the mathematical answer is that the same number of people die on both tracks. notice how the first track constructs a way to enumerate a set of people. the same enumeration can then be applied to the second set, because you're doing the exact same thing. the property that makes the reals dense and uncountable is precisely that it is impossible to assign one discrete element of an enumerable set to each real. "each real number" as a phrase doesn't make sense mathematically - the real numbers are the continuum.
it's a very similar reasoning error as the one that leads people to think that an infinite stack of $20 bills must be worth more than an infinite stack of $1 bills.
this is the joke in the OP - it doesn't matter whether you pull the lever or not, a false choice - and I've now thoroughly ruined it.
an infinite set is countable if there is a one to one mapping between it and the natural numbers. this is easy with the first set as you can literally count off, 1, 2, 3, etc..
the second set is countable in exactly the same way.
this is extremely basic set theory. you're deeply misinformed.
no shit. I'm saying you can't use an enumerable set to produce a mapping with the reals. the natural numbers are an infinite set yet are definitionally countable as they are the ordinals.
disengage, you're arguing nonsense with someone with a literal degree in mathematics.
that's the conceit of the joke, the idea that you can use an enumerated list and map them to the reals. if you could do such a thing, you'd immediately fall prey to Cantor's diagonalization argument. the train tracks are a continuum. they can be mapped to the reals. a neverending list of people cannot.
Do you pull the lever killing one person for every integer
Or do you do nothing, allowing the trolley to kill one person for every real number
The meme establishes the same mapping on both infinities so both infinities have the same cardinality meaning that actually the second infinity is not continuum but aleph null
idk i just don't think it's fun to point out that the problem is inherently poorly posed. you're of course right that you can't actually consistently assign individual people to the reals.
i propose that we set up a third track that lets us mow down a transfinite number of innocents.
the mathematical answer is that the same number of people die on both tracks. notice how the first track constructs a way to enumerate a set of people. the same enumeration can then be applied to the second set, because you're doing the exact same thing. the property that makes the reals dense and uncountable is precisely that it is impossible to assign one discrete element of an enumerable set to each real. "each real number" as a phrase doesn't make sense mathematically - the real numbers are the continuum.
it's a very similar reasoning error as the one that leads people to think that an infinite stack of $20 bills must be worth more than an infinite stack of $1 bills.
this is the joke in the OP - it doesn't matter whether you pull the lever or not, a false choice - and I've now thoroughly ruined it.
I disagree I think people killed per second is a metric that can be minimised here
This sentence is a a more concise description of American voting
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I didn't say it was? I'm comparing the sizes of sets by noticing the enumeration of the first set and that same enumeration applies to the second set.
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no, emphatically:
this is extremely basic set theory. you're deeply misinformed.
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no shit. I'm saying you can't use an enumerable set to produce a mapping with the reals. the natural numbers are an infinite set yet are definitionally countable as they are the ordinals.
disengage, you're arguing nonsense with someone with a literal degree in mathematics.
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Respect people's right to disengage
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Respect people’s right to disengage
that's the conceit of the joke, the idea that you can use an enumerated list and map them to the reals. if you could do such a thing, you'd immediately fall prey to Cantor's diagonalization argument. the train tracks are a continuum. they can be mapped to the reals. a neverending list of people cannot.
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i fucking hate maths
mate, I've already asked you to disengage, please do so
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I'm pretty sure it's just a VOOOOTE joke about how there's no difference between the two parties, except aimed at math nerds.
The meme establishes the same mapping on both infinities so both infinities have the same cardinality meaning that actually the second infinity is not continuum but aleph null
idk i just don't think it's fun to point out that the problem is inherently poorly posed. you're of course right that you can't actually consistently assign individual people to the reals.
i propose that we set up a third track that lets us mow down a transfinite number of innocents.