I’ve been discussing with a friend on what makes big cities worth living in and one of the point raised was that just by putting a lot of people in a small space, you get much more innovation than spreading out the same amount of people in a wider area.

This is one of the reasons why Edward Glaeser dubs city as “the man's greatest invention“ in his book. He brings up the rate of new patents to back up the above claim but the blog post offers another mathematical reason.

I can think of a few extensions: make it more realistic with a global map of fiber-optic cable networks and local extensions, and then compare how information spreads through things like peer-to-peer sharing vs. information posted to 'central authorities' like Twitter. (Notably there was also that study that showed false information spread faster across Twitter than accurate information, attributed to the 'surprise factor'). This could also be modified to include the authoritarian filter effect (i.e. how does China's 'Great Firewall' affect the spread of information, for example).

With respect to this simple nearest-neighbor model, I suppose a complicating factor would be long-distant transport from a given node to a distant node by some out-of-plane connection method (i.e. Covid spread rapidly by airplane, for example).

The article really shows that graph-based network thinking is a great way of approaching these problems, nice work.

Great essay. The simulations sure make this point hit hard. I feel the author's jadedness coming out here.

Should one feel like a small colored dot encircled by immune grey, it is essential to maintain a belief in agency: believing oneself capable of networking, relocating, and modifying the surroundings.