"We have dramatically compelling non-interactive digital (= electronic) entertainment: sit down and watch The Matrix (see Figure 1) or T2 (see Figure 2). We have compelling interactive digital entertainment; my favorites include console-based sports games.2 We have dramatically compelling interactive entertainment; for example, improvizational theatre. What we don't have is dramatically compelling interactive digital entertainment. People sometimes tell me that there is a counter-example to my negative view to be found in online multi-player games, but though such games are digital, interactive, and entertaining -- they have zero literary power (which explains why, though T2 engages young kids through at least middle-aged professors, such games are demographically one-dimensional). The same can be said, by my lights, for all other electronic genres. Can we build systems that imply and affirmative answer to the title of this paper? My answer is: ``Maybe, maybe not; but at any rate I can tell you, at least in broad strokes, what some of the hurdles are, from the standpoint of AI. And I can tell you, today, about one specific hurdle.""