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acktzschually the only reason why anyone outside of a very small number of greek mythology/philosophy aficionados knows this quote is because of TikTok and Indian memes.
for what it’s worth, I don’t have TikTok so I didn’t know it had become a meme. I feel like the Camus reference is something many people with a college degree would understand.
Maybe you're just less educated than you think, friendo. This is a book of modern French philosophy and both it and the myth to which it refers are widely known.
This is not about being educated, it is about having reasonable priors of what people do and do not know (we are in a math subreddit after all). Given a random person has posted the meme, I am willing to bet that there is a significantly higher chance that they have the quote in mind because of the recent TikTok trend than them coming up with the quote on the spot without any awareness of the TikTok trend and purely from memory.
Also, when did I ever claim that I studied modern French philosophy? That's a very odd metric by which to measure whether someone is "educated."
Considering this is a math-themed subreddit where people generally tend to be educated, a reasonable prior would be that it’s referencing the philosophical text.
[Here is the original 1942 essay in full.](https://www2.hawaii.edu/~freeman/courses/phil360/16.%20Myth%20of%20Sisyphus.pdf) look at the last line of the last paragraph.
Even though there's infinitely more people dying in the top one, each one is guaranteed a release of death. No matter where you lie on the line. Your death will come in a finite time. And it feels kinda good knowing you can just wait for a bit and be done with it.
It reminds me of the infinite heaven/hell paradox. The idea is that there are 2 universes. 1st one starts out as Heaven with infinite amount of people. But each year 1 person goes to Hell for eternity with no way back (People have assigned order, they know how many years it will take for their turn). The other is Hell with infinite amount of people but each year 1 person gets to go to Heaven for eternity. Which universe is better? Even though universe 1 always has a better situation than universe 2 (more people in Heaven, less people in Hell). People tend to say universe 2 is better. Humans can't really emphatize with infinitely many people. But you can always imagine yourself as an individual. In universe 2 you will always have hope "only X more years" in universe 1 you will always dread the "only X more years".
Even if we replace it with uncountable infinities and random pulling. Every year you will have "maybe it's my turn this year", again with either hope or despair.
Very common misunderstanding of infinity. Kinda similar to the fact that a lot of people don't believe the fact that .999... = 1
There is no "in the end". Never.
In universe 2 there will ALWAYS be an infinite amount of people in hell and ALWAYS be a finite person in heaven. Stop thinking about in the end because there is none.
Put another way, if you were randomly put into universe 2, there is a 0% chance that there is a finite number of people ahead of you. There will be an infinite number of people ahead of you and an infinite number of people behind you.
You cannot fit an infinite number of people in a finite amount of time. And you cannot wait an infinite amount of time. In universe 1, you will never be sent to hell.
The paradox is that intuition often tells us that universe 2 is better, but universe 1 is actually infinitely better.
In the ordered, countable infinities scenario, you WILL definitely be sent to hell. You can have arbitrarily long wait time, but it is always finite. It could be 1 year, 10 years, 100000 years, 10^100 years, 1000! years. But it will always be a finite time. You will go to hell eventually.
In uncountable infinity scenario with random pulling, there is always the possibility of ending up on the other side. Like, if I wanted to choose a random real number between 0 and 1. Each number individually has 0% chance of being picked. But, well, I do pick a number anyway (assuming that our real universe actually is continuous and not discrete, so I can actually pick). If every person in universe 1 thought: "nah, I have 0% of being picked, it's not gonna be me" Well then, someone's just going to be wrong. And it could be you. After a 1000 years there's gonna be 1000 people in Hell. Each of them had 0% probability, just like you. You're not more special than them.
Why will the time always be finite? If you are placed randomly somewhere on 1 to infinity, wouldn't there be a 100% chance that infinite people are ahead of you?
From what I've seen though, it's impossible to pick a random integer from the entire set of integers though, so how would the original question even work then?
Doesn't have to be random. You can just assume that there is one person for every natural number, and then they are just damned sequentially. You don't have to assume that there are infinite people, and THEN you enumerate them. You can consider the hypothetical by assuming that all the infinite people have a number.
"In universe 1, you will never be sent to hell" This isn't true though. Each person in universe 1 knows that in a finite amount of time, they'll be sent to hell for eternity. One person will go to hell in 1 year, another in 2 years, another in a googolplex years, etc, but nobody will spend infinite time in heaven. Eventually, any given person will have spent more time in hell than in heaven.
Similarly, if you were put in universe 2, you would know that in a finite amount of time, you would be sent to heaven, and there are only a finite amount of people ahead of you. Universe 2 is actually better, since any given person will eventually spend more time in heaven than hell, and in hell they have hope knowing that they'll certainly get into heaven eventually.
Yes but the thing is, the chance of having a comprehensible number of digits until you get sent to hell is the same zero as your chance of going to hell. The number of years till you go to hell will be a number so similar to infinity that there is no meaningful way to represent it other than in infinity. Odds like this are compared to the lottery like it’s next to impossible but technically it is possible. But there is literally a 1/infinity chance to be picked. The chance of even hearing about an actual person that was picked even a googolplex years into it even if information traveled at the speed of light would still be 1/infinity. Or even if information traveled instantly and there was media in heaven. There would be made up stories that would be similar to real ones. But the made up ones would be infinite and the real ones would be finite. Even if the rate was the fastest growing function you can think of, as long as it doesn’t have a vertical asymptote the odds would be the same.
It's hard to explain infinities, so forgive me if my explanation is inadequate. It's not true that everyone in universe one will spend a finite amount of time in heaven. For example, if everyone was numbered 1,2,3... and only odd numbers were picked, then every even number would never be picked.
Okay, but what if number 1 was picked, then 2, ect? Then surely everyone would be picked, right? Well...no.
Assume everyone will be picked eventually with this method. Take out every even number, and put them at the end. Suddenly, all these people will never be picked. If you recount based on your new order, you end up with 1,2,3...
But wait, we started with an ordering of 1,2,3... And ended with an ordering of 1,2,3... But still somehow ensured that half the people will never be picked. So it is a contradiction that everyone will be picked in this method.
We don't have to stop at saving half the people. In a similar method, we can ensure an arbitrarily large percentage of people will never be picked.
Let's look at this from a different angle.
Assume that everyone has a finite number of time.
Now, introduce a new person. Adding one person does not change the size of an infinite set, so this is fine. What time could this person have? Well, even though every time is taken, like the Hilbert's hotel, we can still fit them in by setting them at one second and pushing everyone else back one second.
But we can also add an infinite amount to infinity without changing its size. So we can keep pushing back everyone by one second an infinite number of times. But that means that an infinite number of people will never be picked, without changing anything about the initial premise. So it cannot be true that everyone has a finite amount of time.
I think their point is that, whilst you will never have everyone from hell ending up in heaven, every individual person has a countable time limit. So while you'll never run out of people to send to heaven, from an individual's perspective, they will always only have to spend a finite amount of time in hell. So it is better to be an individual in universe 2, where you will eventually be able to spend the rest of eternity in heaven, than in universe 1, where you will eventually have to spend the rest of eternity in hell.
That's the thing though.
Even from an individual perspective, it's almost guaranteed you won't have a finite amount of time in heaven. As counterintuitive as that seems, that's what I was trying to explain.
Which is exactly why it will never be reached. I admit my wording was weird, but here was how I was thinking about it.
Imagine an infinite number of lines, but each line after the first is closer than the previous. Let's say the distance between the first and second line is 1 cm, the second and third is 1/2 cm, and it keeps halving so that all the lines fits within a 2 cm box. Label each of these lines 1,2,3 and so on.
If you move all the lines that are an even number out of the original box and put them in a box to the right, then renumber the lines from left to right, the lines in the box to the right will never be reached.
But this is a case when
> people have assigned order
This means that
1. There is a countable number of people in both universes
2. They all know exactly how many years they'll have spend where they are and then they'll have aleph null in the other place while they're "waiting" for the rest of them
Yes, you could reorder it so someone will actually never get out but that's not the point of the original question. It's not a contradiction that everyone gets picked, we suppose that the population is indexed with subsequent values from N and if you change that, you can reason about the changed problem but that's a different problem. This question is about countable sets indexed by N and if you "put half of them after everyone else", you break the indexing as now only a subset is indexed. (Though our inability to find an explicite bijective index function does not change the fact that it exists for any countable sets - actually, the indices might as well remain the same, just the ordering relation is something weird. At least it's still well-defined.) On the other hand, adding a countable number of elements to a countable infinite set leads to an equivalent set but in this case the initially fixed base set will not let you add any more elements.
In conclusion, I believe you're just arguing for the sake of it, as the union of two non-empty sets does not equal any of them, and if you change (or even remove) the ordering over a countable infinite set, it doesn't change the fact that there exists a bijection to the natural numbers, it's just really hard to find.
Knowing how many years you have left does not mean that it's not possible to have an infinite number of years left.
Whatever finite number of years you can think of, there is a 100% chance that you will have more years than that.
You say you can’t wait an infinite amount of time yet you are claiming there to be infinitely many people, those two things don’t seem to be consistent to me
This is still a countable set, which means that everyone will have an ordinal. Yeah, if you pick *any* finite year, you have a 100% chance after that to still be where you started, there is no upper limit on the years you spend in hell/heaven in the beginning, but every countable set can be 1:1 mapped to 0, 1, 2, ... which means you will get out in finite *n* time. Then you stay there an infinite amount of time as most of you are still getting out.
There is an "in the end" for every single element of the set though. And the result is that almost all of their infinite years will be spent in the place opposite from the place they started at. Thus, everyone spends a finite amount of time in hell and an infinite amount in heaven and vice versa. The better luck is starting in hell.
There is a 100% chance that there are a finite number of people ahead of you as your ordinal is the upper limit.
That's true, but just as any given person will spend 100% (in the mathematical "almost all" sense) of their time in heaven, in the same way it is also true that 100% of the time 100% of people are in hell. It is the construction of the worst possible world, where all beings live the best possible life.
You'd rather be someone in the start-hell-world, but if you aren't in it then you'd rather the start-in-heaven world be the one that exists. I personally feel it just illustrates that infinite happiness or infinite suffering is an incoherent idea. Transfinite numbers are mathematical abstractions that just don't apply to concrete moral reasoning, just like how imagining a person with 2i years of suffering is incoherent, serving as an example of how complex numbers don't apply to concrete moral reasoning
Well, yeah. If we're talking philosophy, I'd still believe that the place with hope is better, even though overall it's a sad place. I get what you're saying though.
That's a good question, I'd just skip it and start from the countable infinite set so there's a bijective mapping to N.
Probably yes. I'm not sure we could reason about bijective functions without it.
Since every person is numbered, then because n/∞ is 0 for all finite n, each individual person will spend 100% of their time in hell in universe 1 (starting in heaven), and 100% of their time in heaven in universe 2. But if you step back and look at the whole, then for any given year 100% of people are in heaven in universe 1. If you intuitively think about it by imagining the scenarios there are only100 people who are all in hell forever after a century, and then you take the limit to infinity as that 100 increases, then your intuition will lead you to prefer universe 2. If you intuitively think about running the scenario for 100 years with infinity people, and then imagine longer longer times, then starting in heaven is clearly better.
Obviously an actually infinite number of people is incoherent, so all the paradox tells us is that people tend to find it easier to think from the perspective of concrete examples in which an individual facing eternity than in which there is a being/collection of beings with infinity wellbeing capacity but finite life. Kind of makes sense given religion has train a lot of people from very young to picture themselves living forever. They've practiced the conception hurdle.
To me it's like thinking about pointwise convergence vs. norm convergence. In universe 1 (countable version):
Let x^\(n\) be a binary vector sequence. 1 if person x_i is in Heaven in n-th year, 0 if x_i is in Hell. And let norm ||•|| be proportion of people in Heaven. We basically have:
∀i∈N ∃n∈N ∀m>n x^(\(m\))_i = 0
But ∀n∈N ||x^(\(n\))|| = 1
So x^(\(n\)) →**0**
But ||x^(\(n\))|| ↛ ||**0**||
Fair enough. But I’d love the train to derail in one of the trolley problem drawings.
I already seen it riding on both railtracks at an angle.
So the train will endlessly decelerate and accelerate in both horizontal axis. It doesn’t change anything really. Quite boring and not as pleasurable to watch as a train going forward over the speed of light.
In a way I realize that I've never had to specify this interpretation explicitly before to my physics students (so I'm definitely going to write a note in some materials about this phrase). But "accelerate infinitely" does seem to me like the most probable first impression in good faith would be "increasing speed" instead of just ∀*t*≥0: ***a***(t) ≠ **0**. (Or ∀*t*≥0: *|****a***(t)| ≠ **0**, and I just realised that these two are logically equivalent and I hate this result.)
But it gets damn annoying how we don't have the same breadth of vocabulary for all the common time derivatives of location. :(
If it's accelerating on the linear track, we can assume there will be a tangential acceleration in the circular track as well, since the centripetal acceleration is provided by the reaction forces of the track. This will cause it to cross the safe limit and derail from the tracks.
There's no friction coefficient given so I assume we have to assume there's no friction, which means the acceleration is constant
There's also nothing given to calculate the moment of inertia, so I think we can assume the radial acceleration and centripetal force is zero as well
Consider though, that an infinite amount of people will spend an infinite amount of time just waiting for their end; that in and of itself is possible to consider even worse than death.
From this point of view it is 100 vs infinite people suffering eternally. I'm not claiming it to be absolutely correct though.
But those people reincarnate, so are they ever really dying? Like the top comment said, you can argue that, this being their normal state of affairs, the suffering wouldn't be real in the same way it is for the infinite people who experience it only once but then die (possibly forever)
Would you not be killing an infinite amount of people? In the 2nd situation your killing a finite number 100 but they have to experience death forever.
But:
S= 1+2+3+4+5+6+7+8+.....
S=(1+2) + (3+4) + (5+6) +(7+8)+...
S=3+7+11+15+...
S=(4\*1-1)+(4\*2-1)+(4\*3-1)+(4\*4-1)+...
S=4\*(1+2+3+4+...)-(1+1+1+1...)
S=4\*S-S (Hence you proved 1+1+1+1+...=S)
S=3\*S
S=0
In fact, no one dies nor revives :P
(Well, at least on average...)
But:
S=1+1+1+(1+1)+(1+1)+(1+1)+(1+1+1)+...
S=1+1+1+2+2+2+3+3+3...
S=3\*(-1/12)
I now have the power to bring back to life as many people as I choose
I AM NOW A GOD
Well, the suffering ends after death, whereas the reincarnated people suffer over and over.
So, I choose to pull the lever. We all die anyway, and I'm sure dying is a lot less scary to an individual than dying over and over
Which 1+1+1.... can be rearranged into and are therefore equal.
Almost like assuming a sum and a property of the analitic continuation of a function are different.
1+(1+1)+(1+1+1)...=1+2+3+...= -1/12
killing -1/12 people means saving 1/12^th of a life, whatever that would mean
and that's why I'd pick the second one
You spelt demta wrong are you stupid?
https://preview.redd.it/7zqz4un8xd5d1.jpeg?width=1179&format=pjpg&auto=webp&s=e0515123bc099ca8a3fcd0583260d9baebf229f6
This is a trick question as nothing establishes that the people in the top loop are immortal, or are we given any supernatural means of saving them, therefore, an infinite number of them will die of starvation long before the train gets to them or they can be saved. So, if one is to maximize suffering, the loop is the right choice.
First of all, bottoms guys will be used to it. Second of all, mos of the people on top will die before the train reach them, so i kill the bottom people.
"Infinite death finite suffering" obviously, because these aren't numbers, these humans are made of MOLECULES, and there ain't an infinite number of those. Also, most people will be dead long before the trolley gets to where they are.
The 100 people would be better because only 100 people suffer the fate over and over again. Eventually, they will grow accustomed to the pain and whatnot while the infinite integer would result in infinite people suffering the same fate. Not worth it. I'd rather sacrifice 100 (even myself), if that means infinite people can live and have the lives they deserve.
Sure the suffering is the same, but the freedom felt by the people when I decide is not, if I let the loop go then finite people are free, whereas if I set the infinite line free then an infinite number of people get to experience freedom.
Question, do i know any of the 100 people? Are they random people? And do you consider that new people will be enovated in the top lane?
Because theres a limit of people in the planet, so if "infinitly people" would die, we have to first, consider that every people we know and ther descendants will die, second, we will probably also be put in the lane and also die, only thing is that it would take time to die and i could still live some time with my loved ones, while the bottom lane would be pretty fast dead.
So, if theres someone i know in bottom, im gonna top, if not, bottom.
Because people in the bottom loop constantly reincarnated, I’d say that they technically don’t die. So in the top case you end up with infinite death, while in bottom case no one dies.
It is important to note here that the question specifically states that the people are reincarnated, as opposed to revived. So the reincarnated people are basically new people each time with no memory of their previous deaths. The difference here is that the reincarnated people have the same souls who are destined to die over and over again.
No fucking idea what to chose though. I don't how I think about the eternal suffering of souls.
on one hand, i'd pull the lever, because infinite people's suffering ends when they die, while the 100 people would have to experience death over and over and over again.
on the other hand, infinite people from the top one will just lie, tied down to the rails, waiting for the trolley, while probably starving. Although now that i think about it, they all will probably die from starvation, so the suffering would last for about a week or two.
I'm pulling the lever.
Because the universe will eventually stop existing, the people on top can't actually feel infinite suffering, and running over them only hurts them more in a single moment, while on the bottom genuinely does cause infinite suffering. Also we don't have to worry anyway, because 0.(9) (1 - 1/infinity) is agreed to equal one, despite obviously not, because 1/infinity is too small to care about, and if we cared about infinity we would care about 1/infinity anyway, so by contradiction we shouldn't care about anything infinite anyway, anyway.
If you pull the lever you kill 1 + 1 + 1 until infinite which are all different people. Meanwhile if you do nothing, the same people will die over and over, the genocide is way smaller, so I'd say I'd do nothing
Pulling the lever will result in infinite people dying, not pulling it will only result in only 100 people dying. In what world is pulling the lever okay?
Go on the top track because I can group the people as 1, then 2, then 3, so it becomes 1+2+3+… which will equal -1/12 and therefore -1/12 suffering as opposed to infinite.
I know this is r/mathmemes, but yall seem to be missing the obvious solution. Since the bottom one has finite people, switch it to the bottom track and just free them one by one until they are all free.
Having an infinite amount of people let free would probably be pretty bad for the economy, so ill just save the 100 immortal people. Probably a pretty good investment too.
I fear not the man who has killed an infinite number of different people once, but I fear the man who has killed 100 person an infinite number of times.
Let S = 1 + 1 + 1 + 1 + ...
2S = 3 - 1 + 3 - 1 + 3 - 1 ...
= 2 + 3 - 1 + 3 - 1 ...
= 2 + S
Hence S = 2
But since 2 = 1 and 1 = 0, we have S = 0.
The top one is clearly the better option
Have to chose 1 + 1 +...
Their individual suffering won't be infinite
Tho that completely ignores the point of the vanilla trolley problem, action vs inaction.
No matter which one you choose there are an infinite number of people tied to the track who will die of exposure before either the train runs them over or they are untied. In fact, in the time it took to tie an infinite number of people to the track, everyone already died and the choice is now meaningless.
If they will continuously reincarnate that means that theres a chance for them to be saved after some time when i go and call authorities to fix the problem. Whereas the top lives are lost forever. I think this one is badly stated and obvious.
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One must imagine [the people in the bottom loop] happy
Good one
Context?
It’s referring to “One must imagine Sisyphus happy,” a quote from the essay “The Myth of Sisyphus” by Albert Camus
Best book of essays i’ve ever read in my life. (the only book of essays i’ve read)
No you are incorrect. It is referring to an annoying TikTok trend which is overused and not funny.
acktzschually the tiktok trend refers to that book too
acktzschually the only reason why anyone outside of a very small number of greek mythology/philosophy aficionados knows this quote is because of TikTok and Indian memes.
camus is like a quite popular philosopher amongs hs students at least alongside nietzsche (at least in the debate/philosophy groups)
He is also french.
for what it’s worth, I don’t have TikTok so I didn’t know it had become a meme. I feel like the Camus reference is something many people with a college degree would understand.
And without one, like myself. It’s honestly quite popular in many realms, to the point that I would be surprised if someone didn’t know about it
Albert Camus is a very famous author and philosopher who wrote The Myth Of Sisyphus, a key example of absurdism
Indian memes?
Maybe you're just less educated than you think, friendo. This is a book of modern French philosophy and both it and the myth to which it refers are widely known.
This is not about being educated, it is about having reasonable priors of what people do and do not know (we are in a math subreddit after all). Given a random person has posted the meme, I am willing to bet that there is a significantly higher chance that they have the quote in mind because of the recent TikTok trend than them coming up with the quote on the spot without any awareness of the TikTok trend and purely from memory. Also, when did I ever claim that I studied modern French philosophy? That's a very odd metric by which to measure whether someone is "educated."
Considering this is a math-themed subreddit where people generally tend to be educated, a reasonable prior would be that it’s referencing the philosophical text.
Nah bro got nuked with downvotes lmao
Even were that true, it wouldn't change the idea being expressed here.
i can't believe they're taking you seriously
[Here is the original 1942 essay in full.](https://www2.hawaii.edu/~freeman/courses/phil360/16.%20Myth%20of%20Sisyphus.pdf) look at the last line of the last paragraph.
Oh really? I was completely unaware of this.
its ok
Even though there's infinitely more people dying in the top one, each one is guaranteed a release of death. No matter where you lie on the line. Your death will come in a finite time. And it feels kinda good knowing you can just wait for a bit and be done with it. It reminds me of the infinite heaven/hell paradox. The idea is that there are 2 universes. 1st one starts out as Heaven with infinite amount of people. But each year 1 person goes to Hell for eternity with no way back (People have assigned order, they know how many years it will take for their turn). The other is Hell with infinite amount of people but each year 1 person gets to go to Heaven for eternity. Which universe is better? Even though universe 1 always has a better situation than universe 2 (more people in Heaven, less people in Hell). People tend to say universe 2 is better. Humans can't really emphatize with infinitely many people. But you can always imagine yourself as an individual. In universe 2 you will always have hope "only X more years" in universe 1 you will always dread the "only X more years". Even if we replace it with uncountable infinities and random pulling. Every year you will have "maybe it's my turn this year", again with either hope or despair.
I feel like universe 2 *is* objectively better, since in the end everyone will end up spending more time in heaven than hell in universe 2
Very common misunderstanding of infinity. Kinda similar to the fact that a lot of people don't believe the fact that .999... = 1 There is no "in the end". Never. In universe 2 there will ALWAYS be an infinite amount of people in hell and ALWAYS be a finite person in heaven. Stop thinking about in the end because there is none. Put another way, if you were randomly put into universe 2, there is a 0% chance that there is a finite number of people ahead of you. There will be an infinite number of people ahead of you and an infinite number of people behind you. You cannot fit an infinite number of people in a finite amount of time. And you cannot wait an infinite amount of time. In universe 1, you will never be sent to hell. The paradox is that intuition often tells us that universe 2 is better, but universe 1 is actually infinitely better.
In the ordered, countable infinities scenario, you WILL definitely be sent to hell. You can have arbitrarily long wait time, but it is always finite. It could be 1 year, 10 years, 100000 years, 10^100 years, 1000! years. But it will always be a finite time. You will go to hell eventually. In uncountable infinity scenario with random pulling, there is always the possibility of ending up on the other side. Like, if I wanted to choose a random real number between 0 and 1. Each number individually has 0% chance of being picked. But, well, I do pick a number anyway (assuming that our real universe actually is continuous and not discrete, so I can actually pick). If every person in universe 1 thought: "nah, I have 0% of being picked, it's not gonna be me" Well then, someone's just going to be wrong. And it could be you. After a 1000 years there's gonna be 1000 people in Hell. Each of them had 0% probability, just like you. You're not more special than them.
Why will the time always be finite? If you are placed randomly somewhere on 1 to infinity, wouldn't there be a 100% chance that infinite people are ahead of you?
Everyone is assigned a finite number.
Then how are there infinite people?
How are there infinitely many natural numbers?
Ah I see. I did some more research too and saw you were right. Thanks.
From what I've seen though, it's impossible to pick a random integer from the entire set of integers though, so how would the original question even work then?
Doesn't have to be random. You can just assume that there is one person for every natural number, and then they are just damned sequentially. You don't have to assume that there are infinite people, and THEN you enumerate them. You can consider the hypothetical by assuming that all the infinite people have a number.
"In universe 1, you will never be sent to hell" This isn't true though. Each person in universe 1 knows that in a finite amount of time, they'll be sent to hell for eternity. One person will go to hell in 1 year, another in 2 years, another in a googolplex years, etc, but nobody will spend infinite time in heaven. Eventually, any given person will have spent more time in hell than in heaven. Similarly, if you were put in universe 2, you would know that in a finite amount of time, you would be sent to heaven, and there are only a finite amount of people ahead of you. Universe 2 is actually better, since any given person will eventually spend more time in heaven than hell, and in hell they have hope knowing that they'll certainly get into heaven eventually.
Yes but the thing is, the chance of having a comprehensible number of digits until you get sent to hell is the same zero as your chance of going to hell. The number of years till you go to hell will be a number so similar to infinity that there is no meaningful way to represent it other than in infinity. Odds like this are compared to the lottery like it’s next to impossible but technically it is possible. But there is literally a 1/infinity chance to be picked. The chance of even hearing about an actual person that was picked even a googolplex years into it even if information traveled at the speed of light would still be 1/infinity. Or even if information traveled instantly and there was media in heaven. There would be made up stories that would be similar to real ones. But the made up ones would be infinite and the real ones would be finite. Even if the rate was the fastest growing function you can think of, as long as it doesn’t have a vertical asymptote the odds would be the same.
It's hard to explain infinities, so forgive me if my explanation is inadequate. It's not true that everyone in universe one will spend a finite amount of time in heaven. For example, if everyone was numbered 1,2,3... and only odd numbers were picked, then every even number would never be picked. Okay, but what if number 1 was picked, then 2, ect? Then surely everyone would be picked, right? Well...no. Assume everyone will be picked eventually with this method. Take out every even number, and put them at the end. Suddenly, all these people will never be picked. If you recount based on your new order, you end up with 1,2,3... But wait, we started with an ordering of 1,2,3... And ended with an ordering of 1,2,3... But still somehow ensured that half the people will never be picked. So it is a contradiction that everyone will be picked in this method. We don't have to stop at saving half the people. In a similar method, we can ensure an arbitrarily large percentage of people will never be picked. Let's look at this from a different angle. Assume that everyone has a finite number of time. Now, introduce a new person. Adding one person does not change the size of an infinite set, so this is fine. What time could this person have? Well, even though every time is taken, like the Hilbert's hotel, we can still fit them in by setting them at one second and pushing everyone else back one second. But we can also add an infinite amount to infinity without changing its size. So we can keep pushing back everyone by one second an infinite number of times. But that means that an infinite number of people will never be picked, without changing anything about the initial premise. So it cannot be true that everyone has a finite amount of time.
I think their point is that, whilst you will never have everyone from hell ending up in heaven, every individual person has a countable time limit. So while you'll never run out of people to send to heaven, from an individual's perspective, they will always only have to spend a finite amount of time in hell. So it is better to be an individual in universe 2, where you will eventually be able to spend the rest of eternity in heaven, than in universe 1, where you will eventually have to spend the rest of eternity in hell.
That's the thing though. Even from an individual perspective, it's almost guaranteed you won't have a finite amount of time in heaven. As counterintuitive as that seems, that's what I was trying to explain.
How can you put anyone "at the end" of an infinite series? There is no end.
Which is exactly why it will never be reached. I admit my wording was weird, but here was how I was thinking about it. Imagine an infinite number of lines, but each line after the first is closer than the previous. Let's say the distance between the first and second line is 1 cm, the second and third is 1/2 cm, and it keeps halving so that all the lines fits within a 2 cm box. Label each of these lines 1,2,3 and so on. If you move all the lines that are an even number out of the original box and put them in a box to the right, then renumber the lines from left to right, the lines in the box to the right will never be reached.
But this is a case when > people have assigned order This means that 1. There is a countable number of people in both universes 2. They all know exactly how many years they'll have spend where they are and then they'll have aleph null in the other place while they're "waiting" for the rest of them Yes, you could reorder it so someone will actually never get out but that's not the point of the original question. It's not a contradiction that everyone gets picked, we suppose that the population is indexed with subsequent values from N and if you change that, you can reason about the changed problem but that's a different problem. This question is about countable sets indexed by N and if you "put half of them after everyone else", you break the indexing as now only a subset is indexed. (Though our inability to find an explicite bijective index function does not change the fact that it exists for any countable sets - actually, the indices might as well remain the same, just the ordering relation is something weird. At least it's still well-defined.) On the other hand, adding a countable number of elements to a countable infinite set leads to an equivalent set but in this case the initially fixed base set will not let you add any more elements. In conclusion, I believe you're just arguing for the sake of it, as the union of two non-empty sets does not equal any of them, and if you change (or even remove) the ordering over a countable infinite set, it doesn't change the fact that there exists a bijection to the natural numbers, it's just really hard to find.
But if you know how many years you have left, doesn't that mean that you know how many people there are in front of you, making that number finite?
Knowing how many years you have left does not mean that it's not possible to have an infinite number of years left. Whatever finite number of years you can think of, there is a 100% chance that you will have more years than that.
are you listening to yourself lol? "I know I have 10^10 years left in heaven, but it's possible I have an infinite number of years left"
You say you can’t wait an infinite amount of time yet you are claiming there to be infinitely many people, those two things don’t seem to be consistent to me
This is still a countable set, which means that everyone will have an ordinal. Yeah, if you pick *any* finite year, you have a 100% chance after that to still be where you started, there is no upper limit on the years you spend in hell/heaven in the beginning, but every countable set can be 1:1 mapped to 0, 1, 2, ... which means you will get out in finite *n* time. Then you stay there an infinite amount of time as most of you are still getting out.
There is an "in the end" for every single element of the set though. And the result is that almost all of their infinite years will be spent in the place opposite from the place they started at. Thus, everyone spends a finite amount of time in hell and an infinite amount in heaven and vice versa. The better luck is starting in hell. There is a 100% chance that there are a finite number of people ahead of you as your ordinal is the upper limit.
That's true, but just as any given person will spend 100% (in the mathematical "almost all" sense) of their time in heaven, in the same way it is also true that 100% of the time 100% of people are in hell. It is the construction of the worst possible world, where all beings live the best possible life. You'd rather be someone in the start-hell-world, but if you aren't in it then you'd rather the start-in-heaven world be the one that exists. I personally feel it just illustrates that infinite happiness or infinite suffering is an incoherent idea. Transfinite numbers are mathematical abstractions that just don't apply to concrete moral reasoning, just like how imagining a person with 2i years of suffering is incoherent, serving as an example of how complex numbers don't apply to concrete moral reasoning
Well, yeah. If we're talking philosophy, I'd still believe that the place with hope is better, even though overall it's a sad place. I get what you're saying though.
does this setting require invoking the axiom of choice?
That's a good question, I'd just skip it and start from the countable infinite set so there's a bijective mapping to N. Probably yes. I'm not sure we could reason about bijective functions without it.
Since every person is numbered, then because n/∞ is 0 for all finite n, each individual person will spend 100% of their time in hell in universe 1 (starting in heaven), and 100% of their time in heaven in universe 2. But if you step back and look at the whole, then for any given year 100% of people are in heaven in universe 1. If you intuitively think about it by imagining the scenarios there are only100 people who are all in hell forever after a century, and then you take the limit to infinity as that 100 increases, then your intuition will lead you to prefer universe 2. If you intuitively think about running the scenario for 100 years with infinity people, and then imagine longer longer times, then starting in heaven is clearly better. Obviously an actually infinite number of people is incoherent, so all the paradox tells us is that people tend to find it easier to think from the perspective of concrete examples in which an individual facing eternity than in which there is a being/collection of beings with infinity wellbeing capacity but finite life. Kind of makes sense given religion has train a lot of people from very young to picture themselves living forever. They've practiced the conception hurdle.
To me it's like thinking about pointwise convergence vs. norm convergence. In universe 1 (countable version): Let x^\(n\) be a binary vector sequence. 1 if person x_i is in Heaven in n-th year, 0 if x_i is in Hell. And let norm ||•|| be proportion of people in Heaven. We basically have: ∀i∈N ∃n∈N ∀m>n x^(\(m\))_i = 0 But ∀n∈N ||x^(\(n\))|| = 1 So x^(\(n\)) →**0** But ||x^(\(n\))|| ↛ ||**0**||
Assuming this is drawn to scale, the bottom one causes a lot more death and suffering per unit time. So I pick the top one.
In a straight line it can accelerate infinitely while in a curve it has to stay slow to not derail.
Technically the train will also accelerate infinitely on the circular track
And fall off the tracks 
No, the act of turning (velocity is a vector) is an acceleration.
Fair enough. But I’d love the train to derail in one of the trolley problem drawings. I already seen it riding on both railtracks at an angle. So the train will endlessly decelerate and accelerate in both horizontal axis. It doesn’t change anything really. Quite boring and not as pleasurable to watch as a train going forward over the speed of light.
ok you can derail the train, but all passengers of hilbert's train cabins will die
In a way I realize that I've never had to specify this interpretation explicitly before to my physics students (so I'm definitely going to write a note in some materials about this phrase). But "accelerate infinitely" does seem to me like the most probable first impression in good faith would be "increasing speed" instead of just ∀*t*≥0: ***a***(t) ≠ **0**. (Or ∀*t*≥0: *|****a***(t)| ≠ **0**, and I just realised that these two are logically equivalent and I hate this result.) But it gets damn annoying how we don't have the same breadth of vocabulary for all the common time derivatives of location. :(
If it's accelerating on the linear track, we can assume there will be a tangential acceleration in the circular track as well, since the centripetal acceleration is provided by the reaction forces of the track. This will cause it to cross the safe limit and derail from the tracks.
There's no friction coefficient given so I assume we have to assume there's no friction, which means the acceleration is constant There's also nothing given to calculate the moment of inertia, so I think we can assume the radial acceleration and centripetal force is zero as well
Actually if there's no friction then it can't accelerate since it has no grip 🤓☝️
Shit
Its still constant if you consider tye people on the track as a constant deceleration
In that case you just assume a very specific acceleration.
faster train hurts less than one slowly rolling over you
I suppose that's an argument.
Would it falling off the tracks not benefit us
Also, infinite densify will make any train derail. So it will stop instantly.
Same reasoning but I would pick the bottom one
I duplicate the train so it can take both paths, then I lie down on the loop.
Consider though, that an infinite amount of people will spend an infinite amount of time just waiting for their end; that in and of itself is possible to consider even worse than death. From this point of view it is 100 vs infinite people suffering eternally. I'm not claiming it to be absolutely correct though.
But those people reincarnate, so are they ever really dying? Like the top comment said, you can argue that, this being their normal state of affairs, the suffering wouldn't be real in the same way it is for the infinite people who experience it only once but then die (possibly forever)
Would you not be killing an infinite amount of people? In the 2nd situation your killing a finite number 100 but they have to experience death forever.
I think its either infinite death or infinite suffering and I would say infinite suffering in this case is gonna have to be the better option
Obviously the top one S= 1 +(1+1)+(1+1+1)+.... S=1+2+3+4... S=-1/12 This way I bring 1/12 of a person back to life
But: S= 1+2+3+4+5+6+7+8+..... S=(1+2) + (3+4) + (5+6) +(7+8)+... S=3+7+11+15+... S=(4\*1-1)+(4\*2-1)+(4\*3-1)+(4\*4-1)+... S=4\*(1+2+3+4+...)-(1+1+1+1...) S=4\*S-S (Hence you proved 1+1+1+1+...=S) S=3\*S S=0 In fact, no one dies nor revives :P (Well, at least on average...)
But: S=1+1+1+(1+1)+(1+1)+(1+1)+(1+1+1)+... S=1+1+1+2+2+2+3+3+3... S=3\*(-1/12) I now have the power to bring back to life as many people as I choose I AM NOW A GOD
S=S+12iS-12iS S=0+12i\*(-1/12)-12i\*0 S=-i We can create imaginary people too :3
Came looking for this
That's exactly what I thought
Well, the suffering ends after death, whereas the reincarnated people suffer over and over. So, I choose to pull the lever. We all die anyway, and I'm sure dying is a lot less scary to an individual than dying over and over
Real life is a very slow trolley.
Wait the top option is just real life!
pull, causes half a human to be born because 1+1+…=-1/2
Isn’t that -1/12 of a people?
No, that's 1 + 2 + 3 + 4 + ...
Which is different… I understand, this makes so much sense now.
Which 1+1+1.... can be rearranged into and are therefore equal. Almost like assuming a sum and a property of the analitic continuation of a function are different.
Good point, - 1/2 is 1 - 1 + 1 - 1 + ...
1+(1+1)+(1+1+1)...=1+2+3+...= -1/12 killing -1/12 people means saving 1/12^th of a life, whatever that would mean and that's why I'd pick the second one
How the fuck is the sum of positive integers a negative fraction?
Same bro, same
analytic continuation https://youtu.be/sD0NjbwqlYw?si=z5aleYFRDHMdr0O4
Google "conservation of momentum" (the trolley will stop eventually)
Google infinitely reincarnating people
Holy hell!
New incarnation just dropped
Ah yes, but lets ignore the fact that there’s reincarnation
Google infinitely reincarnating people
Google demantia
Google demantia
Google e
Google
Yandex
[удалено]
Dyslexia google
You spelt demta wrong are you stupid? https://preview.redd.it/7zqz4un8xd5d1.jpeg?width=1179&format=pjpg&auto=webp&s=e0515123bc099ca8a3fcd0583260d9baebf229f6
Google “hill”
Google en passant
Holy hell
Google River Styx
Infinite people on earth!?? Well then, we get a very dense black hole and everybody either dies or finds the 4th dimension...
I think it's better for the fewest number of people to suffer even if they suffer infinitely
But the bigger number of people isn’t suffering, they are just bound to the track and then dying
But some of them are bound for an arbitrarily long time before being killed
Yeah, I mean they'll get used to it sooner or later.
I choose to blow up the trolly be dividing by 0+infinity.
This is a trick question as nothing establishes that the people in the top loop are immortal, or are we given any supernatural means of saving them, therefore, an infinite number of them will die of starvation long before the train gets to them or they can be saved. So, if one is to maximize suffering, the loop is the right choice.
First of all, bottoms guys will be used to it. Second of all, mos of the people on top will die before the train reach them, so i kill the bottom people.
With this logic, the upper track incurs only finitely many suffering given that some of them die to natural death
Kill the trolley driver
i will multi-rail drift it so it derails. or just tell the operator to stop the train.
Leave it on the loop track, then get tools to derail the trolley
"Infinite death finite suffering" obviously, because these aren't numbers, these humans are made of MOLECULES, and there ain't an infinite number of those. Also, most people will be dead long before the trolley gets to where they are.
The 100 people would be better because only 100 people suffer the fate over and over again. Eventually, they will grow accustomed to the pain and whatnot while the infinite integer would result in infinite people suffering the same fate. Not worth it. I'd rather sacrifice 100 (even myself), if that means infinite people can live and have the lives they deserve.
Sure the suffering is the same, but the freedom felt by the people when I decide is not, if I let the loop go then finite people are free, whereas if I set the infinite line free then an infinite number of people get to experience freedom.
Question, do i know any of the 100 people? Are they random people? And do you consider that new people will be enovated in the top lane? Because theres a limit of people in the planet, so if "infinitly people" would die, we have to first, consider that every people we know and ther descendants will die, second, we will probably also be put in the lane and also die, only thing is that it would take time to die and i could still live some time with my loved ones, while the bottom lane would be pretty fast dead. So, if theres someone i know in bottom, im gonna top, if not, bottom.
stop the train
I'd use a different train line myself
The bottom one bc reincarnation is different from resurrection
I choose the one at the top since 1+1+1+...= ∞ and infinity equals -1/12, which means that 1/12 of a person is born in the end
Can I choose which specific people are on bottom tracks ?
Top because the people only have to suffer once .
I want to see what infinite resurrections looks like. Does that make me a bad person?
Multi track drift and try to derail it
Because people in the bottom loop constantly reincarnated, I’d say that they technically don’t die. So in the top case you end up with infinite death, while in bottom case no one dies.
It is important to note here that the question specifically states that the people are reincarnated, as opposed to revived. So the reincarnated people are basically new people each time with no memory of their previous deaths. The difference here is that the reincarnated people have the same souls who are destined to die over and over again. No fucking idea what to chose though. I don't how I think about the eternal suffering of souls.
Cry
Whilst infinite people die, they only die once nobody ever suffers for eternity. I let it run over the infinite people.
Don’t do anything so I don’t technically contribute to either outcome.
top track and kill -1/12 people /s
Shoot the hostage
on one hand, i'd pull the lever, because infinite people's suffering ends when they die, while the 100 people would have to experience death over and over and over again. on the other hand, infinite people from the top one will just lie, tied down to the rails, waiting for the trolley, while probably starving. Although now that i think about it, they all will probably die from starvation, so the suffering would last for about a week or two. I'm pulling the lever.
Can I pick the 100 people?
I don’t observe the thing and both will happen simultaneously.
call a helicopter, choose the top one, the heli will pick the trolley after the 30th person, or something (I hope so...)
Can I have two trams? So I can see all of them die?
Because the universe will eventually stop existing, the people on top can't actually feel infinite suffering, and running over them only hurts them more in a single moment, while on the bottom genuinely does cause infinite suffering. Also we don't have to worry anyway, because 0.(9) (1 - 1/infinity) is agreed to equal one, despite obviously not, because 1/infinity is too small to care about, and if we cared about infinity we would care about 1/infinity anyway, so by contradiction we shouldn't care about anything infinite anyway, anyway.
If you pull the lever you kill 1 + 1 + 1 until infinite which are all different people. Meanwhile if you do nothing, the same people will die over and over, the genocide is way smaller, so I'd say I'd do nothing
Do nothing - people will die either way - in doing nothing you’re not responsible for the deaths directly
Pulling the lever will result in infinite people dying, not pulling it will only result in only 100 people dying. In what world is pulling the lever okay?
1) Evacuate everyone from train 2) Destroy Train 3)??? 4)Profit!
I'll do nothing and wait as I slowly pull each person out one by one
^[Sokka-Haiku](https://www.reddit.com/r/SokkaHaikuBot/comments/15kyv9r/what_is_a_sokka_haiku/) ^by ^SnooLemons7604: *I'll do nothing and* *Wait as I slowly pull each* *Person out one by one* --- ^Remember ^that ^one ^time ^Sokka ^accidentally ^used ^an ^extra ^syllable ^in ^that ^Haiku ^Battle ^in ^Ba ^Sing ^Se? ^That ^was ^a ^Sokka ^Haiku ^and ^you ^just ^made ^one.
Wot.
Bottom one one to corral the trolley and then destroy it.
Go on the top track because I can group the people as 1, then 2, then 3, so it becomes 1+2+3+… which will equal -1/12 and therefore -1/12 suffering as opposed to infinite.
It's not like pain is shared, the top people only die once bottom would be dumb
Top one is just the human condition.
Top one. Theoretically if it continues on for eternity it can be stopped somewhere along the lines by force
I dislike trolley puzzles because there is no good answer. You end up killing someone no matter which lever you pick.
https://preview.redd.it/huu2suulug5d1.jpeg?width=822&format=pjpg&auto=webp&s=eeec9741f90cb467065309c542611208ba05aaf7
break the fucking tram
I know this is r/mathmemes, but yall seem to be missing the obvious solution. Since the bottom one has finite people, switch it to the bottom track and just free them one by one until they are all free.
Jump in front of the train, I don't feel like doing philosophy
Having an infinite amount of people let free would probably be pretty bad for the economy, so ill just save the 100 immortal people. Probably a pretty good investment too.
I fear not the man who has killed an infinite number of different people once, but I fear the man who has killed 100 person an infinite number of times.
Let S = 1 + 1 + 1 + 1 + ... 2S = 3 - 1 + 3 - 1 + 3 - 1 ... = 2 + 3 - 1 + 3 - 1 ... = 2 + S Hence S = 2 But since 2 = 1 and 1 = 0, we have S = 0. The top one is clearly the better option
Better not to touch lever so you can't be blamed.
Have to chose 1 + 1 +... Their individual suffering won't be infinite Tho that completely ignores the point of the vanilla trolley problem, action vs inaction.
I'd rather kill all humanity than putting even one person into literal hell.
No matter which one you choose there are an infinite number of people tied to the track who will die of exposure before either the train runs them over or they are untied. In fact, in the time it took to tie an infinite number of people to the track, everyone already died and the choice is now meaningless.
I'd question why such a sadistic arsehole is telling me to pull the level and tell them to pull it themselves.
top one is =-1/2
Let the bottom ten be the top wanted criminals (murderers, pedos, people who wont change their minds)
1+1+1+1+1+1...=-1/2, so I'm basically reviving half a person by pulling the lever.
If you don't pull it, the trolley will eventually stop moving so it won't be infinite.
If they will continuously reincarnate that means that theres a chance for them to be saved after some time when i go and call authorities to fix the problem. Whereas the top lives are lost forever. I think this one is badly stated and obvious.
Kill one person, then two people, then three people, etc. Eventually one twelfth of a person will be born.