The top one will never actually reach infinity, unless the trolly accellerate in such a way that it reaches infinity in finite time (not physically possible). The bottom one reaches infinity in an instant.
this post was submitted on 30 Mar 2026
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Is the top case the smallest possible infinity? What about an infinite set of all even integers? What about an infinite set of integers divisible by 10? What about an infinite set of integers divisible by 100?
it is. those sets all have the same cardinality
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.
I stop the trolley using its brake, no one dies.
Save two infinity lives. Blow up the trolley.
We live in the modern era. The trolley was stopped by modern signal systems and a call by a passerby to the dispatcher (look for the blue sign near the crossing) reporting a lunatic tying hundreds of people to the rails. The police were dispatched and due to the numerous descriptions from the would-be victims, the lunatic was caught and jailed, awaiting trial.
Not philosophical, but the trolley on track two would have to have infinite energy otherwise it would get hung up on all the bodies rather quickly.
Philosophically it is a matter of utilitarianism for me with less death over time being preferable.
What option is more profitable? No money -- no action. Especially if we are talking about infinitely moving tram over infinite amount of people.
Pull the lever when the trolley is halfway over the switch, trolley gets derailed
laughs in ramanujan.
Pull the lever and then start working on stopping and or derailing the train.
there's no such thing as "a person for every real number." people are countable, and an infinite set of countable things cannot have a cardinality that is uncountable (i.e. greater than that of integers)