It seems to me this is important, because this precisely why games are fun. In almost any other aspect of human existence, all these things are ambiguous. Think of a family quarrel, or a workplace rivalry. Who is or is not a party to it, what’s fair, when it began and when it’s over, what it even means to say you won—it’s all extremely difficult to say. The hardest thing of all is to understand the rules. [...] Games allow us our only real experience of a situation where all this ambiguity is swept away. Everyone knows exactly what the rules are. And not only that, people actually do follow them. And by following them, it is even possible to win! This—along with the fact that unlike in real life, one has submitted oneself to the rules completely voluntarily—is the source of the pleasure.
Games, then, are a kind of utopia of rules.
— utopia-of-rulesch. 3
This is what makes possible the utopia of math: the insistence on definitions, games that are played by the rules. Where do the rules come from? The founders of mathematical fields, who ultimately derive them from observations of the world around them (are other sources of "the rules" possible?)
Graeber makes this distinction between play and games
In fact, if it were possible to come up with a workable definition of “play” (this is notoriously difficult) it would have to be something along these lines: play can be said to be present when the free expression of creative energies becomes an end in itself. It is freedom for its own sake. But this also makes play in a certain sense a higher-level concept than games: play can create games, it can generate rules—in fact, it inevitably does produce at least tacit ones, since sheer random playing around soon becomes boring—but therefore by definition play cannot itself be intrinsically rule-bound. [...]
[...] Here’s a quote from Indian philosopher of science Shiv Visvanathan:
A game is a bounded, specific way of problem solving. Play is more cosmic and open-ended. Gods play, but man unfortunately is a gaming individual. A game has a predictable resolution, play may not. Play allows for emergence, novelty, surprise.
All true. But there is also something potentially terrifying about play for just this reason. Because this open-ended creativity is also what allows it to be randomly destructive. Cats play with mice. Pulling the wings off flies is also a form of play. Playful gods are rarely ones any sane person would desire to encounter.
Let me put forth a suggestion, then.
What ultimately lies behind the appeal of bureaucracy is fear of play. For the social theorist, there is one obvious analogy to play as a principle that generates rules, but is not itself bound by them. This is the principle of sovereignty. [...] Basically, the question was: is it possible to say that the supreme ruler of a kingdom is in any sense bound by its laws?
— utopia-of-rulesch. 3
Specifically, while play can generate rules, games only work when there is a fixed set of rules that everyone agrees to abide by.
Sovereignty in this sense is ultimately identical to play as the generative principle that produces games; but if so, it is also play in its most terrifying, cosmic form. Some have called this the notion of “top-down” play, a concept that seems to be most explicitly developed in Indian theology, where the cosmos itself is essentially the play of the divine forces.161 But as Brian Sutton-Smith notes in his book The Ambiguities of Play, this was the dominant view throughout the ancient world, where human beings were the playthings of destiny and fate; the exemplary human game, in such a universe, is gambling, where we willingly submit ourselves to the random whims of the gods.162
In such a universe, freedom really is a zero-sum game. The freedom of gods or kings is the measure of human slavery.
— utopia-of-rulesch. 3
Graeber doesn't make explicit mention of Gödel, but I wonder if he was at least indirectly influenced by the Incompleteness Theorem, which basically states that formal systems (e.g. arithmetic, algebra, etc.) cannot "prove their own correctness", so to speak. Something else outside of the system must have generated those rules (axioms) in the first place. A sovereign something, here in the context of the social theorist.
Penrose criticises the idea that the human mind and consciousness can be boiled down simply to computability, as the practitioners of "strong AI" had it in 1989 (IIRC he counts Hofstadter amongst them). Citing Gödel,
Thus, once we have seen how to mechanize some part of our mathematical understanding (into [some computational procedure] P, say), then we can also see how to transcend this mechanization. To me, this provides a clear-cut reason for believing that our mathematical understanding contains elements that lie beyond purely computational action.
— emperors-new-mindch. Preface
Recall: Hofstadter claims that life arises when there is a strange loop, when a system begins to change the rules of the game it itself abides by, a "computer rewriting its own source code". godel-escher-bach
In the social sphere, perhaps the analogue might be "popular sovereignty", in which laws can nominally be changed, constitutions can nominally be amended according to the "will of the people", but Graeber questions what that even really entails:
It shouldn’t be hard to see where all this is going. Modern states are based on a principle of popular sovereignty. Ultimately, the divine power of kings is in the hands of an entity called “the people.” In practice, though, it’s increasingly unclear what popular sovereignty in that sense is even supposed to mean. Max Weber famously pointed out that a sovereign state’s institutional representatives maintain a monopoly on the right of violence within the state’s territory.163 Normally, this violence can only be exercised by certain duly authorized officials (soldiers, police, jailers), or those authorized by such officials (airport security, private guards …), and only in a manner explicitly designated by law. But ultimately, sovereign power really is, still, the right to brush such legalities aside, or to make them up as one goes along.164 The United States might call itself “a country of laws, not men,” but as we have learned in recent years, American presidents can order torture, assassinations, domestic surveillance programs, even set up extra-legal zones like Guantanamo where they can treat prisoners pretty much any way they choose to. Even on the lowest levels, those who enforce the law are not really subject to it. It’s extraordinary difficult, for instance, for a police officer to do anything to an American citizen that would lead to that officer being convicted of a crime.165
— utopia-of-rulesch. 3
In an example of a society with only sovereignty (sans knowledge-control or charismatic politics):
How exactly are we to understand this situation? It might seem paradoxical – but historically such arrangements are not particularly unusual. The Great Sun was a sovereign in the classical sense of the term, which is to say he embodied a principle that was seen as higher than law. Therefore no law applied to him. This is a very common bit of cosmological reasoning that we find, in some form or another, almost anywhere from Bologna to Mbanza Congo. Just as gods (or God) are not seen as bound by morality – since only a principle existing beyond good and evil could have created good and evil to begin with – so ‘divine kings’ cannot be judged in human terms; behaving in arbitrarily violent ways to anyone around them is itself proof of their transcendent status. Yet at the same time, they are expected to be creators and enforcers of systems of justice. Such with the Natchez too. The Great Sun was said to be descended from a child of the Sun who came to earth bearing a universal code of laws, among the most prominent of which were proscriptions against theft and murder. Yet the Great Sun himself ostentatiously violated those laws on a regular basis, as if to prove his identification with a principle prior to law and, therefore, able to create it.
— dawn-of-everythingch. 10
Reputation for illegal violence w/o consequences "proves" their divinity and their being above the law, and hence their right to create and enforce it. (... smells like auth-rule-of-law)