# Network dynamics

Saw a very cool talk this morning about dynamics of and on networks.

A large fraction of the talk was an introduction to network theory. The general point was introducing network dynamics as an alternative approach to the study of middle-order complex systems.

Small systems (with only a few interacting pieces), see, you can just do the math for. And really large systems (like, 10^23 interacting molecules) can be handled with statistical mechanics. But systems with too many components to do the math, but not enough to apply stat-mech to, are really, really hard.

However, if you can represent your system as a bunch of nodes connected together in a network and interacting via the links, you can do some cool stuff, because the topology of the network imposes strong constraints on the system behavior regardless of what's actually passing across the links!

He talked about a whole bunch of stuff, but here's one of the neat ideas: network structure determines how big your system can get before it goes unstable. One of the features that large, stable networks have is that they are disassortative -- the high-degree nodes (the hubs) will not be adjacent to each other, they will be separated by low-degree nodes.

Now, a system that's optimized for information transfer, like a social network, needs to be assortative, with the hubs close to one another.

So there's a possible explanation for the "natural size limit" on human communities of about 100 people. It's not an arbitrary limit to how many people a human brain can keep track of, it's that the human brain has never needed to evolve the capacity to keep track of communities larger than that, because they become unstable above that size...

(Note: I'm not saying that you can't keep a system stable above a certain size, because that's obviously not true. I think it's more like once a system has gotten as big as it can get and still be naturally stable, you have to put another system on top of it in order for things to be stable at the new scale. Informal decision-making only works for small companies; once your company gets to a certain size, you have to create formal structures to keep functioning.)

Anyway, there was lots of other neat stuff (like network instability being a possible contributor to the collapse of the Maya), but the assortative limit idea was the thing I had to share.
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