| > It sounds like your assertion is more that a system cannot be deterministic because the complete state is not knowable and without the complete state of a system, there is no way for it to be deterministic because state form outside of it will influence it? Not quite. The choice of perfect knowledge of state is irrelevant. Even with perfect knowledge you can't, for example, predict the thought you think next. If you did, you didn't predict it, you experienced it, because the very act of predicting it was the act of thinking it. There are leading edges to the computation. It is a hindsight bias upon thinking them to think they were predictable. > I definitely think there is probably a contradiction between perfect knowledge and self reference, thus it is impossible to have perfect knowledge of a system from within the system. This is a lot closer to what I'm actually trying to say. Critically, that leading edge of information is a barrier that is very important and agents can use it to cause other agents to be unable to predict what will happen before they experience it. > I don't think I understand why game theory is relevant The reason it becomes relevant is because of optimal decision structure. From the math of game theory we learn that the optimal structure of an agent's decision making isn't to play rock or to play paper or to play scissors. If you choose any of these then an argument from the equilibrium considerations - which is basically an argument from the consequences of self-reference - shows the choice is exploitable. So in game theory we don't select rock and we don't select paper and we don't select scissors. Instead we select a probability vector over those choices. Basically it turns out that when things become unknowable the appropriate response is to change the level of abstraction over which actions are taken. |