Hello all

Thanks for the insight into linear vs non-linear models.

I have found it interesting to compare discussions about linear vs non-linear models in OE with discussions about linear vs non-linear models models in health and social care. So here are my ramblings and some references should they be useful.

I am currently reading  ‘Chaos & Complexity; Implications for Psychological Theory & Practice’ by Michael Butz and 'Complexity and Healthcare; An Introduction’ edited by Sweeney and Griffiths. Both use Chaos and Complexity Theory to offer insight into non-linear models, in healthcare and psychology. The details are beyond this posting but the discussions about the value of non-linear models in another context may be of interest to this thread. 

There is a lot of talk about linear models working for simple closed system models working on simple cause and effect relationships between say, heart rate and adrenalin (eg fight or flight response), or consciousness and fluid loss (eg volume shock). But for for more complex open systems like diabetes and insulin or disease and treatment in public health (eg the epidemiology of the  SARS-CoV virus) there are so many variables, linear models don’t predict outcomes of interventions. 
This makes me think of Jay talking about Dewey’s “Quest for certainty”. The chaos theory proponents suggest that in complex systems, the capacity for linear models to predcict certainty is limited, so mathematical models which allow for uncertainty are a useful alternative. So for a chaotic model, the mathematics allows for uncertainty, and non-linear or complex outcomes. The outcomes for a range of initial conditions will vary widely, but for a specific set of conditions, chaos mathematics will give a precise and repeatable outcome.  

This has led to a plethora of suggested applications of chaotic, non-linear models. In ‘Using chaos theory: the implications for nursing.’ by Carol Haigh, the broad application of non-linear models is critiqued.  Haigh criticises the metaphorical application of chaotic, non-linear models, beyond their precise mathematical and evidence based applications. The danger she sees is the predictive or empirical mathematical model improperly used in a broader, metaphorical application or context. She describes this as pseudoscience.

Also in ‘Arrows in Time : The Misapplication of Chaos Theory in Education’ by William J. Hunter and Garth Benson, the authors argue, amongst other things, that non-linear models are sometimes an antithetical or reactionary response to linear models and that we need to look at applications of both. They say ‘Attempts to promote chaos theory as the solution to problems in educational research, teacher thinking, and school re- organization (Cziko, 1989; Rockler, 1990; and Braggett, 1992) are a matter of replacing the devil you know with the devil you don't.’

When Roger states “I think I have been consistent in questioning linear process models. But I have been a bit ambivalent about whether the vacuum or questions left behind...” I have to agree. Linear models help us when the relationships are simple. Chaotic, non-linear models help use with more complex systems, but can be predictive for only a precise set of initial conditions. But to assume because a linear model may be flawed, we replace it with a non-linear model may be false economy.

Groups and groupwork, in an adventurous outdoor environment, must fall under the category of a complex system with a wide range of initial conditions for any given predicted or desired outcome. In ‘Chaos & Complexity; Implications for Psychological Theory & Practice’ by Michael Butz, there is some useful stuff however. I work on a family project at the moment and worked an adventure therapy programme for families in the USA. Families are without a doubt complex systems. Butz also talks about larger social groups and offers much to ponder and some useful ideas about non-linear models. Part 4 of Butz could be of interest to anyone working with families or groups. 

Of particular interest to group workers wanting a non-linear model for group work could be a family therapy technique, developed by the Milan Group (Selvini-Palazzoli). In this article at http://www.anzjft.com/pages/articles/940.pdf called ‘Circular Questioning: An Introductory Guide’  by Jac Brown, the idea of a non-linear model to work is expressed literally in the process. ‘This interview style stimulates the release of information into the system in a manner that encourages new ways of viewing the problem’. This would in chaos parlance be called a bifurcation which could initiate a transition to a new phase space. Pseudoscience or practical application ? Depends on your initial conditions I guess.

Chris Reed