But for sake of argument, let's move N down to 10,000 (a small city or large crowd). How do you manage that without hierarchical organization and government?
So you have a billion Facebook friends?
> commerce, et cetera.
So you go to a billion different grocery stores? A billion different drugstores? A billion different restaurants?
The fact that, ultimately, there might be a billion or more people involved in the processes that bring you your food, household items, etc., or visiting the same social media sites that you do, does not mean you interact with all of those people directly. Nobody does. All of that activity is coordinated spontaneously, driven by individual voluntary interactions involving much smaller numbers of people.
In fact, talking about the social media case, centralization of power, as in the case of Facebook, has arguably done more harm than good.
> let's move N down to 10,000 (a small city or large crowd). How do you manage that without hierarchical organization and government?
You will most likely have hierarchical organization in these cases. But hierarchical organization is not the same thing as government. Hierarchical organizations evolve all the time through the voluntary interactions of people. Governments impose their rules on people by force. Those are very different things.
The functional health of an organization is directly determined by how closely its constituents are following a loose language of agreed-upon behaviors -- protocols. If you pretend such protocols don't exist, or explicitly refuse to enforce them, your organization will simply disintegrate.
How many gatherings of a billion people have you attended?
Nobody actually has direct relationships with a billion people. That's why there is no need to "solve" the "problem" of how to centrally coordinate a network with a billion nodes. The coordination happens spontaneously as people voluntarily interact with the people they directly know. In economics, this mechanism is called a "free market".