Culturomics meets random fractal theory: insights into long-range correlations of social and natural phenomena over the past two centuries

Jianbo Gao,Matjaž Perc,Xiang Mao,Jing Hu

doi:10.1098/rsif.2011.0846

Abstract

Culturomics was recently introduced as the application of high-throughput data collection and analysis to the study of human culture. Here, we make use of these data by investigating fluctuations in yearly usage frequencies of specific words that describe social and natural phenomena, as derived from books that were published over the course of the past two centuries. We show that the determination of the Hurst parameter by means of fractal analysis provides fundamental insights into the nature of long-range correlations contained in the culturomic trajectories, and by doing so offers new interpretations as to what might be the main driving forces behind the examined phenomena. Quite remarkably, we find that social and natural phenomena are governed by fundamentally different processes. While natural phenomena have properties that are typical for processes with persistent long-range correlations, social phenomena are better described as non-stationary, on–off intermittent or Lévy walk processes.

Highlights

Observational data are often very complex, appearing without any structure or pattern in either time or space
We show what new insights are attainable by applying random fractal theory to this vast culturomic dataset
Our goal is to try and go beyond the interpretations of trajectories provided in Michel et al [15] by means of an accurate determination of scaling parameters [33], and in particular, the Hurst parameter H, which enables us to characterize the nature of correlations, if any, contained in the irregular time series

Summary

Introduction

Observational data are often very complex, appearing without any structure or pattern in either time or space. Examples of such observations can be found across the whole spectrum of the social and natural sciences, ranging from economics [1] to physics [2], biology [3] and medicine [4]. Attention has begun to shift from chaos to noise and random processes as alternative [11] (or, in many cases, as even more probable) sources of irregularity. Investigations based on these theoretical foundations may provide an elegant statistical characterization of a broad range of heterogeneous phenomena [14], and in this paper, it is our goal to extend this theory to culturomics, as recently introduced in Michel et al [15]

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Results

Conclusion