A Survey of Causality and Directed Information

Causality has been an important concept in philosophy at least since the days of Aristotle and his "four causes" theory. Just for how long causality has been studied mathematically is uncertain due to the often blurred lines between mathematics and philosophy, but even today assigning causality (let alone culpability) to a pair of events requires some degree of human intuition. This paper will survey Granger Causality, a tool with applications in aiding the researcher in determining causal influence in complex systems. We will also present Directed Information, a generalization of causality with applications beyond the philosophical. Discussion of the philosophical consequences of these tools is intertwined throughout, just as philosophy is intertwined with science and engineering in life.