 The reader must have noticed that in the equation for \(P_{\opt,M}\) we have not elaborated on \(\bE\) and \(U\) and how equation \eqref{eq1} might be used to construct an agent if the class of environments \(\bE\) is quite general, or if the true environment \(E\) is simply unknown. Depending on the task for which one is constructing an artificial agent, \(E\) and \(U\) would vary. The mathematical form of the environment \(E\) and the utility function \(U\) would vary wildly from, say, chess to Jeopardy!. Of course, if we were to design a globally intelligent agent, and not just a chess-playing agent, we could get away with having just one pair of \(E\) and \(U\). What would \(E\) look like if we were building a generally intelligent agent and not just an agent that is good at a single task? \(E\) would be a model of not just a single game or a task, but the entire physical-social-virtual universe consisting of many games, tasks, situations, problems, etc. This project is (at least currently) hopelessly difficult as, obviously, we are nowhere near to having such a comprehensive theory-of-everything model. For further discussion of a theoretical architecture put forward for this problem, see the  Supplement on the AIXI architecture.  