Computer Analysis of Human Belligerency

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.

[1]  M. Jackson,et al.  The Reasons for Wars: An updated survey , 2011 .

[2]  Roman M. Sheremeta,et al.  Theories of conflict and war , 2019, Journal of Economic Behavior & Organization.

[3]  T. Blanning.  The Oxford history of modern Europe , 2000 .

[4]  J. Talbott.  Soldiers, Psychiatrists, and Combat Trauma , 1997 .

[5]  A. Taylor,et al.  The Struggle for Mastery in Europe, 1848-1918. Vol. II of Oxford History of Modern Europe. , 1955 .

[6]  J. T. Tenreiro Machado,et al.  Integer and fractional-order entropy analysis of earthquake data series , 2016 .

[7]  H. Srivastava,et al.  Local Fractional Integral Transforms and Their Applications , 2015 .

[8]  O. Marichev,et al.  Fractional Integrals and Derivatives: Theory and Applications , 1993 .

[9]  António M. Lopes,et al.  Fractional Rényi entropy⋆ , 2019, The European Physical Journal Plus.

[10]  Vincent Kanade,et al.  Clustering Algorithms , 2021, Wireless RF Energy Transfer in the Massive IoT Era.

[11]  H. Srivastava,et al.  Theory and Applications of Fractional Differential Equations , 2006 .

[12]  Hall Gardner.  A reader in international relations and political theory , 1994 .

[13]  Alan Trounson,et al.  The persistence of memory , 2010, Nature Medicine.

[14]  R. Sokal,et al.  THE COMPARISON OF DENDROGRAMS BY OBJECTIVE METHODS , 1962 .

[15]  G. Mortimer.  The Origins of the Thirty Years War , 2015 .

[16]  A. Clauset.  On the Frequency and Severity of Interstate Wars , 2019, Pioneers in Arts, Humanities, Science, Engineering, Practice.

[17]  Richard K. Beatson,et al.  Surface interpolation with radial basis functions for medical imaging , 1997, IEEE Transactions on Medical Imaging.

[18]  Vaughn H. Standley,et al.  Modeling Interstate War Combat Deaths , 2020 .

[19]  V. E. Tarasov.  Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media , 2011 .

[20]  Humberto Bustince,et al.  A Practical Guide to Averaging Functions , 2015, Studies in Fuzziness and Soft Computing.

[21]  Ranchao Wu,et al.  Design and implementation of grid multi-scroll fractional-order chaotic attractors. , 2016, Chaos.

[22]  K. B. Oldham,et al.  The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order , 1974 .

[23]  Karen A. Mingst,et al.  Essentials of International Relations , 1998 .

[24]  José António Tenreiro Machado,et al.  Multidimensional Scaling Visualization Using Parametric Similarity Indices , 2015, Entropy.

[25]  Christopher J. Coyne,et al.  The Handbook on the Political Economy of War , 2012 .

[26]  M. Newman.  Power laws, Pareto distributions and Zipf's law , 2005 .

[27]  Sven Strauss,et al.  The Elements Of Law Natural And Politic , 2016 .

[28]  J. A. Tenreiro Machado,et al.  A review of power laws in real life phenomena , 2012 .

[29]  K. Miller,et al.  An Introduction to the Fractional Calculus and Fractional Differential Equations , 1993 .

[30]  Elena Deza,et al.  Encyclopedia of Distances , 2014 .

[31]  Deniz Erdogmus,et al.  Renyi's Entropy, Divergence and Their Nonparametric Estimators , 2010, Information Theoretic Learning.

[32]  L. Cederman.  Modeling the Size of Wars: From Billiard Balls to Sandpiles , 2003, American Political Science Review.

[33]  Charu C. Aggarwal,et al.  On the Surprising Behavior of Distance Metrics in High Dimensional Spaces , 2001, ICDT.

[34]  Tang,et al.  Self-Organized Criticality: An Explanation of 1/f Noise , 2011 .

[35]  M. Rivero,et al.  Fractional calculus: A survey of useful formulas , 2013, The European Physical Journal Special Topics.

[36]  Clara-Mihaela Ionescu,et al.  The Human Respiratory System: An Analysis of the Interplay between Anatomy, Structure, Breathing and Fractal Dynamics , 2013 .

[37]  E. Jones,et al.  The European Miracle: Environments, Economies and Geopolitics in the History of Europe and Asia , 1983 .

[38]  Henrik Jeldtoft Jensen,et al.  Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems , 1998 .

[39]  Ulrich Amsel.  War Economy And Society 1939 1945 , 2016 .

[40]  K. Diethelm,et al.  Fractional Calculus: Models and Numerical Methods , 2012 .