Ontology of the Rule
How State Transition Functions Manufacture Human Behavioral Norms
Permanent Identifier: https://doi.org/10.5281/zenodo.1089203
Scholarly Abstract
A game is not merely an artistic artifact; it is an executable state machine whose formal transition constraints manufacture artificial scarcity, strategic incentives, and emergent psychological norms. This treatise deconstructs the mechanics-dynamics-aesthetics (MDA) framework to show how trivial syntactic rules compound into profound sociological phenomena.
1. The Formal State Transition Function
At its computational core, any formal game is modeled as a state machine $M = \langle S, A, T, s_0, Z, U \rangle$, where $S$ is the state space, $A$ is the alphabet of legal actions, $T: S \times A \to S$ is the transition function, $s_0$ is initial state, $Z \subset S$ is terminal states, and $U: Z \to \mathbb{R}^n$ assigns player utilities.
2. The Magic Circle as an Epistemic Boundary
Johan Huizinga's concept of the 'magic circle' describes a temporary, dedicated spatial and temporal arena where ordinary real-world meanings are suspended and replaced by the arbitrary normative constraints of the rules.