@hazel the trolley hypothesis.......

@hazel I don't think it's possible to have 2^​ people in a line, since there is a clear answer to what person is immediately after another

@hazel unless they're point-object people I guess

@jacethechicken @hazel They become point-object people near the horizon

@jacethechicken @hazel imagine they are in a "very long line", where by "very long line" I mean "uncountably infinite but well-ordered set"

@jay @jacethechicken [0,1] times the first uncountable ordinal?

@jay @hazel well-ordered just means that any given subset has a smallest element -- that doesn't solve the problem that no elements of an uncountable set are ever truly adjacent

@jacethechicken @jay how would you accurately portray uncountability with regards to the trolley problem meme

@hazel @jay maybe copy-paste the person on the tracks many more times overlapping each other, to the point that you cannot parse any individual person

@hazel @jacethechicken I mean like, each person has a successor, but also you can take limits. I guess aleph_1 would be the first uncountable ordinal, and 2^aleph_0 would be the power set of the naturals, but with a well-ordering (idk if there's a canonical way to do this or if you need choice). Either way the "first bits" would look like the naturals, but it would just go on "longer"

@hazel @jacethechicken for a picture I guess just imagine something like this but where each line is a person, and it goes on "long enough" to get whatever wacky cardinality you want. upload.wikimedia.org/wikipedia

finally, my trolley problem

@hazel [math crackpot voice] the so-called proof that $2^a$ is a larger cardinal than $a$ even for infinite $a$ rests on an unconvincing sleight of hand. in this essay i will

@hazel sweet little Continuum Hypothesis

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