Essential concepts of causal inference: a remarkable history and an intriguing future

ABSTRACT Causal inference refers to the process of inferring what would happen in the future if we change what we are doing, or inferring what would have happened in the past, if we had done something different in the distant past. Humans adjust our behaviors by anticipating what will happen if we act in different ways, using past experiences to inform these choices. ‘Essential’ here means in the mathematical sense of excluding the unnecessary and including only the necessary, e.g. stating that the Pythagorean theorem works for an isosceles right triangle is bad mathematics because it includes the unnecessary adjective isosceles; of course this is not as bad as omitting the adjective ‘right.’ I find much of what is written about causal inference to be mathematically inapposite in one of these senses because the descriptions either include irrelevant clutter or omit conditions required for the correctness of the assertions. The history of formal causal inference is remarkable because its correct formulation is so recent, a twentieth century phenomenon, and its future is intriguing because it is currently undeveloped when applied to investigate interventions applied to conscious humans, and moreover will utilize tools impossible without modern computing.