Going critical

The agent-based modelling approach to the spread of ideas is, in my naive opinion, a fascinating and extremely important development. Nicky Case has an excellent website with a whole bunch of them (looks like more have been added since last I checked), in particular exploring how the structure of crowds can impede or aid the spread of ideas. It's obvious enough that the property of the idea and the pre-existing beliefs of the people are crucial. What's less obvious - or at least can be more easily and precisely revealed through simulations - is that the structure of the network is at least equally essential.

Here Keven Simler presents another excellent set of interactive simulations (Cases' are better at showing the structure, Simler's are better at demonstrating the results; Case also explores complex contagions). You should definitely run them for yourself (it's an easy and not that lengthy read), but here are some choice highlights. I thought it was particularly interesting just how versatile such network-based approaches can be - if I had to guess, I wouldn't have suspected that the spread of measles could be similar to wildfires, but apparently sometimes that expression can be an accurate metaphor.

It turns out that there's a precise tipping point that separates subcritical networks (those fated for extinction) from supercritical networks (those that are capable of neverending growth). This tipping point is called the critical threshold, and it's a pretty general feature of diffusion processes on regular networks. The exact value of the critical threshold differs between networks. What's shared is the existence of such a value.
Below the critical threshold, any finite infection on the network is guaranteed (with probability 1) to eventually go extinct. 

But above the critical threshold, it's possible (p > 0) for the infection to carry on forever, and in doing so to spread out arbitrarily far from the initial site. Note, however, that an infection on a supercritical network isn't guaranteed to go on forever. In fact, the infection will frequently fizzle out, especially in the very early steps of the simulation.

Which I suppose suggests that the timing of interference in the spread of whatever it is that's spreading can be critical, and the nature of the intervention is equally important. Simler goes on to explore one such simple intervention - the presence of nodes who are immune. Interestingly this also includes nodes which can become immune after exposure, as well as those who are temporarily afflicted but then become vulnerable again after some time.

Changing how many nodes are immune absolutely changes whether the network is sub- or supercritical. And it's not hard to see why. When many nodes are immune, each infection has fewer opportunities to spread to a new host. This turns out to have a number of very important practical implications. One is preventing the spread of wildfires... Another outbreak that's important to stop is infectious disease... Finally, we can use the concept of immune nodes to understand what happens in a nuclear reactor.

And then we look at how the connections help spread and restrict transmissions :

Up to now, our networks have been completely homogeneous. Every node looks the same as every other node. But what if we subvert this assumption and allow things to vary across the network? For example, let's try to model cities. We'll do this by creating patches of the network that are denser in connections (have higher degree) than the rest of the network. This is motivated by data that suggests that people in cities have wider social circles and more social interactions than people outside cities.

What surprises me is that some of this cultural variety can arise based on nothing more than the topology of the social network. What I learned from the simulation above is that there are ideas and cultural practices that can take root and spread in a city that simply can't spread out in the countryside. (Mathematically can't.) These are the very same ideas and the very same kinds of people. It's not that rural folks are e.g. "small-minded"; when exposed to one of these ideas, they're exactly as likely to adopt it as someone in the city. Rather, it's that the idea itself can't go viral in the countryside because there aren't as many connections along which it can spread.

Anyone want to take a stab at how this applies to political ideologies, e.g. people in the countryside seem to be more right wing and conservative ? It would be interesting to see if people who move from rural to urban areas become more liberal, and vice-versa. And networks can be intensely local as well as global, which is why behaviour among some groups can be radically different from the prevailing norms :

We tend to think that if something's a good idea, it will eventually reach everyone, and if something's a bad idea, it will fizzle out. And while that's certainly true at the extremes, in between are a bunch of ideas and practices that can only go viral in certain networks. I find this fascinating.

Cities aren't the only place we find dense networks. High schools are an interesting example. Consider, in a given neighborhood, the network that exists among the students vs. the network that exists among their parents. Same geographic area and similar population sizes, but one network is many times denser than the other. And it's no surprise, then, that fashion and linguistic trends proliferate among adolescents, and spread much slower among the adults.

 Finally we get an interesting case study of how all this can work in academia :

Suppose we distinguish two ways of practising science: Real Science vs. careerist science. Real Science is whatever habits and practices reliably produce knowledge. It's motivated by curiosity and characterised by honesty. (Feynman: "I just have to understand the world, you see.") Careerist science, in contrast, is motivated by professional ambition, and characterised by playing politics and taking scientific shortcuts. It may look and act like science, but it doesn't produce reliable knowledge. 

Of course, there's no categorical distinction between careerists and Real Scientists. We all have a little careerism in us. The question is just how much the network can carry before going quiet.

In the simulation it's fun to watch a fairly small percentage of Careerists block the successful propagation of ideas, in which one idea triggers the formation of another. I suspect there are very few scientists who are so strongly career-oriented as to be damaging for knowledge, but on the other hand it might explain why my citations are so low... :P

Though, this does make me wonder why people tend to - for example - like posts on social media but not reshare them : particularly those cases where a post gets lots of likes but few reshares. Why does this happen ? What makes something likeable but doesn't leave one with the urge to tell anyone else about it ?* I do this as much as anyone, though I do make a conscious effort to more preferentially reshare content from people I directly interact with. Content creation and dissemination seems like a major feature of social media - having conversations about the news is fine and all, but a secondary goal. (Somewhat related : people who present their own very good content but never like or reshare anyone else's. What's with that ?)

* For posts such as this one, I totally understand why people might prefer to share the original link rather than this, which is mostly my own comments.

It's also interesting to watch ideas interact with each other, though this simulation makes the assumption that successive ideas always replace the previous one. I wonder if it would be possible to model this more accurately, allowing some ideas to be replaced with others or with agents to have multiple infections independently. Or if agents could change connections depending on their current beliefs, seeking out other, similar agents and moving through the network...

It's also fun to see (though sadly you can't control) that it's not just numbers that matter but structure. If there's no key connection between two nodes that generate key ideas, then key ideas don't get started. These connection routes can be blocked with only a very few Careerists, if they're in the right places. Coherent structures, as I found out personally, don't necessarily need to be statistically significant to be important.

Going Critical

Learn how things spread with playable simulations