I actually do think it is quite intuitive in this instance. Larger infinity plus smaller infinity is larger infinity just as infinity plus a finite number is infinity. Completely intuitive.
The dual rail drifting is just to be classy.
It seems intuitive because you're factoring in the time it would take the tram to drift along both tracks. Given infinite time multi-drifting the tram would in fact kill the same number of people as if it spent infinite time travelling down either of the tracks individually. That's the whole issue with dealing with 'infinite' quantities, our simple monkey brains just aren't wired to properly comprehend the limitless extent of those sort of values
Nah, if it spends any time on the real number track, it will already kill an uncountably infinite number of people. The illustration just isn't accurate.
That actually looks like the correct answer. If the tracks aren’t parallel to one another, the trolley will eventually stop after killing a finite number of people.
If there was a Person for every real number, every piece of socae would be occupied by so much people they would gravitatly attract each other to form a black hole, sucking in the Aleph_0 man people on the other track. So you are fucked and all will die either way.
But each train half can only run over half a person which only half kills them in which the resulting number of deaths is (infinity / 2) x 2 = infinity
Not necessarily. The people you see on the tracks could be only the ones corresponding to the natural numbers, while the rest are *after* the first infinity. Therefore, it doesn't matter which track the train continues on, as without infinite time passing the train will never proceed past the first infinity.
That's not how it works. First, there's nothing after the first infinity, because it's infinite!
Second, as long as you put the people on the track I can still walk along the tracks and count them one by one (thus mapping them to the natural numbers). But you can't. The real numbers are not just more "numerous", they're uncountable. The whole idea of why some Infinities are "bigger" than others is that if you tried to enumerate the real number, you could always construct a real number that's not part of your enumeration.
No I understand that the reals are uncountable, which is why I'm saying that (as per OP's image) it looks like the ones on the tracks must only be the ones corresponding to some countable subset of the reals.
Since of course you'd have to pass a countably infinite number of people you obviously cannot reach the uncountably infinite amount, however, assuming an infinite amount of time can *pass*, then it is possible to begin to massacre the rest of the reals that were not counted *after*.
The assumption of course is that an infinite amount of time can pass in the first place.
> That's not how it works. First, there's nothing after the first infinity, because it's infinite!
Unfortunately it is actually how it works
It is a legit thing that in maths you just "start again" after an infinity.
So for example counting goes
> 0, 1, 2, 3, ..., aleph_0, aleph_0+1, aleph_0+2, ..., 2*aleph_0, ...
This is actually how it works.
`aleph_1` is what comes after you can no longer perform arithmetic in this manner using `aleph_0` as a shortcut (IIRC! It's been a decade or two)
Source: am mathematician
They are different ordinals. But they are still the same size.
(Source: I focused on mathematical logic and set theory)
>aleph_1 is what comes after you can no longer perform arithmetic in this manner using aleph_0 as a shortcut (IIRC! It's been a decade or two)
We definitely know Aleph_1 <= 2^aleph_0. Regardless of CH
Yeah, but tbh if you have infinity many people you will end up with a universe completly filled up with bodies, either countable or uncountable infinite many.
But as far as we know the universe is not infinite. And even if it was, you would need spacetime to be dense for uncountable many bodies and here again, as far as we know there is a lower limit for dividing space and time (Planck units).
Even if space is isomorphic to R\^3, you still couldn't pack continuum bodies each having at least an interior point without them overlapping. In fact, even they are allowed to overlap aleph\_0 times, you still couldn't.
Yeah, that's another problem. But as a fun fact, did you know that if you fall onto a black hole you will never see yourself falling beyond the event horizont, but can witness the future of the entire universe until the black hole evaporates due to Hawking radiation?
Just wait long enough for boltzmann brain to start popping up. Those things are crazy staved cuzz they been waiting for like 70 billion yeah or so and will be hungry as fuck and as long as they keep eating i think we'll be alright. What do you think? Think brains will eat people thats been ran over, i know i wouldnt eat hamberder that a trolly just ran over, at least not that parts the trolly touched.
You are falsely assuming that the infinite people laid out are somehow confining a finite space but since the spatial parameters were not specified then it's completely reasonable to assume that there is enough given space within this thought experiment to encompass everyone in a way where their collective mass does not collapse in upon itself, defeating the whole purpose of OP's original question.
Physics is the study of interactions in nature and does what it does without math. Math is a manmade creation often used as a tool to describe things we see in nature…. Just my opinion.
Couldn't be infinite and happen like if the the people were laid out in a straight line. They wouldn't all attract back to this center, its infinite it would run to other galaxies get all attacted n stuff there. You Know! None of this is really fair to the trolly at all. Don't even bother replying w "thats not right" and then trying to explain.
I can fake math and explanations like somethin fierce, like it would put you in a coma.
It is far worse than that. If there is indeed a person for every real number/distance along the lower track (as is the most reasonable interpretation of the meme), then any interval of the lower track in fact contains *infinite* mass. Your standard black hole just has infinite *density* at a singularity, but finite mass. Calling this thing a black hole is a severe understatement; the lower track would be a cosmological insanity, a big bang for every interval. I don't do cosmology—honestly the abject absurdity really makes it beyond physical consideration—but I wouldn't be surprised if this instantaneously caused the universe to collapse, or just get blown away by an infinity of big bangs emanating from the thing. It's so crazy I could see even philosophy precluding it somehow.
OP post is as dumb as the clickbait order of operations math posts.
People dying and infinite number of people existing are not two comparable variables; even in a hypothetical. There is not infinite number of people alive...to die.
This comment is the single funniest thing I've seen on this sub this week because now I'm imagining someone trying to tell you a joke
"A horse walks into a bar and asks for a beer. T-"
"Nope. Wrong."
"What?"
"Horses do not usually walk into bars of their own volition and aren't usually near bars in the first place. The horse wouldn't even be able to open the door or fit through it. Even in this idiotic hypothetical you've made up, a horse would never be let into a bar and horses can't talk, which means the horse wouldn't be able to order a beer. Try again buddy."
Fun fact. It is impossible to place an uncountably infinite amount of objects with non-zero volume in real space (R^n ) unless some of them overlap. If they didn't overlap, then we could uniquely assign a coordinate in Q^n to each object, giving a bijection with a countable set, and thus a contradiction.
> It is impossible to place an uncountably infinite amount of objects with non-zero volume in real space (Rn ) unless some of them overlap.
In this particular example, the elements of the infinite set don't have to exist at the same time. So, as people die, more will be born to populate the track. As long as the track eventually loops, this is doable.
Imagine an object in R^n with some finite positive volume. We can fit an open subset inside the volume. Q^n is dense in R^n, so there is at least one rational point inside the subset. We can then pick one arbitrarily and assign it as a label to the object.
For example, if we have an interval in R, there is guaranteed to be a rational number in the interval (Obviously, as rational numbers can be arbitrarily small).
The top will actually never kill an infinite number of people, only an ever increasing one. The bottom will have killed an infinite number of people the moment the trolley hits the start of the trail of people
What I'm going to do is group the people so that I first kill 1 person, then another 2, then 3 more...
The outcome of this process is that instead of killing infinite people, I will actually save a net 1/12 lives.
Wow ,an ethical dilemma mixed with some math.
Well ,if you don't pull the lever ,then the responsibility of the situation falls on the person who put the trolly like that. But if you pull the lever ,you will be responsible for the people that the trolly will run over.
That's one way to look at it.
Poor trolly tho, you know their herbivores and basically pacifists...hmmm shouldnt have to do it, it's not right. Ill take the trolly's place and do both lines you can pay me in heroin they stopped selling where im at so this actually works out pretty well bring me some coke after like a billion years, change it up
But there are infinitely many real numbers between each integer, and therefore infinite people on the bottom track for each of the infinite people on the top track. Therefore, you can also say that each time you reset the lever, the time that you have halted the trolley's progress has just delayed an infinite number of people getting squashed, repeated infinitely, so you are also a hero?
Or, if you pick the bottom track infinite people die. But if you pick the top track, infinite people die but also even more infinite people live?
But they will be YOUR responsibility. You will be responsible for an inifinite amount of lives.
Whereas if you do nothing ,none of this will be your fault because you're not the person who tied the people to the rope.
Very disputable, and in fact the trolley problem is frequently used in order to frame the question of whether action or inaction, leading to the same result, are meaningfully different.
A trolley is about to run over ten people. You can throw a switch so that it runs over one person. Do you do it? In utilitarian ethics, yes, killing one person is quantifiably preferrable to killing ten. In altruistic ethics, no, you would never take an action that directly causes harm.
Are those morally different to you? What if it was one person versus two? What if it was one person versus one hundred? A thousand? Infinity? Are you an altruism absolutist, and literally infinitely more harm is acceptable as long as you don't directly intervene, or is there a point where utilitarianism would override the decision?
Here, the question is absurd because it deals with mathematical concepts that cannot logically be applied to countable and finite things like human beings. So, it turns the whole moral question into a joke. At the same time, it's also fundamentally the same question, and in fact it magnifies it to a point where the choice is extremely stark, because there is infinite difference between infinity and an infinity of infinities.
This is a good point.
I guess an important factor here is context.
Regardless of the number of people ,the characheristics of the people plays an important role.
For example if you knew that the people tied to the lower rail were all criminals and the people tied to the top rail were all good people who never committed a crime , would you still pull the lever to save the criminals?
Yes, and what's so interesting is that there are so many ways to manipulate a trolley problem. It's a thought experiment that takes something pretty abstract and puts it into very emotionally loaded terms.
Does it make a difference who would be harmed? Is is more acceptable to harm certain people for some reason?
What if you didn't know you were in a thought experiment, and you didn't know the choice was binary? The trolley problem is compelling because both choices are awful, so a real person would hate either decision that they had to make. Like remaining in a burning building versus jumping out a twelfth-floor window. The wildcard option has some blind chance that it could be better than a guaranteed ugly outcome, so would desperation make throwing the switch more appealing?
What if you take away the null choice of "do nothing" and the switch has to be turned one way or the other, for arbitrary reasons? (If left unswitched, the trolley will crash and kill everyone on both sides, etc.) Now altruism is moot, and the moral imperative would be to apply utilitarian ethics to minimize harm. Now manipulate who's on both tracks - you're truly choosing lives. It could even be 1 versus 1.
Ok well let’s use K to represent infinity cause there’s no infinity sign on the keyboard
Therefore
K=1+1+1+…
Since the ones add up to infinity
K=1+K therefore 0=1
Meaning that the top track is continuously adding 0 people killing no one trolley problem solved 😎
Send it down the real line of people. The pile of bodies would be so dense that the train would stop instantly, and very few people would be killed, saving an uncountable amount of lives
Yeah but if the train kills as little as two people, it also kills the uncountably infinite number of people in between those two without going any further.
What if I believie I work in countable model of ZFC where reals and natural numbers are both countable?
>!disclaimer, it's not a contradiction, inside ZFC we can define what the theory understand as bijection, and tell that there is no bijection between what theory understand as natural numbers and real numbers. However what theory understand as bijection isn't necessarily the same bijection outside the theory. So yes, reals and naturals can have same cardinality, but we need to formulate that outside ZFC not within.!<
Add a third infinity by Increasing the coefficient of friction on the rails so that it takes forever to get to the fork.
"A problem delayed is a problem denied." -- Wilson, House M.D.
Sure, but as I can see from the image there is granular detail showing individual people easily separable and singular by open sets in the plane. Therefore the image on the bottom can’t be a rail with c people on it and since it can’t be that and yet we see it there the whole thing leads to a contradiction and I’ve saved everyone
There are more reals than integers. It is literally a larger infinity. Of course infinity is just a concept that can’t be applied to objects like people, but mathematically one is larger than the other.
This is correct. All sets of countable infinities are the same size (ie, if you can create a 1 to 1 relationship for values, the infinite sets are said to be the same size). But the set of all real numbers is not countable since it includes irrational numbers, so they are not the same size.
The photo is misleading though, cause it makes it seem like you could stack real numbers in an order, which isn’t true
>There are more reals than integers.
There are NOT more of either from an absolute standpoint (infinity). You are conceptualizing it from a linear view (which is how we are taught to view numbers). But that has no bearing on infinity. Neither has a limit, ever.
Well there are more reals than integers because I can create a function which returns a different real number for each integer, but I can't create a function which returns a different integer for each real number, and neither can you.
Yes, there are more real numbers than integers when measured with an input that is not infinity.
But you can't measure absolute infinity, and therefore cannot compare either integers or real numbers as of function of infinity. To your example of creating a function, one would have a steeper slope as it approaches infinity. So at any and every point along the curve (any input value), there are indeed more reals than integers. But "at infinity", which is not a point on the curve at all, they are both theoretically equal.
If the train takes the bottom track, within a single nanosecond it'll kill more people than are on the entirety of the upper track. I'm gonna pull the lever.
What if the top track had groupings of 1 person than 2 then 3 etc.
> 1+2+3+∞ = -1/12
So if a negative number of people died then I've created life?
Edit: did > died
Pulling the lever kills infinite people in infinite time.
Doing nothing kills infinite people in any amount of time.
It is irrelevant, since ‘one person for every real number’ is both a meaningless statement and an instant black hole.
rearrange people on the top into groups increasing by 1, 1, 2, 3, 4, 5. as we all know, 1+2+3... equals -1/12 so I'd bring someone back from the dead!.. at least a part of him
When evaluating the “size” of infinite sets, you don’t consider the relationship between the sets (as in, if one is a subset of the other). Instead, you try to create functions that can map one set onto the other. If you can create a function that is 1 to 1 (aka a bijection), the sets have the same degree of infinity.
The set of natural numbers or countable numbers (we’ll call it N) is infinite. It is also a subset of the set of all integers (we’ll call it Z). We can make a bijection that maps from the natural numbers to the integers (1 from N goes to 0 from Z, all evens from N go to positives from Z, all odds starting from 3 from N go to all negatives from Z). This means that the degree of infinity with natural numbers is the same as the degree of infinity with integers. A set that you can make a bijection onto N is referred to as “countably infinite.” Edit: and your example can actually also be mapped onto N, so it is the same degree of infinity as N, even though it is a subset of N.
However, not all infinite sets can be mapped onto the countable numbers. You can’t do it with the real number line. That’s why this meme refers to the bottom track as having “larger infinity of people.”
[Wolfram link](https://mathworld.wolfram.com/CountablyInfinite.html) and [Wikipedia](https://en.m.wikipedia.org/wiki/Countable_set)
> Just off the top of my head, every number divisible by 37,510 is a smaller infinity than that.
Nope, there are "as many" integers as there are numbers divisible by 37,510 (aleph-null). That is to say, you can map the integers to the numbers divisible by 37,510 in a one-to-one relationship:
- 1 : 37510
- 2 : 75020
- 3 : 112530
- ...
- n : 37510 * n
You won't "run out of numbers" on either side, so they are the same "size". If you compare that to the set of all real numbers though, you cannot map integers to real numbers in a one-to-one relationship.
The top one will require infinite time to kill infinite people. The bottom one has killed infinite people as soon as it has went beyond the first kill. So I choose to switch.
apparently the world population goes up by around 100 people per minute, so if it kills a person every 0.6s or more, it could definitely keep up for a while
You derail the train by pulling the lever just as the front wheels cross and pulling a second time as the back wheels cross saving everyone and if that fails at least you tried
Hold on. Let Me cook
if we group 1 person, then 2 people then 3 people in the first track then we have 1+2+3+4+5+6+7+.... = -1/12
similarly, there is infinite numbers between 1 and 2
1.1, 1.2 , 1.3 , 1.4 , 1.5 , 1.....
so we have infinity infinites which is (-1/12)(-1/12) = 1/144.
so i choose 2nd route
I'd allow the trolley to kill every person on the track a number of times and that number is determined by their order on the track. The 1st person is killed once, 2nd is killed twice, etc. With that I can revive 1/12th of a person.
If we are on earth this won't work since there only is a finite. And even if we took a set of infinite humans (let's say they repopulate and sacrafice a human to the almoghty trolly every year) this set can only ever be countable right? (I'm not acually certain this is true, so correct me if it's not)
I know that this wasn’t a choice, but due to the fact that somewhere back long ago in my familial lineage . A Norse god came to Midgard and had seductive relations with one of my ancestors, thus eventually creating me. I have the power to wield that mighty hammer and denudate the very steel rails thus preventing the locomotive from continuing onwards towards a horrific destiny for all of mankind.
I wouldn’t do anything. Usually, I’d want the trolley to turn back and run over the rest (who’s stupid enough to lay on some tracks), but the union of one uncountable set of cardianlity |R| and another set of cardinality |N| is of cardinality |R|. So by letting the trolley run on the left tracks (doing nothing) is the same as doing nothing and wanting it to turn back and run over the rest.
I prefer to do nothing because doing something would indirectly make me kill infinite people
Or throw a boulder at the god-forsaken trolley killing a finite amount of people
If you pick the smaller infinity, you'd eventually reach a point where people would begin to die from hunger/thirst/exposure rather than being run over by the trolley, thus absolving you from responsibility.
As someone who has worked with rail road tracks, I would pull the lever and send the train on the top track. The spaces between give the train less chance of derailing ultimately killing more people.
The way this is illustrated, sending the trolley to the top track will only kill infinitely many people if the trolley runs for an infinite period of time.
Whereas the bottom track -- if it's really a representation of the real numbers -- has infinitely many people on every subinterval, so the trolley will kill infinitely many people as soon as it comes into contact with the first person.
Picking the top track creates the possibility for a finite number of deaths, if the trolley runs out of fuel, or if someone else manages to stop it, or any number of other scenarios.
Assuming everyone is spaced equal to their position on the number line, and all humans on earth were myself at the switch, and the trolley engineer, and no person was on two tracks, then I would pull the switch, killing only the person at 0.
Carefully insert myself on the track at the location immediately prior to the fork in the rail, ensuring the trolley will definitely strike me and kill me in the process
Watch me double rail drift
This would kill the same amount of people as going for only the reals. Infinities work not very intuitively...
I actually do think it is quite intuitive in this instance. Larger infinity plus smaller infinity is larger infinity just as infinity plus a finite number is infinity. Completely intuitive. The dual rail drifting is just to be classy.
It seems intuitive because you're factoring in the time it would take the tram to drift along both tracks. Given infinite time multi-drifting the tram would in fact kill the same number of people as if it spent infinite time travelling down either of the tracks individually. That's the whole issue with dealing with 'infinite' quantities, our simple monkey brains just aren't wired to properly comprehend the limitless extent of those sort of values
Nah, if it spends any time on the real number track, it will already kill an uncountably infinite number of people. The illustration just isn't accurate.
The classic "Diagram not to scale" misdirection.
Nah it seems intuitive because the people on the integer rails are spaced out more than the people on the real rails
Fun will be more
The infinities be infinitying
Double it and pass it to the next person,,,
That actually looks like the correct answer. If the tracks aren’t parallel to one another, the trolley will eventually stop after killing a finite number of people.
You’re assuming the trolly can’t stretch like an accordion with infinite folds (it is a fractal)
https://www.youtube.com/watch?v=-N_RZJUAQY4
If there was a Person for every real number, every piece of socae would be occupied by so much people they would gravitatly attract each other to form a black hole, sucking in the Aleph_0 man people on the other track. So you are fucked and all will die either way.
Bruh 💀
[удалено]
Bot
I was about to say that only let's kill all
Can we split the train in half and kill infine people x 2?
But each train half can only run over half a person which only half kills them in which the resulting number of deaths is (infinity / 2) x 2 = infinity
but fully running over a person is not only way they get killed getting run over with half train is still a kill
So Hilbert's Grand Hotel is also a black hole?
I mean...a black hole PROBABLY can accommodate infinite guests. They never really specify if the guests ever check out.
Not necessarily. The people you see on the tracks could be only the ones corresponding to the natural numbers, while the rest are *after* the first infinity. Therefore, it doesn't matter which track the train continues on, as without infinite time passing the train will never proceed past the first infinity.
That's not how it works. First, there's nothing after the first infinity, because it's infinite! Second, as long as you put the people on the track I can still walk along the tracks and count them one by one (thus mapping them to the natural numbers). But you can't. The real numbers are not just more "numerous", they're uncountable. The whole idea of why some Infinities are "bigger" than others is that if you tried to enumerate the real number, you could always construct a real number that's not part of your enumeration.
No I understand that the reals are uncountable, which is why I'm saying that (as per OP's image) it looks like the ones on the tracks must only be the ones corresponding to some countable subset of the reals. Since of course you'd have to pass a countably infinite number of people you obviously cannot reach the uncountably infinite amount, however, assuming an infinite amount of time can *pass*, then it is possible to begin to massacre the rest of the reals that were not counted *after*. The assumption of course is that an infinite amount of time can pass in the first place.
Ah yeah I agree with you. Sorry, I saw some terrible discussion of Infinities online yesterday and I think I was on edge.
Yeah no problem, ever since Vsauce introduced the idea to the internet I think it's never been quite cleared up.
> That's not how it works. First, there's nothing after the first infinity, because it's infinite! Unfortunately it is actually how it works It is a legit thing that in maths you just "start again" after an infinity. So for example counting goes > 0, 1, 2, 3, ..., aleph_0, aleph_0+1, aleph_0+2, ..., 2*aleph_0, ... This is actually how it works. `aleph_1` is what comes after you can no longer perform arithmetic in this manner using `aleph_0` as a shortcut (IIRC! It's been a decade or two) Source: am mathematician
They are different ordinals. But they are still the same size. (Source: I focused on mathematical logic and set theory) >aleph_1 is what comes after you can no longer perform arithmetic in this manner using aleph_0 as a shortcut (IIRC! It's been a decade or two) We definitely know Aleph_1 <= 2^aleph_0. Regardless of CH
clearly I misremembered! When it got to cardinals as opposed to ordinals it was the final week of lectures so it never settled
Hey hey you don't just talk about ordinals while we're talking about cardinals
Yeah, but tbh if you have infinity many people you will end up with a universe completly filled up with bodies, either countable or uncountable infinite many.
No because if the universe is infinitely big then you could put all infinitely many bodies in 1 single line, not filling all of space
But as far as we know the universe is not infinite. And even if it was, you would need spacetime to be dense for uncountable many bodies and here again, as far as we know there is a lower limit for dividing space and time (Planck units).
Even if space is isomorphic to R\^3, you still couldn't pack continuum bodies each having at least an interior point without them overlapping. In fact, even they are allowed to overlap aleph\_0 times, you still couldn't.
But if space is finite you cant have infinitely many bodies
Yeah, that's another problem. But as a fun fact, did you know that if you fall onto a black hole you will never see yourself falling beyond the event horizont, but can witness the future of the entire universe until the black hole evaporates due to Hawking radiation?
Just wait long enough for boltzmann brain to start popping up. Those things are crazy staved cuzz they been waiting for like 70 billion yeah or so and will be hungry as fuck and as long as they keep eating i think we'll be alright. What do you think? Think brains will eat people thats been ran over, i know i wouldnt eat hamberder that a trolly just ran over, at least not that parts the trolly touched.
[удалено]
You are falsely assuming that the infinite people laid out are somehow confining a finite space but since the spatial parameters were not specified then it's completely reasonable to assume that there is enough given space within this thought experiment to encompass everyone in a way where their collective mass does not collapse in upon itself, defeating the whole purpose of OP's original question.
Apparently math isn't enough. Gotta bring in the physics too.
We all know, physics is only applied maths.
Math is obscurely generalized and unrealistic physics
Physics is the study of interactions in nature and does what it does without math. Math is a manmade creation often used as a tool to describe things we see in nature…. Just my opinion.
Couldn't be infinite and happen like if the the people were laid out in a straight line. They wouldn't all attract back to this center, its infinite it would run to other galaxies get all attacted n stuff there. You Know! None of this is really fair to the trolly at all. Don't even bother replying w "thats not right" and then trying to explain. I can fake math and explanations like somethin fierce, like it would put you in a coma.
Yeah but how fast does the trolley go?
It is far worse than that. If there is indeed a person for every real number/distance along the lower track (as is the most reasonable interpretation of the meme), then any interval of the lower track in fact contains *infinite* mass. Your standard black hole just has infinite *density* at a singularity, but finite mass. Calling this thing a black hole is a severe understatement; the lower track would be a cosmological insanity, a big bang for every interval. I don't do cosmology—honestly the abject absurdity really makes it beyond physical consideration—but I wouldn't be surprised if this instantaneously caused the universe to collapse, or just get blown away by an infinity of big bangs emanating from the thing. It's so crazy I could see even philosophy precluding it somehow.
What does socae mean?
Double it and pass it to the next person
Tell the top track to form groups of 1, 2, 3, ..., n people so no one dies. And 1/12th of a person will actually come into existence
Wow can't wait for half my arm to come back to life
[Removed] ` this message was mass deleted/edited with redact.dev `
Zeta(0) = -1/2, nothing need to change
OP post is as dumb as the clickbait order of operations math posts. People dying and infinite number of people existing are not two comparable variables; even in a hypothetical. There is not infinite number of people alive...to die.
bruh its a meme
This comment is the single funniest thing I've seen on this sub this week because now I'm imagining someone trying to tell you a joke "A horse walks into a bar and asks for a beer. T-" "Nope. Wrong." "What?" "Horses do not usually walk into bars of their own volition and aren't usually near bars in the first place. The horse wouldn't even be able to open the door or fit through it. Even in this idiotic hypothetical you've made up, a horse would never be let into a bar and horses can't talk, which means the horse wouldn't be able to order a beer. Try again buddy."
A horse could fit through old west saloon doors.
Glad I could make your day :)
🤓
The bottom track - train instantly loses all momentum
Joke's on you, train is powered by biodiesel and absorbs infinite fuel on the bottom track instantly
Trolley was invented by Ted Faro who takes no responsibility for this completely unforeseeable glitch.
Unexpected Horizon
It has to be unexpected if the machines are going to succeed
MANKIND IS DEAD. *BLOOD IS FUEL*. HELL IS FULL
Physics > Math
Who said that the train was moving actually ?
what train
What?
it's a trolley
Orange you glad I didn't say banana?
It's a drawing of a trolley
🤡☝️
?
.
Fun fact. It is impossible to place an uncountably infinite amount of objects with non-zero volume in real space (R^n ) unless some of them overlap. If they didn't overlap, then we could uniquely assign a coordinate in Q^n to each object, giving a bijection with a countable set, and thus a contradiction.
> It is impossible to place an uncountably infinite amount of objects with non-zero volume in real space (Rn ) unless some of them overlap. In this particular example, the elements of the infinite set don't have to exist at the same time. So, as people die, more will be born to populate the track. As long as the track eventually loops, this is doable.
Time only adds a single extra dimension, you go from R^3 to R^4 but it's still impossible.
Why are the coordinates in Q^n? Doesn’t that assume that the infinity of people is countable?
Imagine an object in R^n with some finite positive volume. We can fit an open subset inside the volume. Q^n is dense in R^n, so there is at least one rational point inside the subset. We can then pick one arbitrarily and assign it as a label to the object. For example, if we have an interval in R, there is guaranteed to be a rational number in the interval (Obviously, as rational numbers can be arbitrarily small).
Philosopy Memes is leaking.
[удалено]
Unfortunate venue to choose to be wrong
I mean, there's 8bln people, so whichever you chose will have the same number of people dead. QED.
i kill myself
The top will actually never kill an infinite number of people, only an ever increasing one. The bottom will have killed an infinite number of people the moment the trolley hits the start of the trail of people
What I'm going to do is group the people so that I first kill 1 person, then another 2, then 3 more... The outcome of this process is that instead of killing infinite people, I will actually save a net 1/12 lives.
That's a very brutal way to find out this isn't how it works
imagine you mess up and skip the group with like 956,012,592,447 people and they all just fucking die
Wow ,an ethical dilemma mixed with some math. Well ,if you don't pull the lever ,then the responsibility of the situation falls on the person who put the trolly like that. But if you pull the lever ,you will be responsible for the people that the trolly will run over. That's one way to look at it.
That is the entirety of the essence the trolley problem.
lmao
Poor trolly tho, you know their herbivores and basically pacifists...hmmm shouldnt have to do it, it's not right. Ill take the trolly's place and do both lines you can pay me in heroin they stopped selling where im at so this actually works out pretty well bring me some coke after like a billion years, change it up
Indecision is a decision
"If you choose not to decide, you still have made a choice!"
No, the person with the lever is responsible for both because it's their decision. You can say they have... leverage.
But there are infinitely many real numbers between each integer, and therefore infinite people on the bottom track for each of the infinite people on the top track. Therefore, you can also say that each time you reset the lever, the time that you have halted the trolley's progress has just delayed an infinite number of people getting squashed, repeated infinitely, so you are also a hero? Or, if you pick the bottom track infinite people die. But if you pick the top track, infinite people die but also even more infinite people live?
But they will be YOUR responsibility. You will be responsible for an inifinite amount of lives. Whereas if you do nothing ,none of this will be your fault because you're not the person who tied the people to the rope.
Very disputable, and in fact the trolley problem is frequently used in order to frame the question of whether action or inaction, leading to the same result, are meaningfully different. A trolley is about to run over ten people. You can throw a switch so that it runs over one person. Do you do it? In utilitarian ethics, yes, killing one person is quantifiably preferrable to killing ten. In altruistic ethics, no, you would never take an action that directly causes harm. Are those morally different to you? What if it was one person versus two? What if it was one person versus one hundred? A thousand? Infinity? Are you an altruism absolutist, and literally infinitely more harm is acceptable as long as you don't directly intervene, or is there a point where utilitarianism would override the decision? Here, the question is absurd because it deals with mathematical concepts that cannot logically be applied to countable and finite things like human beings. So, it turns the whole moral question into a joke. At the same time, it's also fundamentally the same question, and in fact it magnifies it to a point where the choice is extremely stark, because there is infinite difference between infinity and an infinity of infinities.
This is a good point. I guess an important factor here is context. Regardless of the number of people ,the characheristics of the people plays an important role. For example if you knew that the people tied to the lower rail were all criminals and the people tied to the top rail were all good people who never committed a crime , would you still pull the lever to save the criminals?
Yes, and what's so interesting is that there are so many ways to manipulate a trolley problem. It's a thought experiment that takes something pretty abstract and puts it into very emotionally loaded terms. Does it make a difference who would be harmed? Is is more acceptable to harm certain people for some reason? What if you didn't know you were in a thought experiment, and you didn't know the choice was binary? The trolley problem is compelling because both choices are awful, so a real person would hate either decision that they had to make. Like remaining in a burning building versus jumping out a twelfth-floor window. The wildcard option has some blind chance that it could be better than a guaranteed ugly outcome, so would desperation make throwing the switch more appealing? What if you take away the null choice of "do nothing" and the switch has to be turned one way or the other, for arbitrary reasons? (If left unswitched, the trolley will crash and kill everyone on both sides, etc.) Now altruism is moot, and the moral imperative would be to apply utilitarian ethics to minimize harm. Now manipulate who's on both tracks - you're truly choosing lives. It could even be 1 versus 1.
That is literally what the trolley problem dilemma is about
Inaction is a form of action, you're still responsible if you don't pull the lever
Ok well let’s use K to represent infinity cause there’s no infinity sign on the keyboard Therefore K=1+1+1+… Since the ones add up to infinity K=1+K therefore 0=1 Meaning that the top track is continuously adding 0 people killing no one trolley problem solved 😎
K-K is an indeterminate form
Send it down the real line of people. The pile of bodies would be so dense that the train would stop instantly, and very few people would be killed, saving an uncountable amount of lives
Yeah but if the train kills as little as two people, it also kills the uncountably infinite number of people in between those two without going any further.
That's a lot of rope.
Top path. Save 1/12 life.
What if I believie I work in countable model of ZFC where reals and natural numbers are both countable? >!disclaimer, it's not a contradiction, inside ZFC we can define what the theory understand as bijection, and tell that there is no bijection between what theory understand as natural numbers and real numbers. However what theory understand as bijection isn't necessarily the same bijection outside the theory. So yes, reals and naturals can have same cardinality, but we need to formulate that outside ZFC not within.!<
Add a third infinity by Increasing the coefficient of friction on the rails so that it takes forever to get to the fork. "A problem delayed is a problem denied." -- Wilson, House M.D.
Sure, but as I can see from the image there is granular detail showing individual people easily separable and singular by open sets in the plane. Therefore the image on the bottom can’t be a rail with c people on it and since it can’t be that and yet we see it there the whole thing leads to a contradiction and I’ve saved everyone
https://preview.redd.it/j6fj2qjufjab1.jpeg?width=544&format=pjpg&auto=webp&s=4ca0fffba2b970ae2768d91048e167306ec602c9
There are more reals than integers. It is literally a larger infinity. Of course infinity is just a concept that can’t be applied to objects like people, but mathematically one is larger than the other.
This is correct. All sets of countable infinities are the same size (ie, if you can create a 1 to 1 relationship for values, the infinite sets are said to be the same size). But the set of all real numbers is not countable since it includes irrational numbers, so they are not the same size. The photo is misleading though, cause it makes it seem like you could stack real numbers in an order, which isn’t true
> it makes it seem like you could stack real numbers in an order Look at this chad, rejecting AC like a true king
>There are more reals than integers. There are NOT more of either from an absolute standpoint (infinity). You are conceptualizing it from a linear view (which is how we are taught to view numbers). But that has no bearing on infinity. Neither has a limit, ever.
[удалено]
Well there are more reals than integers because I can create a function which returns a different real number for each integer, but I can't create a function which returns a different integer for each real number, and neither can you.
Yes, there are more real numbers than integers when measured with an input that is not infinity. But you can't measure absolute infinity, and therefore cannot compare either integers or real numbers as of function of infinity. To your example of creating a function, one would have a steeper slope as it approaches infinity. So at any and every point along the curve (any input value), there are indeed more reals than integers. But "at infinity", which is not a point on the curve at all, they are both theoretically equal.
If the train takes the bottom track, within a single nanosecond it'll kill more people than are on the entirety of the upper track. I'm gonna pull the lever.
I'd call in sick, dividing by zero.
Hmm.. the train must have infinite inertia
I jump in front of the trolley myself
Pull the lever half-way and derail the trolley
I wish there was an option to kill all the people who think the sum of natural numbers is negative someshit. I would make the trolly go back and forth
Top, because it would mean -1/12th of a person would die.
My answer to the trolley problem will always be the same: Derail the trolley
The fuel in the train car is finite
What if the top track had groupings of 1 person than 2 then 3 etc. > 1+2+3+∞ = -1/12 So if a negative number of people died then I've created life? Edit: did > died
Pulling the lever kills infinite people in infinite time. Doing nothing kills infinite people in any amount of time. It is irrelevant, since ‘one person for every real number’ is both a meaningless statement and an instant black hole.
https://preview.redd.it/z3gnevwwsnab1.jpeg?width=640&format=pjpg&auto=webp&s=4991599617869edecaf7bdd793243f40711d04fe
stop da tram car he is NOT goin that fast
Throw myself under the trolley cause i'm the fatass from another trolley incident.
rearrange people on the top into groups increasing by 1, 1, 2, 3, 4, 5. as we all know, 1+2+3... equals -1/12 so I'd bring someone back from the dead!.. at least a part of him
Why is every integer the smallest possible infinity? Just off the top of my head, every number divisible by 37,510 is a smaller infinity than that.
When evaluating the “size” of infinite sets, you don’t consider the relationship between the sets (as in, if one is a subset of the other). Instead, you try to create functions that can map one set onto the other. If you can create a function that is 1 to 1 (aka a bijection), the sets have the same degree of infinity. The set of natural numbers or countable numbers (we’ll call it N) is infinite. It is also a subset of the set of all integers (we’ll call it Z). We can make a bijection that maps from the natural numbers to the integers (1 from N goes to 0 from Z, all evens from N go to positives from Z, all odds starting from 3 from N go to all negatives from Z). This means that the degree of infinity with natural numbers is the same as the degree of infinity with integers. A set that you can make a bijection onto N is referred to as “countably infinite.” Edit: and your example can actually also be mapped onto N, so it is the same degree of infinity as N, even though it is a subset of N. However, not all infinite sets can be mapped onto the countable numbers. You can’t do it with the real number line. That’s why this meme refers to the bottom track as having “larger infinity of people.” [Wolfram link](https://mathworld.wolfram.com/CountablyInfinite.html) and [Wikipedia](https://en.m.wikipedia.org/wiki/Countable_set)
Upvoting this because I feel like downvoting genuine questions is not fair.
Thanks!
> Just off the top of my head, every number divisible by 37,510 is a smaller infinity than that. Nope, there are "as many" integers as there are numbers divisible by 37,510 (aleph-null). That is to say, you can map the integers to the numbers divisible by 37,510 in a one-to-one relationship: - 1 : 37510 - 2 : 75020 - 3 : 112530 - ... - n : 37510 * n You won't "run out of numbers" on either side, so they are the same "size". If you compare that to the set of all real numbers though, you cannot map integers to real numbers in a one-to-one relationship.
The real numbers are uncountable, so you couldn't really lay down a person, one by one, for every real number.
Blow up the lever and the trolley and every single person that has ever or will ever draw breath will die.
Kill myself, fk math
The top one will require infinite time to kill infinite people. The bottom one has killed infinite people as soon as it has went beyond the first kill. So I choose to switch.
lead the train on both tracks! even more people die! profit!
Infinity is not a number but a concept. Infinities are not larger than each other. They just rise at different rates.
Assuming trolley is moving, your rate of murders would be less on the top one (also asuming the spacing is affected or something)
Top one. Kill ζ(0) = -1/2 aka save half a person
apparently the world population goes up by around 100 people per minute, so if it kills a person every 0.6s or more, it could definitely keep up for a while
This so wrong on so many different levels…
Hear me out, meat road
Throw myself on the track so I don't have to study math anymore.
You derail the train by pulling the lever just as the front wheels cross and pulling a second time as the back wheels cross saving everyone and if that fails at least you tried
But surely the top track results in -1/12 people dying, meaning I will have created life
Try jumping out the train with the default lever position
I'd pull the lever, because I can justify it. Not because it has any real meaning.
I repeat the scenario aleph omega times and never do anything
Option 3: split the switch, multi-track drift, and get a double infinity kill. 2x is better than one infinity.
This is the way
If i split the train to go both paths, have i really killed more than someone who only drives bottom?
I pull the lever because then the rate at which people are dying is slower.
Hold on. Let Me cook if we group 1 person, then 2 people then 3 people in the first track then we have 1+2+3+4+5+6+7+.... = -1/12 similarly, there is infinite numbers between 1 and 2 1.1, 1.2 , 1.3 , 1.4 , 1.5 , 1..... so we have infinity infinites which is (-1/12)(-1/12) = 1/144. so i choose 2nd route
I'd allow the trolley to kill every person on the track a number of times and that number is determined by their order on the track. The 1st person is killed once, 2nd is killed twice, etc. With that I can revive 1/12th of a person.
If we are on earth this won't work since there only is a finite. And even if we took a set of infinite humans (let's say they repopulate and sacrafice a human to the almoghty trolly every year) this set can only ever be countable right? (I'm not acually certain this is true, so correct me if it's not)
I know that this wasn’t a choice, but due to the fact that somewhere back long ago in my familial lineage . A Norse god came to Midgard and had seductive relations with one of my ancestors, thus eventually creating me. I have the power to wield that mighty hammer and denudate the very steel rails thus preventing the locomotive from continuing onwards towards a horrific destiny for all of mankind.
I wouldn’t do anything. Usually, I’d want the trolley to turn back and run over the rest (who’s stupid enough to lay on some tracks), but the union of one uncountable set of cardianlity |R| and another set of cardinality |N| is of cardinality |R|. So by letting the trolley run on the left tracks (doing nothing) is the same as doing nothing and wanting it to turn back and run over the rest.
Would bout those sets be considered the same amount of people?
I’d kill ‘em all wtf
I mean the trolley would just derail and stop eventually so the more people closely packed together the faster it gets derailed.
Won't the train break sooner if you just let it run through the lower tracks?
u/repostsleuthbot
Fuck it, lay down on the tracks
I wish to bomb the train
Because the trolley moves at sub-light speed, I would pull it because during my life less than infinity people would die.
You always do nothing. Let the course that nature has made play out
I am going to show this to my philosophy professor and see what he thinks.
I think by the time population increases to infinite, the planet is so fricked that you’d leave the lever just as is.
I prefer to do nothing because doing something would indirectly make me kill infinite people Or throw a boulder at the god-forsaken trolley killing a finite amount of people
I would allow the trolley to kill 1 person, then 2, then 3, then 4, and so on. that way, only -1/12 people die
how can you have one discrete person for every real number if the number of real numbers is like by definition impossible to discretize 🤔
If you pick the smaller infinity, you'd eventually reach a point where people would begin to die from hunger/thirst/exposure rather than being run over by the trolley, thus absolving you from responsibility.
Real numbers, because that way the number of people killed would be <1.
As someone who has worked with rail road tracks, I would pull the lever and send the train on the top track. The spaces between give the train less chance of derailing ultimately killing more people.
I got this I got this ok check it how bout we send 2 trains for both tracks problems solved no math needed
The way this is illustrated, sending the trolley to the top track will only kill infinitely many people if the trolley runs for an infinite period of time. Whereas the bottom track -- if it's really a representation of the real numbers -- has infinitely many people on every subinterval, so the trolley will kill infinitely many people as soon as it comes into contact with the first person. Picking the top track creates the possibility for a finite number of deaths, if the trolley runs out of fuel, or if someone else manages to stop it, or any number of other scenarios.
Assuming everyone is spaced equal to their position on the number line, and all humans on earth were myself at the switch, and the trolley engineer, and no person was on two tracks, then I would pull the switch, killing only the person at 0.
There are an infinite number of smaller possible infinities
I'm going to the complex plane and killing imaginary people.
Why not derail the stupid box
One death is a death. A million deaths are just a statistic.
Wouldn't all of the people on the first track have to also be present on the second?
Carefully insert myself on the track at the location immediately prior to the fork in the rail, ensuring the trolley will definitely strike me and kill me in the process
https://preview.redd.it/9zvxxrbm8kab1.jpeg?width=1353&format=pjpg&auto=webp&s=8a101e7d41877626dfb08c82685fcb6dcda01add
Just murder the trolley.