Scale-Independent Aggression: A Fractal Analysis of Four Levels of Human Aggression

Julia J C Blau,Alexandra Paxton,Diego R Amancio

doi:10.1155/2020/2047157

Julia J C Blau, Alexandra Paxton + Show 1 more

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https://doi.org/10.1155/2020/2047157

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Abstract

Using fractal analyses to study events allows us to capture the scale-independence of those events, that is, no matter at which level we study a phenomenon, we should get roughly the same results because events exhibit similar structure across scales. This is demonstrably true in mathematical fractals but is less assured in behavioral fractals. The current research directly tests the scale-independence hypothesis in the behavioral domain by exploring the fractal structure of aggression, a social phenomenon comprising events that span temporal scales from minutes of face-to-face arguments to centuries of international armed conflicts. Using publicly available data, we examined the temporal fractal structure of four scales of aggression: wars (very macrolevel, worldwide data), riots (macrolevel, worldwide data), violent crimes (microlevel, data gathered from cities and towns in the United States of America), and body movement during arguments (very microlevel, data gathered on American participants). Our results lend mixed support to the scale-independence hypothesis and provide insight into the self-organization of human interactions.

Highlights

Some phenomena are fig not suited for typical summary statistics such as means and standard deviations [1]
From neurons [2] to nebulae [3] and geology [4] to geography [5], many phenomena exhibit fractality, a phenomenon where patterns recur at all spatiotemporal scales
Fractals generated by purely mathematical processes [6] exhibit perfect self-similarity, with patterns that recur identically at all possible levels of observation

Summary

Introduction

Some phenomena are fig not suited for typical summary statistics such as means and standard deviations [1]. From neurons [2] to nebulae [3] and geology [4] to geography [5], many phenomena exhibit fractality, a phenomenon where patterns recur at all spatiotemporal scales. Fractals generated by purely mathematical processes [6] exhibit perfect self-similarity, with patterns that recur identically at all possible levels of observation. Natural fractals (e.g., coastlines, clouds, and branching of the lungs; for review, see [7, 8]) have only rough self-similarity, in other words, having patterns that recur in similar but not identical ways across most possible levels of observation. E perfect self-similarity of mathematical fractals and the rough self-similarity of natural fractals have led to the scale-independence hypothesis. While fractal analyses have been performed on different types of events at different scales, (e.g., [11,12,13,14]), no single study—to our knowledge—has explored a single type of event across all feasible temporal scales of human activity

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