo graphically specific.

Limitations of Traditional Methods of Pattern Recognition and Forecasting

Predicting adolescent births is immensely difficult, in part, because of the problems in under standing the abundant ragged ups and downs that characterize this and many other changes in natural populations (Catalano & Selxner, 1987; Heckman & Walker, 1989; Joyce, 1989; Schaffer & Kot, 1985). In Figure 1. you can see the jagged appearance of the adolescent birth data. It looks very much like a plot of static or noise in a radio signal. High frequencies appear to be interspersed randomly with low frequencies. However, there has been great progress made in analysis of nonlinear dynamics leading to findings that suggest even the noisiest variation may have its origin in simple deterministic mechanisms (West, 1990). Only recently have advanced methods for nonlinear analyses been developed that can distinguish between chaos and noise.

There is a traditional assumption that causal factors at work in the pattern of a changing phenomenon exert their influence in a uniform, or stationary, way. The nonstationary nature of birth data has been a persistent problem for current methods of modeling. Texas adolescent birth data are no exception; they exemplify a process that is markedly nonstationary (Gilliam, 1992).

Distribution of age and race as well as patterns of sexual behavior of the population changed dramatically in Texas between 1964 and 1990. There has been a dramatic upward shift in the age distribution of Texas females over the last 20 years, most of which is due to the maturation of the post WWII baby boomers. For example, in 1970, women aged 15-19 years comprised 9.5% of all females in Texas, while those aged 30-34 years accounted for only 5.8%. By 1990, women aged 15 -19 years had fallen to 7.4% of the female population, those aged 30-34 had risen to a full 9% of the total (Adolescent Pregnancy Prevention: a Progress Report, 1992).

In addition to the shift in age distribution there has been behavioral change among women of reproductive age. Assuming that Texas women have been following the national trend, there has been a marked increase in the percentage of older women (over 30) who have not yet given birth. However, the first birth rate for women aged 15-19 years has consistently been about twice as high for blacks and Latinos as it has been for whites.

The diversity in ethnicity indicates the increasingly multicultural character of the state. Compared to 1987, the number of white births in 1991 decreased by 6.6%, while there were increases of 24.6% for Latinos, others (primarily Asians) increased by 20.8% and blacks by 2.2%. Among blacks and Latinos fertility rates rise quickly between the ages of 15 and 24 and then begin to decrease. Among whites and others, however, fertility peaks and tapers off slowly in the 25-29 group (Adolescent Pregnancy Prevention: a Progress Report, 1992). The constantly changing background factors influencing adolescent births in Texas illustrate the non-stationarity of the process.

Analysis

The data were obtained from birth certificates at the Texas Department of Health. Data included dates and frequency of births to women 10 to 19 years old on each day from January 1, 1964 to December 31, 1990. Preliminary analysis revealed that the average number of births to adolescents in Texas each month over the 27 year period was 3,984. The average daily incidence was 126 with a standard deviation of 17.2. The number of babies born to adolescents during the study period was in excess of 1,200,000. No data regarding abortions or repeat pregnancies were analyzed in this study. Analysis of more detailed data is planned for subsequent studies.

The total number of young women ages 10 to 19 during each year of the study period was obtained. The birth data was normalized by dividing frequencies of births in a given year by the number of young women in that age group in the same year. This normalization offset the effect of changes in age distributions during the 26 year period.

Traditional time series analyses, including power spectral density analysis (PSD), were used to display the data. The time series plot of the data is shown in Figure 1.

Visual inspection of the data indicated an apparently random, noisy process. In fact, the histogram shown in Figure 2. indicates a good fit of the fluctuations to a normal distribution as shown by the solid curve. Normality is evidence of random or noisy distribution of the frequencies.

The PSD of the time series is shown in Figure 3. The PSD is used to expose the periodic components in the data (indicated by the sharp peaks) and determine the amount of variance attributable to the background fluctuations. Very large effects were found at periods of 7, 182, and 372 days. In other words there are peaks in the number of births to adolescents at these intervals. The number of ado lescent births at other times seems to be random with no distinct pattern.

These results are consistent with two quite different interpretations. The first one is the most familiar. This interpretation suggests that the process is a deterministic, linear process embedded in random process. The peaks in the spectrum would, in this case, correspond to the deterministic linear process and the noise would correspond to random occurrences.

The second interpretation is that of a nonlinear deterministic process, in which case, the "noise" would actually be chaos and the peaks would correspond to strong correlations in the dynamical system. Using methods specific to nonlinear analysis, the dominant variables in the system can be isolated, i.e. separated from the "noise" (Broomhead & King, 1987). To accomplish this the daily incidence of adolescent births were first plotted as points in a multidimensional phase space.

In order to imagine how this is done pretend that you are taking the pulse, blood pressure and temperature of a patient every hour and you want to graph the relationships among all three vital signs as they change over time. You could construct a three dimensional graph which had three axes, one for each of the vital signs (See Figure 4). The three dimensional construction formed by the three axes is called phase space. Each hour the vital signs would be graphed as a point in three dimensional space. Connecting these points in temporal sequence forms a trajectory. In nonlinear dynamical analysis this trajectory is referred to as an attractor.

In the adolescent birth example there were not three separate variables to be plotted. Instead, the daily incidence of adolescent births was graphed as a continuous series of three values of the single variable as it changed over time ( t) at (x)t, (x)t +1, (x)t +2. This represents a major innovation in graphing changes in a system as a series of measures of only one of the variables in the system James Gleick calls this method "one of the most enduring practical contributions to the progress of chaos" (p. 265). The method is based on the assumption that a single variable from within a chaotic system has been influenced by all the other variables within the system. Therefore, knowledge of the entire system can be deduced from knowledge of a single variable as it evolves (Gleick, 1987).

There are a number of diagnostic procedures which can be applied to determine the dimensions of the attractor. The characteristic dimensions of the attractor correspond to the number of dominant features in the dynamical process. By examining the dimensional characteristics of an attractor knowledge of the evolving pattern of the system can be determined. Figure 5. shows the attractor formed from the adolescent birth data. The spacing between data points along each axis in the phase space is denoted by t (tau). Tau simply refers to the number of days that separate any two data points. One can construct time series and trajectory analyses using a variety of values of tau in order to examine patterns with different time-dependent features.

One method used in this study to determine the number of dominant factors influencing the phenomenon of births to adolescents was singular value decomposition (SVD). In Figure 6. the singular values (depicted as eigenvalues) are plotted against the singular value index. The two curves indicate a time separation of t = 1 and t = 7 . The results are suggestive of factor analysis.

In the SVD analysis the eigenvalues indicate the degree of relationship among points occurring in phase space over time. Just as in a scree plot, the singular values above the floor, or leveling off point, indicate the number of dominant deterministic variables in the process. The SVD illustrates that for t = 1 perhaps six variables are dominant (repre sented by the 6 circles above the scree line on the curve), but for t = 7 only four variables are domi nant (represented by 4 triangles above the scree line on the curve). This would suggest that at least in one case (looking at points separated by 7 days) a four variable model of the process would provide an adequate description of the dynamics of this very complex process of adolescent births.

The nonlinear interpretation of the adolescent birth process is further supported by means of what is called a return map. If one were to 'slice' the attractor on which the trajectories evolve by inserting a plane transverse to the attractor, one could see how closely related the points on the attractor were as they crossed the plane. If the points are closely related they form a return map. In Figure 7 we see some indication of the existence of a return map function relating successive values of the data.

The diagonal cluster of closely spaced points suggests the existence of a low dimensional attractor. A low dimensional attractor is indicative of a process dependent on few variables for the pattern of its change over time. For an uncorrelated random time series this return mapping function would be a random spray of points. When very complex systems appear random but can be modeled by a low dimensional attractor they are said to be chaotic. Additional analyses of the data will be required to determine the detailed structure of this function and identify which variables are appropriate to model the data.

Conclusions

Preliminary evidence indicated a nonlinear component to the data. Visual inspection of the time series and the frequency histogram revealed a data pattern that was noisy and showed superficial signs of randomness. However, when more advanced nonlinear methods of analysis were applied, there seemed to be a complex, but deterministic (non-random), process at work. IronicaIly, one property of low dimensional, nonlinear processes is that their pattern of change can often be reconstructed using very few parameters (here, only four would be needed). Therefore, it was concluded that the "noise" was chaos and the peaks correspond to strong correlations in the dynamical system. In other words, what had at first appeared random was constrained by a deterministic process still to be identified.

Further analysis of the effects of ethnicity, culture, economics and other variables thought to contribute to adolescent pregnancy and birth will provide a more accurate description of the dynamic process reflected in the data over time. According to Schaffer and Kot (1985), "The time is past for models that are only caricatures of the data" (p. 349). Advanced computer technology and theory from physics and mathematics have provided the foundation for more sophisticated modeling of adolescent births. Through this study it was hoped that linear, stationary representations of the data might be replaced with richer descriptions of the patterns modeling the complexity with which the process actually occurs.

The findings of this study shall become the foundation for a long-term program of research which shall compare patterns of adolescent births across ages, races and sociodemographic conditions in various states and regions of the United States. These very detailed comparisons may provide more precise identification of the influence of individual and community characteristics on births to adolescents. The findings also may provide a much more sensitive epidemiologic measure for the community-wide evaluation of interventions. A long range result of improved pattern identification would be the descriptions of patterns which might become epidemiological "markers" for the influence of specific factors on the incidence of adolescent births. At certain regions of the attractor the process might speed up or slow down. Such "markers" could be used to identify particular times and targets for intensified interventions. For example, perhaps certain characteristics of attractors were found to correlate highly with periods of time in which school drop out rates were high. This might warrant intensified efforts to modify educational programs for at -risk students.

Summary

The research described here was conducted to describe, in detail, the pattern of adolescent births in Texas and to demonstrate and evaluate the application of advanced analytic procedures derived from mathematics and physics which are now available to nurse scientists.

The methods presented may greatly enhance analysis of the complex changes in natality in Texas during the period under investigation. The methods can address the "problem" of nonstationarity of the data and can describe the complexity of the orbit of the dynamic process through phase space. These methods of analysis are appropriate for data gath ered at equal time intervals. The amount of data required is dependent on the dynamics of the process. The more complex the process (or the more variables or parameters it takes to reproduce the attractor) the more data is required.

Examples of the types of data which might lend themselves to nonlinear analysis and which are of interest to nurse researchers, would include repeated measures of heart beats, respiration, blood pressure, temperature, blood gases, or other indicators of physiological function in individuals. At the community level of analysis, data might include population changes, incidence of disease, resource utilization, immunization levels or mortality rates.

Advanced mathematics and nonlinear analysis have been proposed as possible tools appropriate for nursing analysis (Coppa, 1993; Davidson & Ray,

1991; Phillips, 1991). The use of nonlinear dynamics has been suggested specifically for research involving nursing at the community level (Vicenzi & Hamilton, 1990). The investigation of phenomena at the community level, and the parallel development of appropriate analytic techniques with which to do that, are among the priorities for research identified by the Association for Community Health Nursing Educators in 1991 (ACHNE, 1991).

Resources For Further Investigation of Methods of Nonlinear Dynamical Analysis

James Gleick's book, Chaos: Making a New Science , provides a general overview of chaos theory and some of the methods mentioned above. It was published in 1987 by Viking Press. Chaos: the Software is also available through Autodesk in Bothell, Washington. This software program will allow the user to explore principles of chaos theory by inter actively manipulating the excellent color graphics. However, more complex programs are required for actually analyzing data. One such program is Dynamical Software which is available in basic and advanced versions from Aerial Press in Santa Cruz, California. Both versions are designed for teaching and research but are more expensive and less user friendly than Chaos: the Software.

One book that illustrates the concepts of chaos in deterministic systems and describes explicit techniques for detecting each of these concepts is, Global Bifurcations and Chaos: Analytical Methods by Wiggins. This book was published in 1988 by Springer Publishing Company. A more recent collection of methodological articles can be found in the June, 1992 issue of IEEE Engineering in Medicine and Biology. The computer programs used in the analyses conducted in our study were developed by the research team and incorporated new technical information as it became available. Many of the articles referenced above also provide more techni cal information about the methods.

This new science is evolving quickly and is dependent on technical expertise from mathematics, physics and computer science. It is unlikely that nurses will be using these methods independently in the near future. Therefore, interdisciplinary research teams seem far more likely to be successful in applying the methods to nursing research problems with nurse researchers contributing vital insights to such studies. Nurse researchers are expert in identification of appropriate research questions and in obtaining available and appropriate data for analysis using these methods. Interpretation of the findings is also dependent on the nurse's knowledge of the substantive variables and systems involved. Nurses can play a new and important role in focusing the power of these non -linear quantitative techniques to improve the quality of health for their clients.

References

Adolescent Pregnancy Prevention: A Progress Report. (1992). Presented to the 72nd Legislature by Texas Department of Human Services: Client Self-Support Services.

Catalano, R. & Serxner, S. (1987). Time series de signs of potential interest to epidemiologists. American Journal of Epidemiology. 126, 724-731.

Coppa, D. (1993). Chaos theory suggests a new paradigm for nursing science. Journal of Advanced Nursing, 18, 985-991.

Davidson, A. & Ray, M. (1991). Studying the human environment phenomenon using the science of complexity. Advances in Nursing Science, 73-87.

Gleick, J. (1987). Chaos: making a new science. New York Viking. Press.

Heckman, J. & Walker, J. (1989). Forecasting aggregate period-specific birth rates: The time series properties of a microdynamic neoclassical model of fertility. Journal of American Statistical Association. 84 (408), 958-965.

Jones, E., Forrest, J., Goldman, N., Henshaw S., Lincoln, R., Rosoff, J., Westhoff, C., & Wulf, D. (1985). Teenage pregnancy in developed countries: Determinants and policy implications. Family Planning Perspectives, 53-63.

Norr, K. (1991). Community-based primary prevention of adolescent pregnancy. Cited in Adolescent Pregnancy: Nursing Perspectives on Prevention. White Plains, NY: March of Dimes.

Phillips, J. (1991). Chaos in nursing research. Nursing Science Quarterly 4 (3), Fall, 96-97. Schaffer, W. & Kot, M. (1985). Do strange attractors govern ecological systems? BioScience. 35: (6), 342-350.

Vicenzi, A. & Hamilton, P. (1990). Concerning partnerships between theoretical physics, mathematics and community health nursing. In B. Chambers (Ed.). State of the art of community health nursing education. research and practice , (pp. 42-51). Lexington, KY: Association of Community Health Nursing Educators.

West, B. (1990). Fractal physiology and chaos in medicine. New Jersey: World Scientific. Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1 Ray: Complex Caring Dynamics

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The Society for Chaos Theory in Psychology and the Life Sciences brings together researchers and practitioners interested in applying dynamical systems theory, self -organization theory, neural nets, fractals, and other forms of chaos and complexity theory to the study of nonlinear interdependent systems. Our members hail from numerous specialties in psychology plus sociology, economics, mathematics, physics, philosophy, and literature. The Society publishes a newsletter, holds an annual conference, maintains the CHAOPSYC bulletin board, and is hosting a workshop on nonlinear methods in June 1994.

For more information on becoming a member, send a note WITH YOUR MAILING ADDRESS to Katherine E. Robertson at The Society for Chaos Theory, P.O. Box 7226, Alhambra CA 91802-7226 or via e-mail to 0005699249@mcimail.com.

Complex Caring Dynamics: A Unifying

Model Of Nursing Inquiry

Scientists from different disciplines are seriously attending to what knits the nature of the universe together. A new understanding of the concepts of wholeness and the discovery of nonlinear dynamical or chaotic (unpredictable) systems are at the center of the scientific revolution. This new, unified science is called the science of complexity (Waldrop, 1992; Lewin, 1992) and it has made it possible for scientists studying bio-physical, chemical, economic, environmental and sociocultural phenomena to arrive at similar conclusions about their holistic and relational nature. Their findings include the way patterns are established in living and non-living systems, how these patterns are interconnected and how they are linked to corresponding principles of order.

Reexamination of the nature of nursing also promises to revolutionize nursing science. Nursing paradigms which include the concepts of unitary human beings, human field patterning, self-organization and caring, now appear as the central phenomena of the discipline (Rogers, 1970; Leininger, 1981; Watson, 1985; Newman 1985; Newman, Sime, & Corcorran-Perry, 1991). Not only is caring becoming more clearly defined as the essence of nursing (Leininger, 1984; Ray, 1981; Watson, 1985; Chinn, 1991) but recently, caring in the human health experience has been identified as nursing's domain of inquiry (Newman, Sime, & Corcorran-Perry, l991).

Caring in nursing has been conceptualized in various ways: a human trait, a moral imperative, an affect, an interpersonal interaction, and an intervention (Morse, Bottoroff, Neander & Solberg, 1991). Despite the diversity, the primary focus of these conceptualizations is caring's relational character; a sense of belongingess and interconnectedness which manifests itself in actions that evoke, direct or facilitate understanding and change in terms of health, illness, dying and healing.

This article will examine the science of complexity movement, discuss the dynamics of the phenomenon of caring in the human health experience, examine the relationship between caring and choice, and propose a unifying model of complex caring dynamics for nursing inquiry.

The Science of Complexity Movement

The fundamental idea in the science of complexity is that all things in nature are interrelated and organize themselves into patterns. Over time these patterns exhibit no rational predictable behavior but produce new, more complex structures, known as nonlinear, emergent properties (Waldrop, 1992; Lewin, 1992). Complexity scientists state that the future is open and all must participate in a new dialogue with nature (Nicolis & Prigogine, 1989); a dialogue where all phenomena are "an integral part of the time-bound, spontaneously organized movement of nature, not a low probability accident" (Briggs & Peat, 1989, p. 151). Rather than maintaining a view of the universe as mechanistic, controllable, objective and predictable, there is acknowledgment of a new perspective that links the notions of spontaneous activity, uncertainty, and unpredictability (Briggs & Peat, 1984). The new science provides a foundation for a clearer understanding of the universe as holistic, complex and dynamic. A universe that is interdependent and relational; where the observer cannot be separated from the observed; and the future is open and always changing. While phenomena are spontaneous, changing and nonlinear they are, however, dependent upon their earlier historical past states. That is, there is a causal past with an unpredictable, possible future.

The essential picture of complexity or dynamic relational activity is seen at the boundary between evolving systems. At the boundary, there are forces of reciprocity between order and chaos (unpredictability) where new forms of order emerge. Creativity takes place at the boundary line between order and chaos, between systems that are considered settled, rigid, and orderly, and systems that are turbulentwhat complexity theorists call the edge of chaos (Waldrop, 1992; Briggs & Peat, 1984, 1989).

This tension between chaos and order drives change and a creative reordering in self-organizing systems (Capra, Steindl-Rast with Matus, 1991). For example, chemical and biological systems, or even social or economic systems, are driven to change and creative reordering. The edge of chaos is, thus, a communication and information process which feeds back on itself and coordinates system behavior through continual, mutual interaction (Capra, Steindl-Rast with Matus, 1991). "If amplifications have increased to the level where the system is at maximum instability (a crossroads between death and transformation known technically as a bifurcation point), the system encounters a future that is wide open" (Wheatley, 1992, p. 96). One fluctuation then becomes dominant and a new pattern forms with greater order. The system then remains stable until at some point too much change again creates a chaotic system and new arrangements for order are activated (Briggs & Peat, 1989).

What is most interesting in these systems is the creative or autocatalytic (self-organizing) process. At the potential decay point (entropy or equilibrium state) there is a phase space "which exerts a "magnetic" appeal for a system, seemingly pulling the system toward it" (Briggs & Peat, 1989, p. 36). The system seems to hesitate in this phase space, to be offered a choice among various possible directions of evolution. Through the interweaving of iterations or feed back loops, the chaotic state containing the possibilities for self-organizationstructure, pattern and process is free to seek out its own solution to the current environment (Prigogine & Stengers, 1984). The unpredictable system "chooses" one possible future while leaving others behind (Briggs & Peat, 1989) Chaos, rather than merely a mindless jiggling, has awareness; it seeks out and chooses its own subtle form of order (Briggs & Peat, 1989; Capra, Steindl-Rast with Matus, 1991).

Enfolded and etched in all patterns and processes of a living organism or sociocultural system are numbers of these bifurcation points Since it is assumed that time is irreversible and that all phenomena in the universe are interconnected, these bifurcation points constitute a living history of the choices by which we evolved from primordial beginnings to the complex cellular and social forms of today. Therefore, "every complex system is a changing part of a greater whole, a nesting of larger and larger wholes leading eventually to the most complex dynamical system of all "the universe (Briggs & Peat, 1989, p. 148).

The Philosophy, Epistemology and Metaphysics of Complexity Science

Capra and Steindl-Rast with Matus (1991) identified belongingness or belonging to the universe as the central metaphor of the new science of complexity. Belongingness represents a vision of reality that is relational; the self can be understood in the context of belonging because we first belong to the self and our personhood is defined through relationships. The new paradigm is embedded in the social paradigm which is also a pattern of relationships. This is congruent with a philosophy which holds that the kind of society we live in, to a large extent, determines the kind of science we have. If we believe that the parts (individuals) can be understood only from the dynamics of the whole (society) and that a complex, global society with different co-existing cultures illuminates our social interrelatedness, then, the only way to understand any one culture is to understand its relationship to the whole (Capra, Steindl-Rast with Matus, 1991).

The new epistemology recognizes that the wholeness of the universe is brought forth as a process of "knowledge-in-process" (Harmon, 1991, p. 27). Complexity science reinforces the perspective that science cannot provide any complete and definitive understanding of reality. Because all phenomena in the universe are interconnected and dynamic, all knowledge (including scientific concepts, theories and research results) is limited and approximate.

In this new scientific theory of living systems, the processes of life are seen as mental processes. There is a relationship between mind and matter which differs from the dualistic philosophy of Descartes which advocated the separation of mind and matter. The new view of unitive consciousness or interconnectedness between mind and matter reveals an unfolding of value, purpose and meaning. Capra, Steindl-Rast with Matus (1991) claim that "Logos [the word] is the pattern that makes a cosmos out of chaos" (Capra, Steindl-Rast with Matus, 1991, p. 126) and further, that the relational pattern of the cosmos is drawn by love "we love what attracts us" (p. 118).

Self-organization in chaos theory, although seemingly without a goal, is influenced by creativity-a vision of a purposeful love, a purposeful God, a force or spirit of life expressing itself intelligently in the universe. As participants in the universe we, thus, say "yes" to belonging. We choose not just at the level of the intellect but within a mode of consciousness that is moral, where the choice to act is a reflection of knowledge and under standing of how to act when people and things belong together (Capra, Steindl-Rast with Matus, l991)in essence, within the realm of caring, the action of love.

In this philosophical treatise there is recognition that again, the notion of consciousness is not an individual thing but is continually formed in and by relationships. It is intrinsically apprehended through a spiritual or loving relationship, and extrinsically understood through shared relationships with persons integral with their environment (Webb, 1988). Relational subjectivity is coupled with the cognitive objectivity of intentional moral operations-attention, understanding and knowing (Lonergan, cited in Webb, 1988). The experiential data of relational knowing now is considered the mark for exploration or inquiry.

The rise of the caring movement in nursing also has paralleled the recent strength of the complexity movement in modern science (Ray, 1981; Leininger, 1981, 1984, 1991; Watson, 1985; Benner & Wrubel, 1989; Newman, Sime, & Corcorran-Perry, 1991). But there is more than temporal coincidence between the two movements. Concepts advanced in complexity science are also well represented in the nursing literature. They include the shared concepts of relationality, belongingness, holism, value, purpose, choice, love, and qualitative measures for seeing the movement of order, chaos and change in the nonlinear world. This overlap is also evidenced by Newman who described a new paradigm for nursing (Newman, Sime, & Corcorran-Perry, 1991). The paradigm called the unitive or unitary transformative paradigm places emphasis on consciousness and complexity and identifies caring in the human health experience as the unifying focus of nursing and nursing inquiry. The following unitive characteristics were identified: self-organization and personal knowing, human-environment integrality, human field patterning, stages of disorganization and organization, change which is unidirectional and unpredictable, and pattern recognition (Fawcett, 1993). These views ground nursing firmly within the new science of complexity and the new philosophy of consciousness.

Expanding on the ideas of Rogers (1970) and Newman (1986), but incorporating additional concepts from the science of complexity and chaos theory, Davidson (1988; Davidson & Ray, 1991) recognized that choice was central to the integral patterning of the human-environment relationship. Davidson's research demonstrated that "choice is a felt capacity within the multidimensional human field that is manifested as knowingness influencing environmental pattern selection" (Davidson & Ray, 1991, p. 81). In like manner, the life pattern of the human field (what has happened) and self-pattern (what will happen) is mediated by choice at the "edge of chaos" (the paradox of far-from-equilibrium and order). Choice mediates "self" organizing phenomena (structure, process, and pattern) at the critical bifurcation point in the complex dynamic of the human-environment relationship.

The Nature of Caring and Choice

Nursing is a relational caring process. Clients need nursing at critical bifurcation points in their lives. "Caring is the coherent 'radiation' of nursing and the energy of nursing research inquiry" (Davidson & Ray, 1991, p. 83). Caring is the energy by which choice is facilitated to bring order (healing or well-being) out of chaos (disease, dis-ease need, pain or crises). See Figure 1.

The caring relationship is the attractor or magnetic appeal in a human system relationship in nursing which pulls the system away from disorder. Caring is a complex phenomenon with philosophical and culturally diverse views, and levels of expression. It is a personal knowing (Polanyi, 1958), an intellectual and emotional commitment to others for whom one has responsibility, thus it is wholly communal.

In my philosophical analysis of caring, I identified the magnetic appeal of caring as love and co-presence (Ray, 1981; 1991). Caring in this sense is a spiritual-ethical knowing-a process understood within the virtues of faith, hope, love and technical competency. Caring as love and co-presence is an existential quality of felt realness, a relational sign of "one with the other" (Levinas, 1982). It is characterized by an inner vision apprehended and understood in consciousness as an ontologic mystery (Marcel, 1949) and the "divine grace within" (Capra, Steindl-Rast with Matus, 1991, p. 59).

The magnetic appeal of caring (the action of love) "pulls" the other in such a way that the power of the relationship brings forth faith and trusta "courageous trust in belonging" (Capra Steindl-Rast with Matus, 1991, p. 24). Within this view of relationship, the nurse instills hope. By anticipating and working through knowledgeable, caring-presence, and using technical competency, the nurse evokes, directs or facilitates reasoned moral choice. These intentional operations, at the edge of chaos, co-create opportunities for choice-making toward the best possible future to enhance well-being, health, healing or a peaceful death. This complex choice-making patterning is a caring moment of insight, a spiritual transformation. The quality of the magnetic appeal enables both the nurse and the client to be "more alive" or "more authentic" than before, and occurs simultaneously within the will to act or choose.

A Case Study Illustrating Choice Patterning

Facilitating choice-making through the professional caring relationship can be clarified, in part, within complexity science. Chaos or unpredictability in far-from-equilibrium systems can be viewed in human systems as disease, dis-ease, dilemmas, crises or need. For example, at the critical or bifurcation point in disease, the client is the specific agent of change to effect a healthier state of self-organization or well-being and participates with the nurse in the choice to change. As a result of the caring relationship, the life pattern of disease is transformed through choice or a series of choices toward a new pattern of relational "self" organization. Both the nurse and client are transformed in the process.

The following is an exemplar of choice patterning. The exemplar illuminates the caring teams' participation in pattern change and shows how the patterns can be a foci of nursing and multi-disciplinary caring inquiry.

A Person With Severe Chronic Pain*

A person with severe chronic pain after years of "doctor shopping", has taken medications with no lasting relief and is in physical, emotional and spiritual chaos. The person arrives at a critical or bifurcation point where a choice must be made either to continue in the same life pattern leading to deterioration and death or to a new beginning in pain management and healing.

By a deep call within, and by encouragement of significant others, the client is motivated to seek pain rehabilitation from a community of caregivers. The pain center is the last hope. The person, deeply connected to the pain, is in a crisis of spirit usually brought upon by abuse or loss of a relationship, either physical, emotional, sexual or spiritual.

The multidisciplinary caregivers offer different views toward healing. The nurse caregivers, in particular, encourage faith in the self, instill hope and through loving compassion, (even against the client's own self-sabotage), motivate and facilitate choice toward a new future and a bifurcation. This new pattern is one of participation in life and living; a renewal of the quality of a life. At the edge of chaos is hope, anticipation of the future possibility of controlling pain. This process of relational self -patterning between the nurse(s) and the client results in an emergent life pattern (new order) for the client.

*J. Howell (personal communication, December 1, 1993)

Unifying Model of Complex Caring Dynamics for Nursing Inquiry

The focus of nursing as caring in the human health experience suggests the need for a new model of inquiry that can deal with the complexity of nursing. Clearly, caring relationality is the ground of nursing, and knowledge-in-process, understanding and choice within a relational reflective consciousness are critical components. As such, nursing research is a reflective journey toward possibilities.

A unifying model assumes that nursing is a holistic, complex and dynamic discipline and a part of the unfolding of the complex phenomena of the universe (Marcel, 1967; Ray, 1981). Seeing complex life patterns (the neuro-biophysical, sociocultural, ethical, personal, aesthetic and spiritual), as well as mapping and recognizing those patterns that potentiate choices toward health, well-being, healing or a peaceful death, become the foci of nursing inquiry.

Organization of the Model of Complex Caring Dynamics for Nursing Inquiry

Figure 2 is a unifying model of complex caring dynamics and represents an overarching metaparadigm which integrates the structural components of nursing inquiry and shows the complexity and dynamism of nursing. The model incorporates the views of the science of complexity and choice patterning (Davidson & Ray, 1991). It is consistent with the tenets of the new paradigm in nursing, the unitary-transformative paradigm of Newman (Fawcett, 1993), which identifies features of the new science and nursing as caring in the human health experience. Moreover, it includes components of other paradigms identified in nurs ing: the simultaneity paradigm of human-environment integrality and, in part, the more technically oriented particularistic-deterministic paradigm (Newman, Sime, & Corcorran-Perry, 1991; Fawcett, 1993). The model also reflects Habermas' comprehensive approach to inquiry which integrates competing social paradigms, technical, practical and emancipatory (Bernstein, 1983).

Assumptions

In the Complex Caring Dynamical model of inquiry, there are three fundamental assumptions: first, that caring is the essence of nursing; second, that the nurse researcher engages in a caring relationship, a "participatory we" (Marcel, cited in Speigelberg, 1982) in the process of inquiry; and third that the caring consciousness of the researcher is central to the inquiry both at the levels of data generation and of data analysis. The caring consciousness of the researcher offers significant challenges to the research process, and reinforces the point in complexity dynamics that the observer and the observed are inseparable.

Explanation of the Model

All components of caring inquiry (see Figure 2) are considered relational and reflect a process of engagement or mind-matter connectedness on the part of the researcher. All knowledge generated for research is considered "approximate, that is, all concepts, theories, and findings are limited and approximate" and open to possibilities (Capra, Steindl-Rast with Matus, 1991, p. xv), rather than considered final, predictable, linear or causal. The Technical Caring Dynamics' component especially should be recognized as addressing approximate or limited knowledge because, historically, knowledge generated in traditional science through quantitative or technical means has been represented as the "truth".

The model illuminates nursing and consciousness as mutually embedded in the same way that human beings and the world are mutually embedded. The model is holistic and organized to facilitate research of the complex patterns of nursing's relational caring. Although the model is presented linearly, the arrows indicate that it is dynamic. Each component of the model reflects the complex processes involved in researching life patterns and relational caring patterns in the human health experience. The model attends to the many research voices of nursing (Schultz, 1992).

As diagrammed in Figure 2, the defining concepts of the model of inquiry are depicted as the following:

Life Pattern Forms: Pattern Seeing

Life pattern forms include all human-environment or human-field processes, both material and nonmaterial that are available to be researched. The forms (structures of life processes) can be either ontological, spiritual, religious, ethical, aesthetic, biophysical or psychoneuroimmunological, and be concerned with health, healing, death or dying. In addition, there are sociocultural forms: technical, historical, economic, legal, political, social, organizational and educational. The forms obviously shift from abstractions to concrete life experiences when they are considered for inquiry. They can be researched either separately or in conjunction with each other through the four ways of pattern seeing: Technical, Practical, Critical and Creative. Each has its corresponding methodologic framework and integrative synthesis (to be discussed later).

Pattern seeing is a way of organizing or visualizing caring inquiry. Pattern seeing recognizes the movement of chaos, order and change in nursing phenomena. It shows the critical bifurcation points at the edge of chaos and the movements to a new order in the caring relationship.

Within the four types of inquiry, the researcher seeks to generate data from different foci: through observation, interviewing, the use of instruments, or contemplation. Data are recorded through hand written notations, computer assisted means or audio/video tapes in preparation for data analysis. The Technical, Practical, Critical or Creative Caring Dynamics are the lenses for generating data for pattern seeing.

1) Technical caring dynamics. The focus of inquiry is primarily on the more mechanical, techni cal or biophysiological aspects of life patterns. Quantitative analysis through technical reflective processes (including the role that intuition and interpretation play in the process of mechanical or technical research) is emphasized to identify and recognize patterns (findings). The patterns or findings in this research approach are designated as approximations rather than causal, predictable outcomes.

2) Practical caring dynamics. The focus of inquiry is primarily on the meaning of patterns of actual, practical experience. Ethnographic, grounded theory, historic, phenomenologic and hermeneutic approaches (singularly or in combination) are methods that can be used to describe and interpret diverse cultural life and self patterns. Processes of intentional reflection (dwelling with data, intuition, and interpretation of past, present, and future possibilities) enhance understanding of choice patterns of life, self, and human relationships in the movement of chaos, order and change.

3) Critical caring dynamics. The focus of inquiry is primarily on the praxis of ethical and political social life (Bernstein, 1971). The meaning of "how ought we to live" or "how ought we to care", as we socially interact with culturally diverse persons or groups, is explored. The purpose is to ensure sociocultural change, emancipation or liberation from oppressive conditions. Action, evaluative, or focus group research approaches are used with critical reflecting (reflection focusing on issues that elicit ethical or feminist responses). In this way, new choices for change in human-environment relational patterning can be initiated.

4) Creative caring dynamics. The focus of inquiry is primarily on ideas, imagination and experiential sociocultural life patterns. These can be of a philosophic and aesthetic nature (creative nursing, music, dance, visual art, theater), and spiritual, religious, or ethical nature. Creative Caring Dynamics, as a process of inquiry, facilitates wisdom. It encourages the use of traditional or creative research methods to integrate all interconnected pattern recognizing goals. The creative caring component of inquiry uses transformative reflecting, and affirms the view that knowledge is always in process and continually being revealed. The mystery of the invisible, unfolding meaning of the universe and human experience is "sustained by Divine Imagining "cosmic powers of space, time, and life which are open to creation in the process of becoming (Harmon, 1991 p. 76). Furthermore, human beings are anticipating, always in a state of hoping in relation to future possibilities (Rosen, 1988).

Methodologic Frameworks: Pattern Mapping

Each component: Technical, Practical, Critical, and Creative Caring Dynamics have a corresponding methodological framework for analytical pattern mapping. The methods corresponding to each dynamical view of the caring relationship are ways of capturing data by reflection (see Figure 2). Pat tern mapping details and plans out the strategies which a researcher uses to reveal the meaning of the caring relationship. It makes known the choice-making patterns used in the complex movement from chaos, to order and transformation.

Reflection is a process of thinking and apprehending human environment integral patterning and responds to the question, "How do these data fit into the whole?" or "How is the whole intuited and interpreted by the data?" All methodological frameworks are subject to the reflective process, albeit differently with each particular caring dynamic. Reflection reinforces the active role that consciousness now plays in the process of inquiry.

1. This is especially evident in Technical Caring Dynamics with its corresponding methodological framework of Quantitative Analysis and Technical Reflecting. Even with the use of quantitative tools, the observer cannot be separated from the observed and interpretation enters into this form of inquiry. Within this perspective, the researcher utilizes a qualitative understanding of the whole to obtain a richer view of a phenomenon with the use of different or new quantitative methods. Examples are ARIMA, Discriminant Analysis, Logistic Regression, Spectral or Cosigner Analysis (A. Davidson, personal communication December 28, 1993).

2. The Practical Caring Dynamics component has a corresponding methodological framework of Qualitative Analysis and Intentional Reflecting. This includes the use of qualitative methods of any type for pattern mapping. Examples are phenomenology, hermeneutics or their combination, ethnography, grounded theory or other methods, such as caring inquiry (Ray, 1991).

3. The Critical Caring Dynamics component has a corresponding methodology of Dialectical Synthesis. It uses qualitative and quantitative analysis to comprise Critical Reflecting.

4. The Creative Caring Dynamics component with its corresponding framework of Interconnected Holism uses Transformative Reflecting to map patterns.

Integrative Synthesis: Pattern Recognizing

The integrative synthesis or pattern recognizing relates to the goal of inquiry. Goals differ depending on which method is selected.

1. The goal of Technical Caring Dynamics is patterning studied through different or select quantitative mappings. It seeks technical knowledge that is considered limited or approximate rather than seeking knowledge that is considered absolute or final.

2. In Practical Caring Dynamics, the goal is understanding. Understanding is achieved through recognizing the human health experience and the descriptive and interpretative analysis of patterns of meaning. There is however no complete understanding of reality.

3. The goal of Critical Caring Dynamics is change. Focusing research on praxis, the ethical-political life of interacting cultural groups in different contexts, brings forth patterned knowledge of meaning and a commitment to facilitate liberation from situations that bind or destroy.

4. Wisdom is the goal of the Creative Caring Dynamical inquiry. Creative and imaginative questions are addressed through this approach to research. Wisdom is the result of awareness or insight which, through the use of any, all or new research approaches, recognizes holistic and trans-formative choice patterning in the human field processes. It is the fusion of complexity science, caring, aesthetics and spirituality.

Transformative reflecting allows for the unfolding of a deep sense of personal, interpersonal and spiritual knowing; a knowing wherein the spirit of the researcher and the research interest are nourished so that there is a true and profound attention to the "heart". By opening up to the totality of our being, to creative possibilities, the presence of the mystical can be felt in and through creative action. Faith, hope, and love are apprehended, and greater order or harmony of body, mind and spirit are anticipated.

Implications of Complex Caring Dynamical Model of Inquiry for Nursing

Key considerations of a Complex Caring Dynamical model for nursing inquiry are summarized in the following points:

1. The Complex Caring Dynamical Model was constructed as a unitive foundation for nursing because of nursing's complexity. The discipline of nursing is neither purely science nor purely art, but is greater than the combination of the two. "David Bohm has proposed that science and art in the future should move closer to art" (Briggs & Peat, 1989 p. 200). Complex Caring Dynamics points the way.

2. Complex Caring Dynamics illuminates the role of nurses/nursing in the human health experience by emphasizing the focus of nursing inquiry as caring in the human health experience within the unitive-transformative paradigm (Newman, Sime, & Corcorran-Perry, 1991).

3. Complex Caring Dynamics identifies the caring relationship as the complexity in nursing science. This view offers a challenge to the concept of self-organization which is a central thesis of the science of complexity. Perhaps scientists should entertain the view that all living systems in an interconnected universe do not self-organize at all, but organize through caring relationships, both visible and invisible.

4. Complex Caring Dynamics calls for a reevaluation and dialogue of nursing's fragmented philosophy (ontology, metaphysics, epistemology, ethics and teleology).

5. Complex Caring Dynamics combines approaches to inquiry into a unified whole that responds to the many voices of nursing (Schultz, 1992).

6. Complex Caring Dynamics incorporates the different extant paradigms in nursing to facilitate an approach to inquiry that is in tandem with the holistic and complex nature of nursing.

7. Complex Caring Dynamics highlights the primordial nature of caring as the action of love, the magnetic appeal or pull in the universe.

8. Complex Caring Dynamics shows that the nature of complexity is always anticipating (Rosen, 1988), always hoping and is, therefore, the foundational process of creative evolution (Bergson, cited in Harmon, 1991).

9. Complex Caring Dynamics shows that in accepting knowledge-in-process as the epistemological basis of reality, faith must be placed in both the esoteric phenomena of human consciousness, the deep intuitive inner knowing (interiority, Lonergan, cited in Webb, 1988), as well as, the esoteric encountering of physical sense data.

In his book, Beyond the Quantum, Talbot (1987 /1988) characterized the nature of truth as growing, changing, and transforming by stating, "The human race has reached a threshold of wisdom in which it can at long last abandon the lure of completeness and recognize that whatever form they take, there will always be new vistas to be discovered in science, and new worlds awaiting us beyond the quantum" (p. 224). In nursing, we hold the key to these new vistas because through caring for others, we hold "in the center of our hearts" the conscious ness of the universe, love, the magnetic appeal and pull of the universe.

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Theoretic and Applied Chaos in Nursing á Summer 1994 á 1:1 Sabelli et al.: The Process Method

The Process Method of Comprehensive Patient Evaluation BASED ON THE EMERGING SCIENCE OF COMPLEX DYNAMICAL SYSTEMS

Hector C. Sabelli, M.D., Ph.D., Linnea Carlson-Sabelli, R.N., Ph.D., Joseph Messer, M.D.

Introduction

The complexity of biological, social and psychological processes creates the conflicting needs of professional specialization and cross-disciplinary integration. There is a hope that the newly evolving science of complex dynamical systems chaos theory (Baker & Gollub, 1990; Lorenz, 1963), catastrophe theory (Thom, 1975, 1983), thermodynamics of processes far-from- equilibrium (Prigogine, 1980; Prigogine & Stengers, 1984), fractal geometry (Mandelbrot, 1983) and process theory (Sabelli & Carlson-Sabelli, 1989) may serve to integrate clinical care.

This article presents a method for the comprehensive evaluation of patients based on process theory. The process theory notion of physical priority and psychological supremacy serves as the foundation for a comprehensive physiological and socio- psychological evaluation which leads to a comprehensive approach to patient care (Sabelli & Carlson-Sabelli; 1989, 1991). In a companion article (Carlson-Sabelli et al., accepted for publication) a process theory application to electrocardiography, a new method that provides time graphs of changes in patterns of cardiac timing associated with emotional and biological processes, will be introduced. Process theory and its application to evaluating patients and developing strategies for intervention will be illustrated in both with the same case of a person with coronary artery disease.

Physiology is a term that originally meant the study of nature, both physical and psychological. The early physiologists, Heraclitus (the originator of process philosophy, who introduced the concepts of "psyche" and "logos", hence psychology) and Empedocles (the Italian physician who authored the first theory of biological evolution) focused on the process of change rather than on static structures. They stressed the essential unity of natural and psychological processes, the interconnection of opposites (inspiration and expiration, growth and decay, sleep and wakefulness, priority and supremacy, simplicity and complexity, structure and spontaneity, health and illness), and the creativity of evolution. After centuries of focus on static structures, mechanical processes, and analytic separation, modern science has returned to these general principles (Prigogine & Stengers, 1984). Process theory formulates them as a set of scientific, empirically testable hypotheses, from which arises a methodology to study complex processes using the techniques of mathematical dynamics.

Process theory (Sabelli, 1989, 1991a, 1991b; Sabelli & Carlson-Sabelli, 1989, 1991, 1992; Carlson -Sabelli & Sabelli, 1990, 1992a) focuses on long-term patterns of interactions rather than on isolated events, stable structures or stationary processes. Over time, these processes co-create new and more complex forms of organization, in contrast to evolving towards equilibrium and other simple forms of stability. Process theory operationalizes process philosophy via the mathematics of nonlinear dynamics. This linkage allows one to test its postulates, study processes mathematically, and plot patterns of complex relationships among biological, social and psychological dynamics. Here we shall introduce process theory from a biological perspective and discuss practical applications to patient care.

Human anatomy the most complex product of natural selection and evolution embodies the most fundamental forms of natural processes (VanÐdervert, 1988; Sabelli, 1989). Consider the three basic dimensions of body and brain. First, there is a dorso- ventral asymmetry that reflects the forward direction of movement ( asymmetric action). Second, there is a bilateral organization, including pairs of limbs, sensory organs, lungs, and brain hemispheres, that display significant asymmetries, alternate in dominance, and complement each other (union of opposites). Third, there is a vertical hierarchy of organization in which the simple levels have biological priority over the more complex, while the more complex levels have supremacy. Thus, the circulatory system has priority over the brain which depends on it for nourishment, and the brain has supremacy over the body,. The concept of priority/supremacy was developed by the 19th century British neurologist, H. Jackson, with regard to the central nervous system. Here the lower levels (bulbar and spinal cord) have priority in the evolution of the species, as well as in mediating the input and output for the higher levels, whereas the higher level (brain cortex) controls the function of the lower levels.

This hierarchy of neural levels parallels the levels of organization of nature. The brain cortex relates to consciousness, emotions and knowledge, while lower levels deal with the physical processes of temperature, movement and oxidation (respiration). Using the brain as an exemplar, other natural processes and structures may be expected to (1) exhibit an asymmetry which reflects the unidirectionality of action in time; (2) include a pair of complementary opposites (alternating in predominance in time); and (3) be hierarchically organized in levels of complexity. For example, simple biologic patterns are ever-present (priority), and the more complex components have supremacy (local generation of complex patterns through interaction of simple components). Process theory postulates that all processes include these three basic forms: asymmetry, opposition, and hierarchical structure. And each process has three corresponding and inseparable aspects: energy, information, and material structure. Energy is a unidirectional flow; information is a difference between two opposites; and matter is a tridimensional structure which is the fundamental level upon which more complex forms of organization are developed.

As the same fabric, energy and matter, makes up physical as well as psychological processes (monism), it is their form, or in-for-mation, that differentiates one from another. Information never exists alone, but it is always carried by energetic or material tokens (Shannon, 1964). Likewise, energy and matter always carry information such as a pattern of change in time, and the external shape and the internal structure of a material structure in space. Information can be described by numbers, as in a computer or in a digital recording. The patterns of processes can be described as a sequence of numerical properties (arithmetical hypothesis) and can be easily remembered because they are named for the number of dimensions each law addresses: (0) Symmetric flux; (1) Asymmetric oneness (action); (2) Union of opposites; (3) Organization: Co -creation of a third higher dimensional organization by the interaction of two or more processes.

(0) Symmetric flux: Zero represents the absence of energy, matter and information, but paradoxically, it is inseparable from them. Matter is contained in space and contains vacuum; in turn, the vacuum is a state of constant flux of subatomic particles. Energy flows towards equilibrium, which also is a reversible flux rather than absolute rest. Information is always mixed with uncertainty, ignorance and error. Order mixes with disorder the 0 order of chance. The recognition of chance implies the use of statistical methods in research, and the acceptance of "bad luck" as a sensible explanation of illness and conflicts. All processes are immersed in, and contain, random, symmetric flux, unobservable except as an absence, while observables (matter, information, energy) are asymmetries within the symmetric flux.

(1) Action asymmetry and oneness (asymmetry): Everything is a flow of energy in time (action = energy x time in physics), and hence everything changes, acts and interacts. There is a oneness in nature; biological, social and psychological processes all are physical processes. One is many and many is one, said Heraclitus, the originator of process theory. There is a unidirectionality to nature; processes share the uni-directional form of time, its asymmetry from past to future (like a life or a personal narrative) which makes all processes irreversible (in contrast to the reversibility of time postulated by mechanical theory). Each process, no matter how complex, includes a component of unidirectional flow of energy and can be described by point attractor models in dynamics. The universe as a totality flows in the one direction of time; uni-verse means unidirectional flow.

(2) Union of opposites (opposition): There is a duality to nature, everything contains difference and a difference implies information. Two-values are required to code information according to Boolean mathematical logic and Shannon's (1964) mathematical theory of communication. Opposition, the co-existence of two complementary processes is a universal form. These opposite actions create cycles. The phases of respiration and cardiac contraction illustrate how biological processes always include an alternation of opposites. Opposites that co-exist in any one process are, by necessity, more similar than different. Because opposites have both synergic and antagonistic components, pairs of coexisting opposites cannot be represented as extreme poles in a lineal continuum; since oppo sites can vary independently, they are better represented as orthogonal axes defining a plane (Carlson -Sabelli & Sabelli, 1992b; Carlson-Sabelli, Sabelli, Patel & Holm, 1992; Sabelli, 1992).

Opposite processes alternate in predominance, so they never co-exist in the same place, at the same time, and in the same respect. Even in quasi-cyclic processes, one process has priority over its opposite, while its opposite eventually predominates ( supremacy); inspiration and expiration, systole and diastole, are obvious examples. More interesting is the coexistence of opposites in unidirectional processes: in physics, the maximization of entropy (second law of thermodynamics) coexists with cosmological and biological evolution (enantiodromia) (Sabelli, 1989; Sabelli et al., 1994). Similarly, we can grow up and grow old simultaneously, but each opposite predominates at different times.

Because opposition is universal, all processes have at a minimum a tridimensional structure, which is evident in our perception of tridimensional space. There are many other systems with 3 or more opposites. Color theory specifies three primary colors, each the inverse of the addition of the other two [Red = - (Yellow + Blue)]. A similar system of three complementary opposites governs the combinations of quarks in elementary particles. Topology (the third pillar of mathematics according to Bourbaki) describes this nonlinear organizational form of processes.

(3) Organizational diversification: the co-creation of higher dimensional organization : Development, individuation and evolution are processes of diversification that increase the number and complexity of processes. The interaction of two opposites produces processes of three or more dimensions. For instance, when a couple procreates they move from a two to a three member family system. Similarly, interpersonal choices result from the interaction of opposite motivations of attraction and repulsion. Physical, biological, social and psychological evolution does not simply follow a lineal, predetermined succession of stages as does embryological development. They include diversification and the creation of novelty and complexity; even simple physical processes can spontaneously create complexity when fed with energy. Energy polarizes opposites and thereby can engender an all or none switch or produce high intensity fluctuations leading to turbulence and chaos from which novel patterns and structures emerge.

Prigogine described the creation of new and more complex structures in chaotic chemical systems that are far-from-equilibrium. Just as the intercourse of opposites is the main mechanism of novelty in biological processes, the interaction between opposite feelings or ideas can co-create novel perspectives.

Beyond its applications to psychophysiology, the process method provides a comprehensive approach to patient care which we shall illustrate with a clinical case. A 47-year-old man enters the emergency room of a small town hospital complaining he felt chest pains while driving to see his father, who just had a myocardial infarct. The man looks anxious and pale, perspires conspicuously, and voices fear he is having a heart attack "as my father did." He is rushed into an examining room, hooked up to an electrocardiogram, and a nervous young doctor, on the first day of his internship, yells at a nurse, "Quickly, please. This is an emergency." Starting an intravenous line proves difficult, and the nurse becomes flustered, tense, and angry with himself. A few minutes later, the doctor and nurse unsuccessfully struggling to find a vein, comment to each other about the patient's excessive weight and smoking. The EKG, which up until then had been unremarkable, begins showing elevation of the S-T segments in V 2 to V 4, followed by ventricular fibrillation, with loss of consciousness. Defibrillation is successful, and the next day, the nurse praises the patient, for having come to the hospital immediately. "It's lucky, John, you were already in the emergency room when you had the bad episode."

There is, however, another possibility: Anxiety may have caused his chest pains, and the events in the emergency room may have worsened, rather than relieved, this anxiety. The consequent cat echolamine release may have been the immediate cause of the infarction and/or the fibrillation. Although fear and anxiety commonly accompany medical emergencies, they are not trivial psychological concomitants that we can afford to ignore. Relieving the patient's anxiety, may have made a major difference in the outcome, and it requires no more than appropriate communication with the patient, being in control of oneself, and reassurance. Once the patient is in the emergency room, there is no point in confronting denial, and it is much to the point to decrease anxiety, whether pharmacologically or psychotherapeutically. These steps which are no more than good patient care, illustrate an integrative approach that attends at the same time to biological priorities and to the supremacy of psychological factors. This two-pronged approach attends simultaneously, rather than sequentially, to the biological and psychological aspects of the illness. It thus differs from an exclusively biological focus of depersonalized medicine. Sharing the fundamental tenets of the bio-psycho-social approach of systems theory (Engel, 1980), the process method is a bio-socio-psychological approach (Sabelli & Carlson-Sabelli, 1989, 1991; Sabelli, 1991a, 1991b, 1991c; Carlson-Sabelli & Sabelli, 1992a). As the psychological aspect is considered the highest level, personalization is viewed as the criterion for excellence in patient care. The consideration of social roles (e.g. family roles and employment behaviors) is secondary to the analysis of individual psychology.

The emotional trigger of coronary events illustrates the supremacy of the more complex psycho logical and personal processes. On the day of the infarct, John K. was feeling angry and anxious regarding both his father and his current work. In the emergency room, John K. reported feeling even more fearful when the difficulties in starting an intravenous line were compounded by the nurse's apparent nervousness. Was the doctor unable to treat him? Why did the nurse ask about negative prognostic factors, his weight and his smoking, but never once reassure him that effective treatment would be provided? This made him angry, as well as anxious. The coexistence of anger and fear, two emotional opposites, illustrates the union of opposites.

In the emergency room, patient, nurse, and doctor interact with one another as a function of their respective social roles, rather than as individual persons. In the patient's eyes, white coats give professionals the authority to cause, or to relieve, anxiety. Social roles are more important than personal characteristics in the emergency room because patient, nurse and doctor interact as a function of their respective roles before they know each other as individuals. This is true for other social roles: adult and child; women and men; employer and employee. Generally, social processes occupy an intermediate level between biological and psychological processes, and often are mediators between them. In this case, it is unlikely that the emergency room staff was intentionally callous toward the patient's psychological needs. Rather, they focused exclusively on his biological care and disregarded the patient's anxiety because their training focused them on the biological aspects of illness.

It is the current climate of economic and scientific materialism that is leading professional education, and hence patient care, down the narrow path of primarily biological care. Technological progress, emphasizing the scientific treatment of illness, often overshadows traditional practices which were more personal and humanistic. But this bias toward medical bio-technology should encourage, not discourage, nursing to complement it with an approach that includes the psychological and interpersonal dimensions of illness and its therapeutic treatment.

The bio-socio-psychological approach recognizes that while the more personal aspects of the patient may not be apparent early in treatment, they must eventually be addressed and then should dominate the plan of action. Either the care of the patient is adapted to her or his personal needs, or the person is reduced to a case. In this example, John K was referred to by the emergency room staff as "the M I." In the coronary care unit, he graduated to "John." This casual use of his first name, becoming standard in American hospitals, was particularly unsatisfactory to John K., who preferred to be known as Mr. K. This loss of status also contributed to his sense of loss of control.

In view of the limitations of the small town hospital, it was decided to transfer Mr. K. to a large medical center for bypass surgery. At the Coronary Care Unit, Mr. K roomed with an elderly lady who could not sleep without her radio on; both felt embarrassed sharing the room with a person of the opposite sex. The nurse told John K. to learn to sleep with the music, making him angry. He felt the nurse was not simply violating his rights, but endangering his life. Even after John K. was transferred to a clinical ward of the hospital, his sleep continued to be systematically interrupted by the nursing staff. A dissolution of the normal sleep /wakefulness pattern by fragmentation of nighttime sleep, and a considerable amount of daytime sleep, has been observed in cases of myocardial infarction. This suggests a generalized disruption of biological rhythms (Broghton & Baron, 1978). Since hospital routine is probably the cause of this disruption of biological rhythms, hospital care has negative, as well as, beneficial effects a union of opposites which can be remedied, at least in part.

On a smaller scale, when Mr. John K complained that his bed sheets were one foot short, and his heels rested on the mattress, he was told all the sheets in the hospital were too short for the beds because of a purchasing error. John K. felt anger, not unusual for him, and he felt depersonalized, which was a new and unpleasant experience. The reader may doubt this factual report of treatment, but these occurrences took place in a large medical center. Serious mistakes may remain infrequent in patient care, but significant annoyances frequently occur as a result of the depersonalization of hospital care (Anderson, 1981). To the public, hospitals feel not only impersonal, but also depersonalizing. The alternative is personalization (Sabelli & Synnestvedt, 1990). This is a desirable goal because of the moral progression from the biological level of interaction, to the social, to the personal.

But personal care is not a part of high technology medical care. During the month he remained in the hospital, the attending physician talked to John K. for no more than five minutes each day. It was too short a time to attend to his psychological needs and he was always surrounded by medical students. When John K. asked when he would be able to eat solid food the doctor expressed surprise that he was still on a liquid diet. "The resident obviously forgot to change your diet," he said. John K. felt angry that his needs were being ignored, and fearful that more important ones were also being neglected. Once again the coexistence of emotional opposites is illustrated.

A week later, John K. realized he was receiving intravenous saline and, at the same time, was on a salt-free diet to protect his heart. At this point, he began to assert greater control over his own care. By gaining control, John K. felt relief as he eliminated the contradiction generated by an impersonal and uncaring process, replacing it with a personalized plan.

Personal issues significantly affect the course of hospitalization. During one of the wife's visits, an argument developed. John K. blamed his wife for creating the argument, and accused her of potentially endangering his health. His fear has a measure of truth. Chaotic attractors are exquisitely sensitive to external influences, and minor variations in input produce unpredictable changes in output ("butterfly effect"). The prominence of chaotic processes in cardiac rhythms may explain how psychosocial stresses can produce major-at times fatal-changes in cardiac patients. The nurse did not confront either spouse, as this would have further escalated their anger, nor did she accept their behavior, which needed change. She was at once supportive of both, and firm with both in redirecting their behavior. This is what we call a partial contradiction, the main psychotherapeutic maneuver that derives from the union of opposites.

In later visits, conflict between John K. and his wife persisted and escalated. The spouses grew irritable, and both developed sleep, energy, and mood disturbances indicating depression. This depression may explain their inability to reduce their conflict. The parallel development of symptoms in each spouse exemplifies the concept that opposites are more similar than different. Once again, the nurse, closer to the patient and family, served as an intermediary to obtain necessary psychological assistance to resolve the conflict.

III. Process Guidelines for developing psychotherapeutic interventions

The process method allows nurses to integrate biological, social, and psychological processes as factors in patient care the bio-socio-psychological method (Sabelli & Carlson-Sabelli, 1991). It also provides concrete guidelines for psychotherapeutic interventions including the use of action methods, partial contradiction, and diversification (Sabelli, 1989). Conceptualizing life as a process which includes unidirectional, cyclic and creative aspects provides a framework to guide therapy, which contrasts with the naive desire of many patients to have their problem "fixed" by returning to the past.

Both patients and clinicians can benefit from conscious use of the three types of processes in their behavior. The basic guidelines are: Act, do not react. Respond, do not ignore. Co-create.

Act: the clinician must display her or his initiative and spontaneity. Simply awaiting the patients' complaint fails to elicit their trust, to demonstrate nursing ability or to use our knowledge to its full. It seems equally important never to react with anger or panic to the patient, as this can only increase the already existing conflict or fear.

Respond: the clinician must incorporate in her or his action a clear response to the patient's needs or requests. Appearing to ignore needs can only increase uncertainty, fear, anguish, or anger.

Co-create: active participation in one's treatment, rather than simply being a patient, promotes health and diminishes conflicts with the treatment team. Creative solutions can make the difference for the amputee, the man with cardiac failure, the post-hysterectomy woman, the neurologically-impaired patient, as well as for all psychiatric patients. It is a fallacy to see illness as having a predetermined course. Illness is an open process, subject to environmental influences and to the creative action of therapists and patients.

Patients' attitudes towards illness and treatment are ultimately dependent upon their beliefs regarding determinism, luck, choice and creativity. The clinician should learn the patients' assumptions and point out how every one of these factors enters into the therapeutic situation. It is useful that patients learn the causal factors which influence the course of their illnesses, so they can modify them. But it is also necessary for the clinician to recognize the elements of "luck" and of ignorance regarding pathogenesis. Otherwise we may actually be blaming the patients for their illnesses and thus reducing their well-being and self-esteem. These are precious components of health and healing.

The union of opposites guides the development of these process concepts regarding patient care. For instance a healthy heart rate varies, adapting itself to the needs of the organism. In contrast, reduction in the range of variability (bradycardia as well as tachycardia) represents pathological conditions. The most severe pathology is a fixed heart rate, a predictor of imminent death (Goldberger & West, 1987). Recognizing the asymmetry of time (unidirectionality) serves to promote the use of available capabilities now. Life can actually pass by those who wait for full health to live. It encourages us to construct new avenues for ourselves rather than think of old expectations that may not be consistent with our current potentialities. Just as hardly anyone is totally healthy, sick persons are to a great extent healthy -a union of opposites.

In evaluating a situation, one must give priority to the objective data but also recognize the unavoidable supremacy of the subjective interpretations (Carlson-Sabelli & Sabelli, 1984). The meaning of illness, and the reaction to it, can only be under stood in the context of the person's life. A heart attack represents an irreversible event that high lights the asymmetry of time from youth to old age and death. The event makes the patient aware of time's irreversible flow. Illness reduces competitive ness, and shortens the time available for attainment. When John K. returned to his job, he found that he had been displaced by others. He reacted by increasing, rather than decreasing Three traits associ ated with coronary illness: to compete, to rush and to become angry.

When work, entertainment, travel, and/or family life become curtailed, process theory suggests that the psychosocial treatment should focus on the development of alternatives-diversification. Whereas growing old is unavoidable, growing up may be continued until the time of death. Competitiveness should be reduced and competition redirected. Irrational rushing should be channeled into greater selectivity of goals. Anger should be lessened by reducing conflict and by raising the tolerance to conflict inherent in everyday life. Reducing conflict makes use of the concept of the union of opposites. First, by using the role reversal technique to increase the insight of spouses into each other's feelings (Carlson-Sabelli & Sabelli, 1984). And second, to understand deep feelings obscured by outward emotional expressions. Thus, for every strong emotion, behavior, or statement, one should explore how the opposite emotion, behavior or statement is implied, included, or is also true. When a strong emotion is expressed, we should look for the presence and enhancement of its opposite: love /hate, anger/fear, pain/pleasure, self-righteousness /guilt are examples. When someone expresses a strong fear, one explores how this is also a wish and vice versa. Examples that can be both wishes and fears are success, responsibility, intimacy and peace. It is particularly important to pay attention to what is not said and to explore the opposite of what is said.

IV. A Process Approach to Psychocardiological Research

Are psychological interventions as important as controlling cholesterol levels? Only research can give an answer, research that must be done. Meanwhile, practicing clinicians need to respond to the presenting characteristics of the patient being treated. Is angina triggered by exertion or by emotions? What are the emotional triggers for angina? Are there relevant patterns of emotional activity that influence the course of action?

Many of these questions may have answers which only apply to a particular individual. This is because human development includes, not only a predetermined sequence relating to age, but also variable components relating to social roles and unique components resulting from the individuation of each person. It is therefore necessary to study each person individually. In principle, mathematical dynamics provides a methodology, however, studying the temporal dynamic pattern of emotions is very difficult because the data is subjective and difficult to gather. Dynamic analysis requires numerous observations that are impossible to record during the course of daily behavior. We are now studying the patterns of cardiac activity (changes in heart rate over time) that accompany emotional activities (electropsychocardiography [EPCG]). By linking information recorded in the patient's diary to time graphs of PQRS Wave recurrences, a process theory application (Carlson-Sabelli et al., 1994; Sabelli et al., 1994, Sabelli et al., in press) of recurrence plot method (Eckmann, Kamphorst & Ruelle, 1987; Webber & Zbilut, 1994; Zbilut, Webber, Sobotka & Loeb, 1993; Zbilut & Webber, 1992) is being developed. We are beginning to see relationships between emotional states, behaviors and cardiac timing. This objective evaluation of patterns of cardiac activity that are largely controlled by the central nervous system, will serve to clarify the interactions between biological and psychological processes. They will be illustrated in a companion article in the next issue of this journal.

Acknowledgement: We are thankful to Mrs. Maria McCormick of the Society for the Advancement of Clinical Philosophy, for her invaluable assistance in supporting this project.

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ANNOTATED BIBLIOGRAPHY

CHAOS THEORY Nonlinear Dynamics

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An in-depth discussion of the major components of Chaos theory, using understandable illustrations to clarify very complex ideas without reducing them to simplicity. It is a good overview and progresses from simple to complex concepts.

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This is a large picture book which provides lots of graphic, computer generated, and naturally occurring illustrations of the various components, characteristics, and principles of Chaos theory. This is very helpful for the visual learner.

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This book is a compilation of several authors who presents basic nonlinear mathematical formulas used to determine chaoticity. Several chapters explain how to measure chaos quantitatively using Lyapunov exponents and fractal dimensions. Holden's book would be a useful reference for understanding the math once the concepts of chaos are fully understood. It is helpful for the non- mathematician.

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Chaos and Fractals was written by mathematicians for both technical and nontechnical audiences. This comprehensive text presents a broad overview of Chaos theory, fractal geometry, and nonlinear dynamics. Each chapter suggests relevant "experiments" as well as a computer program the reader may use to enhance understanding of the chapter's content. Students and scientists interested in learning about the mathematical foundations of Chaos theory will benefit from this text.

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This book uses a creative approach in presenting the modern mathematics that have emerged in the later half of this century. Approximately half of the book is devoted specifically to basic chaos concepts. It is user friendly, interesting, and has several full color plates depicting what is happening mathematically. Inexpensive.

Schuster, H. G. (1988). Deterministic chaos (2nd ed.). New York: Federal Republic of Germany, VCH.

The author does a very nice job of introducing the reader to the basic concepts of Chaos, and provides explanations of Chaos theory using mathematical equations. Several chapters provide pictures which aid in understanding the concepts. This book is very helpful for understanding the implications for using Chaos theory. Intermediate level reading.

Stewart, I. (1989). Does God play dice?: The mathematics of chaos. Cambridge: Blackwell.

This is a terrific reference for the non-mathematician who is trying to understand the mathematics of Chaos theory. It is very readable.

Vicenzi, A. E. (1994). Chaos theory and some nursing considerations. Nursing Science Quarterly, 7(1), 36-42.

The chaotic concepts of aperiodicy, attractors, sensitive dependence on initial conditions, phase space and fractals are discussed. Each concept's connection to physics and mathematics is cited and suggested applications for nursing science are outlined. Conclusions include redefining health, nursing, and community in chaotic terms.

Waldrop, M. M. (1992). Complexity: The emerging science at the edge of order and chaos. New York: Simon & Schuster.

Waldrop identifies the edge of chaos as the balance point between order and chaos where the components of a system never quite lock into place, yet never dissolve into turbulence. The goals of the science of complexity is a general law of pattern formation in nonequilibrium systems. Key concepts in the new science, such as emergence, collective behavior, spontaneous organization and evolution are discussed.

West, B. J. (1990). Fractal physiology and chaos in medicine. Singapore, NJ: World Scientific.

West uses examples from biomedical data to demonstrate nonlinear processes. The author explains fractal physiology, and includes explanations of terms and nonlinear formulas. Intermediate reading.

Wheatley, M. J. (1992). Leadership and the new science: Learning about organization from an orderly universe. San Francisco: Berrett-Koehler.

This is an interesting application of Chaos theory to management and leadership within organizations. Chaos theory gives new understanding to the concepts of change and disorder as they are encountered in organizations.

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