Emergence

Definition

Emergence refers to the appearance of novel organizational principles, properties, or behaviors at coarser scales that are not present (or not apparent) at finer scales. Emergent phenomena arise from the interactions of system components but cannot be straightforwardly reduced to properties of those components in isolation.

In the context of nested systems, emergence is understood as a structural phenomenon: the macroscopic system ${\mathcal{S}}^{+}$ exhibits properties and dynamics that, while functionally dependent on microscopic configurations, represent genuinely new organizational principles governing interactions among coarse-grained entities.

Key Characteristics

• Novelty: New properties or patterns appear at higher organizational levels
• Non-reducibility: Emergent properties cannot be simply predicted from component properties alone
• Downward causation: Higher-level organization can constrain lower-level dynamics
• Scale-dependence: Emerges specifically in the transition between organizational levels
• Relational origin: Arises from interactions and relationships, not individual components

Emergence in Nested Systems

Walloth’s framework treats emergence as fundamentally tied to nested system hierarchies. Systems are “emergent nested systems” when:

1. Lower-level entities interact to produce higher-level structures
2. These structures become elements at the next organizational level
3. The enclose relation connects levels: ${\mathcal{S}}^{\prime }\text{encl}\mathcal{S}\text{encl}{\mathcal{S}}^{\prime \prime }$
4. Novel properties appear that govern interactions among these new elements

The superlevel operation formalizes this: the partition of $\mathfrak{u}({\mathcal{S}}^{+})$ is coarser than that of $\mathfrak{u}(\mathcal{S})$, but the relations $\mathfrak{r}({\mathcal{S}}^{+})$ represent new organizational principles not present at the lower level.

Von Bertalanffy’s Constitutive vs. Summative

Von Bertalanffy’s distinction between constitutive and summative characteristics illuminates emergence:

• Summative characteristics: Properties that remain the same whether elements are isolated or within the system (additive, reducible)
• Constitutive characteristics: Properties that depend on specific relational configurations within the system (emergent, irreducible)

Emergence involves constitutive characteristics: properties that arise from the system’s organization and cannot be understood by examining components in isolation.

Example: Molecular Isomerism

Two chemical compounds with identical molecular formulas but different structural arrangements (isomers) have the same atomic composition but different emergent properties:

• Same atoms (summative)
• Different bond configurations (constitutive)
• Different emergent properties: boiling points, reactivities, chemical behaviors

The emergent chemical properties exemplify constitutive characteristics arising from specific relational configurations.

Types of Emergence

Weak Emergence

Properties that are in principle deducible from micro-level descriptions but are computationally or practically irreducible. The macro-level description provides explanatory and predictive value despite being ontologically reducible.

Strong Emergence

Properties that are fundamentally irreducible to micro-level descriptions, involving genuine novelty. This is more controversial philosophically but captures the intuition of “downward causation.”

Structural Emergence

The specific formulation in nested systems theory: emergence as the appearance of new organizational structures and interaction patterns at coarser scales. The superlevel-system has relations $\mathfrak{r}({\mathcal{S}}^{+})$ that govern coarse-grained entities in ways not present at finer scales.

Emergence and Multi-Scale Modeling

The superlevel and sublevel operations capture emergence bidirectionally:

• Upward (superlevel): Coarse-graining reveals emergent patterns
• Downward (sublevel): Fine-graining reveals underlying mechanisms

Understanding emergence requires tracking:

1. How micro-level interactions produce macro-level structures (superlevel-system)
2. How macro-level constraints influence micro-level dynamics (sublevel-system)
3. The functional dependencies between levels (supersystem)

Examples

Biological Systems

Cellular to tissue level:

• Micro: Individual cells with membrane potentials, chemical gradients
• Emergent: Coordinated tissue contraction, collective calcium waves
• Novel property: Mechanical tissue properties (elasticity, strength) not possessed by individual cells

Neural networks:

• Micro: Individual neurons firing action potentials
• Emergent: Consciousness, memory, pattern recognition
• Novel property: Cognitive capabilities that cannot be localized to individual neurons

Physical Systems

Thermodynamic emergence:

• Micro: Molecular positions and velocities
• Emergent: Temperature, pressure, entropy
• Novel property: Thermodynamic laws (second law) that don’t apply to individual molecules

Convection patterns:

• Micro: Random molecular collisions
• Emergent: Coherent convection cells, Bénard cells
• Novel property: Large-scale flow organization from microscopic chaos

Social Systems

Organizational culture:

• Micro: Individual beliefs, values, behaviors
• Emergent: Organizational norms, collective identity
• Novel property: Culture that persists even as individuals change

Market dynamics:

• Micro: Individual buying and selling decisions
• Emergent: Price equilibria, market trends, bubbles
• Novel property: Market-level phenomena (crashes, booms) not predictable from individual actions

Philosophical Significance

Emergence challenges both:

• Reductionism: The view that wholes are nothing but sums of parts
• Holism: The view that wholes are completely independent of parts

Instead, emergence suggests a middle path: wholes have properties arising from part-interactions, but these properties represent genuine novelty requiring their own explanatory frameworks.

The formalization through nested systems provides mathematical rigor to this middle path: relations at level $n+1$ are functionally dependent on (but not reducible to) relations at level $n$.

Underdetermination and Non-Uniqueness

A key insight: the non-uniqueness of supersystems reflects that emergence permits multiple distinct macroscopic descriptions compatible with a single microscopic configuration.

This underdetermination is not a limitation but a feature: it captures that the same underlying dynamics can give rise to different emergent organizations depending on observational scale, boundary conditions, or contextual constraints.

Key References

Emergent Nested Systems

C. Walloth (2016) View in Semantic Scholar DOI: 10.1007/978-3-319-27550-5

Comprehensive treatment of emergence in the context of nested system hierarchies, emphasizing structural and multi-scale aspects.

General System Theory

Ludwig von Bertalanffy (1968)

Introduces the distinction between summative and constitutive characteristics, foundational for understanding emergence in systems.

The definition of system

Alexander Backlund (2000) View in Semantic Scholar DOI: 10.1108/03684920010322055

Discusses how different system definitions capture (or fail to capture) emergent properties.

Related Concepts

• nested-system - Hierarchical structures where emergence occurs
• superlevel-system - Formalization of coarse-graining and emergence
• sublevel-system - Revealing mechanisms underlying emergence
• supersystem - Aggregation and functional dependencies
• hierarchy - Multi-level organization enabling emergence
• complexity - Related concept of system behavior from interactions

Bibliography Keys

• Walloth2016
• Bertalanffy1968
• Backlund2000
• Simon2012
• Mesarovic1970