This is from a casual note by Cosma Shalizi about graphical causal models. I'm publishing it here: 1) to park it where I can find it readily, 2) because it bears on a favorite example of Graham Harman's, and 3) sheds light on the 'tissue' of indirect causality (Harman's concept) that is the basis of my conception of Realm of Being:
Part of what we mean by "cause" is that, when we know the immediate causes, the remoter causes are irrelevant --- given the parents, remoter ancestors don't matter. The standard example is that applying a flame to a piece of cotton will cause it to burn, whether the flame came from a match, spark, lighter or what-not. Probabilistically, this is a conditional independence property, or a Markov property: a variable is independent of its ancestors conditional on its parents. In fact, given its parents, its children, and its childrens' other parents, a variable is conditionally independent of all other variables. This is called the graphical or causal Markov property. When this holds, we can factor the joint probability distribution for all the variables into the product of the distribution of the exogenous variables, and the conditional distribution for each endogenous variable given its parents.