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.

First, I start moving people to hotel rooms...

fossilesque you’re one of my fav posters

The first one, because people will die at a slower rate.

The second one, because the density will cause the trolley to slow down sooner, versus the first one where it will be able to pick up speed again between each person. Also, more time to save people down the rail with my handy rope cutting knife.

I think it was numberphile, or maybe vsauce, who did a video on infinities. It was really interesting. I learnt a lot, then forgot it all.

Bottom.

Killing one person for every real number implies there’s a way to count all real numbers one by one. This is a contradiction, because real numbers are uncountable. By principle of explosion, I’m Superman, which means I can stop the train by my super powers. QED

Is there a way to take both routes?

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.

Top case is not the smallest infinite; going for prime number would save a lot of time for a lot of people before they die

I mean, the bottom. The trolley simply would stop, get gunked up by all the guts and the sheer amount of bodies so close together. Checkmate tolley.

I thought that the correct answer to these was making a loop on the right, merging the lines.

Bottom has infinite density and will collapse into a black hole killing everyone, and destroying the tram and lever.

The second one. It'll be a bit rough, but overall should be a smoother ride for the occupants.

I don't think we want a world where there are any sort of infinity of people, and I don't think a tram is the solution to revert a world from having its infinities to having a finite number

I also see practicality problems in tying even a small infinity of people to railway tracks, as that requires yet another infinity of people to hold people down, and another infinity of people people to do the tying (as well as the infinities of people to do the tying and holding on the other track) and all of those people will have to be fed and watered with infinite amounts of food and water (some infinities of people for infinite time), the infinities of people tying people down would need some education, implying infinite teachers

It's a logistic nightmare

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.

Good to know there are roughly 6 real numbers for every integer

This hypothetical post is a thought crime!

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?

You've misunderstood "some infinities are bigger than others." Both of these infinities are the same size. You can show this since each person on the bottom track can be assigned a person from the top track at 1 to 1 ratio. An example of infinities that are different sizes are all whole numbers and all decimal numbers. You cannot assign a whole number to every decimal number.

Matt parker does a good video on this. I can't remember the exact title but if you search "is infinite $20 notes worth more than infinite $1 notes" you should find it.

An infinite amount of people on the track implies that the track is infinitely long. If that is not the case and the track is a normal length then the sudden addition of all that bio-mass in a finite space will cause a gravitational collapse. But will the collapse start on the first track or the second? Either way I hope you saved your game because you might lose your progress.

In the top case has it been arbitrarily decided to include space in between the would-be victims? Or is the top a like number line comparison to the bottom? Because if thats the case it becomes relevant if there is one body for every real number unit of distance. (One body at 0.1 meter, and at 0.01 meter, at 0.001, etc)

If so then there's an infinite amount of victims on the first planck length of the bottom track. An infinite number of victims would contain every possible victim. Every single possible person on the first plank length. So on the next planck length would be every possible person again.

Which would mean that the bottom track is actually choosing a universe of perpetual endless suffering and death for every single possible person. The top track would eventually cause infinite suffering but it would take infinite time to get there. The bottom track starts at infinite suffering and extends infinitely in this manner. Every possible version of every possible person dying, forever.

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

Getting killed by a train is apparently just an inevitability in this universe. Either choice is just the grand conductors plan.

3. I lay some extra track so the train runs over the perverts that come up with these "dilemmas" instead. Problem solved. 👍

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.