The New York Giants were inside the Green Bay five-yard line, maybe at around the two. The Packers jumped offside. Normally, that would be a five-yard penaty, but inside the defensive team's five, it's half the distance to the goal line. The teams line up again. Green Bay jumps offside again. Half the distance.
"Hey," I said to my friend Sandy, with whom I was watching the game, "the Packers are implementing the Zeno strategy!" I figured, they knew the Giants were going to score and take the lead unless they did something desperate, so they intended to continue jumping offside forever, allowing the Giants ever closer to the goal line but never able to cross it.
That whimsy brought up an interesting point: What could be done about a team really trying to implement such a strategy. Say, there's twenty seconds left in a game, and the team trailing by four has a first-and-inches to the goal line. The defensive team figures there's no way to stop each of four successive QB sneaks from getting the ball in the endzone, in which case they lose. And so they jump offsides the first moment the offensive team lines up, intending to do so forever -- meaning, until everyone gives up.
What can the officials do about this? Is there a response available within the current rules?
More realistically, what if a team just has a tired offensive unit it wishes to rest for a while, and a desire to flummox their opponent. On x-and-inches to the goal, why not jump offsides 10 or 20 times in a row? Certainly, the odds of giving up a touchdown are only changed minutely by a series of sub-centimeter advances towards the goal line.
By the way, the Wikipedia entry is excellent in explaining why the notion of a limit from calculus does not solve Zeno's paradox:
"A suggested problem with using calculus and mathematical series to try to solve Zeno's paradoxes is that these solutions miss the point. To be precise, while these kinds of solutions specify the limit point of infinite series, they do not explain how such a series can actually ever be completed and the limit point be reached. Thus, calculus and mathematical series can be used to predict where and when Achilles will overtake the tortoise, assuming that the infinite sequence of events as laid out in the argument ever comes to an end. However, the problem lies exactly with that assumption, as Zeno's paradox points out that in order for Achilles to catch up with the Tortoise, an infinite number of physical events need to take place, which seems to be impossible in and of itself, independent of how much time such an act would require if it could actually be done.
"Indeed, the problem with the calculus and other series-based solutions is that these kinds of solutions beg the question. They assume that one can finish a limiting process, but this is exactly what Zeno questioned. To be precise, Zeno started with the assumption that a finite interval can be split into infinitely many parts, and then argued that it is impossible to move through such a landscape. For calculus and other series-based solutions to make the point that the sum of infinitely many terms can add up to a finite amount therefore merely confirms Zeno's assumption about the landscape (geometry) of space, but does nothing to answer Zeno's question of how we can actually (dynamically) move through such a space."
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