Causality, information and time

Any scientific discipline strives to explain causes of observed phenomena. Quantitative, mathematical description of causality is possible when studying phenomena that evolve in time and provide measurable quantities which can be registered in consecutive instants of time and stored in datasets called time series. As examples we can mention long-term recordings of air temperature, or recordings of the electrical activity of the human brain, known as the electroencephalogram.

In this talk we will follow ideas of the father of cybernetics, Norbert Wiener, and Nobel prize winner Sir C.W.J. Granger. We will explain how to detect causality using probability distribution functionals from information theory and the interpretation of causal relations as information transfer. We will study the information transfer in chaotic systems on the route to synchronization. The time and the arrow of time play a natural role in the definition of causality: the cause precedes the effect. We will investigate whether this principle is obeyed by chaotic dynamical systems. Another role of time can be seen in complex systems evolving on multiple time scales. We will show how to measure the information transfer across time scales. As an application we will demonstrate a causal influence of climate oscillations with a period about 7-8 years on the amplitude of the annual temperature cycle and the inter-annual variability of the mean winter temperature in central Europe.