Abstract
We present a new approach to exoplanet characterization using techniques from complexity science, with potential applications to biosignature detection. This agnostic method makes use of the temporal variability of light reflected or emitted from a planet. We use a technique known as epsilon machine reconstruction to compute the statistical complexity, a measure of the minimal model size for time series data. We demonstrate that statistical complexity is an effective measure of the complexity of planetary features. Increasing levels of qualitative planetary complexity correlate with increases in statistical complexity and Shannon entropy, demonstrating that our approach can identify planets with the richest dynamics. We also compare Earth time series with Jupiter data, and find that for the three wavelengths considered Earth’s average complexity and entropy rate are approximately 50% and 43% higher than Jupiter’s, respectively. The majority of schemes for the detection of extraterrestrial life rely upon biochemical signatures and planetary context. However, it is increasingly recognized that extraterrestrial life could be very different from life on Earth. Under the hypothesis that there is a correlation between the presence of a biosphere and observable planetary complexity, our technique offers an agnostic and quantitative method for the measurement thereof.
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Data availability
Source data for all time series as well as the data points in the figures in the main text are provided with this paper.
Code availability
C++ code for the EMR process used in this study can be accessed here: https://nicolas.brodu.net/recherche/decisional_states/index.html.
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Acknowledgements
We acknowledge partial funding support from the NASA Exoplanet Research Program NNH18ZDA001N-2XRP. A portion of this research was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with NASA (80NM0018D0004). Y.L.Y. was supported in part by an NAI Virtual Planetary Laboratory grant from the University of Washington. We thank the members of the Caltech GPS ‘Astrobiothermoevoinfo’ reading group for the various inspiring discussions that have helped catalyse ideas such as those presented here. We also thank T. Ewald at Caltech for valuable help with the processing of Jupiter data from Cassini. Finally, S.B. thanks S. Bullock for being his guide into the world of complexity.
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S.B. conceived of the idea of using EMR to analyse planetary complexity and the hypothesized correlation between planetary complexity and the presence of life. He performed the complexity analysis, produced the figures and wrote the manuscript. J.L. provided the Jupiter Cassini data. L.G. and S.F. produced the synthetic Earth and recomposed datasets. L.S. assisted with the complexity analysis, results interpretation, literature review and manuscript editing. V.N. assisted with results interpretation and manuscript editing. J.H.J., D.C. and Y.L.Y. provided essential guidance, assistance with data provision, results interpretation and manuscript editing.
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Extended data
Extended Data Fig. 1 Epsilon machine example.
A simple epsilon machine with a set of discrete states (blue circles), a start state (double circle on the left), a set of state-to-state transitions (orange arrows), and a set of measurement observables for each transition (green numbers). Each transition has a certain probability of occurrence (not shown in the diagram). The Shannon entropy measures the intrinsic randomness of the model (technically the state probability-weighted information content of the transition probability distributions). The statistical complexity measures the information content of the state space of the model. Notation follows that of26.
Extended Data Fig. 2 Time series processing.
Examples showing the pre-processing of time series in preparation for EMR. a) Original, unaltered time series from the 10 reflectance channels, b) Original time series after normalization and discretization, c) Synthetic time series generated by replacing all pixels with a characteristic desert spectrum, d) Normalized and discretized versions of the series in (c).
Extended Data Fig. 3 Earth, Jupiter time series.
Time series for Earth (blue, 443nm wavelength) and Jupiter (red, 450.9nm wavelength) used for the complexity comparison.
Extended Data Fig. 4 Earth, Jupiter complexity comparison.
Statistical complexities of Earth and Jupiter time series in three wavelength bands for a range of kernel width parameter values.
Supplementary information
Supplementary Information
Supplementary Figs. 1–5, Tables 1 and 2 and Sections 1–4.
Source data
Source Data Fig. 1
Data points for Fig. 1.
Source Data Fig. 2
Data points for Fig. 2.
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Bartlett, S., Li, J., Gu, L. et al. Assessing planetary complexity and potential agnostic biosignatures using epsilon machines. Nat Astron 6, 387–392 (2022). https://doi.org/10.1038/s41550-021-01559-x
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DOI: https://doi.org/10.1038/s41550-021-01559-x
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