This contribution revisits Joseph Weizenbaum’s reflections on the limits of ELIZA, the first chatbot intended as a provocative probe into human-machine communication (1966, 1976), and my own critical analyses of the same problem (Suchman 1987, 2007). Based in an associated critique of the project of artificial intelligence, I argue that across significant shifts in technologies and techniques the differences that matter between humans (and other beings) and machines (of our making) persist (see Dreyfus 1992). These differences turn on the capacity for generative (in the old sense of that term) co-construction of mutual intelligibility in and through the contingencies of the open worlds that we inhabit together. Crucially, those capacities are irreducible to their translation into digital input, the sensorial prerequisite for computation. This reflection reiterates the incomputable capacities that human interaction presupposes and that escape incorporation into the computational sensorium. The point is not to diminish the capacities of computational systems, but rather to demystify their operations, acknowledge their limits, and foreground the human agencies and political economies that are responsible for their consequences.