In this note we will dig deeper into the idea of Emergence - as used the term in Science Modelling.

Note: The term emergence can refer generally to the appearance of something, but in science it has a technical meaning: the appearance of a radically new dynamical regime.

Note: Emergence is still an almost undefined term in general usage, but in if offers us a way to communicate a loose sense - a very relevant change in the dynamics of a piece of reality. To define emergence rigorously, we need a formal method to characterize radical changes in the system’s dynamics.

QA:

• Is the claiming that a system is strongly emergent is a type of ignorant / faith-based claudication?
• What are the type of emerges?
  • Strong emergence refers to the idea that certain properties or behaviors at the macro-level are fundamentally new and cannot be reduced to or predicted from the properties of the system's individual components, even in principle. These emergent properties arise spontaneously and are not explainable by the underlying micro-level laws.
  • Weak emergence suggests that macro-level properties do emerge from the micro-level components, but they can, in theory, be explained or predicted by the underlying rules and interactions of the system's parts. These emergent properties are complex but ultimately reducible to the behavior of the individual elements.
  • Coarse-grained Emergence: Emergent phenomena that arise at a level of abstraction, which may not be immediately visible at the micro-level but can be discerned at higher levels of analysis.

Formulation

Emergence is a property of the change of change—that is, a higher-order transformation—observed when a system or piece of reality transitions to a qualitatively new dynamical regime. This can occur either through:

1. Interaction of components — the relational dynamics between existing elements drive the system into new behaviors.
2. Addition of new elements combined with interaction — new components are introduced and interact with the existing system, producing new collective behavior without altering the intrinsic nature of the original elements.

In both cases, what emerges is not just a cumulative sum of parts, but a novel pattern or regime—a structural and dynamical novelty that could not be predicted by analyzing components in isolation.

References

• Emergence
• Carroll, S. M., & Parola, A. (2024). What Emergence Can Possibly Mean. ArXiv.
• Philip W Anderson (1972). More Is Different: Broken symmetry and the nature of the hierarchical structure of science. American Association for the Advancement of Science.
• Self-Organization