Editing Openai/693343d7-a38c-8012-a67c-11cbed4c0fd9 (section)

===== Mathematically, the actor primitive can be described as a system that follows certain rules for change. The nature of the change determines if the actor is an entity or an agent. =====

====== An actor could be described by a state space SSS, where its state evolves over time based on external factors Ω\OmegaΩ and internal rules RRR: ======

St+1=f(St,Ωt,Rt)S_{t+1} = f(S_t, \Omega_t, R_t)St+1=f(St,Ωt,Rt)
Where:
* StS_tSt is the state of the actor at time ttt,
* Ωt\Omega_tΩt represents the external factors that influence the actor,
* RtR_tRt represents the internal rules that guide the actor's state transitions (e.g., decision-making, rules of behavior).

====== For passive actors (entities), the internal rules are either absent or rule-based and driven solely by external stimuli: ======

St+1=f(St,Ωt)S_{t+1} = f(S_t, \Omega_t)St+1=f(St,Ωt)
Here, the actor's state change depends purely on the external environment, and there is no internal decision-making involved. These are typical of entities like resources, inanimate objects, or passive data points.

====== For active actors (agents), the internal rules are complex and allow for autonomous decision-making: ======

St+1=f(St,Ωt,Rt,Πt)S_{t+1} = f(S_t, \Omega_t, R_t, \Pi_t)St+1=f(St,Ωt,Rt,Πt)
Where Πt\Pi_tΠt represents the intentional decisions or policy of the agent. In this case, the actor uses its internal mechanisms to make decisions based on its goals, beliefs, and experiences, allowing for adaptation and learning. This is typical of agents with goals and learning capabilities.