like the infinite monkeys with typewritters, universal limits to the rescue. Trolley's are slow. Each bump makes them slower. Some of the people in the discrete line will have long lives until an excruciatingly painful death from dehydration.
this post was submitted on 02 Oct 2025
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- I lay some extra track so the train runs over the perverts that come up with these "dilemmas" instead. Problem solved. π
Some infinities are bigger than other infinities
Is this actually true?
Many eons ago when I was in college, I worked with a guy who was a math major. He was a bit of a show boat know it all and I honestly think he believed that he was never wrong. This post reminded me of him because he and I had a debate / discussion on this topic and I came away from that feeling like he he was right and I was too dumb to understand why he was right.
He was arguing that if two sets are both infinite, then they are the same size (i.e. infinity, infinite). From a strictly logical perspective, it seemed to me that even if two sets were infinite, it seems like one could still be larger than the other (or maybe the better way of phrasing it was that one grew faster than the other) and I used the example of even integers versus all integers. He called me an idiot and honestly, I've always just assumed I was wrong -- he was a math major at a mid-ranked state school after all, how could he be wrong?
Thoughts?
It's pretty well settled mathematics that infinities are "the same size" if you can draw any kind of 1-to-1 mapping function between the two sets. If it's 1-to-1, then every member of set A is paired off with a member of B, and there are no elements left over on either side.
In the example with even integers y versus all integers x, you can define the relation x <--> y = 2*x. So the two sets "have the same size".
But the real numbers are provably larger than any of the integer sets. Meaning every possible mapping function leaves some reals leftover.
It is true! Someone much more studied on this than me could provide a better explanation, but instead of "size" it's called cardinality. From what I understand your example of even integers versus all integers would still be the same size, since they can both be mapped to the natural numbers and are therefore countable, but something like real numbers would have a higher cardinality than integers, as real numbers are uncountable and infinite. I think you can have different cardinalities within uncountable infinities too, but that's where my knowledge stops.
What about a time loop where only one person dies, but infinite times?
The second one. It'll be a bit rough, but overall should be a smoother ride for the occupants.
The top one, because time is still a factor.
Sure, infinite people will die either way, but that is only after infinite time.
you know, I'm not sure you can have an uncountably infinite number of people. so whatever that abomination is I'll send the trolley down its way. it's probably an SCP.
I ignore the question and go to the IT and maintenance teams to put a series of blocks, physical and communication-system-based, between the maths and philosophy departments. Attempts to breach containment will be met with deadly force.
Math is the philosophy department in that math is an extension of logic, which is in turn an extension of philosophy. You'd have a better chance of divorcing math from applied math (engineering/physics) than separating math from philosophy.
That sounds an awful lot like someone looking to arrange a containment breach.
That's like just your axiom man
Considering that there's a small but non zero chance of surviving getting ran over by a train some of them are gonna survive this and since there are infinite people that will result in infinite train-proof people spawning machine
I pull the lever, if the cart goes over the real numbers it will instantly kill an infinite amount of people and continue killing an infinite amount of people for every moment for the rest of existence.
If I pull the lever a finite amount of people will die instantly and slowly over time tending twords infinity but due to the linear nature of movement it would never actually reach Infinity even if there are an infinite number of people tied to the track a finite amount is all that could ever die.
All the people tied to the track will die after a few days anyway.
So you're going to let those infinite people on top stay tied to the track and starve to death slowlyβ½
I mean, in that case itβs not really a matter of the trolley killing them, per se. The number will tend towards infinity, until it suddenly spikes to real infinity as people starve.
I assume the people spawn into existence as the render distance comes into frame.
Probably better than an infinite number of people waiting an infinite amount of time for there impending doom and then also an infinite number of people starving to death.
you have to remember β΅^0 in this case is included in β΅^1 or at least the numerical value is, which is the only information given.
I guess technically you could value one human soul above the other and technically this is philosophy? So I guess technically you should? but anyway everything that happens on β΅^0 will also happen on β΅^1 except more will always happen on β΅^1 than β΅^0 so whether there is unintended consequences or not doesn't really matter. it's always safer to pick the countable infinities.
Unless there is something innately good about physically having more people exist no matter there condition. but you would have to ask a philosopher about that one, I'm paid to pull lever's not philosophize.
Geez, disconnect the trains so you can hit both lines at the same time, obviously.
Bottom.
Killing one person for every real number implies thereβs a way to count all real numbers one by one. This is a contradiction, because real numbers are uncountable. By principle of explosion, Iβm Superman, which means I can stop the train by my super powers. QED
Wait until your league of super heroes is up against the axis of choice.
Can I group the people into groups of 1, then 2, then 3 and so forth? When the trolley is done with the killing, it will have killed -1/12 people.
In the top one you will never actually kill an infinite number of people, just approach it linearly. The bottom one will kill an infinite amount of people in finite time.
Edit: assuming constant speed of the train.
I'm going bottom.
NOT LIKE THAT. Not like sexually. I just mean I want to kill all the people on the bottom with my train.
So still sexually
Too late! Now bend...
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Bottom has infinite density and will collapse into a black hole killing everyone, and destroying the tram and lever.
I masturbate until I forget about the decision I have to make and then put off cleaning my apartment until I finally just run out, randomly pull the lever, and never think of the consequences again.
Of course by that point everyone has already starved to death which is the worst possible outcome.
Ah, procrasturbation.
I reject the premise since there will only ever exist a finite number of people. They will all die. One day the last human will die.
Use the fact that a set people corresponding to the real numbers are laying in a single line to prove that the real numbers are countable, thus throwing the mathematics community into chaos, and using this as a distraction to sabotage the trolley and save everybody.
Hey, maybe they're infinitely thin people, in which case you can (and necessarily must, continuum hypothesis moment) have one for every real number.
I use the lever to kill the train driver.
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