This article was published in Scientific American’s former blog network and reflects the views of the author, not necessarily those of Scientific American
“How many days will you be staying?” The immigration officer’s question made my blood run cold. I could easily tell him my origin city, nationality, flight number, and eventual destination, but this question was different. It was a fencepost question.
Fencepost questions, dealing as they do with the difference between count and duration, discrete and continuous, have always been difficult for me. May 1st and 8th were both Sundays. There are 7 days in a week, and 8-1 is 7. 9 am on May 8th is 7 days after 9 am on May 1st, but if I do something every day from the 1st to the 8th, I do it 8 times. If someone asks me about something that takes place from the 1st to the 8th, mere subtraction is not enough. I need to know the context of the question and what type of answer is expected.
For this trip, I left on the 14th and would return on the 24th. 24-14 is 10, but I would be there for portions of 11 calendar days and the entirety of only 9 of them. I arrived at 5 pm and would leave at 10 am, so I would be there for less than 240 hours, the length of 10 days. On the other hand, I would be away from my home for well over 240 hours. Would the officer just look at my arrival and departure dates, subtract, and be done with it? Would it confuse him if I said 11? Or did he know about fenceposts too? Was he trying to trap me? Luring me into the false certainty of subtraction, ready to pounce when I gave him a number that failed to reflect the nuances of my visit?
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I felt like a cornered animal who doesn’t know whether, if I do something every other day, I do it 3 or 4 times in a week, and if I do it 4 times, whether that means a week has 8 days in it.
My mind was racing, my palms sweaty. The officer looked at me expectantly. Would he think I was flustered because I had something to hide? Would I be dragged away for more questioning, as another mathematician was last week?
Trying to keep my voice steady, I replied: “Ten.” I resisted the urge to explain the situation further.
I held my breath. As if in slow motion, he looked down, reached for the stamp, and flipped to a blank page in my passport. “Have a nice visit.”