The Do-Operator

The do-operator, written do(x), is Judea Pearl's central technical contribution: a piece of mathematical notation that distinguishes intervening on a variable from merely observing it. To observe that patients who take the drug recover is to make a statement about the world as it is; to compute what would happen if you gave everyone the drug—do(drug)—is to make a statement about a world you have not yet created. The first is a fact about data, the second a fact about mechanism, and no amount of the former, Pearl proves, will ever yield the latter. This is the formal boundary between the first and second rungs of the Ladder of Causation, and the engine of what he calls the do-calculus—a set of rules for deciding when an interventional question can be answered from observational data combined with a causal model, and when it cannot. It is also the precise instrument that locates the large language models of the present, which are trained only on what was observed