Correlation is not causality: a conceptual and mathematical framework

Causal relations are a crucial aspect of the human understanding of the world. On the other hand, most statistical and machine learning tools are completely blind to the distinction between correlation and causality. This lack of discrimination capability can be catastrophic for control, particularly of complex and chaotic systems. In this contribution, a conceptual framework is provided to distinguish between correlation and causality. A new definition of causality for the sciences is proposed. How this can be converted into mathematical criteria is also covered. The extraction of causal relation directly from the data, the field of so called observational causality detection, is introduced as well.