Essential Concepts of Causal Inference: A remarkable history and an intriguing future

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Causal inference is a major topic in any field that tries to understand the kinds of treatments (i.e., interventions) we humans are considering in order to effect particular changes in the world around us, whether those treatments involve business decisions, pharmaceuticals to ingest, educational programs to offer, military actions to take ÿ effectively everything that involves choices in our lives. Despite the ubiquity of this topic to the lives of unconscious and later conscious humans for tens of thousands of years, it has a remarkable history, with solid mathematical foundations beginning only in the early 20th century, with the development of crucial ideas tied to related ideas in physics, namely those arising in quantum mechanics. This formulation of causal inference has an intriguing future because of the increasing application of causal inference to treatments with conscious units, humans, despite its mathematical origins with unconscious units: plants, animals, industrial objects. Conscious units do not necessarily comply with their assigned treatments and can suffer from complications such as placebo effects; moreover, humans may depart from study protocols by dropping out early, or may use the internet to interfere with each other in ways that were considered impossible in the middle of the twentieth century. The proper handling of such complexities comprises an intriguing collection of topics,which are currently virtually unstudied with any mathematical rigor.