Intelligence as Relational Leap: A Dual-Domain Framework for State, Impulse, Connection, and Higher-Order Transition

This paper proposes a dual-domain relational framework for describing intelligence not primarily as a stock of knowledge, a test score, or a property contained within a single agent, but as a transition that emerges through a changing relation between two analytically defined domains, L and R. The framework begins from a minimal claim: a system’s operative state is determined not by L or R in isolation but by their coupling. A perturbation in that coupling—termed an impulse—can create conditions for a new functional connection. When the new connection reorganizes the space of possible states rather than merely selecting among already available responses, the transition is defined as a relational leap. The model distinguishes ordinary state change from higher-order transition: a first-order leap changes the state generated by a transition rule, whereas a higher-order leap changes the transition rule itself. An atemporal relational network is introduced only as an analytical representation for viewing many historical pathways simultaneously; it is not offered as a causal account of the origin of intelligence. The framework is positioned relative to cybernetics, dynamical systems, enactive cognition, predictive processing, complex adaptive systems, network neuroscience, and theories of scientific change. The paper concludes with operational definitions, formal notation, empirical propositions, and possible applications to human–AI coupling. The aim is to turn an intuitive relational model into a falsifiable research program.