Sunday, February 24, 2008

9 plots and Dunbar's number - computer science, anthropology and literature

It has been said that there are only nine different plots (lots of people claim seven, but I think this is just for mystical reasons), and after hearing and Robin Dunbar talk about the social structure of human societies, I think I can explain this.

Social groups organise in a hierarchy of trust of degree (3+epsilon), so you get a social group of size (3+e)^n (1, 3, 9, 27, 81, 243) roughly - the epsilon varies with smartness and species. Dunbar also observes that the neocortex size of primates directly correlates with effective maximum group size (chimps 40, humans 150), and that this shows up in human societies in may many organisations (villages, armies, companies that are succesful). The explanation is that this is the maximum size that a group can maintain complete cohesion over, since everyone in the group has a model of everyone else - this reflects a species ability to infer intentionality (humans can do 5 levels reasonably well) and therefore trust relationships. One aspect of this is that humans have spoken language which abstracts, and therefore accelerate (expand, in graph terms) the range of grooming (essentially, by being able to gossip) rather than relying on physical grooming as a mechanism to achieve pairwise (or indeed, (3+e)-wise) cohesion.

OK - so now consider how we encode (neurologically speaking?) a simple description of another person's behaviour? We can use the distributed systems folks' model- BAR (Byzantine, Altruistic, Rational) - this has a game theoretic interpretation - but is also (I think) respectable in anthropology terms -

- Rational is basically selfish (think, selfish gene) and is just what Nash said. selfish is not bad since it is predictable, but it isn't "nice" in the normal selnse - it is also how naive economists describe the "market" and claim it is good - bah humbug

- Altruism is what happens (often, not always) when an individual behaves for the "greater good" at a disproportionally negative cost to themselves.

- Byzantive is mad/bad/sad - bonkers, people that do random harm - in network terms, hackers, script kiddies, whatever, that don't do it simply for personal gain.

Interestingly enough, one can reasonable assume that anyone can choose any of these behaviours, but that various incentives keep one in a particular state (kinship keep you mostly rational, occasionally atruistic), and social pressure will keep most people rational, but, and here's an observation about cities and the internet and the p2p systems and online games and facebook, once a group size is too big, there are enough places for people to go to other social groups, that there are ways one can be a serial byzantine bad person, and still survive - alienation, disaffection, etc, we all know about this - at a certan scale, if the rate of such behaviour is high enough, one sees social collapse...

ok - so in literature, (plays books films) many stories have 3 main characters. A plot consists of social dynamics. Lets think "eternal triangle", or "three princes" or any other archetype (or if you like, shakespeare tragedy, or wuthering heights or lord of the rings).

So 3 characters, 3 states- change 1 state
(gollum helps or hinders, heathcliff loves or hates, othello trusts or doesn't trust)
gives 9 plots.


indeed, classes of literature (jacobean tragedy - everyone starts luvvy, everyone dies) can be captured in this simple, elegant and ultimately futile and reductionist model:)

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