As a lifelong California suburbanite, spending nine weeks in Manhattan was an adjustment. The first difference I noticed was having to wait for everything: the elevator, the subway, restaurants, matcha, and the city's latest trend, frozen yogurt.
Enter Mimi's and Myka, the two shops everyone was lining up for. Every weekend or so, my friends and I would line up too. Our record was 80 minutes for Myka, at midnight, right before they closed. That made the next weekend's 30 minutes at Mimi's feel like nothing. Once it started pouring and people waited anyway, including the ones without umbrellas.
This was pretty ridiculous, and people walking by taunted us: "no way the froyo is that good." Cool, they were free thinkers, not sheep. I thought I was like that too. My friends and I would agonize over whether to keep waiting, but we'd already waited so long and the yogurt was so good!
All this time waiting for necessary (subway) and unnecessary (froyo) things in New York lent itself to thinking. I thought about the concept of the line. Here are some things that came to mind, including three claims that I had previously muddled together.
(1) Structural. The last person in line occupies the unique position with no one behind them. This is true by construction. Let's remember this as the base case for now.
(2) Phenomenological. Positional value is relational. Being 33rd in line felt like an accomplishment only because 25 people queued up behind us. The same 33rd place, with nobody behind it, would have felt silly.
(3) Dispositional. What kept me there was the people behind me, not the time I had already spent (that was a sunk cost). The 25 people behind us were evidence: 25 others who judged the line worth joining, though what they were judging was mostly each other.
Now, grant three premises:
Then run backward induction. Given (C), waiting is pure cost. The last person waits the longest, so being last is the costliest position in the line. By claim (1), that position is also unique in having nobody behind it. So, if you knew with certainty that you were last, the case for staying is the weakest it will ever be. Suppose you leave. Now the person ahead of you is last, facing the same reasoning and reaching the same conclusion, so they leave too. Repeat and the line empties.
The line did not empty though. In fact it was pretty much that long all day. So at least one premise must be false. I argue that all three are.
The objection to (A) and (B) is trivial. The argument needs everyone to know the cutoff, and everyone to know that everyone else is reasoning this way. Nobody in line has either. Someone in front of us said yesterday they let us go to 00:20, which is exactly the kind of thing that circulates in a line and cannot be verified.
Premise (C) is the most damaging one. The argument treats the frozen yogurt as the only thing valued intrinsically and the waiting as purely instrumental. It follows then that being last is the worst position, since the waiting is nothing but cost. But if the waiting is also valued intrinsically, then being last costs you nothing you were not already getting, so the base case is false and the induction collapses.
Standing there, the waiting felt like cost. I felt sillier the longer I waited, and I would have told you at minute 60 that the whole thing was indefensible. For most of my life, I treated friction as something to be minimized and time spent not arriving as time lost.
What I find odd is that the logic was available to me yet the answer was not. I could work out, standing there, exactly why the line should have emptied. I could not work out why it hadn't, because the reason was the thing I was doing at the time.