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Space-time nature of causality.

Ezequiel Bianco-Martinez1, Murilo S Baptista1

  • 1Institute of Complex Sciences and Mathematical Biology, University of Aberdeen, SUPA, AB24 3UE Aberdeen, United Kingdom.

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Summary

This study defines causality based on time

Area of Science:

  • Causal inference
  • Information theory
  • Time series analysis

Background:

  • Causality is traditionally understood through the lens of time's arrow, where past events influence future outcomes.
  • Predictability of future states in a variable Y is key to defining causality, based on past observations of X and Y.

Purpose of the Study:

  • To propose a spatiotemporal definition of causality.
  • To develop methods for detecting the direction of influence (arrow of influence) between variables X and Y.

Main Methods:

  • Exploiting the temporal nature of causality by comparing time-series lengths of X and Y.
  • Leveraging the spatial nature of causality by analyzing the precision of measured time-series data for X and Y.

Main Results:

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  • Causality exhibits distinct space and time signatures.
  • A break in symmetry in probabilistic space or time-series length indicates information flow from X to Y.

Conclusions:

  • The proposed spatiotemporal definition offers a novel approach to causality detection.
  • Information flow direction can be identified by analyzing asymmetries in time-series data.