This rather elderly paper by Paul Cilliers peters off to an unsatisfyingly vague and obvious conclusion, but it does have some quite useful clarifications and observations about the nature of boundaries as they relate to hierarchies, networks and complex systems in general. I particularly like:
“We often fall into the trap of thinking of a boundary as something that separates one thing from another. We should rather think of a boundary as something that constitutes that which is bounded. “
This simple observation leads to further thoughts on how we choose those boundaries and the (necessary) ways we create models that make use of them. The thing is, we are the creators of those boundaries, at least in any complex system – Cilliers mentions neural networks as a good example – so what we choose to model is always determined by us and, like any model, it is and must be a partial representation, not an analogue, of the impossible complexities of the world it models. In a very real sense, we shape our understanding of the world through the boundaries that we choose to (or are hard-wired to) consider significant and there are always other places to draw those boundaries that change the meaning of what we are observing. It makes the analysis of complex systems quite hard, because we can seldom see beyond the boundaries we create that simplify the complexity in them and we have a tendency to over-simplify: as he points out, even apparently clear hierarchies shift and interpenetrate one another. This is more than, though related to, categories and metaphors of the sort examined by the likes of Hofstadter or Lakoff.
Since this paper was written, John Holland has done some mind-bending and deeply thought-provoking work on signals and boundaries in complex systems that delves far deeper and that begins to address the problem head-on, but which I have been struggling to understand properly for many months: I’m pretty certain that Holland is onto something of staggering importance, if I could only grasp precisely what that might be! He is not the clearest of writers and he tends to leave a lot unsaid and assumed, that the reader has to fill in. It’s also complicated stuff – suffice to say, stochastic urns play a significant role. This paper by Cilliers is a good stab at the issue from a high altitude philosophical perspective that makes a few of the wicked and profound issues quite clear.