That's almost exactly one of the parables between Achilles and the Tortoise that Hofstadter gives in Godel, Escher, Bach, where the Tortoise keeps breaking Achi

That's almost exactly one of the parables between Achilles and the Tortoise that Hofstadter gives in Godel, Escher, Bach, where the Tortoise keeps breaking Achilles' record player by playing records of the machine's resonant frequency. Hofstadter gives it as an example of the 2nd Incompleteness Theorem, that in any mathematical system there are always statements that can neither be proven true nor false using the system's axioms (although I'm not fully convinced this resonant frequency example is actually an example of Godel's theorem). In any case, that's funny, I bet Hofstadter based the example on this story of the Black Team.