Allotaxonometry and rank-turbulence divergence: a universal instrument for comparing complex systems
Computational Story Lab, Vermont Complex Systems Center, MassMutual Center of Excellence for Complex Systems and Data Science, Vermont Advanced Computing Center, University of Vermont, 05405, Burlington, VT, USA
2 Department of Computer Science, University of Vermont, 05405, Burlington, VT, USA
3 Santa Fe Institute, 1399 Hyde Park Rd, 87501, Santa Fe, NM, USA
4 Department of Mathematics & Statistics, University of Vermont, 05405, Burlington, VT, USA
5 Institute for Data, Systems, and Society, Massachusetts Institute of Technology, 02139, Cambridge, MA, USA
6 MassMutual Data Science, 01002, Amherst, MA, USA
Accepted: 16 June 2023
Published online: 19 September 2023
Complex systems often comprise many kinds of components which vary over many orders of magnitude in size: Populations of cities in countries, individual and corporate wealth in economies, species abundance in ecologies, word frequency in natural language, and node degree in complex networks. Here, we introduce ‘allotaxonometry’ along with ‘rank-turbulence divergence’ (RTD), a tunable instrument for comparing any two ranked lists of components. We analytically develop our rank-based divergence in a series of steps, and then establish a rank-based allotaxonograph which pairs a map-like histogram for rank-rank pairs with an ordered list of components according to divergence contribution. We explore the performance of rank-turbulence divergence, which we view as an instrument of ‘type calculus’, for a series of distinct settings including: Language use on Twitter and in books, species abundance, baby name popularity, market capitalization, performance in sports, mortality causes, and job titles. We provide a series of supplementary flipbooks which demonstrate the tunability and storytelling power of rank-based allotaxonometry.
© The Author(s) 2023
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