I’ve been reading John Miller and Scott Pages’ Complex Adaptive Systems – an introduction to computational models of social life, and Melanie Mitchell’s Complexity – a guided tour, both of which have set my wheels to turning.

Of the two, Mitchell’s book is the more accessible. Miller & Page dive heavily into cellular automata, and it takes some real leaps of the imagination to see how any of that applies to social life. One thing that they do discuss (and as does Mitchell) are Stephen Wolfram‘s theories that certain kinds of automata are universal computers. In principle this then suggests that simplified models such as cellular automata or more complicated ABM are widely applicable: that with a conceptual shift, a model may do double duty.  A model about predator-prey interactions becomes a model about shopping malls.

Mitchell also explores by-ways where the distributed, no-central-control system has as an emergent property the ability to compute solutions to problems facing the ant colony, the bee hive, the group, as a whole. Ants explore their world, and leave pheromone trails behind them. Another ant encounters the pheromone trail, leave its own traces, which reinforces the route. Trails that lead nowhere evaporate away; trails that lead to food sources are reinforced, and soon you have a map of all local food sources for the colony.  (or the Tokyo rail network, as the case may be.) No central direction.

Mitchell’s book is also quite good when it comes to explaining how networks figure into all of this, and some basic statistical properties of networks and how they conform/are formed by various behaviors.

Which is sparking a thought in my head, as a route to a new project. In my thesis work, I was able to compute the statistics for a variety of networks in Rome. I was then able to model these networks, to see how decentralized control solved the problem of resource exploitation (in this particular case, building materials to Rome). It would be interesting to compare the statistics of various patronage systems from various cultures at various times around the world. How did these systems solve the problems of resource management? I would then reanimate these various networks in a ‘sugarscape‘ type world. Which ones are more effective? How do I measure effectiveness? Which social configurations are more fit? Then, translating that back into history & culture, it would be interesting to see how that plays out when you’ve got two cultures in roughly the same environment – Medieval Florentine patronage vs Ancient Roman patronage…

Another thought sparked by these readings: in a patronage system where clients have choice over who their patron is – ie, they can insert themselves into the train of a new patron- naturally evolve to a state where there is a single patron.  In this, I’m recasting Miller and Page’s City Formation model (pg 151, section 9.4) in patronage terms.

In this model, imagine a world where all of the available patrons are standing in a ‘police-lineup’ style line in the town square.  The population of the town is randomly sorted in lines in front of each patron.  There are a host of reasons why a client might wish to swap patrons; let’s collapse all these into two variables: displayed support (# of clients the patron already has, hence the desirability of becoming a client) and ‘difficulty’ in switching allegiances – it is hard to gather knowledge about patrons further down the chain to either side, so the further away a patron is in the line, the more difficult it is to get into that chain.  A patron’s success depends on his ability to marshal the resources made available via his client base.

So – behavior. Following Miller and Page, the agents want to have access to the most successful patron.  A client can stay where it is, or move one step to the right, or the left. If the model is run, allowing clients to assess the entire line of patrons, this ‘society’ sorts itself out so that all clients are clients of a single patron. (situation a)

That’s quite neat.

If the ability of clients is restricted so that they can only see locally (a step to the right, or a step to the left), you end up with multiple ‘poles of power’, a handful of patrons with all the clients. (situation b)

So… if we have a society in history characterized by patronage… is it more like situation a, or is it more like situation b? In this model, it’s all about the clients. They choose where to go: so the key dynamic is in how they ‘learn’ about the world. The daily display, in ancient Rome, of a patron walking to the Forum with his clients then is a way through which clients learn about the relative fitness or desirability of potential patrons: thus leading to a single patron….?

…I’m just riffing off the top of my head here, but I think there’s something to this…