Cross-posted at Pharoz

I want to try to use the idea of bifurcations in non-linear systems as a model that might help to place political theories, and some political history maybe, in a context. All models are abstractions and include some kinds of simplications; they ignore some things and highlight some other aspects.

Bifurcation diagram - Wikipedia, the free encyclopaedia:

This is a bifurcation diagram for a dynamical system [from the Wikipedia]. Chaos theory applies to natural processes, and it helps us understand complexity in the real world. Even quite simple iterative mathematical rules can result in complex images.

I want to try to use this idea of bifurcations in non-linear systems as a model that might help to place political theories, and some political history maybe, in a context. All models are abstractions and include some kinds of simplications; they ignore some things and highlight some other aspects. Its a model.

Marx claimed that there was some kind of teleology behind history, and that society will culminate in Communism. This was proved to be wrong, but has the increasing complexity in society changed the political framework for those societies over time? My suggestion here is that they have, and that this change could perhaps be modelled in a similar way to that of a dynamical system as it changes to become chaotic.

Chaos is possibly the wrong word for these complex political structures and societies. They are DIVERSE, and still adhere to the rule of law and human rights, rather than falling back into a state-of-nature. That pre-modern state-of-nature kind of lawlessness is NOT what I am talking about here.

A simple progression:

1. Social groups (group identity mostly based around ethnicity, religion or church) [one point - eg r=2.6 on the graph above]

2. Modern states after the American and French revolutions (individual and the nation state) [two points - eg r=3.2 above]

3. Polarised modern states and individuals after the First World War  (Left versus Right) [four points - eg r=3.5 above]

4. Postmodern maybe (left and right start to loose meaning and fragment) [eight points, 16 points - eg ~3.54 above] - we are here now I think

4. Diversity perhaps (where the state is counter-balanced by the 'individual', so that people are free to participate and create culturally as they please) [the chaotic regions - eg r=3.6 or 3.7]

Much of the political confusion today is around how to find a way to integrate individuals, society and state. Religious fundamentalists want us to move back to the first kind of ordering around the social group - patriarchal mostly. The French Republic model [ordering around the secular individual and nation state, to the exclusion of the social and religious] seems to be in question after the riots in Paris. We also now find an attempt to return to the polarised politics of the 1930's in Australia with the Howard Government and its proposed IR and anti-terror legislation. These are all regressive moves, trying to grasp at some sense of certainty and some sense of secure and well known ordering.

Interesting times...

This post ties in with a number of issues to do with politics and history. Marx and Hegel both postulated a dynamic behind the way that history changes. I have not researched these ideas in any depth, but I wonder whether the new understanding of complexity and chaotic system could provide a better model for understanding changes in politics over time.

Many of the posts on my blog look at these issues. Perhaps the old idea of the separation of church and state reflects the early modern perspective after the first bifurcation in the diagram above.

One point that I didn't draw attention to in my post is that once a bifurcation happens, the original trajectory continues, but instead of being an attractor point, it becomes a repelling point. The new attracting points go to either side of the original trajectory. As an idea it provides a model for how an idea that worked in a previous time may not work now, when things become more sophisticated.

So in terms of the separation of church and state, before modern states started to take form the social group was organised mainly around religion and church. In the modern state the emphasis moved towards BOTH the state and the individual. The idea of the separation of church and state is one way of expressing this change.

Another thing to note about this post-postmodern chaotic realm is it represents a way to integrate all three levels; individual, society and state. And in ways that enable maximal autonomy for individuals, societies and the the state. This is in contrast to the world that fundamentalists of all colours try to impose on others.

Please let me know what you think about these ideas in the comment section.