 There is also a “regressive” version of the Dichotomy supertask that has no initial step. Suppose that Achilles does reach the finish line. Then he would have had to travel the last ½ of the track, and before that ¼ of the track, and before that ⅛ of the track, and so on. In this description of the Achilles race, we imagine winding time backwards and viewing Achilles getting ever-closer to the starting line (Figure 1.1.2). But now there is no initial step in the task.