this post was submitted on 30 Mar 2026
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Don't switch. The trolley will be brought to an almost instant halt by the viscera of the first n people it hits. As they are packed together at infinite density this stop will be very sudden, probably derailing the trolley. Whilst this will certainly kill an uncountably infinite number of people due to that density, you will save a larger uncountably infinite number. You can demonstrate that the number saved is larger by considering the finite length of track the trolley covers before stopping against the infinite length left after it stops. Probably.
The biggest problem will be the release of energy when the speeding trolley hits the infinite mass of bodies. The acceleration will be prodigeous, akin to hitting a solid, immovable, wall. All that kinetic energy has to go somewhere and I would prefer to be a long way away, wearing a Sou'wester and a Macintosh, when it does.
The amount of people killed in a finite track length on the real numbers track is larger than the total number of people on the entire length of the integer track.
That's true, but the number saved us even larger. This clearly make you a hero as you saved the largest possible number of people, and the unfortunate death toll of infinity can be swept under the carpet as a mere rounding error, at least that's what most action movies have taught me.
that's not true. any interval of reals has the same cardinality as all reals, e.g. (0,1) is the same "size" as (-∞,∞). the number killed is equal to the number saved
I was, perhaps, not being entirely serious in my previous comments. I still save an uncountably infinite number of people though, so Im feeling pretty good about my day.