In 1950, Alan Turing proposed his eponymous test of machines -- based on verbal indistinguishability from humans -- which he intended as a replacement for the question "Can machines think?" Since then, the primary philosophical question concerning the Turing Test is whether or not it is well-founded as a sufficient condition for intelligence. The state of play on the question has led to the following stalemate: On one hand, conventional wisdom among philosophers is that the Test is conceptually flawed as a sufficient condition for intelligence; Ned Block's "Aunt Bertha Machine" thought experiment is the crispest argument for this view. On the other hand is the overwhelming sense that were a machine to pass a real live full-fledged Turing Test, it would be a sign of nothing but our orneriness to deny it the attribution of intelligence; this, roughly speaking, is Daniel Dennett's view. In this talk, we present the background for the debate, and apply ideas from theoretical computer science and physics in novel ways in order to cut this Gordian knot: We conclude that both Block and Dennett are right.