Using chaos theory: the implications for nursing

N U R S I N G T H E O R Y A N D C O N C E P T D E V E L O P M E N T O R A N A LY S I S Using chaos theory: the implications for nursing Carol Haigh BSc MSc RGN Senior Lecturer, Pain Management, Faculty of Health, University of Central Lancashire, Preston, UK Submitted for publication 7 March 2001 Accepted for publication 30 November 2001 Correspondence: Carol Haigh, Department of Nursing, Faculty of Health, University of Central Lancashire, Preston PR1 2HE, UK. E-mail: loracenna@hotmail.com Journal of Advanced Nursing 37(5), 462±469 Using chaos theory: the implications for nursing Aims of the paper. The purpose of this paper is to review chaos theory and to examine the role that it may have in the discipline of nursing. Background. In this paper, the fundamental ingredients of chaotic thinking are outlined. The earlier days of chaos thinking were characterized by an almost exclusively physiological focus. By the 21st century, nurse theorists were applying its principles to the organization and evaluation of care delivery with varying levels of success. Whilst the biological use of chaos has focused on pragmatic approaches to knowledge enhancement, nursing has often focused on the mystical aspects of chaos as a concept. Conclusions. The contention that chaos theory has yet to ®nd a niche within nursing theory and practice is examined. The application of chaotic thinking across nursing practice, nursing research and statistical modelling is reviewed. The use of chaos theory as a way of identifying the attractor state of speci®c systems is considered and the suggestion is made that it is within statistical modelling of services that chaos theory is most effective. HAIGH C. (2002) Keywords: chaos theory, statistical modelling, nursing theory, nursing research Introduction The genesis of chaos The science of chaos has been used in many disciplines that contribute to health care systems. It is not overly fanciful to suggest that chaos theory is itself a dynamical system and that the application of the theory has changed focus over time. However, as the discipline evolved, chaos thinking was applied to a variety of disciplines as diverse as epidemiology and economics. By the 21st century, North American nurse theorists were applying its principles to the organization and evaluation of care delivery. This paper has two sections. The ®rst half of the work is an exploration of the concepts inherent in chaos theory. The second half concerns itself with a critical evaluation of the contribution that chaos thinking has made to the discipline of nursing, and a consideration of the function that chaos may have in the future development of nursing care. The suggestion that the universe does not run rigidly in accordance with the laws of classical physics was expressed within the uncertainty that was inherent in quantum physics. Hawking (1987) noted that this uncertainty undermined the notion of a completely deterministic universe, in that this reformulation of classical physics opened the way for unpredictably and randomness. Feynman (1965) had earlier challenged this view to some extent by suggesting that quantum mechanics should not be viewed as an escape from a completely deterministic universe. However, he did go on to acknowledge that classical laws showed a degree of ¯exibility in that tiny ¯uctuations could be ampli®ed by the interactions of dynamic systems until they become large scale effects. The person who would explain this notion and articulate the foundations of chaos was not a physicist but a meteorologist. 462 Ó 2002 Blackwell Science Ltd Nursing theory and concept development or analysis Edward Lorenz, meteorologist at the Massachusetts Institute of Technology, had set up his computer to model weather systems with 12 variable patterns. One day, when reviewing a particular sequence, Lorenz took what he thought was a short cut and began running the sequence in the middle instead of at the beginning; this was the ®rst step towards encountering chaos. The second step was when, instead of typing his data with its normal six decimal places, he only input three decimals in order to ®t all of the numbers onto one line. These two apparently tri¯ing changes were enough to alter the sequence dramatically. What Lorenz had discovered was that the smallest change in the initial circumstances of a dynamical system can drastically affect the longterm behaviour of that system. The popular expression of this is the `butter¯y effect', the implication being that if a butter¯y ¯aps its wings today the tiny changes in air pressure will eventually lead to a hurricane at some future point. Stewart (1997) argues that this is a somewhat simpli®ed example, and contends that the most the butter¯y could hope to achieve would be to make a hurricane (which was going to occur anyway) occur a little earlier or later than it would have otherwise. The important part of Lorenz's discovery was that these small changes in initial conditions could be mapped and calculated to identify chaotic elements in the system. This meant that the mathematics that allowed chaos to be plotted and replicated had been found. The fundamental components of chaotic systems could be identi®ed and the effect of parameter manipulation could be tested. By altering his data in an apparently unimportant manner, Lorenz had brought about a dramatic change. For the ®rst time, apparently disordered systems were shown to exist with an underlying `order' beneath the disorder. The elements of chaos had been identi®ed and, given suf®cient system parameter information, could be predicted and represented graphically. The elements of chaos The technically accepted de®nition of chaos has been suggested to be Processes that appear to proceed according to chance, even though their behaviour is in fact determined by precise laws (Lorenz 1993, p. 4). At ®rst glance, this de®nition is reminiscent of the classical physics view of a deterministic universe. However, on closer inspection this interpretation is a great deal more complex. It must be emphasized that what Lorenz refers to as `processes' in the de®nition cited above most other authors, notably Gleick (1987), Stewart (1997) and Kosko (1994), refer to as Chaos theory and nursing systems. Chaos is seen to be merely one outcome of some systems' evolution. The elements of chaos can be identi®ed as: · a dynamical system; · identi®ed system parameters; · a speci®ed equilibrium state; · a speci®ed state attractor. Each of these elements contributes towards chaotic outcomes in system development and, as such, deserves explanation at this point. Dynamical systems Chaos, in any system, depends upon that system being a dynamical one. A dynamical system is one that changes with time. Kosko (1994) argues that, in theory, everything is a dynamical system in the sense that all systems begin with an initial condition and traverse through transient states to an equilibrium state. The initial condition of any dynamical state will be that of maximum potential energy. The end equilibrium state is typi®ed by minimum potential energy. The initial state potential is transformed into kinetic energy as the system moves through its intervening transient states to equilibrium. System parameters A fundamental characteristic of a dynamical system is change. In mathematics, equations that express rates of change are referred to as differential equations. The rate of change is ascertained by the difference in values of either temporal or spatial parameters (Stewart 1997). This change in system parameters is a fundamental element of chaos theory. It is encapsulated by the phrase `sensitive dependence upon initial conditions'. It suggests that if you pick two different starting points in a system, no matter how closely they can be plotted mathematically, they will give rise to two different paths that will eventually diverge over time. Equilibrium states When a dynamical system has reached a state of minimum potential energy, it is said to be in an equilibrium state. A dynamical system can have two sorts of equilibrium states: periodic and aperiodic. Thus, it can be seen that a dynamical system will eventually settle into one state or another: it will be stable (periodic) or unstable (aperiodic). It may appear to be an oxymoron to describe an equilibrium state as unstable, as `equilibrium' typically describes a balanced state. However, Lorenz likens these two states, stable and unstable, Ó 2002 Blackwell Science Ltd, Journal of Advanced Nursing, 37(5), 462±469 463 C. Haigh to the difference between balancing a pencil on its ¯at end or its sharpened end. If balanced on the ¯at end the pencil is stable, in a state of periodic equilibrium. It will stay in that state forever, unchanged as time passes If the pencil is balanced on its sharpened end it will only balance for a matter of microseconds before it becomes unstable: its equilibrium is aperiodic. The equilibrium of the pencil is unstable because any slight disturbance in the plane in which it is resting will presently evolve into a different state, that is, a horizontal pencil rather than a vertical one. In practice, it is impossible for the human eye to distinguish between a pencil that is vertical and one that is tilted by a minute amount. This small change means that the maximum energy potential of the balanced pencil is dissipated by the changes in balance until a minimum energy potential is reached when the pencil overbalances. Once a dynamical system has reached equilibrium, whether periodic or aperiodic, it manifests itself as an attractor. Speci®c state attractors Stewart (1997), rather unhelpfully, suggests that an attractor is whatever a system settles down to be. However, it is true that the end state of a system will dictate what sort of attractor the system will become. An attractor can also be de®ned as a mathematical mapping concept that allows the geometry of a chaotic system to be represented graphically. The simplest attractor that a system can settle into is a ®xed-point attractor. In this case, the system will stop at a ®xed point. For example, if you drop a stone from your outstretched hand, gravity will bring the stone to a stop when it hits the ground. The stone will not continue to drop through the ¯oor: it has reached equilibrium. The dynamical system that was the stone moving through a gravitational potential becomes a ®xed-point attractor. The second example of a periodic equilibrium state is that of the limit cycle attractor or the closed loop attractor. The clearest example of a closed loop attractor is that demonstrated by the Volterra two-species differential model of predator/prey populations (Cohen & Stewart 1994, Kosko 1994). Basically, Volterra postulated that as prey population rises, so will predator population, until the balance tips and the prey population begin to fall as a result of over-successful predator breeding. As prey population falls, so will predator breeding rates until the original scenario is replicated and the cycle can begin again. As long as all the other parameters remain unchanged, the predator/prey population will move around in this cycle forever. Both ®xed-point attractors and limit cycle attractors are manifestations of periodic stable systems. When represented 464 graphically, both ®xed-point attractors and limit cycle attractors tend towards classical shapes, such as straight or curvy lines. The converse is true of aperiodic equilibrium. Aperiodic equilibrium in the system will appear to wander through its state at random. The slightest change in the system state will cause the state to diverge. There is no classical shape to a chaos attractor, and its randomness when plotted gives rise to fractals. Fractals are a way of demonstrating and measuring qualities that otherwise have no clear de®nition, such as degree of roughness or irregularity. In contrast to Euclidian shapes that are regular, squares, circles, triangles and so on, fractals are irregular (Sardar & Abrams 1999). Fractals show self-similarity which implies that any subsystem of the fractal is structurally identical to the overall fractal shape (Figure 1). Thus, the end state of any dynamical system can be plotted mathematically. However, although the system may diverge from a classical pathway, two important things must be borne in mind. First, although the system appears `random', its behaviour is deterministic and can be predicted via mathematical formulae. Second, the system will never diverge to the extent that it leaves its attractor state. A further concept that is closely allied to chaos theory is that of nonlinearity. Chaos is nonlinear in nature although nonlinearity does not necessarily imply chaos. Lorenz (1993) highlights that the term nonlinearity has become synonymous with `chaos' but states that this is an oversimpli®cation of the facts, although he accepts that chaos demands nonlinearity. A linear equation means that any change in any variable at any Figure 1 Fractal showing self-similarity (Sprott 1995, reproduced with permission). Ó 2002 Blackwell Science Ltd, Journal of Advanced Nursing, 37(5), 462±469 Nursing theory and concept development or analysis point in time will produce an effect of the same size further down the continuum. Data from a linear equation, when plotted graphically will produce a straight line ± hence the name. Non-linearity is a mathematical representation of the chaotic concept of, `sensitive dependence upon initial conditions'. If we return to the butter¯y effect, for example, Lorenz suggests that the ¯apping wings of the butter¯y could produce a 10° rise in temperature. If chaotic systems were linear and we then postulate a disturbance of air current 100 times greater than that of a butter¯y ± that produced by a seagull, for example ± we would expect a temperature rise of 1000 degrees, which is clearly nonsense. This provides an elegant illustration of the nonlinearity of chaotic systems. Chaos systems within nursing Chaos theory has been applied in a practical manner by various disciplines, such as the neurosciences. However, nursing has not been particularly successful in its attempts to use chaos in such a pragmatic way. Chaos theory, as an investigative, explanatory and predictive tool, has not been well served by the (predominantly American) nurse theorists who have espoused its cause. Chaos as metaphor and pseudoscience Writing in 1997, Vincenzi noted that the application of chaos thinking was changing. There was less emphasis on ®nding chaos in various phenomena, and more focus on using chaos techniques to understand the world of nursing. In this approach there is no real need to identify the chaotic elements of nursing (if, indeed they exist) rather the presence of chaos is taken as a given `fact' without troubling to provide data to support such an assertion. Hayles (2000) refers to this approach as a `metaphorical approach', and suggests that chaotic concepts ± such as sensitive dependence upon initial conditions ± are presented as truths but should really be viewed as metaphors, which illustrate the phenomenology of nursing. She further suggests that adherents to this metaphorical approach tend to `blur the lines between metaphor and analysis' (p. 3). Hayles acknowledges that this metaphorical approach will free researchers from seeking chaos, and permit them to predict system dynamics. However, she warns that this may be a dangerous approach as there is no empirical evidence that the assumption that chaos dynamics exist within nursing is a reasonable one. Data gathered from a ¯awed perspective will be neither meaningful nor useful. Hayles makes the point that nurse theorists who wish to integrate positivist techniques with `softer' elements of nursing research use this metaphorical approach. The result Chaos theory and nursing is often a blend of the `scienti®c' and the `mystical' which serves to weaken both the application of chaos theory and the status of nursing research. This point is well illustrated by the work of Ray (1994). Ray sees nursing as a complex dynamical system and argues that four fundamental dynamic processes can be identi®ed, contributing to the concept of nursing enquiry (which, she explains, means the history-taking element of nursing care). She further postulates the existence of `caring attractors', which one can only assume (as she does not clarify her thinking) are somehow the nursing equivalent of chaotic attractors, as described earlier. Ray does not elaborate how the concept of `caring' can be mapped mathematically ± which signi®cantly weakens the `caring attractor' argument. In addition, she suggests that chaotic systems are unpredictable, which is patently a false premise. However, she not only suggests that accepting a chaotic dimension in nursing is necessary to decision-making in nurse±patient relationships, but also highlights that this element of chaos allows, `Interconnected pattern-recognizing goals sustained by cosmic powers of space, time and life' (p. 30). Ray attempts to adopt a positivist stance by continually referring to scienti®c theory; however, she weakens this stance by spurious claims for a `new scienti®c theory', which sees life processes as mental processes, suggesting interconnectedness between mind and matter. Overall, the work leaves the reader with the impression that chaos theory is being used as a crutch to give some `scienti®c' credibility to a metaphysical analysis of the discipline of nursing. There is no indication that the author has any insight into the requisite elements of chaos thinking. The focus of the work is so deeply impressionistic that the incorporation of any positivist thinking is redundant. Similar concepts can be found in the work of Sabelli et al. (1994), who regard the `oneness' of the individual with the universe as a point attractor. They take the stance that a biopsycho-social paradigm is an extension of the bio-physiological approach typical of systems theory, and argue that the manifestation of system equilibrium is health, whilst illness is manifested as a chaotic attractor. There is no evidence that even the most fundamental understanding of the components of chaotic thinking are understood or applied here. In an illustrative case study, Sabelli et al. introduce the concept of `butter¯y effect' when examining the psychological effects of stress on cardiac activity. However, they do not demonstrate how these psychological effects can be mathematically plotted to identify end state attractors. Once again, the spiritual and mystical view of the nature of humans and their place in the universe is at the heart of the work. This may re¯ect the condition of American nursing theory, which has Ó 2002 Blackwell Science Ltd, Journal of Advanced Nursing, 37(5), 462±469 465 C. Haigh often sought the more esoteric side of nursing and attempted to incorporate it into mainstream nursing care. To the uninformed chaos theory, with its method of demonstrating underlying order and predictability in super®cially disordered systems, may appeal as a way of seeking some spiritual understanding and overall plan for the nature of life and the universe. Such paradigms resonate with the work of theorists like Rogers who, in de®ning the environment as a four dimensional energy ®eld composed of waves that evolve towards increasing complexity and diversity, incorporated an incomprehensible amalgamation of chaos theory and the second law of thermodynamics into her work (Rogers 1980, Fawcett 1984). Although in¯uential in American nursing circles, in the United Kingdom (UK) Rogers has been justly criticized for the using science in inappropriate ways and undermining of the credibility of nursing knowledge (Johnson 1999). As a vociferous critic of what he terms `pseudoscience', Johnson warns of the dangers of the application of scienti®c principles in inappropriate and uninformed ways. A further concern is noted by Hayles, One of the reasons that chaos theory lends itself to application in so many different disciplines is that the analysis of chaotic data does not require a detailed understanding of the mechanisms involved (Hayles 2000, p. 1). Whilst acknowledging the point that human knowledge increases because individuals strive to understand the unknown, it is dif®cult to imagine a quantum physicist, for example, embarking on any project without a detailed understanding of the fundamental mechanisms involved. This contention, that lack of understanding does not necessarily stand in the way of a theorist's application of chaos to health, is also illustrated by the work of Pediani (1996) and Walsh (2000). Pediani bravely attempts to identify elements of chaos within the concrete nursing issue of poor analgesia administration by nurses. Although his premise is never clearly articulated, his hypothesis can be inferred from the early part of the paper, which uses chaos to gain insight into the basic features of the dynamics of complex areas. Lodged in the metaphorical approach outlined by Hayles, Pediani assumes that chaotic elements are present in the basic nursing task of ensuring adequate analgesia administration to the patient. He implies that an understanding of these elements will provide insight into nurses' concerns regarding iatrogenic addiction. However, before embarking upon any consideration of the chaotic elements of the issue in question, Pediani arbitrarily abandons his task in favour of a consideration of meme theory. Meme theory concerns itself more with the evolution and transmis466 sion of concepts and ideas than systems analysis. Whilst it can be argued to contribute in some cases to chaotic systems, meme theory is not in itself fundamental to chaos theory (Dawkins 1989). Walsh (2000) aligns himself with the stance of the American theorists previously considered, in that he argues strongly that chaos theory can contribute to a holistic consideration of individual patients. He rejects the notion of conceptual role boundaries, arguing that they are arti®cial. Although he acknowledges that these boundaries may be blurred in some instances, he does not develop this thinking towards the identi®cation of attractor states. Furthermore, Walsh introduces philosophical concepts ± such as the nature of the life/death divide into his argument ± which do not sit comfortably with the empiricist nature of chaos thinking. Chaos as a research tool The nursing profession seems to be having dif®culty in applying chaotic thinking to reality-focused clinical practice. Therefore, the contention of Mark (1994), that the major role of chaos thinking is not necessarily in health care delivery but in nursing systems research, does not appear inappropriate. She suggests that, whilst we can incorporate the notion that nursing is a dynamical and chaotic system into our thinking, it is as a tool for examining system parameters that it excels. She suggests that chaos thinking can help a researcher to identify the attractor state of a particular aspect of a nursing care system, and predict service stresses as the system moves towards unstable equilibrium. Whilst acknowledging that this approach to chaos theory use offers enormous methodological challenges to researchers, she argues that the data obtained would be of enhanced richness and would re¯ect the nonstatic status of care organization and provision in a valid and reliable manner. The weakness in Mark's argument is that at no time does she acknowledge that the data sets which facilitate the identi®cation of chaotic systems are not yet available to nurse researchers. The development of such data sets would require the careful use of a multiplicity of research methods, and systematic validation, before the wholesale categorization of dynamical systems of nursing could even be considered. The generation of these data sets would be wholly reliant on the identi®cation, formatting and manipulation of theoretical, conceptual and contextually dependent boundaries ± all of which would be required before the notion that nursing is composed of dynamical and chaotic systems could be seen as a viable assumption. The dif®culty in implementing this approach to data set production re¯ects the attitude of nursing research to using research methodology in a less than Ó 2002 Blackwell Science Ltd, Journal of Advanced Nursing, 37(5), 462±469 Nursing theory and concept development or analysis `pure' way. Johnson et al. (2001) make a persuasive case for plurality in qualitative health research. It is unfortunate that they do not include a similar consideration of quantitative approaches in their paper, because the argument for pluralistic approaches such as they outline can also be made in the context of identi®cation of chaotic data sets. This is because the collection of such data may require the implementation of qualitative methods to clarify the nature of a speci®c nursing system, before individual elements of that system can be examined using quantitative methods. The data obtained for this quantitative approach will in its turn contribute to the identi®cation of chaotic attractors within the system. Haigh (2000) used this pluralistic approach when applying chaos theory to the estimation of potential longevity of a speci®c specialist service. Qualitative methods such as focus groups and nonparticipant observation were used to identify key nursing systems, which, in turn, were subjected to mathematical analysis, allowing chaotic attractor states to be plotted. Byrne (1997), writing from a social science perspective, cited Trisollio's contention that complexity is a representation of `the sharing of ideas, methods and experience across a number of ®elds' (p. 1), has elaborated on this concept. Byrne argues that the plurality of chaos serves to highlight the limits of conventional science in describing the world. He attacks the rei®cation of quantitative methodologies and suggests that the quantitative can be viewed as inherently qualitative, and that within the social sciences the generation of anything other than very general noncontextual laws is impossible. Copnell (1998), suggests that, even when apparently divergent methodologies are used, the underlying belief systems of the researcher remain the same, and further supports this stance. Application of nonlinear thinking in nursing will require the plurality of approaches espoused by Johnson et al. (2001), coupled with the multiparadigm approach highlighted by Copnell (1998). However, the contention that transitory laws can be drawn from data resonates with attitudes within what are traditionally viewed as the `hard' sciences, such as physics, where the view is held that the notion that all scienti®c laws are immutable is nonsense. Scienti®c law is constantly under review, and constantly altering in the light of new knowledge. This supports the work of Coppa (1993), who submits that the role of chaos theory in nursing should be viewed within the framework of Kuhn's views about paradigms, normal science and revolutions. Chaos theory can be used, Coppa argues, to build a new paradigm of nursing science that would facilitate the integration of practice and research. Contexualizing this within the work of Kuhn (1970), Coppa maintains that the boundaries of the existing nursing Chaos theory and nursing paradigm are relaxing, the nature of nursing research problems are changing, and the science of nursing is in a prerevolutionary or preparadigm stage. The thrust of her argument is that using the concepts of nonlinear dynamics will allow nurses to move outside the traditional philosophies of their science, and that nurse researchers will be freed from reductionist viewpoints and constraints of order and predictability. In this, Coppa can be seen to be misleading. She adheres to the notion that reductionism is in some way `bad', and that order and predictability have no role in chaos thinking. Byrne (1997) notes that one way of analysing a system from a chaotic perspective is the construction of time-ordered classi®cation within data sets. This addresses the issue of the manipulation of contextually dependent boundaries, as all systems in the physical world operate in a time-dependent capacity. Reed and Harvey (1996) refer to `nested systems' that can be seen as characteristic of the whole system. They postulate that the characteristics of the whole can be extrapolated from the characteristics of the contributory system. These nested systems are seen as microcosms of the whole, which can be evaluated as chaotic attractors and will facilitate statistical modelling of care. This can be argued to be an appropriate use of chaos theory, and one that may be attractive to nurse researchers. However, such statistical modelling is reductionist in nature and diametrically opposed to the stance of Coppa (1993), namely that chaos theory will free nurses from reductionism. Statistical modelling using chaos theory The effectiveness of such modelling has been shown in the neurosciences. Martinerie et al. (1998) suggested that deterministic nonlinear processes are involved in preseizure cerebral neural reorganization. The application of nonlinear analysis was facilitated by the use of electroencephalogram (EEG), which allowed the dynamical system of a patient's neuro-electrical activity to be studied. EEG recordings are time-series studies, allowing the mapping of attractor topology and the potential identi®cation of chaos within the system. In this case, the recruitment of preictal neurones can be viewed as a nested system, in that their characteristics allow for extrapolation of events to take place. Haigh (2000) also used a nested system approach by evaluating the patient contact element of an acute pain service as a method of identifying the chaotic attractor status of the whole service. By treating patient contact as a timeseries nested system within the overall system, she was able to model chaotic end points via parameter manipulation that provided insights into the evolution of the entire service. Ó 2002 Blackwell Science Ltd, Journal of Advanced Nursing, 37(5), 462±469 467 C. Haigh Grif®ths and Byrne (1998) have suggested that only a small number of variables will control the end state of a system; both Martinerie et al. (1998) and Haigh (2000) found this to be the case. Grif®ths and Byrne (1998) have likewise postulated that statistical modelling of nested systems can contribute to mapping the perspective of patient outcomes in general practice. Ireson (1998) has suggested that this type of modelling has a function within the organization and management of nursing care. Hamilton et al. (1994) have used chaos theory as a method of carrying out cluster analysis in the nonlinear dynamics of births in adolescents. This application permitted the identi®cation and manipulation of variables in order to carry out predictive modelling, and the identi®cation of epidemiological markers that may contribute to the incidence of teenage pregnancy. This role in the statistical modelling of health care systems, rather than in research methodology, may be the ideal niche for chaos theory. Conclusion The purpose of this paper has been to review chaos theory and to articulate the contribution that it may make to the discipline of nursing. When evaluating the application of chaos theory to speci®c aspects of care delivery, it is clear that the efforts made to use chaos on speci®c clinical exemplars have been both ill-advised and ill-informed. This may well be because the conceptual fundamentals of nursing do not readily lend themselves to quantitative analysis, but may also re¯ect the pragmatic nature of nursing in general, and the problems that its practitioners may have in grappling with abstract concepts. Many theorists, notably Coppa (1993) and Mark (1994), have suggested that chaos theory will contribute in a meaningful way to research disciplines rather than to practical nursing. Whilst this is a seductive notion, it is clear that chaos theory is an ingredient of nursing research rather than a methodology in its own right. Copnell (1998) has, to a certain extent, pre-empted the case that Johnson et al. (2001) presented for pluralistic approaches to research, in that she has disputed the use of chaos theory as a stand-alone research technique. She argues that, taken on its own, chaos theory cannot contribute to knowledge synthesis, and that it relies on a synergistic relationship with other research methodologies if it is to be an effective research tool. It is apparent from the work of Hamilton et al. (1994), Byrne (1997), Martinerie et al. (1998), Ireson (1998) and Haigh (2000) that the individual elements of chaos can be identi®ed within a wide range of health care systems ± from 468 social sciences to neurosciences, via epidemiology and nursing care management. These elements can be identi®ed within parameters that are amenable to theoretical manipulation, and which contribute to statistical modelling. Such modelling allows for an appropriate use of quantitative methods, which may be blended with qualitative approaches in the setting of boundaries. 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