Abstract

War is a cause of gains and losses. Economic historians have long stressed the extreme importance of considering the economic potential of society for belligerency, the role of management of chaos to bear the costs of battle and casualties, and ingenious and improvisation methodologies for emergency management. However, global and inter-temporal studies on warring are missing. The adoption of computational tools for data processing is a key modeling option with present day resources. In this paper, hierarchical clustering techniques and multidimensional scaling are used as efficient instruments for visualizing and describing military conflicts by electing different metrics to assess their characterizing features: time, time span, number of belligerents, and number of casualties. Moreover, entropy is adopted for measuring war complexity over time. Although wars have been an important topic of analysis in all ages, they have been ignored as a subject of nonlinear dynamics and complex system analysis. This paper seeks to fill these gaps in the literature by proposing a quantitative perspective based on algorithmic strategies. We verify the growing number of events and an explosion in their characteristics. The results have similarities to those exhibited by systems with increasing volatility, or evolving toward chaotic-like behavior. We can question also whether such dynamics follow the second law of thermodynamics since the adopted techniques reflect a system expanding the entropy.

Highlights

  • Wars have played a major role in human history, because they have long accounted for violence.According to Blum [1], we presently live in a paradox of power, because on the one hand our means and methods of war have become both more devastating, and on the other hand less devastating.Campbell [2] asks what conception of war to adopt

  • Wars have been an important topic of analysis in all ages, they have been ignored as a subject of nonlinear dynamics and complex system analysis

  • We can question whether such dynamics follow the second law of thermodynamics since the adopted techniques reflect a system expanding the entropy

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Summary

Introduction

Wars have played a major role in human history, because they have long accounted for violence. The mathematical analysis of war has relied on developing and interpreting the statistical distributions of casualties [8,9] Such distributions reveal fat-tails, meaning that the size of an event is inversely proportional to its frequency. The entropy analysis of the war casualties, interpreted as the output of a complex system, reveals the human-belligerency trend towards “chaotic-like” behavior over time. This evolution toward a state of higher confusion reveals increasing an entropy, somehow compatible with systems following the second law of thermodynamics.

Distance Indices
Hierarchical Clustering
Multidimensional Scaling
Spectral Domain
Entropy
The Spans of Wars
Description of the Dataset
The HC Analysis and Visualization of the Spans of Wars
The MDS Analysis and Visualization of the Spans of Wars
Sociological Interpretation of the Spans of Wars
Entropy Analysis of the Span of Wars
Discussion and Conclusions

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