alt Hacker News>we do need and should have good fine-grain computational models of complex systems such [...] the global economy.
Many years ago when 'social graphs' were still a hot area to do research in I started building a simulation of the equivalent of a small medieval village.
What became quickly apparent is that you didn't just need interactions between any two individuals like classical social graphs talked about, but between any number of arbitrary groups of individuals. Otherwise something as simple as an extended family couldn't be modeled.
That meant that instead of being able to use a matrix as the fundamental data structure you'd need a tensor of rank N, where N is the number of people in the economy. Just to see how intractable this is if the village had 20 people in it with the traditional matrix approach you'd need 400 weights to model interactions. With the tensor approach you need ~1e+26.
In short: it's impossible to have fined grained simulations of complex societies. The best we can do is drastic over simplifications that give us _some_ predictive power.
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A set of size N=20, has total number of subsets equal to 2^N = 1.05 million. You must have had other degrees of freedom to bump that to 1E26.
Use of a dense matrix is an artificial constraint you've imposed yourself, but that only disproves feasibility of your proposed solution, not the entire problem in general.
A similar problem, n-body simulation*, has n² gravitational interactions. You will similarly hit a wall if you try to do it with a dense n² matrix. However, there's a hierarchical solution that takes advantage of the sparsity and exponential decay, and can solve it in (n log n) with an imperceptibly low loss of precision.
Social interactions are sparse, and group interactions can be optimized with clustering. Fine-grained simulation of the entire society is such a massive chaotic problem with so many variables, that some loss of precision from clustering is completely insignificant compared to the inevitable simplifications you'll have to make in the design of the model itself.
* I mean the naive one with a fixed timestemp, not trying to solve chaos.