[Paper Review] Interdisciplinarity in Socio-economics, mathematical analysis and predictability of complex systems

Didier Sornette|arXiv (Cornell University)|Jul 24, 2008

Complex Systems and Time Series AnalysisEconomics, Econometrics and Finance47 references18 citations

TL;DR

This paper argues that complex socio-economic systems are amenable to mathematical analysis and prediction through interdisciplinary approaches rooted in physics and applied mathematics. Sornette challenges the notion that complex systems resist formal modeling, demonstrating that rigorous mathematical frameworks—especially those from statistical physics—can capture critical phenomena, phase transitions, and predictability in socio-economic dynamics.

ABSTRACT

In this essay, I attempt to provide supporting evidence as well as some balance for the thesis on `Transforming socio-economics with a new epistemology' presented by Hollingworth and Mueller (2008). First, I review a personal highlight of my own scientific path that illustrates the power of interdisciplinarity as well as unity of the mathematical description of natural and social processes. I also argue against the claim that complex systems are in general `not susceptible to mathematical analysis, but must be understood by letting them evolve over time or with simulation analysis'. Moreover, I present evidence of the limits of the claim that scientists working within Science II do not make predictions about the future because it is too complex. I stress the potentials for a third `Quantum Science' and its associated conceptual and philosophical revolutions, and finally point out some limits of the `new' theory of networks.

Motivation & Objective

• To counter the claim that complex socio-economic systems are inherently unpredictable and resistant to mathematical analysis.
• To demonstrate through personal research experience the unifying power of mathematical methods across natural and social sciences.
• To challenge the idea that Science II (interpretive, qualitative science) cannot make future predictions due to system complexity.
• To explore the potential of a 'third science'—analogous to quantum mechanics—offering new conceptual and methodological frameworks for socio-economics.
• To critically assess the limitations of network theory in capturing the full dynamics of complex systems.

Proposed method

• Drawing on personal research in extreme events and critical phenomena in financial and social systems.
• Applying statistical physics concepts such as power laws, phase transitions, and self-organized criticality to socio-economic data.
• Using mathematical models of complex systems to analyze predictability, including fat-tailed distributions and critical slowing down.
• Contrasting simulation-based approaches with analytical solutions to demonstrate the feasibility of closed-form predictions.
• Engaging with philosophical distinctions between Science I (quantitative, natural sciences) and Science II (qualitative, interpretive sciences) to reframe the epistemological debate.
• Evaluating the role of network theory in modeling complex systems, identifying its conceptual and predictive limitations.

Experimental results

Research questions

• RQ1 Can complex socio-economic systems be meaningfully analyzed and predicted using mathematical tools from physics?
• RQ2 To what extent is the claim that complex systems are not amenable to mathematical analysis empirically and theoretically justified?
• RQ3 Can scientists in Science II make testable predictions about future socio-economic events despite system complexity?
• RQ4 What are the conceptual and methodological foundations for a 'Quantum Science' in the social sciences, and how might it transform socio-economic research?
• RQ5 What are the limitations of network theory in modeling the dynamics of complex socio-economic systems?

Key findings

• Interdisciplinary approaches combining physics and socio-economics reveal that complex systems exhibit mathematical regularities such as power laws and critical phenomena.
• Mathematical analysis—particularly through statistical physics—can predict extreme events in financial and social systems, challenging the view that only simulations can model such dynamics.
• The claim that Science II cannot make predictions is overstated; interpretive approaches can be formalized and tested using probabilistic and statistical frameworks.
• There is strong potential for a 'Quantum Science' paradigm in socio-economics, offering new conceptual tools to understand emergence, nonlinearity, and irreversibility.
• Network theory, while useful, fails to capture the full dynamics of complex systems when applied without deeper structural and temporal modeling.
• The unifying power of mathematics across natural and social processes is demonstrated through empirical and theoretical evidence from financial crises and social cascades.