Australian EducationalResearcher Vol. 20, No. 2 1993

EDUCATION RESEARCH AND THE NATURAL SCIENCES:

WHAT CAN BE LEARNED FROM CHAOS THEORY?

Michael Amold

Abstract: This article explores some aspects of the relationship between education research and the natural sciences. It begins by pointing out that empirical or positivist science of the Modern era has had a powerful influence on the method and on the products of education research. From there the article moves to discuss the post modern sciences of the current era and speculative examples are given of the way they too may influence the method and the products of education research. In conclusion it is argued that this can and will occur as both education research and post modern science inhabit the same cultural and epistemological field.

I n t r o d u c t i o n

Education research has long been informed by research methodologies developed within the natural sciences. Indeed, positivist or empirical science established paradigms which dominated social and educational theory for decades, provided quantified foundational support for the construction of abstractions, and has developed principles and instruments to assess the truth value of these quantified abstractions, or, in the terms of the empirical discourse, the validity and reliability of the findings.

For better or for worse, empirical or positivist science has thereby provided a productive frame of meaning not only for inquiries into nature, but also for the construction of representations of the human condition. However, whilst acknowledging this, one may join Christine Perrott (1992) and note that there are different theoretical discourses arising from studies of nature which, if applied to education research, have a capacity to tell a different story. Post modem sciences, signposted by quantum mechanics, relativity, the uncertainty theorem and chaos theories are examples of scientific discourses which provide different metaphors, different perspectives and different constructs, and may inform a different

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epistemological approach to education research. As Perrott remarks, this approach may not be as productive, but may offer a way into the 'deep problems' of educationresearch.

The Inf luence of Empirical or Posit ivist Science

Before taking up Perrott's invitation to discuss chaos theory as an alternative epistemological model, it may be useful to create a contrast by revisiting the model which has been so influential for so long.

The empirical or positivist episteme is one which:

a. regards its subject as having an existence in a knowable reality which is a-theoretical, a-historic and a-cultural, and insists that cognisance of that reality should and can be objective, and thus value free; b. considers that essential and characteristic features of this objective reality are quantifiable and thus measurable, and that measurements, being an objective, pure and unambiguous means of representing reality, reflect powerfully upon hypotheses, and thus in principle, reveal truth; c. assumes that causality links an event to its antecedents and that which will follow, and seeks to identify chains of causality by isolating and observing dependent and independent variables; and ct assumes that identified causality is generalisable, and that the outcome of research is the power of prediction.

At the intersection of culture, social theory and scientific theory, conceptual frameworks which cross disciplines to model the universe are created, and are used to organise interpretations of phenomenon at the local site. Thus, as Hayles (1990) points out, for Newton, objects consisted of a collection of points, each of which obeyed general laws; for Adam Smith, the economy consisted of a collection of autonomous consumers and producers, each of which obeyed general laws; for Hobbes, society consisted of individuals, each of which obeyed general laws. In education, researchers were no less enthusiastic in the embrace of a particular scientific method - "a science of educat ion- a body of law like generalisations founded on facts about educational behaviour from which testable predictions can be made" (Broudy et al., 1973: .v)

Thus, through decades of mainstream educational research, students have been constructed as objects of nature which respond in potentially predictable and measurable ways to controlled stimuli. Classroom reality was represented as empirical, objective, quantifiable, contingent, teleological, subject to reduction and generalisable, and a particular methodology, which aimed to reveal an 'objective truth', also defined the realm of truth. Constructs become instruments; an episteme becomes an ontology - anxiety becomes a level on the Byrne's repression-sensitisation scale; authoritarianism becomes a level on the Californian

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F scale (Lefcourt, 1982). The discourse was one of subjects, objects, treatment, measurement, prediction. The researcher in this discourse is cast in the role of Cartesian subject, standing outside the world of objects (students) in a position that enables certain knowledge of these opposing objects (Poster, 1990). The extent to which subject (object) 'responses' were predictable, that is, the extent of support for the hypothesis, was seen to depend upon the precision with which behaviour or the treatment was operationalised, the manner in which inputs to the system were controlled, and the extent to which the 'laws' and assumptions which give rise to the predictions accounted accurately for the relationship between controlled inputs and operationalised behaviour.

A New Scient i f ic Discourse

In the nineteenth century, science presented nature as a group of objects set comfortably and solidly in the middle distance before the eyes of the beholder. In the work of D'Arcy Thompson, published around the turn of the century, nature has disappeared. It has become a set of geometric and mathematical relations that lie under the surface of the visible. It is still however, indubitably there. Today, nature has slipped, perhaps finally, beyond our f ield of vision. We can imitate it in mathematics - we can even produce convincing images of it - but we can never know it. We can only know our own creations (Hardison, 1989: 1).

As a broad generalisation it may be said that the period to about the mid sixties saw social research, including education research, modelled on a view of research in the natural sciences, and that the period mid-sixties to the beginning of the 1980s saw a distancing of social and natural sciences, as social researchers and education researchers looked beyond the natural sciences to phenomenology, phenomenography, semiotics, symbolic interactionism, discourse theory, ethnography, micro-ethnography, event structure analysis, Marx, Freud, Nietzsche, Satre, and so on.

Having broken the model provided by the science of the Modem era, the problem of representing behaviour became if anything, more complex. It was no longer seen as a matter of tracing logical chains of argument from an agreed base in reality through to conclusions, within a paradigmatic episteme which will allow no other component but that behaviour and those chains, to the current position where representations of behaviour are seen to be embedded in both subtle and powerful historical, cultural, disciplinary, ideological, physiological and idiosyncratic constructions. Within this context, methodology is seen as much more an inscription of legitimation to be read within an episteme, rather than a process which helps us get closer to some 'truth', and the post-positivist

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episteme seeks legitimation in Deweyian 'warranted assertability' rather than 'truth' (Lather, 1988: 7).

But if the 60s and 70s are characterised as a time when differences were established between the natural sciences of the Modem era and social theory, on another front similarities between the natural sciences of the post modem era and social theory were becoming evident. For example, it was noted that post modem science was closer to social theory than to Modem science on the question of reductionism:

We may say that reductionism, long a strongly criticised attitude in the social sciences, is found to be inadequate even in the physical sciences. The whole is more than the sum of the parts for such systems (Prigogine and Allen, 1982: 7).

and approaches to observation and interpretation:

quantum scientists deal only with unverified hypotheses. They admit that they are modelling reality rather than actually describing it; they understand 'reality' to be a cognitive construction (Best, 1991: 198).

A closer look at the methods actually employed in the natural sciences during the later part of this century tests the strength of its 'value-free' and doggedly empiricist inheritance from an earlier paradigm, and finds it wanting. Like education research, post modem science:

...acknowledges its metaphysical foundations; acknowledges that scientific theories are always empirically underdetermined and requires an appeal to non-empirical data; and acknowledges that observation is not 'objective' but is theory laden and profoundly impacts upon that which is observed (Carr, 1985: 127).

Giddens is of the view that in the contemporary era:

Natural science is an interpretative endeavour, involving a hermeneutic framework (1989: 251).

and Papert distinguishes between the research work of natural scientists and the formalisms constraining the reporting of this work:

recent work by ethnographers who go into laboratories to see what scientists actually do and how they actually think...puts in question, not only whether traditional scientific method is the only

What Can be Learned from Chaos Theory? 5

way to do good science, but even whether it is even practised to any large extent (1991: 23).

It is widely recognised that nature and our ideas of nature are in a reflexive relationship, or, as Arbib and Hesse put it, "space-time reality is in the head and the head is in space-time reality" (1986: 3). It is recognised that both the quantum theory of the atom and the electron microscope are instruments of 'observation'. Each construction places certain things in view as it focuses upon them, and marginalises others which are at the periphery (Porush, 1985). This understanding of the work of the natural scientist is a far cry from the caricature of Newton sailing through a sea of ignorance to discover islands of truth.

Access to the behaviour of cells and polymers and electrons and galaxies remains indirect, is bound by disciplinary paradigms and therefore the vagaries of cultural and historical epochs, is bound by physiological constraints, is empiricallyunderdetermined, and is reported in language which is a creature of a history and a culture, not a creature of cells, polymers and their nature. The behaviour of cells and polymers, and the behaviour of students and teachers, remains therefore a matter for construction, interpretation, representation, and not simply a matter characterised as the objective description of reality, founded upon the rigorous measurement of aspects of that reality, and reported in transparent, a- historical, a-cultural language. One may conclude from such an examination that the methods of natural science are sometimes presented in quantitative research method text-books and other paradigmatic indicators as a century old 'Boy's Own Annual' Newtonian caricature, and that a more sophisticated view of interpretive methods and theory generation in the contemporary sciences will bring out the overlap between post modem scientific research and education research.

C o m p l e x , n o n - l i n e a r systems

The latest of the post modem scientific discourses to grasp the imagination of natural scientists in a number of disciplines, as well as the media and the public, is 'Chaos Theory' (as it is popularly known) or, in more prosaic terms, 'theories of dissipative structures' or 'theories of complex, non-linear systems'. As Perrott's paper indicates, chaos theory has also drawn the attention of some educationresearchers.

Theories of complexity have arisen from the practices of post modem science and one may therefore trace their origins to theories of thermodynamics, quantum mechanics, relativity and other mainstays of contemporary scientific discourses. Theories of complexity are in this sense then "a dramatic extension of many basic concepts of science" (Turner, 1982: 57) rather than a Kuhnian paradigm shift (Kuhn, 1970). The paradigms which structure chaos theory are however quite different to those which structured empirical or positivist science.

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On a deep level, it (chaos theory) embodies assumptions that bring into question presuppositions that have underlain scientific conceptualisations for the last 300 years. Among the challenges it poses are whether an effect is proportional to a cause; how scale variance affects facts; what it means to model a physical system; and what cosmological scenario we are taking part in (Hayles, 1990: 16).

Best (1991) draws links between post modem scientific theory and social theory. He points to links between Heisenberg's uncertainty theory and Derrida's concept of undecidability; between the concept of a 'quantum' at a sub-atomic level, and Foucault's concept of discontinuous epistemes:

The scientific developments I have described have significant similarities with post modem social theory. In both problematics we find a rejection of classical determinism, in favour of a new logic of indeterminacy; a renunciation of linear models of causation for more complex, plural and perspectival models; a repudiation of modem theories of representation; and a critique of identity logic (1991: 212).

Theories of complex non-linear systems are therefore able to suggest to education researchers the consideration of different sets of metaphors, signifiers and signifieds, constructions of relations and of fields. The scientific, cultural and social ideas which intersect in a post modem era, and are also able to inform education research, are ideas in which disorder, complexity, uncertainty, non- linearity, noise, representational forms, language, the observer, scale, reproducibility, causality, subjects and objects and laws are all reconstituted, and are charged with different roles to those assigned in the modem or empiricist era. Seen as a complex dynamical system the classroom takes on other properties and dimensions, another character and another dynamic, and these properties and dimensions, the character and the dynamic associated with the classroom and chaos, may well form the basis of research aimed at the 'deep problems' Perrott (1992) urges us to tackle.

The idea s suggested below provide some examples of such an approach. They serve not to persuade, but to illustrate the production of new knowledge interests, new conceptual tools and new metaphors, which accompany the mapping of a post modem science discourses over the events of the classroom.

Examples

One challenge offered education researchers by post modem constructions of complex systems is the challenge to modernist theories of cause and effect. Seen

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as a complex dynamical system the classroom is not structured in a serial or linear way, where chains of input/output - instruction/outcome - cause/effect can be isolated and explicated, but is constructed as a system in which the elements are in a state of reciprocal dynamic interplay at every scale. To attend to such a system is to attend to notions of learning in terms used to describe complex dynamic systems, terms which perhaps signify novel concepts to education researchers. Constituents such as feedback loops, modes of disequilibrium, self- regulation and bifurcation points might be used to represent aspects of learning or precursors to learning. The use of these terms is not to express old ideas in new ways, but to signify different concepts and to generate different perspectives. For example, when writing of complex systems Gleick notes that "Non-linearity supposes that both the rules and the variables (the two are inseparable) change as the game is being played" (Gleik, 1987: 24). The perspective offered by the non- linear classroom is therefore a perspective which rejects models which are dependent upon unchanged states - which is to reject the methodological structure of much education research. If observers are caught in a change loop, contributing to change and subject to change, and treatments are caught in a change loop, and controls are caught in a change loop, methodologies which attend only to pre-treatment post-treatment change in the subjects will tell a different story to that told by research which attends to change in process, and to reflexive change in all inhabitants of the space.

An example of education theory which attends to change as an inherent dimension of the space within which learning occurs, is to be found in the work of Lave and Wengner (1991). Lave and Wenger assert that learning is not simply a change situated in the mind of the learner, but assert that learning, and therefore change, is distributed among co-participants in situated action. In the course of learning (or legitimate peripheral participation) the apprentice changes, the master changes, and the skills being mastered change. Within a frame which attends to reciprocal and distributed change, learning outcomes are therefore not accounted for by the mechanistic teleology of Modem science, in which the end state (learning outcomes)is determined by a one-way flow of cause and effect emanating from the properties of the space (treatment, subjects etc.) at the beginning. Attendance to dynamic reciprocal relations, in the form suggested by Lave and Wenger for example, and suggested by the theories of complex systems, is to attend to a problem which is 'deep' in Perrott's terms.

The theory of entropy is one of the landmarks of modem science and notions of negentropy are landmarks of post modem science. From its origins in thermodynamics, theories of entropy and negentropy have migrated, most notably to biological sciences, to theories of communication and to cybernetics. It has long been held for example, that biological forms defy entropy, but the realisation that some complex systems might also be said to defy entropy, by creating order from disorder, makes negentropy a notion with very broad applicability. If complex systems are as common as is now thought, the second law of thermodynamics may well be regarded (as Timothy Leary once remarked) as more

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like a local council ordinance than a law of the tmiverse. Student's cognition may also be regarded as a negentropic system which creates order (internal constructs, competent participation) from disorder (the environment, internal constructs, legitimate peripheral participation, social interaction). The negemropic view is that students can't stop making sense, and that information is therefore created in the classroom rather than lost or simply conserved. Just as theories of entropy informed research in biology, communications and cybernetics, an assertion of negentropy and a denial of entropy is a perspective which might illuminate facets of learning, in particular, a reading of negentropic constructionism which brings together the powerful educational theories of Piaget, Dewey, Vygotski, Papert, Minski and others, with the communications and cybernetic theories of Wiener, Shannon and Weaver.

Another suggestion made by post modem science is that the education research might choose to view the classroom as a space which contains a number of attractors.

In nature attractors are points in state space, or phase space, which are typical, and towards which phenomenon trend. For example, a strong attraction for a pencil's orientation relative to a table is the point at which it is horizontal, rather than say, standing on its point. State space may have as many dimensions as the system has variables (Morris, 1991) and dimensions such as the pencil's orientation at time 0, the pencil's inertia, the stability of the air and so on, form the state space the pencil occupies. The dimensions of this space are then said to attract the pencil from all practically possible orientations to a horizontal orientation. Attractors are weaker and harder to identify in the classroom, and hence the usefulness of the parallel may be limited, but frequently studied classroom constructs - cognitive style, cognitive structures, prerequisites for transfer, problem solving strategies and so on - may be viewed by the researcher in terms of an accumulation of synchronic 'snap-shots' of the state-space associated with a given classroom construct, rather than as teleological events understandable in terms of diachromc changes in the behaviour or condition of the individual students under study.

For example, an experienced teacher will be quick to confirm that under certain circumstances 'bedlam' is an attractor in the classroom, just as the traffic jam is an attractor on the city streets (Porush, 1985). One student assaults another with a spit-ball and the victim responds in outrage. Just as a single immobile car may act as an attractor, drawing previously mobile cars into a larger and larger pool of immobile cars, so others in the class are readily 'attracted' to noise, colour, movement and action. Within a minute the system flips from one state to another and orderly behaviour has become disorder, school work has become rough-house play, quietude has become joking and laughing, planned activity has become spontaneity. Similarly, a theory of 'critical mass' accounts for whole classes of students behaving in an ordered fashion, for if all are, each is inhibited from doing otherwise. Thus, classes of students may be seen to flip from one state to another in a manner not predictable on the basis of the behaviour of

What Can be Learned from Chaos Theory? 9

individuals, but in a manner dependent upon the field - the state of the group as a complex, subtle and dynamical system.

Under what circumstances will the classroom flip from one state to another? Understanding such a system is a 'deep problem', for another characteristic of the space and its occupants, who may themselves be constituted as a complex and dynamical system, is its capacity to bifurcate in accordance with extreme sensitivity to total conditions.

Extreme sensitivity in the complex systems discourse is often referred to as the 'Butterfly Principle', a notion explained by Gleik which points to the theoretical possibility of a meteorologist linking a storm on one side of the Earth to the earlier movement of a butterfly's wings on the other. The classroom and its attractors may also be a system subject to the 'butterfly principle'. A seemingly unrelated, seemingly insignificant event in the playground, in Bosnia, or in the womb, may have major effects at a later time in the class. No degree of meticulous observation, even in theory, can provide an account of the state of relevant variables at any given time. The classroom is therefore un-simulatable by any representation with fewer elements than itself. The corollary of this is that, in the terms of their own discourse, the reliability of studies which take place in a clinical or experimental setting is compromised, if not in the transfer of results from experimental setting to experimental setting, at least in the transfer of results from experimental setting to a natural setting. Indeed, chaos theory also casts doubts upon the replicability of results as a scientific principle, through attending to the extreme sensitivity of systems to initial conditions, although reproducible results are to be expected in stable systems close to equilibrium.

Which student caused the events in the class, the spit-ball shooter or the retaliator? As an alternative to tracing lines of cause and effect through a classroom made up of behavioural individuals, Stanislaw Lem (1981) has provided such a frame, or, in his terms, a model of conceptual ecologies. This model concedes that so many variables are at work within a given culturalfield, that its topology cannot be rigorously determined. However, within any given field, such as a classroom, only certain forms are possible, others being prohibited by the overall conformation of the field. Within the field, those forms which are possible may or may not be realised, depending upon the characteristics of the inhabitants, but all forms which are realised are linked to each other through the common attributes which define the space. In this reading, 'cause' cannot be attributed, but certain things are allowed by the field, and certain things are repressed by the field. For example, without Bragg's Law the current understanding of DNA would probably not be possible, and if constructed, would probably be rejected. Yet the construction of DNA as a fundamental conception in the biological field was not an obvious, direct or necessary concomitant of Bragg's Law. An inhabitant of the space in which quantum mechanics was createdis Hilbert's theory of integral equations; relativity was created in a space which also included differential geometry; the music of Jimi Hendrix exists in the same space as recreational drug use and electric instrumentation, and so on.

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According to the argument, specifics beyond that which is allowed and that which is repressed (specifics such as causal relations), are dependent upon the inherently unknowable, infinitely regressing initial conditions of the field's inhabitants. A complex but interesting perspective.

Perhaps the most obvious implication of theories which are built around a field or state-space, is that reality consists not of discrete objects, but rather, consists of underlying structures which produce those objects. This of course is a theme which re-occurs across many post modem disciplines from the anthropology of Levi-Strauss to the physics of Einstein. In education research it implies that the focus shifts from the individual student (o the space occupied by the individual. In contrast to the modernist construction of the student as an autonomous behavioural object, as the fundamental element in the system, the post modem construction represents the student as the intersection of the organising tropes, signifiers and conceptual structures characteristic of the culture. If the student is constituted by a culture and is defined by an episteme, a study of a student becomes a study of a culture and an episteme, and the student as a behavioural individual recedes from view.

A further feature of a complex dynamical classroom is the view that an understanding of the system is scale dependent, a point also made in Perrott's article. The role of language, crucial as it is to social theory and to education research, shall be used to illustrate the implications of scale dependency. In this scale-dependent view, the meaning attributed by a researcher to an inhabitant of the space, say, a word chosen by a student, may well change when the scale used to focus on the inhabitant changes. If for example, the word is viewed in the context of the sentence, or the exchange, or the whole data-item, or the whole of the data, it is plain that its contribution to the configuration of the space (its meaning) may well be subject to change. Indeed, attributed meaning may continue to change as one expands the contextual frame beyond the texaml data and interprets the word(s) in the light of the whole of one's knowledge of the student, of all students, of life, the universe and everything.

Shifting data-scales up from the phoneme towards the whole body of data, and vice versa, may be interpreted as a shift relative to two axes. One axis is semantic and the other is temporal, and the understanding that meaning is deferred and dispersed as one slips from one signifier to another, up and down each axis, without ever reaching a literal or a referent, is most closely associated with the works of Lacan and Derrida. The semantic axis attends to the context within which the phoneme, word, sentence, utterance, or exchange is situated. At any level meaning may be subject to change (reinterpretation) as the lexical context is changed. On the temporal axis, because the signification of words can derive from words yet to be uttered, as well as words which have been uttered, the meaning to be attributed to words is in a state of becoming, it is never complete, never saturated, never stable, untill perhaps the last word has been uttered (Cherryholmes, 1988). The meaning to be attributed to the words spoken by a student is therefore contingent upon the size of the sample chosen to constitute

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data, and will change as the size is increased or decreased. If one accepts that one never encounters a literal, a final referent, a signified that is not also a signifier, there cannot only be no claim to a stable meaning, but also no claim that one scale provides a peg for a truer meaning than any other scale. Also, as one increases scale along the temporal axis by attending to words gathered over minutes, days, months, years, as a whole, a unity, an unfragmented flow or line, one moves towards a diachronicity in which the development of ideas and the transitions between ideas become products of the frame itself. As one reduces the scale one moves towards synchronicity, which, whilst never reaching a point devoid of a chronistic dimension, progressively affords less room for teleology. The point of this business of scale is not simply that the observer's view has changed and hence what is seen changes, the point is that the scale itself is productive, and that 'meaning' changes as scale changes. There are therefore any number of co-existing meanings which may be attributed to any given data-item gathered in the course of education research, just as the coast of England has no single length, but has a number of lengths each dependent upon the size of the ruler used as a measure (Hayles, 1990: 210).

C o n c l u s i o n

Education research has the task of making order out of disorder. In the performance of this task we have long been informed by research in natural science, and have adopted many of its epistemological assumptions and methods. Having of late recogmsed the limitations of this borrowed paradigm for education research, and having developed new epistemes and methodologies, we see that the natural sciences have also moved, and are now operating under a set of fundamental principles unrecogmsable to the scientist of the Modern era. Is it possible for the education researcher to benefit from the work of contemporary natural science, given that the education researcher has at best a naive understanding of chaos theory, quantum mechanics, the uncertainty theorem and other formative constructions, and given that in any case, the education researcher will not be content to return to a methodological paradigm transplanted from the natural sciences?

This paper has given examples of the manner in which challenging ideas derived from post modem science may be mapped onto classroom practices to create a new perspective. Such a mapping has provided a perspective from which learning is seen as a reciprocal dynamic interplay between co-participants, not as something which occurs in the mind of the individual as the result of a one-way flow of cause and effect. It has provided a perspective which uses entropy and negentropy to deny the conveyance, transmission, or conservation of information in the c lassroom, and brings together educational constructionists, communications theorists and cybemeticists to assert that students (and education researchers) construct order from the environment. It has provided a perspective of

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the classroom as a space. Within this space complex sets of variables intersect and form attractors. Occupants of the space, who are themselves reconstituted to form a complex and dynamical system, show extreme sensitivity to total conditions. Characteristic products of the space are determined by the topology or overall conformation of the space, rather than being determined by the action of identifiable variables. The space has therefore provided a perspective from which the individual is marginalised and recedes into the background, whilst space ceases to be a neutral backdrop and emerges as the protagonist. Lastly, the mapping has provided a perspective from which the importance of scale, particularly in relation to the production of meaning through language, is brought into sharp relief.

To connect education research with research in the natural sciences in the above manner, and to assert that one effects the other, it is not necessary to establish direct links between the two. The concept of a field for example, has been traced by Hayles (1984) as it emerges in multiple sites, and whilst one might expect direct lines of influence to flow between the special and general theories of relativity, quantum mechanics, Goedel's theorem, the Church-Turing theorem, and the Halting problem, one might not expect writers such as D. H. Lawrence, Vladimir Nabokov, Robert Pirsig and Thomas Pynchon, for whom the concept of the field was also an organising construct, to be accessing the literature in the mathematical and scientific discourses in any direct way. Hayles (1990) also points to other examples - John Cage experiments with musical applications of stochastic variations whilst Roland Barthes was extolling the virtues of noisy interruptions in literature and Edward Lorenz was examining uncertainties in the non-linear equations used to describe weather formation. Perhaps each reads, listens to and studies the other, but perhaps not. It is not necessary to assert that James Joyce studied Freud in order to assert that Joyce's work is informed by Freudian concepts. It is not necessary to assert that a toy shop manager studied Piaget in order to account for the toys being arranged in departments according to Piagetian stages of development.

To connect education research with research in the natural sciences, and to assert that one effects the other, requires that the two exist in a shared cultural field. For just as research is immersed in a culture and is empowered and constrained by that culture, so the culture is conditioned by the assumptions which have guided the constitution of knowledge in the scientific paradigms of the day. It therefore benefits the education researcher to a/tend to these influences, to be sensitive to them and to be conscious of their capacity to contribute to analysis and interpretation.

What Can be Learned from Chaos Theory? 13

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Best, S. (1991), "Chaos and Entropy. Metaphors in Postmodern Science and Social Theory", 2(2), pp. 188-226.

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Carr, W. (1985), "Philosophy, Values and Educational Science", Journal of Curriculum Studies, 17(2), pp. 119-132.

Cherryholmes, C.H. (1988), "Construct Validity and the Discourses of Research", May, pp.421-457.

Giddens, A. (1989), "A reply to my critics", in D. Held and J.B. Thompson (eds.), Social Theory of Modern Societies: Anthony Giddens and his critics, Cambridge, Cambridge University Press.

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