What is emergence, after all? (2507.04951v1)

Abstract: The term emergence is increasingly used across scientific disciplines to describe phenomena that arise from interactions among a system's components but cannot be readily inferred by examining those components in isolation. While often invoked to explain higher-level behaviors, such as flocking, synchronization, or collective intelligence, the term is frequently used without precision, sometimes giving rise to ambiguity or even mystique. In this perspective paper, we clarify the scientific meaning of emergence as a measurable, physically grounded phenomenon. Through concrete examples, such as temperature, magnetism, and herd immunity in social networks, we review how collective behavior can arise from local interactions that are constrained by global boundaries. By disentangling emergence from vague overuse, we emphasize its role as a rigorous tool for understanding complex systems. Our goal is to show that emergence, when properly framed, offers not mysticism but insight.