When we apply our abstract tree to the city we expect to find an Avogadro's number. The limit on N is determined by the transaction efficiency in the city center, which should be fixed and known by all the agents.
If this is a 1D + momentum makes 2D, then where is the 1D? The center bulges up, in one spot along one line. We have elevator congestion, and business is quantized in those tall building. The limit N on a human city defined by our willingness to pack into elevators for long rides. There is no miracle theory, just the common abhorrence of getting stuck in boxes.
And it should be that way, that is exactly who we are expect economic theories to work. Everyone is pained by long lines. we want personal space, and we are all about the same size. You will get an abstract tree, made in the center of town.
Economics should not be complex, we are not complex.
Sandbox is always the best known linear model, in self sampled systems. So our quantized city can be constructed backwards, start with a smooth pond of water, compress it suddenly along a concentric perfect circle. You get slosh, like in a cup off coffee, really a large echo from the water colliding without compression. That is aliasing, Gibbs phenomena in extreme, like the squeal of a microphone. Happens when we make a wave of higher energy then the medium can hold, it echos.
OK, assume the fluid will quantize in the center, optimally. Compute is back wards, like a pit problem. Find the generator, and you get the optimum size of your elevators. You have built fluid containers to hold units of stuff called human as a fluid. Working the problem in reverse: 2D -> 1D plus momentum. But we don't, it is easier to measure it directly by riding the things on a semi-repeatable basis, then make sight adjustments to our travel frequencies.
2D -> 1D plus momentum -> 2D is your Hamiltonian, I think.
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