alt Hacker NewsUse 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.
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>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.
The use of a dense matrix is the traditional way of solving the problem. The issue is that it solves the wrong problem. You need a dense tensor which requires more storage than the world currently has for an economy of 20 people.
Social interactions are sparse until they aren't. If you think otherwise try to estimate what every Europeans interaction with Gavrilo Princip was on 27 June 1914 vs 28 June 1914.
As for gravitation: I'm very happy for the planets and asteroids out there. Unfortunately the economy isn't a solar system.
Isn't the naive one hopeless since those systems require perfect measurement, and economic interactions are lagging, the calculations are ordinal, and mathematical systems fail because you can't relabel? (i.e. fails a function test so you end up trying to compare unrelated mathematical objects within differing systems).
Even statistics is fully thrown out with the islands of regularity.
The stochastic nature, lack of measure-ability, and multiple hidden underlying states (value is subjective) require any model to solve chaos somehow.
https://science.ku.dk/english/press/news/2024/islands-of-reg...