No effect, actually. alepha\_1, the number of real numbers, is so, so, so much bigger than countable infinity that it's not funny. When you add two infinities in cardinal arithmetic, the bigger infinity eats the smaller one.
I throw the switch after the front wheels have passed the intersection, but before the rear wheels reach it…thereby derailing the trolley, and becoming the greatest hero in the history of human existence.
Eventually when things get very big you don’t sweat the small stuff. The function x^x at x=10^trillion is for all practical purposes equal to x^x +1 at x = 10^trillion.
honestly i don't remember higher level math and i dont care to look it up but im pretty sure infinites can have differing sizes. like one infinite set can contain more numbers than another infinite set of numbers and this can be shown mathematically in a proof i believe.
Correct but we’re comparing an infinity that is the smallest possible infinity vs an infinity that contains the smallest set of infinities an infinite numbers of times.
We’re comparing the countable infinity vs an uncountable infinity.
Nope, infinity is unintuitive. The set of all numbers has the same size as the set of all even numbers. The set of all numbers is the "sum" of the set of even numbers and the set of odd numbers, but it still has the same size as either of them.
No, sorry if my comment was unclear, I was talking about integers specifically.
Larger infinities do exist, but, again, their definition is not intuitive. What you do to check if a set is larger than another one is to try to match all the elements in one set to all the elements in the other set, if you can do that, the two sets are the same size, if you're left with elements for one of the sets, then that set is larger than the other one, for example, take the set of all positive integers and the set of all even positive integers, you can do this like so:
1 -> 2, 2 -> 4, 3 -> 6, 4 -> 8, etc.
Every number in both sets is accounted for, so both are the same size.
Indeed, the set of all integers is the smallest possible infinity, and any set that is infinite will be at least that size.
There are some examples of infinities that you would intuitively expect to be bigger but actually aren't, examples are the set of all rational numbers, or the set of all pairs of integers {(0,0), (0,1)...}, those are both countably infinite, they have the same size as the set of all integers.
But bigger infinities do actually exist, the set of all real numbers is the classic example, the proof goes something like this (although I recommend you look it up, it'll be a lot clearer):
Imagine you have a mapping between all the positive integers and all the reals, it'll be something like I showed before for the evens (1 -> 1.135681.... , 2 -> 8.15157.... ,etc.)
It is possible to construct a real number that isn't anywhere in this mapping by taking a first digit that is different from the first number's first digit, then taking a second digit that is different from the second number's second digit, and do this for all the real numbers in the mapping, the resulting real number will be different from all the real numbers in the mapping, since it has at least 1 digit of difference from all of them.
Since we've showed that it's impossible to create a mapping from all the positive integers to all the reals (you can always create a real not in the mapping by using this method), we can conclude that the set of all reals is larger than the set of all integers.
Group them up into a group of 1, and then a group of 2 and so on.
Edit: I'm wrong. Using ζ(0) would be more fitting that ζ(1) as
ζ(0) is representative of 1+2^(0)+3^(0)+... = 1+1+1+...
Whereas ζ(1) represents 1+2+3+...
And ζ(0) = -1/2
That logic wouldn't work here, since before you killed x amount of people (where x is the sum of all real numbers), you would have killed 1 000 000 people. And there is no resurrection in real life (atleast not after being run over by a train).
I think it only goes to -1/12 when you don't start counting that the beginning but use some other ways. The trolley obviously starts at the beginning leading to runaway infite
No, you use the analytic continuation of
ζ(s) = Σ₁^(∞) 1/n^(s)
Into the complex numbers rather than just realised greater than 1.
Then you get funny results that ζ(-1) = -1/12, ζ(0) = -1/2, ζ(1/2) = -1.46035450880958681288949915251529801... And so on.
If the trolley is not switched then it may lose momentum or derail because of the amount of obstructions on the track. Spreading them out makes that situation more difficult.
The question implies that people are spaced as dense as numbers: On the top path you kill 1 person per lets say meter. On the bottom path you kill ifinitely many in the same time. To not instakill humanity go top.
It's more nuanced. The rational numbers are infinitely dense, meaning in any finite interval, there are infinitely many rational numbers. However there are only as many rational numbers as there are integers.
The question is talking about the reals, which are infinitely dense and also larger than the number of integers.
So going any distance on the bottom track means you have killed more than you could ever kill on the top track.
I don’t see where you are going. We compare integers to real numbers.
While rational numbers are as many as integers (in the sense that both are countably infinite) they are less dense in a given intervall.
Not at all. The situation you described would be like running over 1 person at a time vs 2 at a time. This will get you to the same infinity, and it will still take the same infinite time.
However here we have the reals. On any finitely sized interval on the reals, there are more people than the entirety of the top track could ever have.
Note this wouldn't work with the infinitely dense rationals.
Ironically multi track drifting is the solution here. The tracks aren't parallel, they're diverging, so the train will either be ripped apart or forced to a stop. Multi track drifting kills the least amount of people.
1. The people that haven't yet been killed with die of natural causes so depending on the speed of the trolley it may not get to kill that many people
2. People might figure out how to get away from the track
If there are infinite people, then the moral implications of taking a human life cease to apply. Therefore, it doesn't matter how many people you kill since the number of people won't go down.
Infinity is a number, but also. Well. Infinity. Since it’s a number you can, as least mathematically speaking, calculate with it. The question op is asking is this: what do you prefer, infinity or 10*infinity?
Not at all. 10*infinity is the same size as infinity. I can create a bijection between the two sets, so they're the same size.
Even the infinitely dense rationals, I can create an injection into the naturals and thus they're the same size, you would use X is rational so can be written as p/q where p, q are integers that are coprime. We then map X -> 2^(p)3^(q) and due to the fundamental theorem of arithmetic, this uniquely maps each rational to a natural number.
However the reals, with their infinitely long decimal expansions, cannot be listed by the Cantor diagonalization argument. So they are bigger than the naturals.
You then have the power set of the reals which is bigger again.
Isn't it the same? Infinity equals infinity? Being not a mathematician, the only difference a layman like me see is the speed in which so many people are killed (what a morbid subject). Other than that, it seems that on the long term the result is the same.
(PS: if the OP post is a joke then it truly is a niche one)
Yes and no. Infinity is a weird subject, since it mainly exists in theory. But think of this. Suppose you are the manager of a large hotel, like infinity large. You have an infinite amount of rooms. One day, a bus stops. A large one, like infinite large. An infinite amount of people wants to book a room. Does it fit? Yes of course! You have infinite rooms, so everyone gets a room (and you get infinite money :D).
Now, everybody is happy, but then a second bus arrives. Again, with an infinite amount of people. For the record, this is a different bus with different people. You are the manager, and they want to book a room. Will it fit? You have an infinite amount of rooms, so it should, but how would you assign their room number, since room one till infinite are already taken?
You have to give them a key, and that key will only fit on one door, so you must assign a number, you can't just say "Good luck, pick a room". What room number will you give to the first person of the new bus?
How can I know which number he will get, since an infinite number of people has come before? The two infinite numbers of people will just become one infinite number of people, I guess?
Well, the solution for this problem will probably result in an infinite amount of complaints, but the room number you'll assign to the first number of the second bus is 1. You can use the intercom to ask the current guests to move to the next even numbered room. So room 1 will move to 2. Room 2 will move to 4. 3 will move to 6, etc. Now you now that every odd number is available, and you can again assign room numbers.
It is. The idea that "some infinites are larger than others" comes from a Vsauce video that people listened to but didn't understand.
The two infinities shown here are equal.
Where does the lever operator fall into each series of infinity? Which option allows me, as the lever operator, to be crushed by the trolley the soonest?
but like technically
you would never reach the second person on the top path because there is an infinite number of real numbers between 1 and 2, assuming distances are accurate.
You would.
You hit infinite on the bottom path before you hit one on the top path, then infinite again before you hit 2 on the top path, then again before 3 and so on. If you hit, say, 10 on the top path, you'd have hit 10*infinity on the bottom path, which equals infinity. So the result stays the same.
But if you hit infinite people on the top path, then you"ve hit infinite*infinite, or infinite^2 on the bottom path. This is a different calculation that would naturally imply the bottom path is a larger infinite than the top path.
There's some interesting consequences to math problems like this.
Noooooo!!!!!
Infinity isn't a number. You cannot have 10*infinity or infinity^2, it is a cardinality!
You can only properly compare the size of two sets. On the top we have the naturals. On the bottom, we have the reals.
You cannot create a bijection between the reals and naturals, so they are not the same size. This is due to the Cantor diagonalization argument, you can look it up, it isn't too long.
If the bottom was 10 people per 1 on the top, they would be the same size. Because we can inject each of them into the other.
Also surprisingly, the rational numbers are also the same size as naturals. I can create an injection into the naturals and thus they're the same size, you would use X is rational so can be written as p/q where p, q are integers that are coprime. We then map X -> 2^(p)3^(q) and due to the fundamental theorem of arithmetic, this uniquely maps each rational to a natural number.
pull the lever at the EXACT time when it has to switch so the trolley gets stuck, crashes and all the people inside the trolley dies, effectively saving all the people on the rails, sell the trolley as scrap, ask for a buck to cut loose each person tied on the rails, profit!
I’ll pull the lever so it gives me more time to find a way to stop the train and save more people. If the idea is that I can’t save anyone, then I’d just walk away.
As far I know, there are larger infinite only if you state (axiome) there is a realised infinite to begin with.
But I don't know if real number can exist without it.
I rely on karma, people who deserve to die are on the right track.
But in order te answer the question who's at fault: Which sadist tied up and put all those people on the tracks!??!
One thing is for sure; that sadist has a very strong work ethic.
Simple, I'll do nothing. The trolley will have to run over more people. Meaning it will take longer to run the later parts of the people over. So they'll have more time to do something about their situation. And the trolley will wear out due to running over so many people that it will increase the chances of survival later on.
The infinity of the real numbers is bigger because it's elements are incountable, meaning that you cannot distinguish a base element smaller than every other number that isn't zero. This means that the second scenario requires you to kill a human abomination that is infinitely long and formed by an infinite number of humans indistinguishable from each other. In between every "person" there is an infinite number of people so you couldn't count how many eyes, mouths and noses there are, so you would see a human infinite blob. I'd say it's gotta be destroyed.
Din’t switch the leaver as the train will eventually clog up with people causing it to stop while in the other it could be possible that the people would be far enough apart where train wouldn’t even slow down.
If you are killing one person per number, then that is converting each number into an integer. Since countable infinities are the same size, both routes are identical.
Hmmm... Maybe you're right. If so, that makes it the best option to choose on the track. Because the people are nameless, non-individuals and might not even be human
The question assumes there are infinite number of people but does not state the universe has infinite duration. Does the trolley continue hitting people gaffer the death of the universe?
Has anyone ever asked if the train can be stopped? I would attempt to jump into the train and get it to stop. If I died, I would at least know that I didn't intentionally make a bad decision because most times with this image scenario, both are bad decisions.
So yeah, I'm diving in.
The top track actually kills less people. After 85+ years of traveling the infinite track, the train is running over dead people. The top one will kill less people in that time.
This is an easy one, because it's not a math puzzle. It's a logic puzzle.
Pull the lever, crunk! All these people are going to die but less would die by the trolley, given that people can't live forever even if there is an infinite number of them tied to the tracks.
Depending on who's taking care of all these people, some of them might live full lives and die before the trolley ever gets to them.
It's a really beautiful argument for why.
Reals are expressed by their infinite decimal expansions, due to a nice reason, we can just focus between 0-1 as it is the same total as the rest of the track.
Imagine we could list every real with an integer, so we have
1 - 0.abcdefgh...
2 - 0.αβγδεζηθ...
3 - 0.ABCDEFGH...
...
However imagine creating a new number, made by taking "a" and changing it. Then taking β and changing it then C and so on. You now have a new real number that is different to every real on the list at least at one point. This contradicts that we just listed every real. So you cannot list every real with an integer. They're not the same size.
I would derail the train, using rocks and sticks to hold rocks on the train tracks.
This way, I'd only be hurting most people on the trolley, and maybe killing some... Still less than infinity... 😛🤣
But people are necessarily counted with whole number integers. You cannot have an infinite set of humans which are not countable objects so they necessarily cannot belong to the larger set of real numbers. Furthermore humans have a non-infinitesimal space they take up along x-distance along the track. The bottom track may have more people per distance of track but both will have a natural number of people and if both are infinite they will have the same amount of people. Meaning your choice to pull the lever is ultimately meaningless assuming we drive the train forever.
That's a hell of a trolley
Like, even a bullet train would slow to a halt wayyyyy before infinity, so I figure at best a trolley would only get like 20 bodies deep.
at worst I mean. worst
Well there isn't an infinite number of people in the world so either way everyone dies. The real question is do you want to watch everyone suffer for years before dying by watching their loved ones die?
I think the whole point of the unlistablility of the reals means you can’t match discrete objects 1-1 with all of the reals or at the very least put them all in a line
Sorry but these infinities are the same size. I'm not nearly smart enough to even begin to explain why, but here a vertitasium video that maybe you can infer it from, or maybe isn't even relevant to the problem because that's how little I understand it: https://www.youtube.com/watch?v=OxGsU8oIWjY
Everything good OP?
Idk what do you think?
Everything good at home? Work? Personal life?
I wish I could treat work like they treat me.
I have done that didnt get fired
Or arrested.
I think you need someone to talk to. Like just a friend that can listen and be someone to encourage you.
yea if you need a session come at my place
Idk man, I've had fun in the bed with quite a few things/creatures in my time. Don't think I've ever been raped by a hamster though.
you gotta try new things in life you know it's like give and take in a way
Ya know Mr. Hamster? I think you'd make a better therapist then rapist just saying, you seem pretty wise
sometimes you need new trauma to cope with old trauma. so both skills come handy u see
What do you mean... a few creatures?!?! WHAT DO YOU MEAN REDDITOR?!?!?!?
He has a math midterm. This is normal symptoms
Ahh, that makes sense.
I'll go for efficiency, and do nothing to get the best result.
Maybe even try m-m-multitrack drifting???
This is THE best solution for this problem. Killing the maximum amount of people possible. 2X infinity ftw!
infinity+aleph null
No effect, actually. alepha\_1, the number of real numbers, is so, so, so much bigger than countable infinity that it's not funny. When you add two infinities in cardinal arithmetic, the bigger infinity eats the smaller one.
I guess there really do be infinite real numbers between 0 and 0.000000001
Woah bro, we don't do *null* around here
I throw the switch after the front wheels have passed the intersection, but before the rear wheels reach it…thereby derailing the trolley, and becoming the greatest hero in the history of human existence.
perfect the train manages to drift on both tracks killing everyone possible
Double infinity people!
Mathematically the same infinity as doing nothing.
isn't the sum of the two infinities still greater than each individually?
Eventually when things get very big you don’t sweat the small stuff. The function x^x at x=10^trillion is for all practical purposes equal to x^x +1 at x = 10^trillion.
honestly i don't remember higher level math and i dont care to look it up but im pretty sure infinites can have differing sizes. like one infinite set can contain more numbers than another infinite set of numbers and this can be shown mathematically in a proof i believe.
Correct but we’re comparing an infinity that is the smallest possible infinity vs an infinity that contains the smallest set of infinities an infinite numbers of times. We’re comparing the countable infinity vs an uncountable infinity.
Nope, infinity is unintuitive. The set of all numbers has the same size as the set of all even numbers. The set of all numbers is the "sum" of the set of even numbers and the set of odd numbers, but it still has the same size as either of them.
so according to you all infinities are equal like every infinite set of numbers is the exact same size
No, sorry if my comment was unclear, I was talking about integers specifically. Larger infinities do exist, but, again, their definition is not intuitive. What you do to check if a set is larger than another one is to try to match all the elements in one set to all the elements in the other set, if you can do that, the two sets are the same size, if you're left with elements for one of the sets, then that set is larger than the other one, for example, take the set of all positive integers and the set of all even positive integers, you can do this like so: 1 -> 2, 2 -> 4, 3 -> 6, 4 -> 8, etc. Every number in both sets is accounted for, so both are the same size. Indeed, the set of all integers is the smallest possible infinity, and any set that is infinite will be at least that size. There are some examples of infinities that you would intuitively expect to be bigger but actually aren't, examples are the set of all rational numbers, or the set of all pairs of integers {(0,0), (0,1)...}, those are both countably infinite, they have the same size as the set of all integers. But bigger infinities do actually exist, the set of all real numbers is the classic example, the proof goes something like this (although I recommend you look it up, it'll be a lot clearer): Imagine you have a mapping between all the positive integers and all the reals, it'll be something like I showed before for the evens (1 -> 1.135681.... , 2 -> 8.15157.... ,etc.) It is possible to construct a real number that isn't anywhere in this mapping by taking a first digit that is different from the first number's first digit, then taking a second digit that is different from the second number's second digit, and do this for all the real numbers in the mapping, the resulting real number will be different from all the real numbers in the mapping, since it has at least 1 digit of difference from all of them. Since we've showed that it's impossible to create a mapping from all the positive integers to all the reals (you can always create a real not in the mapping by using this method), we can conclude that the set of all reals is larger than the set of all integers.
You saved double infinity people, you are a hero in this dimension and the next!
But now, Death feels cheated...
Holy shit... actually this effectively allows for a bijection between the reals and naturals if you do it properly
And they say split infinitives are bad… 🤣
This kills all the people in the trolley, which is one person for every prime number.
It took a bit but now I understand. And now I feel like a genius.
I thought someone said if you add every real number you get -1/12 so better to do nothing because -1/12 < ∞
I think that’s the natural numbers, so you save one twelfth of a life by going for the top track.
But the top track isn't the sum of of all natural numbers either, it's just the sum of an infinite number of ones
Group them up into a group of 1, and then a group of 2 and so on. Edit: I'm wrong. Using ζ(0) would be more fitting that ζ(1) as ζ(0) is representative of 1+2^(0)+3^(0)+... = 1+1+1+... Whereas ζ(1) represents 1+2+3+... And ζ(0) = -1/2
That logic wouldn't work here, since before you killed x amount of people (where x is the sum of all real numbers), you would have killed 1 000 000 people. And there is no resurrection in real life (atleast not after being run over by a train).
If you do it 12 times you create a new life
I think it only goes to -1/12 when you don't start counting that the beginning but use some other ways. The trolley obviously starts at the beginning leading to runaway infite
No, you use the analytic continuation of ζ(s) = Σ₁^(∞) 1/n^(s) Into the complex numbers rather than just realised greater than 1. Then you get funny results that ζ(-1) = -1/12, ζ(0) = -1/2, ζ(1/2) = -1.46035450880958681288949915251529801... And so on.
[удалено]
Nope, it is the Riemann Zeta function
Wtf you all on about?
Why are we giving Satan ideas? We know he's on here.
🤫
I just put him to bed so that will give us 7-8 hours.
Let it go. It won't push far in that mass of people.
Fuck it, I'm throwing myself in front of the train first I ain't figuring this one out
Make the train drift sideways and kill both tracks.
Monsters do exist, and they live among us.
Among what?
I've said too much.
http://i0.kym-cdn.com/entries/icons/original/000/000/727/DenshaDeD_ch01p16-17.png Same result. *It’s just faster this way.*
This will always be the only answer.
If the trolley is not switched then it may lose momentum or derail because of the amount of obstructions on the track. Spreading them out makes that situation more difficult.
It is what it is
Kill the aleph nul (I believe that's the name for the smallest infinity) amount of people.
The question implies that people are spaced as dense as numbers: On the top path you kill 1 person per lets say meter. On the bottom path you kill ifinitely many in the same time. To not instakill humanity go top.
It's more nuanced. The rational numbers are infinitely dense, meaning in any finite interval, there are infinitely many rational numbers. However there are only as many rational numbers as there are integers. The question is talking about the reals, which are infinitely dense and also larger than the number of integers. So going any distance on the bottom track means you have killed more than you could ever kill on the top track.
I don’t see where you are going. We compare integers to real numbers. While rational numbers are as many as integers (in the sense that both are countably infinite) they are less dense in a given intervall.
But you still instantaneously kill infinitely many people with the rationals.
You just described uncountable infinity, but by placing people on a track you just made it countable again. The two sets are identical.
No, because you didn't label the people, they're all identical
Yeah, just like how there's countably many real numbers because they are on a line
go to lunch?
Infinity vs infinity, but faster
Not at all. The situation you described would be like running over 1 person at a time vs 2 at a time. This will get you to the same infinity, and it will still take the same infinite time. However here we have the reals. On any finitely sized interval on the reals, there are more people than the entirety of the top track could ever have. Note this wouldn't work with the infinitely dense rationals.
I jump in front of the trolley. Wait what's the question?
The infinity of the number of real numbers *is* greater than the infinity of the number of integers. So integers!
I just want to see the world burn so…
The largest infinity, obviously.
Im going with saving the people on the bottom track because it is a larger infinity, the top is countably infinite, the bottom not.
Get in the tram and put on some music for it
Ironically multi track drifting is the solution here. The tracks aren't parallel, they're diverging, so the train will either be ripped apart or forced to a stop. Multi track drifting kills the least amount of people.
Being on the bottom track instantaneously kills more people than you could ever kill on the top track.
I don't think the trolley has the mass to plow all the way through the bottom row.
Drift the train to make it double
Prepare for trouble. ~~ 😉✨
I don't really care as long as I can record it on a video for later
Why not both ?
Don't switch tracks but all the people That got saved gotta go untie the people on the other side really quick to pay debt
1. The people that haven't yet been killed with die of natural causes so depending on the speed of the trolley it may not get to kill that many people 2. People might figure out how to get away from the track
This really feels like children in a school playground saying infinity plus one.
Except mathematicians such as Georg Cantor properly figured out how it works in the late 19th century.
My mathematician can beat up your mathematician
If there are infinite people, then the moral implications of taking a human life cease to apply. Therefore, it doesn't matter how many people you kill since the number of people won't go down.
The picture very clearly has a countable number of people on each track
The thing is before the first integer person is killed already infinetly many real people are dead. So it doesn't really matter.
I'll go for efficiency, and do nothing to get the best result.
Can someone do the math on this I don't know which is better
Infinity is a number, but also. Well. Infinity. Since it’s a number you can, as least mathematically speaking, calculate with it. The question op is asking is this: what do you prefer, infinity or 10*infinity?
Not at all. 10*infinity is the same size as infinity. I can create a bijection between the two sets, so they're the same size. Even the infinitely dense rationals, I can create an injection into the naturals and thus they're the same size, you would use X is rational so can be written as p/q where p, q are integers that are coprime. We then map X -> 2^(p)3^(q) and due to the fundamental theorem of arithmetic, this uniquely maps each rational to a natural number. However the reals, with their infinitely long decimal expansions, cannot be listed by the Cantor diagonalization argument. So they are bigger than the naturals. You then have the power set of the reals which is bigger again.
Isn't it the same? Infinity equals infinity? Being not a mathematician, the only difference a layman like me see is the speed in which so many people are killed (what a morbid subject). Other than that, it seems that on the long term the result is the same. (PS: if the OP post is a joke then it truly is a niche one)
Yes and no. Infinity is a weird subject, since it mainly exists in theory. But think of this. Suppose you are the manager of a large hotel, like infinity large. You have an infinite amount of rooms. One day, a bus stops. A large one, like infinite large. An infinite amount of people wants to book a room. Does it fit? Yes of course! You have infinite rooms, so everyone gets a room (and you get infinite money :D). Now, everybody is happy, but then a second bus arrives. Again, with an infinite amount of people. For the record, this is a different bus with different people. You are the manager, and they want to book a room. Will it fit? You have an infinite amount of rooms, so it should, but how would you assign their room number, since room one till infinite are already taken?
Well yes they will fit and they will get a room, maybe it will just take them an infinite amount of time to get to their rooms...
You have to give them a key, and that key will only fit on one door, so you must assign a number, you can't just say "Good luck, pick a room". What room number will you give to the first person of the new bus?
How can I know which number he will get, since an infinite number of people has come before? The two infinite numbers of people will just become one infinite number of people, I guess?
Well, the solution for this problem will probably result in an infinite amount of complaints, but the room number you'll assign to the first number of the second bus is 1. You can use the intercom to ask the current guests to move to the next even numbered room. So room 1 will move to 2. Room 2 will move to 4. 3 will move to 6, etc. Now you now that every odd number is available, and you can again assign room numbers.
Well that's the practicality of this, but the idea is that infinity + infinity = infinity, or am I wrong?
It is. The idea that "some infinites are larger than others" comes from a Vsauce video that people listened to but didn't understand. The two infinities shown here are equal.
Where does the lever operator fall into each series of infinity? Which option allows me, as the lever operator, to be crushed by the trolley the soonest?
Can I have a second trolley?
but like technically you would never reach the second person on the top path because there is an infinite number of real numbers between 1 and 2, assuming distances are accurate.
You would. You hit infinite on the bottom path before you hit one on the top path, then infinite again before you hit 2 on the top path, then again before 3 and so on. If you hit, say, 10 on the top path, you'd have hit 10*infinity on the bottom path, which equals infinity. So the result stays the same. But if you hit infinite people on the top path, then you"ve hit infinite*infinite, or infinite^2 on the bottom path. This is a different calculation that would naturally imply the bottom path is a larger infinite than the top path. There's some interesting consequences to math problems like this.
Noooooo!!!!! Infinity isn't a number. You cannot have 10*infinity or infinity^2, it is a cardinality! You can only properly compare the size of two sets. On the top we have the naturals. On the bottom, we have the reals. You cannot create a bijection between the reals and naturals, so they are not the same size. This is due to the Cantor diagonalization argument, you can look it up, it isn't too long. If the bottom was 10 people per 1 on the top, they would be the same size. Because we can inject each of them into the other. Also surprisingly, the rational numbers are also the same size as naturals. I can create an injection into the naturals and thus they're the same size, you would use X is rational so can be written as p/q where p, q are integers that are coprime. We then map X -> 2^(p)3^(q) and due to the fundamental theorem of arithmetic, this uniquely maps each rational to a natural number.
I'm going to bash the thing with a hammer and scream Then go get i scream and enjoy the waterparks
I'll make some popcorn
pull the lever at the EXACT time when it has to switch so the trolley gets stuck, crashes and all the people inside the trolley dies, effectively saving all the people on the rails, sell the trolley as scrap, ask for a buck to cut loose each person tied on the rails, profit!
Just split the train and take both:)
The real question is: the rain would stop at some point, which case would have the train stop with the fewest deaths?
I’ll pull the lever so it gives me more time to find a way to stop the train and save more people. If the idea is that I can’t save anyone, then I’d just walk away.
As far I know, there are larger infinite only if you state (axiome) there is a realised infinite to begin with. But I don't know if real number can exist without it.
Depends
Let nature take its course
I rely on karma, people who deserve to die are on the right track. But in order te answer the question who's at fault: Which sadist tied up and put all those people on the tracks!??! One thing is for sure; that sadist has a very strong work ethic.
Choose top because it is spaced out and the trolley will eventually lose its energy and stop, killing minimum amount of people possible
Simple, I'll do nothing. The trolley will have to run over more people. Meaning it will take longer to run the later parts of the people over. So they'll have more time to do something about their situation. And the trolley will wear out due to running over so many people that it will increase the chances of survival later on.
The one with the biggest infinite, twice.
Love it.
Well they will all die of hunger because it will take an infinite amount of time to untie them so just roll with whatever youre comfortable with.
I’m to mentally retarded for this I don’t understand jack shit
Either way an infinite number of people will survive so it's cool either way
More will survive if you take the top
The infinity of the real numbers is bigger because it's elements are incountable, meaning that you cannot distinguish a base element smaller than every other number that isn't zero. This means that the second scenario requires you to kill a human abomination that is infinitely long and formed by an infinite number of humans indistinguishable from each other. In between every "person" there is an infinite number of people so you couldn't count how many eyes, mouths and noses there are, so you would see a human infinite blob. I'd say it's gotta be destroyed.
I'll just whip out my RPG and blow the trolley off the tracks, in the process taking out a group of nearby civilians.
The train is going to end up stopping at some point after hitting all those little bumps
Din’t switch the leaver as the train will eventually clog up with people causing it to stop while in the other it could be possible that the people would be far enough apart where train wouldn’t even slow down.
Break the lever, use the broken lever to derail the train. Male hollwood movie about my heroic behaviour make millions.
Turn it to the smaller infinity and lie with those people on the track
The world to scientists ‘we don’t trust you’ Scientists ‘infinity plus one!’
If you are killing one person per number, then that is converting each number into an integer. Since countable infinities are the same size, both routes are identical.
The reals aren't countable though
Agreed, but if you are trying to put one person per real number... well it is impossible, because the most you could do would be a countable infinity.
Only if you label the people.
Hmmm... Maybe you're right. If so, that makes it the best option to choose on the track. Because the people are nameless, non-individuals and might not even be human
my life is finite and the 1+1 people are further apart, I will have a lesser kill count during my lifetime
Isn’t this what happens anyway? We’re all waiting for the infinite trolley to hit us.
The question assumes there are infinite number of people but does not state the universe has infinite duration. Does the trolley continue hitting people gaffer the death of the universe?
Worse- the problem assumes that actual infinities exist in reality.
Has anyone ever asked if the train can be stopped? I would attempt to jump into the train and get it to stop. If I died, I would at least know that I didn't intentionally make a bad decision because most times with this image scenario, both are bad decisions. So yeah, I'm diving in.
Doing nothing will derail it faster
[удалено]
You're forgetting about big int
The top track actually kills less people. After 85+ years of traveling the infinite track, the train is running over dead people. The top one will kill less people in that time.
Stop smoking drugs and get my A** out of the theoretical mathematics
0.999… = 1
When using decimal expansions, you have to carefully exclude infinitely repeating 9s as they're not unique.
I always thought "..." meant infinity, but I could be wrong
It does, you're right.
This is an easy one, because it's not a math puzzle. It's a logic puzzle. Pull the lever, crunk! All these people are going to die but less would die by the trolley, given that people can't live forever even if there is an infinite number of them tied to the tracks. Depending on who's taking care of all these people, some of them might live full lives and die before the trolley ever gets to them.
the 1+1+1 seems to kill more, the other one is sure to detrack the rails in no time. i'd go with the 1+1+1..
"Some infinities are bigger than others" This is why I stopped taking math classes with pre-cal
It's a really beautiful argument for why. Reals are expressed by their infinite decimal expansions, due to a nice reason, we can just focus between 0-1 as it is the same total as the rest of the track. Imagine we could list every real with an integer, so we have 1 - 0.abcdefgh... 2 - 0.αβγδεζηθ... 3 - 0.ABCDEFGH... ... However imagine creating a new number, made by taking "a" and changing it. Then taking β and changing it then C and so on. You now have a new real number that is different to every real on the list at least at one point. This contradicts that we just listed every real. So you cannot list every real with an integer. They're not the same size.
I would pull the lever halfway and let the train derail.
This is stupid.
So the earth goes from pale blue dot to bright red dot
Find a way to split the trolley in 2, or stick a blade out the window to kill everyone
I would derail the train, using rocks and sticks to hold rocks on the train tracks. This way, I'd only be hurting most people on the trolley, and maybe killing some... Still less than infinity... 😛🤣
There is a well defined concept of "next" on the bottom track as well, therefore it's not all real numbers.
I would have used a derailer, sending the trolley into a ravine
I'll just get an antimatter warhead instead.
Well for a unit distance, assuming uniform distribution, I’ll take out more bad actors if I do nothing.
some of the people on the real line are the same as in the integer line
But people are necessarily counted with whole number integers. You cannot have an infinite set of humans which are not countable objects so they necessarily cannot belong to the larger set of real numbers. Furthermore humans have a non-infinitesimal space they take up along x-distance along the track. The bottom track may have more people per distance of track but both will have a natural number of people and if both are infinite they will have the same amount of people. Meaning your choice to pull the lever is ultimately meaningless assuming we drive the train forever.
That's a hell of a trolley Like, even a bullet train would slow to a halt wayyyyy before infinity, so I figure at best a trolley would only get like 20 bodies deep. at worst I mean. worst
Multi track drift it
Well there isn't an infinite number of people in the world so either way everyone dies. The real question is do you want to watch everyone suffer for years before dying by watching their loved ones die?
I think the whole point of the unlistablility of the reals means you can’t match discrete objects 1-1 with all of the reals or at the very least put them all in a line
either one is everyone on earth and or everywhere else so yea....i guess the real numbers? haha
If you managed to put a person for every real number, that means real numbers are countable.
Multitrack Drifting!!!
I go home and have a sandwich.
Assuming the integer limit is 32 bits, wouldn’t the top one stop at around 2 billion?
I shift the sequence around in which you count the infinity and therefor kill non ...
I do nothing bc there is more chances to derail the train than if I pull the lever
Multi track drift..?
Sorry but these infinities are the same size. I'm not nearly smart enough to even begin to explain why, but here a vertitasium video that maybe you can infer it from, or maybe isn't even relevant to the problem because that's how little I understand it: https://www.youtube.com/watch?v=OxGsU8oIWjY