Axelrod's model of cultural dissemination
When introducing this basic grid in my previous post I made the off-hand statement that "proximity is 9/10ths of a relationship". This is something I remember hearing at one time and it has stayed with me. In 1997 Robert Axelrod published his now famous model of cultural dissemination using cellular automata. The model gives computational and theoretical basis for studying the emergence of culture through the interactions between individuals. With simple rules the model enables study of the effect of individuals having similar traits becoming more similar, as well as the possible counter effect in which tendency toward local similarity leads to global polarization.
How to win friends and influence other cellular automata
Every cell takes its random turn to possibly interact with a random neighbor. The likelihood of the active cell adopting a trait of its neighbor is based on the similarities they already share. The more they have in common, the higher the probability the active cell will adopt another trait from its neighbor. But in this model, if they have nothing in common, no trait will be adopted. Neither will a trait be adopted if both cells already share identical traits.
Culture constantly emerges, until it doesn't...
In Axelrod's model regions of contiguous cells with fixed inactive states are said to be stable. This characterization might seem a bit sterile when thinking about the richness or complexity that culture is sometimes meant to convey. But it is the dynamic quality of continual interaction between neighbors and zones that I find strangely expressive of real-world cultural volatility. The visualization may at times show narrow corridors of quiet interaction, while elsewhere broad arenas of chaotic tumult ensues. And then we may also see a few sections behind walled fortresses of quiet stability.
Spare the details, and parameters...
I will not here attempt to document the academic details of Axelrod's model and its permutations. There are many research papers and simulations available online. I am also not providing any ability to vary the input of cultural traits. Such traits are expressed with vectors of arbitrary size and number of numerical values. This decision would seem to defeat the whole purpose of enabling research into the effects that such variation of conditions have. But this blog is not meant for this level of research involvement. (For the record, I have used 5 features with each cell having 5 random trait values. This configuration results in a behavior characteristic which I think gives an good feel for the model. For those who are interested, a link to the code is provided below). For now, I am glad to have explored and experimented with the ideas behind Axelrod's research.
Near and far
In 2016 the idea of physical proximity remains important. I like MeetUps and hacker spaces where I can network with people from my local community. People commute everyday just to work in the same building at computers which are connected over the Internet. Yet the Internet greatly expands the interwoven dimensions of our networked cultures. It connects us to places that are very different, and it shows us the many ways we are similar. Our world is becoming more homogeneous at the same time we are exposed to its richness in variety. There are many implications to explore. Watching this model change over time helps me to appreciate the constant dynamic quality that unfolds at many levels.
The network is coming...
The grid remains a fascinating context to explore graph-like relationships and I want to do more with it. We still walk on floors, drive through blocks of residences or shopping districts, and compare columns and rows of numbers. But we also learn with neural networks and communicate with people around the world. I'm eager to explore cultural dissemination through network models too.