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  • Assuming that it takes some amount of energy to kill one person, and that the trolley doesn't have an engine with infinite power, choosing the bottom track would save lives. The trolley would have to expend an infinite amount of energy to move any distance from the starting point, so it would just get stuck there while trying to crush the unimaginable amount of people bunched up in front of it.

    • But getting anywhere on the lower track will kill infinitely many people. You cannot kill finitely many people on the lower track. Well, unless you derail at exactly the first. On the upper track, a stop at any point will have killed only finitely many.

      • One person can only be on the spot for one number. As soon as more than one gets killed, that would mean that the trolley has traversed some distance, which implies that it has killed an infinite number of people. That is impossible in any finite timespan under the aforementioned assumption. Thus the only logical conclusion is that it gets stuck after the first person is killed, at the exact spot the first number is mapped to.

        I guess there could also be a different solution when you look at the problem from a different angle. Treating infinity with this little mathematical care tends to cause paradoxes.

  • I kill the trolley driver. The Dead Man button makes that the trolley stops.

  • Seeing an infinite number of people lying there I deduce that I must be in some kind of thought experiment and let the trolley roll on while I look for a way to escape back to reality.

  • That trolley is definitely stopping before it makes it through all those people on the bottom track.

  • I know many people despise generative AI, but what do you think of this result from Copilot? I am bad at maths so I wonder if you experts can tell.

    In your scenario, you have two sets: the integers on the top track and the real numbers on the bottom track. The cardinality of the integers is equal to the cardinality of the real numbers, which is called the continuum hypothesis. Therefore, it seems intuitively more ethical to pull the lever and divert the trolley to the bottom track, where you kill fewer people in any finite time.

    • it seems intuitively more ethical to pull the lever and divert the trolley to the bottom track,

      not an expert but the integer one is at the top i think

    • It's completely wrong within ZF set theory the cardinality of the integers is stricly smaller than the cardinality of the real numbers. The continuum hypothesis states that there is no set with a cardinality strictly larger than the natural numbers (or integers) and strictly smaller than the real numbers.

      It accidentally kind of comes to the right conclusion, but even the conclusion isn't really correct, you don't need to be concerned with finite time since integers are a smaller cardinality.

      Let's say people can be placed on a point on the track indexed by the real numbers, given any two seperate, finite, points, there would be more people packed between those two points than the entire integer track.

    • "The cardinality of the integers is equal to the cardinality of the real numbers, which is called the continuum hypothesis."

      The cardinality of the integers is not equal to the cardinality of the reals. The integers are countable (have the same cardinality as the natural numbers). A very famous proof in set theory called Cantor's diagonal argument shows the reals are uncountable (i.e. not countable).

      The continuum hypothesis is also not about comparing the cardinality of the reals and the integers or naturals (since we already know the above). The continuum hypothesis is about comparing the cardinality of the reals with aleph_1.

      Within the usual set theory of math (ZFC set theory), we can prove that we can assign every set a "cardinal number" that we call its cardinality. For finite sets we just assign natural numbers. For infinite sets we assign new numbers called alephs. We assign the natural numbers a cardinal that we call aleph_0.

      These cardinal numbers come with an ordering relationship where one set has a cardinality larger than another set if and only if its associated cardinal number is larger than the other sets cardinal number. So, alepha_0 is larger than any finite cardinal, for example. There is a theorem called Cantor's theorem that tells us we can continually produce larger and larger infinite cardinals in fact.

      So, we know the reals have some cardinality, thus some associated cardinal number. We typically call this number the cardinality of the continuum. The typical symbol for this cardinality is a stylized (fraktur) c. Since aleph_0 is countable, every aleph after aleph_0 is uncountable. By definition aleph_1 is the smallest uncountable cardinal number. The continuum hypothesis just asks if aleph_1 and c are equal.

      As an aside, it is provable that c has the same cardinality as the powerset of the naturals. We let the cardinality of the powerset of a set with cardinality x be written as 2x. Then we can write the continuum hypothesis in terms of 2{aleph_0} and aleph_1. The generalized continuum hypothesis just swaps out 0 and 1 for an arbitrary ordinal number alpha and its successor in this new notation.

    • I'm sure if I tried to rephrase the problem getting every detail wrong, I'd do a worse job than this.

      But I'd change the number of tracks.

  • Infinity people always die. Even if you don't make a decision.

  • EDIT: I rolled a critical fail in reading comprehension and I thought the other track was N per integer instead of 1 per real number in the previous version of this comment.

    The people in the real number track are already dead by the time the trolley arrives due to the forces involved in cramming them so tightly together. I.e. they are basically just a gore pile the moment after the people are somehow arranged like that.

    I pick the real number track so that no one new has to die.

  • I pull the lever and invoke Zeno's paradox to ensure the trolley's position remains < 1 for eternity.

204 comments