On Sunday afternoon, I went to the National Football Conference championship game at Lincoln Financial Field in Philadelphia. At one point early in the fourth quarter, the Philadelphia Eagles were on the 1-yard line of the opposing Washington Commanders, ready to run their unstoppable Brotherly Shove play for a score. (Trust me — this has something to do with Future Perfect.)

Knowing they would almost certainly give up a touchdown, the outmatched Commanders decided to do something a little different. First, a Commanders defender purposefully jumped over the line early, leading to a penalty for encroachment. Then they did it again — same thing. And again — same thing. They seemingly had every intention to keep jumping the line, over and over. And each time, the referees moved the ball half the distance to the goal line, as happens when defensive penalties occur close to the end zone.

Anyone familiar with the principle of infinite divisibility in geometry can see the problem here. A line segment — like the distance here between the line of scrimmage and the end zone — can be infinitely divided, over and over. Which means that theoretically, the Commanders could have kept encroaching, and the Eagles could have kept advancing half the distance to the goal line without ever getting there, until the end of time.

Fortunately for the players, coaches and nearly 70,000 fans in attendance, the referees found a way out of this particular paradox by invoking a little-known NFL rule that allows the offense team to be automatically awarded a touchdown if the defense keeps purposefully committing penalties to stop them. That was finally enough to get the Commanders to cut it out.

All of which brings us to a subject we’ve written about a few times here at Future Perfect: the Doomsday Clock. (See, I told you we’d get there.)

What time is it?

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