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©2015 Herbert Snorrason

On Irreducible Complexity


2011-11-26

Class.

Hooo-boy. There’s a term that gets the blood boiling in most cases. Who’s rich and who’s poor; aren’t we all middle-class? Isn’t the industrialised west as a whole the global rich, while the south of the globe gets the short end of the stick? Can we talk about a class-divided society without invoking the spectre of class warfare?

One interesting thing about class is that people tend to claim, today, that it doesn’t matter in western societies. This denial has two main forms:

Neither is a particularly useful way to look at things. Both paper over very real tensions in global society and create an overly simplistic vision. The first pretends that “we’re all in it together” whereas the second pretends that the interests of everyone in the developed countries aligns against the interests of those in the less developed countries. The most sophisticated advocates of class irrelevance combine both. But ultimately, neither position is tenable. Why?

Because of irreducible complexity. Bear with me for a moment; that’s not as preposterous as it may seem at first. At base lies the question of how you model society: My model of choice is a network with extremely complicated interconnections. (Graph with many and varied edges. Individuals are vertices; their relationships are edges.) You should immediately take note of one important factor: The base unit is the individual. Those individuals are positioned inside a structure (the graph) which they have only very limited control over. So far, so good. This model is relatively non-controversial; we can build pretty much any sort of social structure on top of this grid. What causes tension is the empirical question of how the network is structured.

Obviously, the network is far too complex for anyone to map it out in full. (Not that that has stopped facebook from trying.) But we can discern features in it. The first, and most important feature, is simply the realisation that it is a network. It’s a massive network, and one that scales enormously. That means it should be possible to identify subnets; systems that are internally very tightly interconnected but have looser connections to the larger network. Within those subnets, we should also be able to detect segments. Viewed as a communications network, there are very likely to be trunk lines, of a sort, between various subnets. Picking away the pieces, these subnets are liable to be highly interdependent, but in a limited way. We’re fond of saying “everyone is connected” and that is true in the abstract. But when it comes to concrete analysis, it’s not. Understanding the specifics of social structure means reconstructing pieces of an inordinately complex system.

And that’s the snag. A full representation of this highly complex system must be at least as complex as the system itself. This is a fundamental limit that cannot be overcome; it lies in the nature of information.1 Only if we imagine that the extremely complex system can be generated from a simpler description — not impossible, but unlikely given the role of chance in relationship formation.

“Uh-oh”, says the typical proponent of class-based analysis at this point. “Doesn’t this also mean that the contention of primacy of class is untenable?” Well, yes, it does. What it means is that no single way of dividing up the world is going to give you an accurate picture of human society. It means we have to take a multitude of factors into account and restrict our models appropriately. It means we have to take into consideration the edges of what we’re investigating; the fact that, for instance, the social elites are international and usually more tightly interconnected with each other than they are with the general population of their origin or residence. The fact that, although on a global scale the west is built on exploitation of vastly larger areas (and populations), the spoils go almost exclusively to small groups within those societies who also exploit the vast majority of their own populations. The fact that “middle-class“ has no meaningful definition and instead masks very real differences between a number of social groupings — some of which are surprisingly powerful, and others of which are surprisingly powerless.

As for the spectre of class warfare: Perhaps the spectre needs to be raised again, because if there’s anything we need to be mindful of on this earth, it is the fact that not everyone’s interests are harmoniously aligned.


  1. Refer to Claude E. Shannon and Warren Weaver, The Mathematical Theory of Communication. Basically, there is a minimum information content (measurable in bits) for any given thing to be represented. Things can be represented in less efficient forms than that, but not more.

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