It seems like everyone knows self-organization when they see it, but no one can quite say what makes it a thing. What follows is just three seemingly sensible and intuitive sounding things that people tend to say about self-organization and/or complexity that don’t to alleviate that situation. They’ll get progressively less unhelpful as we go along.
Self-organization is a process whereby pattern at the global level of a system emerges solely from interactions among the lower-level components of the system. The rules specifying the interactions among the system’s components are executed using only local information, without reference to the global pattern.
Camazine, “Self-Organization“, from The Encyclopedia of Cognitive Science
To start off, let’s look at Scott Camazine’s short definition of self-organizing systems. It’s a pretty good definition, especially if you already have an intuitive idea of the kind of systems we’re talking about. They have some interesting global behaviour, which isn’t imposed on the system from outside, it just emerges from the interactions of the parts. As far as it goes, I think what Camazine writes is true. It’s just not very helpful.
To see why, look again at the definition and ask yourself whether it excludes anything. Are there systems which aren’t simply the product of local interactions of their parts? The reductionist, physicalist picture which self-organization is supposed to be a challenge to asserts that everything is just the product of the interaction of its parts. If there is something philosophically interesting about self-organizing systems, it’s supposed to be that they challenge this view! Read in a strict and literal way (ie. without the benefit of implicit, intuitive ideas about what self-organization means), Camazine’s definition tells us precisely nothing about the phenomena of interest.
Every biological system can be viewed either as an organized whole or in terms of its individual parts. Holistic studies focus on the organized whole. Reductionist studies focus on the individual parts.
Grinnell, The Everyday Practice of Science. p. 49
Ok, so Camazine didn’t help much to get a grip on what we really mean by self-organized systems. There was something unspoken in his definition, something about there being interesting global structures that emerge from the interaction of the parts. Surely then the above quote from Frederick Grinnell helps? What we’re talking about is organized wholes versus individual parts, right?
That would be fine, except that ‘part’ and ‘whole’ are entirely relative concepts. Everything is a part relative to some larger whole, and (almost) everything is a whole composed of several parts. Telling us that the sciences of self-organization or complexity or whatever focus on ‘wholes’ rather than ‘parts’ is to say precisely nothing about the style of reasoning being employed. Newtonian mechanics, that blessed paradigm of reductive, analytic sciences, applies perfectly well to extremely complex wholes. If you scooped out my brain (a very complex object if I do say so myself) and tossed it around the yard, it would trace out parabolas as nicely as any other, simpler object. So just saying flatly that self-organization is about ‘wholes’ rather than ‘parts’ is really no help at all.
The distinction between nonlinear and linear interactions provides one way of distinguishing between systems that have emergent processes and systems that do not (Campbell and Bickhard 2002). […] Nonlinear interactions are nonadditive and nonproportional. They give rise (by definition) to systems whose activities cannot be derived aggregatively from the properties of their components.
– Thompson, Mind in Life, p. 419
(Sorry Evan, and thanks for agreeing to be on my comittee!)
So we didn’t get any traction by saying self-organization is about wholes rather than parts. Maybe the trick is to characterize the relationship between the parts and the whole? That seems promising. One popular way of doing this is to say that self-organization happens when the parts interact in non-linear ways, such that the whole cannot be understood in terms of the simple addition of its parts. But what exactly is non-linearity?
Below you’ll find an example of a non-linear function. Are you ready?
Not exactly mind-blowing, is it? But it is, in the strictest and most literal sense, a non-linear graph. Changes in x result in non-proportional changes in y, because going from x=1 to x=2 results in a much smaller change in y than going from x=10 to x=11. And that’s really all there is to non-linearity – that the points on the graph don’t form a line.
The reason why y = x² is so underwhelming as a non-linear graph is that it’s really easy to see how it would be linearized. We just take the 1st derivative to get y = 2x and pow, perfect linearity. Of course, there are lots of graphs where it won’t be so easy to find a nice linear reconstruction – especially if lots of variables are coming together, each interacting with the others in a non-linear way. But now we’re on to a richer notion that linearity vs. non-linearity. We need something like non-linearizability, or non-decomposability.
To be fair to Thompson (hi Evan, thanks again) just paragraphs after the above quote he goes on to discuss exactly those kinds of richer ideas. My aim is just to point out that it is the more subtle and consequently more difficult to formally characterize idea of non-decomposability that does the actual work.
So those are three completely unhelpful things to say about self-organization. I don’t know if pointing those out is itself helpful in any way, which is why this gets to be a blog post rather than a conference paper or what have you. To sum up, we could say that a helpful notion of self-organization has to say something that:
1) Includes the fact that there is interesting organization at the level of the whole that calls out for explanation somehow
2) Says something about the nature of the relationship between parts and wholes, rather than just specifies that we’re talking about ‘wholes’ rather than ‘parts’
3) Doesn’t merely say that the relationship between parts and wholes is ‘non-linear’, but instead includes some richer notion like non-linearizability, or non-decomposability.