Ontogeny and Symmetry

Gregory Bateson's description of symmetry in his paper "A re-examination of Bateson's Rule" provides a way of thinking about the way things grow in relation to other things. The relations are not just between  fingers on a hand, or the divisions in a Beetle's leg, but also the relationship between the processes of reproduction within cells, and the 'informational' context within which that reproduction takes place. Basically, from the environment information is gained or lost which causes particular patterns of growth over time. D'arcy Thompson, many years before, had made this connection between ontogeny and symmetry by demonstrating how symmetrical forms resulted from varying rates of growth within a cellular structure. Indeed, William Bateson (whose 'rule' Bateson is talking about), was a contemporary of Thompson, and there are many overlapping themes in their work. Thompson is worth quoting here:

"The differences of form, and changes of form, which are brought about by varying rates (or 'laws') of growth, are essentially the same phenomenon whether they be, so to speak, episodes in the life-history of the individual, or manifest themselves as the normal and distinctive characteristics of what we call separate species of the race. From one form, or ratio of magnitude, to another there is but one straight and direct road of transformation, be the journey taken fast or slow; and if the transformation take place at all, it will in all likelihood proceed in the self-same way, whether it occur  within the life-time of an individual or during the long ancestral history of a race." (Growth and Form)

I have been recently working on the 'form of thought', looking particularly at the way expectations are structured. Taking the ideas about physical ontogeny and growth metaphorically can help to think about the mechanisms of mental processes. I agree with Bateson that processes of organic growth and processes of mental life both count as 'mental process'.  So it doesn't seem unreasonable to consider them together.

The problem is that unlike looking at a crab, we cannot see a form of thinking. All we can see are the results of actions which are taken in the light of that thinking. One of the key features of action in a society is that the focus of our attention shifts between thinking about what might be going on in peoples' heads and the communication dynamics that exist between people. There's very little we  can see of the former, although perhaps MRI scans and the like might help us to peer into physiological transformations - but it is still a huge organisational task, and methodologically tricky because it is easy to get carried away with our inferences! In  the environment, we have what we call 'information'. But as I argued yesterday, we have to be careful with 'information', because it is really only a bi-product of the expectations of individuals.

A while ago I tried to model communication dynamics assuming that each individual is a viable system communicating with other viable systems, using as a basis for this Beer's Viable System Model. I produced an agent-based model of this (see http://www.tandfonline.com/doi/abs/10.1080/10494820.2012.745434 and http://dailyimprovisation.blogspot.co.uk/2011/05/agent-based-modelling-and-waves-of_01.html). All interesting stuff. But also a bit unsatisfactory because, whilst there was an effective model of communication between agents, none of my agents reflected on their communications. Eveything happened instantaneously, and so whilst there is much realism in the dynamics, something is missing.

More recently, the problem of reflection has led me to consider the way we reason about communications in order to select an utterance. Luhmann called this the 'psychic system' and is the least well-elaborated aspect of his theory. I used Nigel Howard's  metagame theory as a way of talking about this and presenting the challenges involved. There are two key points which have emerged from this:

1. That absences are causally efficacious in determining the choices we make
2. That anticipated communication dynamics are fundamental to the construction of choices

I've spent a whilst recently talking about 1) - and really, that is also the topic of Bateson's paper, and much work in the information sciences besides (especially Deacon).

But what about 2? What it means is that my growth is dependent on your growth. In mental life, where we seek to make communications, that is obvious. But is it a general 'formal principle'? 

When we consider a petal, or the branches on a stem, or the fingers on a hand, we tend to think about the cellular process occurring within an information environment. Missing from this are all the other petals, branches, fingers,  etc. Increasingly, thinking about the ontogeny of a single entity seems to be a mistake. When are we ever looking at a single entity? 

In mental life, my growth is dependent on the growth of others around me. There is a dynamics of communication which feeds a dynamics of expectation which coordinates particular ontogenetic processes. This raises the question that when we see a cell, are we  not seeing "pairs of processes"? Between a pair, there is a communicational dynamics which establishes the patterns of growth in each pair. In other words, symmetry is born out of communication between pairs. 

As I write this, I am reminded of Douglas Hoffstadter's  thought experiment in "I  am a strange loop". There he considers the possibility that each of us individuals is not a 'person' but a 'pairson'. I don't entirely agree with Hodstadter's thinking, but this is highly revealing as a word-play joke because it cuts underneath some fundamental assumptions we have about life. 

So there is a new model to build. One which combines the kind of co-creating communication dynamics of my earlier model, with a model of the growth processes of mental life within an information context. For the latter, I think the Diffusion Limited Aggregation model (see http://dailyimprovisation.blogspot.co.uk/2013/05/expectation-and-redundancy.html) is not a bad place to start. In essence, the question is what  happens when two DLA models communicate with each other, and whose growth processes are determined by the absences which are created as a bi-product of their communications...