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

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.

[1]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[2]  D. Ruelle,et al.  Ergodic theory of chaos and strange attractors , 1985 .

[3]  D L Gilden,et al.  1/f noise in human cognition. , 1995, Science.

[4]  S. Havlin,et al.  Fractals and Disordered Systems , 1991 .

[5]  Albert-László Barabási,et al.  The origin of bursts and heavy tails in human dynamics , 2005, Nature.

[6]  Erez Lieberman,et al.  Quantifying the evolutionary dynamics of language , 2007, Nature.

[7]  H. Stanley,et al.  Effect of nonlinear filters on detrended fluctuation analysis. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Alessandro Vespignani,et al.  Modeling human mobility responses to the large-scale spreading of infectious diseases , 2011, Scientific reports.

[9]  B. Huberman,et al.  Fluctuations and simple chaotic dynamics , 1982 .

[10]  Rosario N. Mantegna,et al.  Book Review: An Introduction to Econophysics, Correlations, and Complexity in Finance, N. Rosario, H. Mantegna, and H. E. Stanley, Cambridge University Press, Cambridge, 2000. , 2000 .

[11]  E. Lorenz.  Deterministic nonperiodic flow , 1963 .

[12]  Jianbo Gao,et al.  Multifractal analysis of sunspot time series: the effects of the 11-year cycle and Fourier truncation , 2009 .

[13]  Alex Arenas,et al.  Traffic-driven epidemic spreading in finite-size scale-free networks , 2009, Proceedings of the National Academy of Sciences.

[14]  Erez Lieberman Aiden,et al.  Quantitative Analysis of Culture Using Millions of Digitized Books , 2010, Science.

[15]  H. Stanley,et al.  Effect of trends on detrended fluctuation analysis. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Jianbo Gao,et al.  Multiscale Analysis of Complex Time Series: Integration of Chaos and Random Fractal Theory, and Beyond , 2007 .

[17]  Alessandro Vespignani,et al.  Multiscale mobility networks and the spatial spreading of infectious diseases , 2009, Proceedings of the National Academy of Sciences.

[18]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .

[19]  Jing Hu,et al.  Facilitating Joint Chaos and Fractal Analysis of Biosignals through Nonlinear Adaptive Filtering , 2011, PloS one.

[20]  David M. Raup,et al.  How Nature Works: The Science of Self-Organized Criticality , 1997 .

[21]  Marek Wolf.  1/ƒ noise in the distribution of prime numbers , 1997 .

[22]  Santo Fortunato,et al.  Characterizing and modeling the dynamics of online popularity , 2010, Physical review letters.

[23]  Albert-László Barabási,et al.  Understanding individual human mobility patterns , 2008, Nature.

[24]  Albert-László Barabási,et al.  Limits of Predictability in Human Mobility , 2010, Science.

[25]  Alessandro Vespignani,et al.  WiFi networks and malware epidemiology , 2007, Proceedings of the National Academy of Sciences.

[26]  H E Stanley,et al.  Scale-independent measures and pathologic cardiac dynamics. , 1998, Physical review letters.

[27]  R. L. Stratonovich,et al.  Topics in the theory of random noise , 1967 .

[28]  H. Stanley,et al.  Introduction to Phase Transitions and Critical Phenomena , 1972 .

[29]  Per Bak,et al.  How Nature Works , 1996 .

[30]  Henry D. I. Abarbanel,et al.  Analysis of Observed Chaotic Data , 1995 .

[31]  A. Pentland,et al.  Computational Social Science , 2009, Science.

[32]  Hunter N. B. Moseley,et al.  Limits of Predictability in Human Mobility , 2010 .

[33]  Jianbo Gao,et al.  Principal component analysis of 1/fα noise , 2003 .

[34]  Y. Moreno,et al.  Spreading of persistent infections in heterogeneous populations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Yanqing Chen,et al.  Long Memory Processes ( 1 / f α Type) in Human Coordination , 1997 .

[36]  Shlomo Havlin,et al.  Scaling behaviour of heartbeat intervals obtained by wavelet-based time-series analysis , 1996, Nature.

[37]  G. N. Gilbert.  Computational Social Science , 2010 .

[38]  J. Finnigan.  How Nature Works; The science of self-organized criticality , 2001 .

[39]  Albert-László Barabási,et al.  Understanding the Spreading Patterns of Mobile Phone Viruses , 2009, Science.

[40]  C. Peng,et al.  Mosaic organization of DNA nucleotides. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[41]  H. Stanley,et al.  Scale invariance in the nonstationarity of human heart rate. , 2000, Physical review letters.

[42]  Jianbo Gao,et al.  Multiscale Analysis of Complex Time Series , 2007 .

[43]  R. Voss,et al.  Evolution of long-range fractal correlations and 1/f noise in DNA base sequences. , 1992, Physical review letters.

[44]  H. Stanley,et al.  Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series , 2002, physics/0202070.

[45]  B. Gutenberg,et al.  Seismicity of the Earth and associated phenomena , 1950, MAUSAM.

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

[47]  Vittorio Loreto,et al.  Cultural route to the emergence of linguistic categories , 2007, Proceedings of the National Academy of Sciences.

[48]  Filippo Radicchi,et al.  Who Is the Best Player Ever? A Complex Network Analysis of the History of Professional Tennis , 2011, PloS one.

[49]  L. Glass,et al.  From Clocks to Chaos: The Rhythms of Life , 1988 .

[50]  From Clocks to Chaos: The Rhythms of Life , 1988 .

[51]  W. Press.  Flicker noises in astronomy and elsewhere. , 1978 .

[52]  Lei Yang,et al.  Detecting chaos in heavy-noise environments. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[53]  Yamir Moreno,et al.  Structural and Dynamical Patterns on Online Social Networks: The Spanish May 15th Movement as a Case Study , 2011, PloS one.

[54]  L. Amaral,et al.  Multifractality in human heartbeat dynamics , 1998, Nature.

[55]  Jeffrey M. Hausdorff,et al.  Physionet: Components of a New Research Resource for Complex Physiologic Signals". Circu-lation Vol , 2000 .

[56]  Vittorio Loreto,et al.  Statistical physics of language dynamics , 2011 .

[57]  J. Collins,et al.  Random walking during quiet standing. , 1994, Physical review letters.

[58]  H. Stanley,et al.  Phase Transitions and Critical Phenomena , 2008 .

[59]  V. Roychowdhury,et al.  Assessment of long-range correlation in time series: how to avoid pitfalls. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[60]  H. Stanley,et al.  Multifractal phenomena in physics and chemistry , 1988, Nature.

[61]  C. Peng,et al.  Long-range correlations in nucleotide sequences , 1992, Nature.

[62]  Chaoming Song,et al.  Modelling the scaling properties of human mobility , 2010, 1010.0436.