Of Downward Causation and Hipsterism

I doubted that I would ever tell this little story in a serious academic context, until a version of it came tumbling out of me in my recent specialist exam. Now that I’ve already suffered the embarrassment of having my committee hear it, I may as well share it with the wider world.

As a bit of background, consider the question of downward causation. Some philosophers (Evan Thompson, R.C. Bishop, Alicia Juarrero) have been arguing that complex systems exhibit downward causation, where the system as a whole constrains or explains the behaviour of its parts. We can’t just look to the intrinsic properties of the parts to understand the overall dynamics, we have to also include their organization as a whole system.

The example I like best is Raleigh-Benard convection, this thing:

So imagine this is water (or some other fluid) and the bottom plate is heated. Above a certain temperature, the water will make these lovely little rolls that form hexagonal cells. That’s Raleigh-Benard convection.

And the argument is that before convection starts, the individual water molecules are just bopping around, doing their own thing. The relevant causes are just the low-level microphysics of the system. But once a convective regime takes hold, the story goes, we need to consider another kind of cause – the constraint put on elements of the system by the organization of the system as a whole. So because the whole system is spiralling, individual molecules can’t just bounce around in any old direction, their set of possibilities is constrained to just rolling action. And that’s downward causation – a kind of systemic constrain on the possibilities of the parts.

I’d like to propose that we look at that same story from a different perspective. Suppose we ask what it would be like to be one of those water molecules. I think that if you look at it from the water molecule’s point of view, it’s pretty clear that whatever these systemic constraints that convection introduces are, they aren’t ‘downward’. They may tell us something about the system as a whole, but they don’t really tell us anything about the parts of the system, and don’t constitute a real constraint on the behaviour of those parts.

To that end, I’m pleased to introduce to Walter the Water Molecule:

The life of a water molecule is a simple but satisfying one. The really nice thing is that, unlike people, water molecules always act perfectly authentically, according to their own Innate Physics. When bounced by something from the left, Walter zooms right..

When something bounces him from the right, Walter always reacts in exactly the way he pleases, bouncing away to the left.

And no matter what his circumstances, Walter would always remain true to his own Innate Physics.

But one particularly hot day, Walter noticed something funny. Despite his doing nothing different than what he always had, it seemed more and more that everyone else was doing exactly what he was doing. He had decided, on account of his Innate Physics, to do vertical loops that day, but for some reason everyone else was doing it as well!

Since he was doing what he had always done, and now everyone else was doing the same, there was only one conclusion that poor Walter could come to: they were all copying him! Walter therefore became an insufferable hipster.

The moral of the story is, don’t be like Walter. His confusion was to think that just because everyone is doing the same thing, they must be following the crowd somehow. He assumed that if the overall behaviour is orderly, that must mean that the individuals involved must somehow be constrained from following their own Innate Physics. But that’s just not true. Water molecules do their own thing, no more and no less, both before and after the onset of convection.

Of course, something does change when the system changes from being disorderly to the orderliness of convection. What I’m rhetorically gesturing at here is that what changes isn’t anything about the parts of the system – they keep on keeping on in exactly the same way no matter what. What changes is at the system level. So there isn’t any good sense in which this self-organized behaviour counts as ‘downward’ causation.

three completely unhelpful things to say about self-organization

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’

and

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.