fossilesque you’re one of my fav posters
ilu2 :)
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
If the next person getting tied down holds down the person currently being tied down then this could work. I’m sure they’d be game so that’s fine.
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.
Is there a way to take both routes?
Hit the hand brake and drift that sucker.
Running in the 90s intensifies
with my knack for drifting i’ll miss both and hit something else entirely even within this imaginary scenario
You dont have to since the set of all positive integers belongs to the set of all real numbers, you actually hit both tracks by just taking the lower track.
never doubt my ability to mess up the unmessable. i just might stumble into disabling clipping and end up falling forever.
First, I start moving people to hotel rooms…
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.
Ah yes, I remember my eyes glazing over as things got too complicated to fit through my thick skull
I thought that the correct answer to these was making a loop on the right, merging the lines.
Unfortunately it’s hard to join the tag end of one infinity to the tag end of another infinity to allow traversing both completely
I don’t really think it’s even sensible to talk about the tag end of an infinity. The bitten/bitter end is at 1, the tag end at infinity in this mental model. I feel that is the correct way to use rope terms for imagined embodied infinities as the small end is clearly bitten to (tied to) zero while the other end is free
The answer is multi track drifting
No, we need a second trolley.
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
The set of all primes is the same size infinity as the set of all positive integers because you could create a way to map one to the other aka you can count to the nth prime. Reals are different in that there are an infinite number of real between any two reals which means there’s no possible way to map them.
The set of primes and the set of integers have the same size, you can map a prime to every integer.
depends on what you mean by “smallest”
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.
Too late! Now bend…
So still sexually
Limits still are not intuitive to me. Whats the distinction here?
If people on the top rail are equally spaced at a distance d from each other, then you’d need to go a distance nd to kill the nth person. For any number n, nd is just a number, so it’ll never be infinity. Meanwhile the number of real numbers between 0 and 1 is infinite (for example you have 0.1, 0.01, 0.001, etc), so running a distance d will kill an infinite number of people. Think of it like this: The people on the top are blocks, so walking a finite distance you only step on a finite number of blocks. Meanwhile the people on the bottom are infinitely thin sheets. To even have a thickness you need an infinite number of them.
Different slopes.
On top you kill one person per whole number increment. 0 -> 1 kills one person
On bottom you kill infinity people per whole number increment. 0 -> 1 kills infinity people
You can basically think of it like the entirety of the top rail happens for each step of the bottom rail.
For every integer, there are an infinite number of real numbers until the next integer. So you can’t make a 1:1 correspondence. They’re both infinite, but this shows that the reals are more infinite. (and yeah, as other people mentioned, it’s the 1:1 correspondence, countability, that matters more than the infinite quantity of the Real numbers)
There are infinitely many rational numbers between any two integers (or any two rationals), yet the rationals are still countable, so this reasoning doesn’t hold.
The only simple intuition for the uncountability of the reals I know of is Cantor’s diagonal argument.
You can assign each rational number a single unique integer though if you use a simple algorithm. So the 1:1 correspondence holds up (though both are still infinite)
There are also an infinite number of rationale between two integers, but the rationals are still countable and therefore have the same cardinality as the naturals and integers.
Makes sense, thanks!
There are an infinite amount of real numbers between 0 and 1. On the top track, when you reach 1, you would only kill 1 person. But on the bottom track you would’ve already killed infinite people by the time you reached 1. And you would continue to kill infinite people every time you reached a new whole number.
On the top track. You would tend towards infinity, meaning the train would never actually kill infinite people; There would always be more people to kill, and the train would always be moving forwards. Those two constants are what make it tend towards infinity, but the train can never actually reach infinity as there is no end to the tracks.
But on the bottom track. The train can reach infinity multiple times, and will do so every time it reaches a whole number. Basically, by the time you’ve reached 1, the bottom track has already killed more people than the top track ever will.
There aren’t infinite trams. There’s one tram that has to step over (roll through) one person at a time. Good luck to it making any progress, it will never get to the person numbered 1
Great explanation, I’d just like to add to this bit because I think it’s fun and important
And you would continue to kill infinite people every time you reached a new whole number.
Or any new number at all. Between 0 and 0.0…01 there are already infinite people. And between 0.001 and 0.002.
That’s still not doing it justice. If there were one person for every rational number there would be infinitely many in any finite interval (but still actually no more than the top track, go figure) but the real numbers are a whole other kind of infinite!
What I still don’t understand is where time comes into play. Is it defined somewhere? Wouldn’t everything still happen instantly even if there are infinite steps inbetween?
I guess it could be implied by it being a trolley on a track, but then the whole mixing of reality and infinity would also kind of fall apart.
Is every person tied to the track by default? If so, wouldn’t it be more humane to just kill them?
and will do so every time it reaches a whole number
Worse. It will kill an infinity every time it will move any distance no matter how small.
The bottom one will kill an infinite amount of people in finite time.
instantaneously FTFY
Good to know there are roughly 6 real numbers for every integer
If there are child real numbers then you can fit more.
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
Wait until your league of super heroes is up against the axis of choice.
Either that or the humans are so “infinitely packed” that they’re probably already dead squashed into each other.
Now, if you put infinite people in a chamber, and then compress the chamber and then put an infinite amount of compressed chambers inside a chamber… Will we have Real People?
Also, almost all real numbers are undefinable. (Unless you’re using a model, that makes them countable.)
So that means, that almost all the “humans” on the bottom track are something we can not even imagine in principle. Wouldn’t be surprised, if infinite Superman’s were among them.
plus uncountable infinity implies there is uncountable supply of humans, which is nice.
This hypothetical post is a thought crime!
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.
How do we know it’s an accurate illustration? They might have jacked up the trolley with monster truck wheels or something.
The illustration can’t be accurate - you can’t picture an infinite number of people between each pair of people, but the description is clear. The trolly can’t progress because it can’t get from the first person to the second due to the infinite people between them, and the infinite people between each of those between them, etc.
Like in the second infinity you can’t count to one, you can’t count from 0 to 1*10^(-1000)
I mean, maybe, but I can only go off what I see here.
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.
So you’re going to let those infinite people on top stay tied to the track and starve to death slowly‽
I mean, in that case it’s 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 ℵ^0 in this case is included in ℵ^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 ℵ^0 will also happen on ℵ^1 except more will always happen on ℵ^1 than ℵ^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.
All the people tied to the track will die after a few days anyway.
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.
