PaperlayerView exact revision on arXiv

Source-linked AI summary

An Introduction to Complex Systems Science and its Applications

Alexander F. Siegenfeld, Yaneer Bar-Yam

arXiv:1912.05088v2physics.soc-ph

TL;DR

Many standard frameworks mischaracterize complex physical, biological, and social systems because their assumptions do not hold at the system level. This review introduces general concepts and analytical approaches for studying such systems, including multi-scale complexity and efficiency–adaptability tradeoffs. It argues that approximate analyses can reveal important mismatches between systems and environments, while organizational structure and decision-making complexity constrain effective responses.

  • Problem

    Standard assumptions used in quantitative studies often do not hold for complex systems as wholes, leading to mischaracterization of large-scale behavior.

  • Method

    The paper presents a conceptual and analytical introduction focused on general system properties, complexity across scales, and when standard assumptions apply.

  • Results

    Complex systems are characterized by multi-scale complexity, efficiency–adaptability tradeoffs, and the need to match system complexity and subdivisions to environmental behaviors.

  • Takeaways & Limitations

    Approximate complexity analysis can diagnose consequential system–environment mismatches, while independent decisions should be handled independently and dependent decisions dependently.

  • Takeaways & Limitations

    High-complexity systems have many configurations that fail, so beneficial changes are generally less likely than harmful ones.

Abstract

from arXiv · show

The standard assumptions that underlie many conceptual and quantitative frameworks do not hold for many complex physical, biological, and social systems. Complex systems science clarifies when and why such assumptions fail and provides alternative frameworks for understanding the properties of complex systems. This review introduces some of the basic principles of complex systems science, including complexity profiles, the tradeoff between efficiency and adaptability, the necessity of matching the complexity of systems to that of their environments, multi-scale analysis, and evolutionary processes. Our focus is on the general properties of systems as opposed to the modeling of specific dynamics; rather than provide a comprehensive review, we pedagogically describe a conceptual and analytic approach for understanding and interacting with the complex systems of our world. With the exception of a few footnotes, this paper assumes only a high school mathematical and scientific background, so that it may be accessible to academics in all fields, decision-makers in industry, government, and philanthropy, and anyone who is interested in systems and society.

I. INTRODUCTION

Complex systems science studies how relationships among components generate system-level behavior, especially where standard quantitative assumptions fail. It provides interdisciplinary concepts and analytical approaches for understanding and making decisions about physical, biological, and social systems.

  • Standard quantitative assumptions may fail for systems as wholes, mischaracterizing the causes and consequences of large-scale behavior.
  • The paper introduces general properties such as complexity profiles, efficiency–adaptability tradeoffs, environment matching, assumption testing, and intervention principles.
  • Complex systems science focuses on relationships among components rather than only on the components themselves.Systems with identical parts can have different properties when their interactions differ.
  • Emergent behaviors, including turbulence, conversation groups, decentralized allocation, ecosystems, and flocking, arise autonomously from interactions among components.
  • Because full descriptions of system details are impossible, analysis must identify properties that do not depend on every detail and consider behavior across relevant scales.The paper presents statistical physics as an analytical lens for characterizing spaces of possible behaviors rather than particular states.

B. What is complexity?

Complexity is defined through the length of a behavior’s description and depends on the scale and behavior space being considered. Complexity profiles reveal how random, coherent, and correlated systems differ across scales.

  • Complexity equals the length of a behavior’s description and increases with the number of possible behaviors: C = log2 N.
  • The relevant complexity depends on how the space of possible behaviors is defined for the task or system under consideration.A light bulb can have two states in operation but many possible part arrangements when being built.
  • Complexity depends on scale because different levels of detail reveal different behaviors and description lengths.A gas is simpler than a human at the scale of human perception, despite being harder to describe microscopically.
  • A complexity profile plots system complexity as a function of scale, capturing complexity across multiple scales rather than only at the smallest scale.
  • Random systems are most complex at fine scales and simplify as scale increases, whereas coherent systems retain similar complexity across scales.Correlated systems have qualitatively distinct profiles, and individual systems may combine aspects of all three.
  • Increasing detail in a human system successively reveals whole-body, limb, facial, organ, tissue, cellular, and subcellular behaviors.

D. Tradeoffs between complexity and scale

Complexity at larger scales requires coordination that limits smaller-scale behaviors, creating a fundamental tradeoff between complexity and scale. This tradeoff appears in factories, militaries, and the balance between adaptability and efficiency.

  • Tradeoff principle: Coordination among smaller-scale components enables larger-scale complexity while limiting their individual behaviors.The tension between small- and large-scale complexity follows from interdependencies among coordinated components.
  • Tradeoff principle: For a fixed set of components and individual behaviors, increasing behavioral variety generally requires sacrificing the scale of coordinated behaviors.Adding machinery or workers can increase both complexity and scale, so the fixed-component condition matters.
  • Factory example: Factories optimized for mass production coordinate workers to produce few goods at large scale, whereas independent workers produce varied goods without scale.Production scale is proxied by copies produced, while complexity is proxied by the number of product types available at that scale.
  • Adaptability and efficiency: Adaptability comes from many mostly independent actions, whereas efficiency comes from coordinated parts performing a designed task at the largest possible scale.Highly efficient systems are less adaptable to unforeseen variation, while highly adaptable systems sacrifice some larger-scale behaviors.
  • Adaptability and efficiency: Mechanisms that create larger-scale complexity necessarily reduce individual complexity, although sacrificing individual freedom can enable larger-scale cooperation.The paper notes that this tradeoff is not inherently harmful; its desirability depends on the system’s purpose.
  • Military example: In military conflicts, larger scale favors one army when possible behaviors are equal, while higher complexity favors one army when scale is equal.When armies differ in both scale and behavioral variety, the favored army depends on terrain.

E. Why be complex?

A system is effective when its complexity matches the environmental behaviors requiring different responses across relevant scales. Approximate complexity comparisons can reveal consequential mismatches, but detailed analysis may be needed to remedy them.

  • Matching complexity: The Law of Requisite Variety requires a system to match or exceed the environmental behaviors to which it must differentially react.A system facing 100 environmental possibilities needs at least 100 possible actions to respond differently to each.
  • Matching complexity: Effectiveness requires matching environmental complexity at every scale where the relevant behaviors occur.The multi-scale formulation treats one military as the system and the opposing military as part of its environment.
  • Applications: Healthcare combines highly complex small-scale tasks such as case management with lower-complexity, larger-scale tasks such as vaccine delivery.Large-scale top-down organizations suit standardized tasks, while case management requires health systems with greater adaptability.
  • Applications: The eurozone illustrates a potential mismatch because fiscal and monetary policies distribute complexity differently across country and eurozone scales.Country-level fiscal policy has limited eurozone-scale complexity, while eurozone monetary policy lacks country-level variation.
  • Consequences: Problems arise from mismatches between task complexity and the complexity of the system performing the task, not from complexity levels alone.A system’s complexity can help it interact with one environment while making it harder for another system to manage.
  • Scope and limitations: Complexity profiles and scales are estimated with proxies, so the resulting analysis is approximate rather than precise.Approximate analysis can still reveal large mismatches; addressing them may require more detailed investigation.

F. Subdivided systems

Subdividing a system is effective only when its internal divisions match the natural divisions of the problems and environments it must address. Academia illustrates how substantial multi-scale complexity can still leave cross-disciplinary problems poorly matched to organizational structure.

  • F. Subdivided systems: Analyzing possible behaviors can remain useful under uncertainty about precise mechanisms and outcomes, while entropy changes can classify phase transitions without determining every quantity from first principles.Some quantities, such as heat generated or transition temperature, still require empirical determination.
  • F. Subdivided systems: Academia has high complexity across multiple scales, including coordinated people and knowledge, enabling it to address many subdivided problems.Its divisions include departments and subfields, while problems also contain natural subdivisions requiring particular knowledge and effort.
  • F. Subdivided systems: Despite sufficient overall complexity, academia may struggle with problems whose subdivisions do not match its disciplinary and sub-disciplinary structure.The growth of interdisciplinary centers suggests recognition of this mismatch, although the overall structure may still hinder progress.
  • F. Subdivided systems: A system must match environmental complexity both overall and within each corresponding subset to react differentially to environmental behaviors.Independent aspects should be handled independently, while dependent aspects should be handled dependently.

G. Hierarchies

Hierarchies differ in how complexity is distributed across scales, and none is inherently superior. Their suitability depends on matching that profile and internal subdivision to environmental tasks, while excessive centralization can exceed human decision-making capacity.

  • G. Hierarchies: Hierarchical complexity depends on control rigidity: centralized structures maintain complexity across scales, whereas decentralized structures have little complexity beyond the individual level.Figure 5 compares hierarchies with equal numbers of people using coordinated man-hours as the scale.
  • G. Hierarchies: A fully centralized hierarchy assigns every decision to the top, while a fully decentralized hierarchy leaves individuals acting independently.Typical hierarchies distribute different decisions across different levels.
  • G. Hierarchies: No hierarchy is inherently better; the best hierarchy matches its complexity profile to the tasks required by its environment.Top-heavy structures fit less variable lower-level environments, whereas loosely controlled structures fit tasks requiring large-scale coordination.
  • G. Hierarchies: Efficiency and scale trade off against adaptability because larger decisions affect more of the system and are harder to reverse when incorrect.Larger-scale changes also tend to require longer timescales to enact.
  • G. Hierarchies: A hierarchy fails when matching its largest-scale behaviors to the environment requires more decision-making complexity than any individual or committee can achieve.The paper uses command economies as an example of resource-allocation problems exceeding centralized decision-making capacity.
  • G. Hierarchies: A separation of scales means that small-scale behaviors are mostly independent at larger scales, so only their average effects matter there.Figure 6 marks the threshold scale as s0.
  • G. Hierarchies: Larger-scale behaviors can also arise through lateral connections, as cities interact and copy policies while remaining within a hierarchical framework.The upper level may retain significant control even when components learn from one another.

III. ANALYZING COMPLEX SYSTEMS

Macroscopic systems can be studied when their relevant behavior is separated from microscopic detail by a gap in scales. Mean-field theory formalizes this approach by modeling averages and treating component deviations as independent fluctuations, though its applicability must be checked.

  • III. ANALYZING COMPLEX SYSTEMS: The tractability of macroscopic systems is notable because even simple mechanical systems contain trillions upon trillions of molecules.The paper presents scale separation as the reason such systems can nevertheless be understood.
  • III. ANALYZING COMPLEX SYSTEMS: A separation of scales makes macroscopic systems tractable by allowing macroscopic and microscopic behaviors to be treated separately.In mechanical systems, Newtonian mechanics describes macroscopic behavior while microscopic molecular behavior is aggregated.
  • III. ANALYZING COMPLEX SYSTEMS: Mean-field theory explicitly models average component behavior and treats individual deviations from that average as statistically independent random fluctuations.This approach works well for systems such as computers, cars, airplanes, and buildings.
  • III. ANALYZING COMPLEX SYSTEMS: Mean-field assumptions are used in biological, social, and economic analyses, but they are not always appropriate for complex systems.The relevant analytical question is determining the conditions under which mean-field theory holds.

B. When mean-field theory breaks down

Mean-field theory breaks down when component correlations cannot be neglected, making relationships between components central to large-scale behavior. Such systems can produce fat-tailed fluctuations, including adaptive responses and systemic risks that mean-field models do not predict.

  • B. When mean-field theory breaks down: Strong correlations cause mean-field theory to break down because large-scale behavior depends on relationships between components, not only individual properties.The paper contrasts muscle behavior, roughly related to individual cells, with brain cognition, which differs fundamentally from individual neurons.
  • B. When mean-field theory breaks down: Complex systems can exhibit large-scale fluctuations that mean-field theory does not predict because small-scale occurrences are not statistically independent.Examples include forest fires, viral social-media content, and economic-market crashes.
  • B. When mean-field theory breaks down: Some large-scale fluctuations are adaptive because they enable a system to respond collectively to small inputs.The paper gives humans’ strong response to hearing their own names amid minor air-density disturbances as an example.
  • B. When mean-field theory breaks down: The failure of mean-field descriptions for some physical phase transitions motivated the multi-scale renormalization-group approach.The paper identifies renormalization group as foundational to complex systems science.
  • B. When mean-field theory breaks down: Large-scale fluctuations can also pose systemic risks.This is presented as a distinct consequence of non-mean-field behavior.

C. Fat-tailed distributions and systemic risk

Complex systems can generate fat-tailed fluctuations when interdependencies violate independence-based assumptions, making extreme events more likely and standard statistical estimates unreliable.

  • Independent components produce approximately normal fluctuations, whereas interdependent components can produce fat-tailed distributions with unusually extreme deviations.Human height is thin-tailed, while human wealth has included deviations exceeding one million times the average.
  • Interdependencies can reduce small-scale fluctuations while increasing the probability of catastrophic failure.Fat-tailed distributions can make standard statistical methods underestimate extreme-event probabilities.
  • Tying individually safer ladders together creates a non-negligible chance that they will all fail simultaneously.With independent ladders, simultaneous failure is astronomically unlikely; interdependence changes the system-level risk.
  • Addressing one crisis does not remove systemic instability, so another crisis is bound to occur sooner or later even when its form is unpredictable.The passage distinguishes uncertainty about a crisis’s precise form from the persistence of underlying instability.
  • Complex-systems analyses often miss interaction data and implicitly assume linearity, undermining estimates of large-scale behavior and tail risk.The supplied passages identify component-level data, interaction effects, and extreme-event estimation as recurring analytical problems.

IV. COMPLEX SYSTEMS AND UNCERTAINTY

Complex systems remain difficult to understand and design because their complexity makes complete knowledge impossible and can make adverse changes more likely than beneficial ones.

  • Complex systems inevitably remain imperfect because plans cannot anticipate every element of a genuinely complex system.

A. Evolutionary processes

Evolutionary processes let systems benefit from uncertainty by generating variation, retaining successful changes, and allowing improvements to spread, while flexibility can prevent systemic failure.

  • Some systems benefit from uncertainty and variability when successful changes are copied and further modified while unsuccessful changes are not.Examples include biological adaptation, immune responses, learning, and strengthening through controlled adversity.
  • Competitive markets improve through parallel experimentation, with successful innovations expanding and unsuccessful businesses failing.Successful innovations can then be improved through the same evolutionary process.
  • High-complexity systems face asymmetric change outcomes because many configurations fail for every configuration that works.
  • Without effectively regulated multi-scale cooperative frameworks, economic subsystems may optimize for wrong goals and settle into harmful societal equilibria.
  • Large organizations can improve when small parts are allowed to fail; suppressing small failures may instead create systemic risk.Flexibility helps organizations adapt to changing internal or external environments.
  • Evolutionary systems need variation to explore possibilities and communication so successful choices can be adopted elsewhere.The paper notes that variation should occur at smaller scales because complexity trades off with scale.

B. Multi-scale evolutionary processes

Multi-scale evolutionary processes combine cooperation and competition across levels, allowing groups with beneficial dynamics to be selected and enabling complexity beyond deliberate design.

  • B. Multi-scale evolutionary processes: Evolutionary processes generally combine competition and cooperation rather than relying on unbridled competition.
  • B. Multi-scale evolutionary processes: Explicit design can produce only systems less complex than the designing system, whereas evolution can produce systems more complex than their designers.
  • B. Multi-scale evolutionary processes: Competition at larger scales can foster cooperation at smaller scales, as groups cooperate internally to compete effectively against other groups.
  • B. Multi-scale evolutionary processes: Competition must be structured so that individual behavior benefits the group, as illustrated by competition within soccer teams and leagues.
  • B. Multi-scale evolutionary processes: Multi-scale selection favors groups with a healthy mix of competition and cooperation that benefits the entire group.
  • B. Multi-scale evolutionary processes: Appropriately regulated market systems can support multiscale evolutionary processes that generate innovations and complexity beyond anyone’s design.

V. FURTHER READING

Complex systems science offers interdisciplinary resources for studying systems through their components, interactions, possible behaviors, and evolving multi-scale structure. The paper points readers to broad references while emphasizing systemic analysis and designs robust to unpredictability.

  • V. FURTHER READING: Emergent system properties arise from interactions among components and cannot always be inferred directly from component behavior.
  • V. FURTHER READING: Analyzing a system’s space of possible behaviors can reveal insights unavailable from examining only proximate causes and effects.
  • V. FURTHER READING: Complexity depends on scale because behaviors that appear identical at low resolution may differ at higher resolution.
  • V. FURTHER READING: Interdependencies reduce complexity at smaller scales while creating larger-scale complexity through coordinated multi-component behaviors.
  • V. FURTHER READING: Complex-system analyses and organizations should be multi-scale and robust to human ignorance and unpredictability.
Loading 1912.05088v2…