From the Aztecs to the Annales school people have always seen cycles in history, in nature and in science, but the principles of chaos show us that these are not the simple, repetitive cycles obeying the models we have traditionally constructed to allow us a better understanding of our world. Reality is infinitely more subtle, complex and beautiful. Chaos is nothing more than another model, and has the same problems of dealing with abstracts rather than real things and so on, but it has a complexity that belies its simple founding principles, and as such, can lead to a greater understanding of any real world system.
The subject of this paper is the application of chaos to social change; to be able to do this it is necessary to analyse what actually constitutes social change. There are myriad aspects of our culture, and of every other culture on earth that could be picked for analysis; every aspect of our existence, from plough technology to sexual habits has changed over time, so we must be selective. As archaeologists, we must attempt to restrict ourselves to those aspects that are visible to us, there is obviously no point in us trying to study slang terms in neolithic Siberia! Also, we must restrict ourselves to phenomena for which there is an significant amount of data, the iterative processes that can display strange attractors can not be seen without a large number of iterations. The final, and perhaps most restrictive of considerations is the fact that the thing studied needs to be quantifiable numerically, in many cases (specifically some of the articles in McGlade and Van der Leeuw, 1997) the numerical value applied has been abstracted from the actual site to the point of uselessness.
The subjects of interest to us as archaeologists (when we are not dancing to the tune of the historians) can be roughly summarised as follows (and I stress the word 'roughly'):
All of this has to be seen through the unreliable medium of material culture.
I will try and give these areas of interest a cursory examination from the perspective of a chaologist, and suggest ways in which chaos could be used for the advancement of these various specialities. Obviously, chaos will not be a panacea, and there are parts of this breakdown that chaos has no immediately apparent relevance to, but so long as archaeologists can be educated into knowing that chaos is a tool available to be used, then we shall reap the benefits.
It goes without saying that the vast majority, if not all, of human cultural activity is affected by the 'butterfly effect', tiny random events affecting the rest of human experience an entirely unpredictable amount. What if Julius Caesar had been struck down by the effectively random infant mortality rife in ancient society? What if the emergence of human bipedalism had been too late to take advantage of the Africa/ Eurasia land bridge? Our past is a fragile entity, if we were to run it again it would go very differently. Unfortunately there is little to be gained on a practical level from this, as it is nonsensical to consider rerunning our past.
Matters relating to subsistence are perhaps the most easy to approach using non-linear methods. The process of domestication of particular species is nought more than evolution with the hand of humans, as well as that of nature, deciding reproductive success, and as such we can productively use the work of those such as Binnings (1989) who have applied chaos to evolutionary systems. In situations where the human population relies on non-domesticated animal resources, then there is no reason that we can't use a version of Gilpin's (1979) strange attractor model of predator-prey interaction. The technologies involved in the production of food will be dealt with later.
Maytz (1989) mentions in passing the spread of rumours as a non-linear process. Rumours are an easy, accessible example of the spread of information which could be modelled without too much trouble; details could easily be ignored as all we are really interested in is how many people know, and in what way the information travels through the group. The experience of dealing with the issues involved in this problem would enable a productive approach to be taken to the more complex and abstruse systems of information flow that are of such interest to archaeology. If we consider an idea as a self contained entity then it is possible to treat all different types of information spread in the same way, be it a technological innovation, or social practice.
It is well understood, and fairly obvious that systems are most prone to change dramatically (bifurcate) when they are under stress, old orders break down and new ones emerge. This process can be perfectly modelled with chaos; if one can find an appropriate variable to plot, which is rather more difficult than at first it seems, one has to find an appropriate indicator which is difficult in systems as complex as culture . Once one has found such indicators - land area of an empire, the population in a city, or the proportion of GNP dedicated to religious activities - one can extract the underlying behaviour of the system studied and it may be possible to model the repertoire of the system, and visualise it in a topological fashion (in the way Smale (in Gleick, 1988) introduced).
If we tie together the two preceding thoughts then we have a coherent picture of the advent and spread of ideas, and hence the bones for understanding which conditions are conducive to social change, and which are conducive to a relatively stable limit cycle or damped oscillator.
As archaeologists we have traditionally spent a lot of our time working on typologies for sites, for artefacts and for cultures in general. All in all this could be seen as something of an obsession - the focus of attention on what could be called 'integer forms' is part of a paradigm falsified by chaos. We could perhaps benefit from letting the objects group themselves, by plotting various numerically visible features and seeing where groupings, and patterns form. For instance, in a very simplified example, one could plot height, rim diameter and the ratio of greatest to smallest circumferences for a pottery assemblage; this would result in a three dimensional plot, with groups of points around common pot types, but it would not require the entirely false morphological taxa that archaeologists usually use. It would also be simplicity its self to view the changing assemblage over time by means of some form of animation. An incidental benefit in this specific case would be that if one had only an incomplete set of values for a sherd, then one could easily read off the most likely originating vessel type, as one could just draw a line encompassing all the unknown sets of values, and the most crowded concentration of points it passed through would be the most likely original form.
Perhaps the most productive application of chaos we as archaeologists could do is analysis of diffusion patterns, of objects, of languages, of technologies and of peoples. We have innumerable distribution maps of all of these, but these are often rendered meaningless by lack of evidence in particular areas, and false patterns created (i.e. if excavation is compulsory when building motorways, then there will be long lines of sites).
It would not be difficult to create a computer model of the map, and program it to take into account the misleading features. It could then search for topological features such as strange attractors or limit cycles in the data, which would allow archaeologists not only to be able to predict the kind of situations in which as yet undiscovered sites/artefacts/technologies or whatever might be found, but also to be able to get a better understanding of the reasons for the site placement. Any variety of variables might be used in this analysis, so links and patterns between diverse factors might be found, these links in themselves providing additional information.
There are a great number of other possible applications for chaos theory in archaeology, and these should become apparent to those working in the field, and those trying to find patterns in the various aspects of our subject if chaos gains the popularity that it deserves amongst all those in social sciences.
© Joe MacLeod-Iredale 1998