this post was submitted on 11 Feb 2026
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There are two super interesting problems in here.
One is: would you bet human lives on a conjecture being true? The collatz conjecture does hold for every number we have tried, but there have been conjectures that were disproven with a very large counterexample. You could kill countless humans if wrong, so even if you think the chance of a counterexample is low, is it low enough to outweigh that potentially very hight value counterexample?
The second one is: Let's say the collatz conjecture holds, and the number of passsengers just loops
4 -> 2 -> 1 -> 4 -> 2 -> 1eventually. What is the 'final' number, when the trolley is done with the infinite loops? It can't be1, because that is always followed by a4. And it can't be4because it's always followed by2and so on. But it has to be one of those, because any other number is not possible. It reminds me of the Vsauce Video Supertasks, which comes to the conclusion that we can't know the answer to these type of questions.So in conclusion, flipping the switch will either give you an arbitrarily large number of deaths, or an unknown number of deaths. Fun!
You can't answer this kind of question because "after infinity" is meaningless nonsense.
It really depends. For example, if you walk 1m, then 0.5m, then 0.25m and continue infinitely, then "after infinity" you will have walked exactly 2m. This is the classic 'Achilles and turtle' example and works fine if the value converges. It's just mathematics.
There is only a problem if the value diverges. Imagine the step example, but on even steps, you raise a blue flag, and on odd steps you raise a red flag. Now the question what flag is raised "after infinity" is impossible to answer. It clearly should be either red or blue, but it also can't really be either, because that would mean infinity is either even or odd, which makes no sense.