I take the square root of the negative trolley, then use my imaginary streetcar to establish a complex track so I can start killing in an additional dimension.
It's always better to gain a full understanding of the system when trying to make important decisions.
The trolley has two sets of wheels, leading and trailing, both of which must remain on the same set of tracks.
The switch is designed to enable the trolley to change course, moving from one set of tracks to the other.
Throwing the switch after the leading set has passed, but before the trailing set has reached the switch points will cause the two sets to attempt travel on separate tracks. The trolley will derail, rapidly coming to a halt. If the trolley is moving slowly enough to permit this action, nobody dies.
Source: former brakeman (one of the people responsible for throwing switches), section hand (one of the people responsible for installing switches), and railroad welder (one of the people responsible for field repairs of switches).
Yes, or come to a halt. You'd be surprised at how little it takes to reduce the already low friction to nothing. A bit of blood and a bit of resistance will bring it to a halt pretty quickly.
Thanks. This is the first time I've seen a jokey enough presentation to feel comfortable in treating it as a hypothetical reality rather than a moral/ethical exercise.
OR... if you can keep the wheels spinning really fast, you could "drift" the trolly, keeping a set of wheels on each track and kill everyone on both tracks into infinity.
If we are already dealing with infinities of peoples then we can deal just as easily with infinities of tracks. I just struggle to see what kind of power source the trolly uses to plow through that many people.
The real question for me is what unit of distance would be used for the integer representation… It could take 1 meter, 1 Km, 1 Au, or even 1 Infinity to represent the distance between every person and the next. Also, are we using a linear or logarithmic scale?
This is not to mention the lack of info on how fast the train is going, and whether or not it’s accelerating.
In these scenarios the trolly is too close to stop before running the victums over.
Although in this particular time, having the trolly stop would save an infinite number of lives compared to the casulaites, which would actually help it stop fatser as bodies do not make good railroad tracks [citation needed].
At any point in time, a finite amount of time has passed, and the trolley has killed a finite amount of people. The correct track is the one that, at any given time, will have killed fewer people. Unless the trolley speeds up to account for that and always kills n people per second, the top track will result in less deaths over any period of time.
Assuming that it takes some amount of energy to kill one person, and that the trolley doesn't have an engine with infinite power, choosing the bottom track would save lives. The trolley would have to expend an infinite amount of energy to move any distance from the starting point, so it would just get stuck there while trying to crush the unimaginable amount of people bunched up in front of it.
But getting anywhere on the lower track will kill infinitely many people. You cannot kill finitely many people on the lower track. Well, unless you derail at exactly the first. On the upper track, a stop at any point will have killed only finitely many.
One person can only be on the spot for one number. As soon as more than one gets killed, that would mean that the trolley has traversed some distance, which implies that it has killed an infinite number of people. That is impossible in any finite timespan under the aforementioned assumption. Thus the only logical conclusion is that it gets stuck after the first person is killed, at the exact spot the first number is mapped to.
I guess there could also be a different solution when you look at the problem from a different angle. Treating infinity with this little mathematical care tends to cause paradoxes.
Or will leaving it cause the higher density of bodies to slow the trolley resulting in slower killing in the lifetime of the universe... which either way is infinite deaths?
Move to the end of the track and undo the constraints of people on the track. You will have infinite time until the trolly reaches the end, and can thusly save infinite lives by doing so.
Sadly, it takes an infinite amount of time to reach the end of the track. Thankfully, you have infinity time, though it's still inconvenient. An infinite number of people people will die (instead of an infinite number of people), but you'll save an infinite number of people in the end. After an infinite amount of time that will be infinitely better!
Actually, that's assuming that the track is a straight line. The distance from the beginning to the end of the track could be just a few feet, and the distance along the rail and thusly the number of people infinite.
I expect it would be more able to cleanly cut through the bodies or throw them out of the way with more momentum. If it's going slow it's more likely to ride up on top of a body. Anecdotally, I've heard that derailers tend not to work on fast moving trains.
"Eventually" on the densely packed track - even if almost instant - means uncountably many deaths. On the upper track, any eventual stop will result in only finitely many deaths.
Do nothing, since an infinite number of people implies an inconceivable population overgrowth, so the best possible good for humanity is to cull the population.
Heck, you could probably go out and genocide the rest of the population that isn't tied to the track and still not suffer any real loss. Then, you face the last true enemy: the bloodsoaked beast responsible for the deaths of untold billions- yourself.
Once you've slain that last creature, all of humanity that still remains will be those tied to the railroad track. The only living people will spend their entire lives knowing nothing but the track and the trolley, and the imposing fear that one day, they, too, shall be crushed under its wheels like those before them.
The only life remaining for the human race is now one of terror and eventual slaughter. There are no good outcomes to this conundrum. There are only the uncaring wheels of the trolley.
Just the existence of infinite people implies an infinite space to contain them, and an infinite ecosystem to have produced them. Concerns related to overtaxing a finite ecosystem don't apply.
The top track can be assumed to be of infinite length, but for the bottom track this is not enough - to fit ℵ people on it, they'll have to be infinitely compressed. And since they are compressed - they are already dead. I'm not pulling the lever - preventing the (farther) desecration of corpses does not merit killing people who are still alive.
As a mathematician, this strikes me as an entirely reasonable interpretation, except for the fact that the compressed bodies would form a black hole, killing everyone regardless.
So you're correct to say that you wouldn't pull the lever, but your reasoning still missed an important detail.
As an Engineer with a Physics background I say the most ethical choice is the real numbers side as the tram, having no room to accelerate between victims, will quickly stop, whilst it's more likely it can keep going for ever on the integer branch of the line.
A more effective vehicle for this would be a tank or maybe a steamroller.
(Note to self: keep this in mind if I ever become an Evil Overlord and need to execute large numbers of people in a gruesome manner)
If you let the train go, it would appear to stop immediately at the first person (assuming it has any reaction whatsoever to hitting a person) as there are infinitely real numbers between any two real numbers you could come up with.
Then you have a choice to do nothing and allow people die, or do a conscious choice to kill people. There's something for everyone, everyone wins (except the people on rails)
I replace the lever with a quantum switch so it can be a superppsition and kill everyone twice be ause they deserve it I mean look at that massive line of people there is no way they didn't know what was going on before egtting added to the tracks no species thos dumb deserves to escape the trolly my god how did they all get there -continues ranting as trolly aproaches-
PAUSE
And this makes about as much sense as the original question so no educating me!
Sorry, but technically you would kill infinite people, which while twice as many as infinite people is still the same amount of infinite people...
Might I suggest getting infinite doctors to try and rescue some run over people so they can in fact go to the end of the line and be killed a second...maybe even infinite times.
Seeing an infinite number of people lying there I deduce that I must be in some kind of thought experiment and let the trolley roll on while I look for a way to escape back to reality.
This is a complex problem, hence I pull an imaginary lever and divert the trolley onto the imaginary number line to kill infinite imaginary people. No one cares because they're imaginary
Did nobody have math class? The pictures are always misleading!
It never actually specifies the density the people are packed onto the track, the image implies an answer.
I'd argue that the densities should be considered to be equal, regardless of whatever that density value may be. We do not need to solve for the exact value to discuss the problem at hand!
Doesn't matter how far appart each person is placed when we are dealing in infinities. We still can map each one on each set without missing any. The cardinality is the same between them.
A representation of the real set would imply infinite superposition of people on the track line... Which means they are already dead lmao
I'd argue such an event would not only kill them but actually delete everything in that universe.
This is all a convoluted way of saying we are already dead in this scenario.
edit: correct integer to natural on first paragraph
I know many people despise generative AI, but what do you think of this result from Copilot? I am bad at maths so I wonder if you experts can tell.
In your scenario, you have two sets: the integers on the top track and the real numbers on the bottom track. The cardinality of the integers is equal to the cardinality of the real numbers, which is called the continuum hypothesis. Therefore, it seems intuitively more ethical to pull the lever and divert the trolley to the bottom track, where you kill fewer people in any finite time.
"The cardinality of the integers is equal to the cardinality of the real numbers, which is called the continuum hypothesis."
The cardinality of the integers is not equal to the cardinality of the reals. The integers are countable (have the same cardinality as the natural numbers). A very famous proof in set theory called Cantor's diagonal argument shows the reals are uncountable (i.e. not countable).
The continuum hypothesis is also not about comparing the cardinality of the reals and the integers or naturals (since we already know the above). The continuum hypothesis is about comparing the cardinality of the reals with aleph_1.
Within the usual set theory of math (ZFC set theory), we can prove that we can assign every set a "cardinal number" that we call its cardinality. For finite sets we just assign natural numbers. For infinite sets we assign new numbers called alephs. We assign the natural numbers a cardinal that we call aleph_0.
These cardinal numbers come with an ordering relationship where one set has a cardinality larger than another set if and only if its associated cardinal number is larger than the other sets cardinal number. So, alepha_0 is larger than any finite cardinal, for example. There is a theorem called Cantor's theorem that tells us we can continually produce larger and larger infinite cardinals in fact.
So, we know the reals have some cardinality, thus some associated cardinal number. We typically call this number the cardinality of the continuum. The typical symbol for this cardinality is a stylized (fraktur) c. Since aleph_0 is countable, every aleph after aleph_0 is uncountable. By definition aleph_1 is the smallest uncountable cardinal number. The continuum hypothesis just asks if aleph_1 and c are equal.
As an aside, it is provable that c has the same cardinality as the powerset of the naturals. We let the cardinality of the powerset of a set with cardinality x be written as 2^x. Then we can write the continuum hypothesis in terms of 2^{aleph_0} and aleph_1. The generalized continuum hypothesis just swaps out 0 and 1 for an arbitrary ordinal number alpha and its successor in this new notation.
Only the real cardinallity must. The integer cardinallity could have them spaced out enough that they won't collapse.
For you to do this trolley problem you'd need to be outside the real track black hole so the question becomes: do you let a trolley go into a black hole or do you switch it to an infinite track that kills an infinite number of people?
Edit: in which case the black hole must be infinitely far away and you don't even know about it. So: do you pull the switch to cause a trolley to start killing a seemingly infinite number of people? Which based on the other replies in this thread the answer is a resounding "yes"
Some infinities are bigger than others but those are both the same sized infinity, ℵ₀. Same if you multi-track drift.
Edit: I didn't read it closely enough, it says "one person for every real number". Which is indeed a larger infinity. However I don't think you can diagram that, the diagram is showing a countable infinity of people on the lower track.
Killing one person for each real number, the train will be killing an uncountably infinite quantity of people in any given finite time slice.
I was gonna say, these 2 infinities are the same. I think Vsauce made a second video on infinity to try and clarify it, but putting "more numbers" in between an infinite amount of numbers doesn't make it larger
I'll do nothing. Either way those people will eventually die - because of the train or because of starvation and dehydration. I would prefer the train.
If the tracks are scaled to the same unit (presumably one where one human width equals an infinitely small number), everyone in the top track would die of exposure before the trolley even reaches its first victim due to there being infinite distance between integer milestones, whereas everyone in the bottom track would be killed instantly due to any distance traveled having an infinite number of infinitesimals*. So I choose the bottom track to be merciful.
If the tracks don't share the same scale then we don't have enough information to make a judgment.
* Even though we already established the one human width rule. Could someone check my logic here? Infinities break my brain.
This was my take too, except I'd send the trolley to the integer track, where it would use infinite time to reach the first victim, thus the trolley never kills anyone. Problem solved.
Them dying to exposure is outside the scope of this task. :)
EDIT: I rolled a critical fail in reading comprehension and I thought the other track was N per integer instead of 1 per real number in the previous version of this comment.
The people in the real number track are already dead by the time the trolley arrives due to the forces involved in cramming them so tightly together. I.e. they are basically just a gore pile the moment after the people are somehow arranged like that.
I pick the real number track so that no one new has to die.
I get that the answer is supposed to be "it doesn't matter" but if you take time into account, it actually fucking does, and also makes it hugely obvious what the actual answer is.
I would take a sledgehammer and smash the trolley to bits, thus solving the problem and saving infinite number of lives. There's always another option available.
Oh.....it didn't state that in the graphic. If it IS an unstoppable object, then I'd have to throw myself in front of it after making either choice, because I couldn't and wouldn't want to live with either of those choices.
Since there's an infinite number of people to kill in either case I can just do nothing, and thus by inaction most of those infinite people will have more than enough time for someone else to rescue them. Maybe the State, that's what they're there for.
The existence of the bottom track would imply an infinite density of people, which would create a black hole and kill everyone involved, regardless of the trolley's presence
I have a tangential question I have been wanted an explanation for:
If there are infinite universes, would there be infinite earth's?
I remember (an) answer is infinite universes doesn't necessarily mean infinite earth's. A cool analogy of a CD rack was used when I read it, but I can't find it. Does anyone else have an explanation and/or analogy for this?
With infinite universes, every possible eventuality is realized an infinite number of times. There are infinite universes without earth and infinite universes with it.
Pull the lever. Save as many lives as you can and hope that someone that now wasn't killed as fast can help come up with a solution for the runaway trolley.
Was this an honest question? Because the answer is 'no'. You can't space them out or else the set of people on the lower track would be countable which is a smaller infinity than the ones of the real numbers.
To space them, you would have to take people of the track. Infinitely many. To be precise not all of them but as many as there are on the track.
If you kill two sets at the same rate, but one set is smaller, is it less bad?
The set with one person for every real number, they're neither spaced nor adjacent. It's kind of a Zeno's paradox scenario: no person can ever be first, next, or last. So I think if we can set the rate of killing the same, I'll choose the real numbers track in hopes that the trolley can't ever begin. If we set the rate at speed down the track, it's gotta be the integers.
Multi-track drifting. Also while some infinities are smaller if you're just counting out an infinite number of individual humans then I'm pretty sure they're the same size infinities one is just social distancing. Smaller infinities are ones like those in between each part of the bigger infinities. To represent a smaller infinity you'd maybe have to have an infinite number of smaller humans crammed into a spot the size of one of the spaces between the humans on the other track, or something along those lines. The real number track does contain smaller infinities between each integer via infinite decimal points but I don't think one track would technically be smaller than the other in this case since they run parallel to each other but neither are technically limited in the "length" of their infinity so to speak. But I could be misremembering how they classify smaller infinities.
The same thing most people would do when presented with a Trolly Problem for real. Analysis paralysis, choose to do nothing, then cry softly every night for the rest of my life.
Infinity cannot be divided, if it can then it becomes multiple finite objects. Therefore there cannot be multiple Infinities. If infinity has a size, then it is a finite object. If infinity has a boundary of any kind, then it is a finite object.
I'm not entirely sure I understand your comment, but the fact that there are more real numbers than natural numbers can be readily shown using something called cantor's diagonal argument. It goes something like this:
Suppose the set of real numbers and natural numbers had the same size. Then we could write down an infinite list, where each line represents some real number written in it's decimal representation. So something like
1: 3.14159265
2: 1.41421356
3: 0.24242424
...
This list goes on forever. We will now construct a new real number r as follows: The first number after the decimal point of r shall be different from the first number after the decimal point of the first number in our list, the second shall be different from the second decimal of the second number on the list, and so on (the name diagonal argument comes from this, we consider the entries on the diagonal from top left towards the bottom right).
The key point now is that this constructed real number is different from every single number on the list: After all, we have made sure it differs from each number on the list in at least one place. Therefore, it is impossible to write down the real numbers in such a way that each real number gets its own natural number: There are simply too few natural numbers for this. In particular, there are at least two different "sizes" of infinities.
The set, that has a measurable starting point, is a finite object. If infinity can be measured, then you have created a finite space, one that can be measured, within an infinite space, infinity itself, which cannot be measured. Infinity remains untouched and undivided. The sets that represent infinity are finite objects, that represent an infinite space, a representation which they can never truly achieve.
Infinity cannot be divided, if it can then it becomes multiple finite objects.
It really depends on what you mean by infinity and division here. The ordinals admit some weaker forms of the division algorithm within ordinal arithmetic (in particular note the part about left division in the link). In fact, even the cardinals have a form of trivial division.
Additionally, infinite sets can often be divided into set theoretic unions of infinite sets fairly easily. For example, the integers (an infinite set) is the union of the set of all integers less than 0 with the set of all integers greater than or equal to 0 (both of these sets are of course infinite). Even in the reals you can divide an arbitrary interval (which is an infinite set in the cardinality sense) into two infinite sets. For example [0,1]=[0,1/2]U[1/2,1].
If infinity has a size, then it is a finite object.
Again, this is not really true with cardinals as cardinals are in some sense a way to assign sizes to sets.
If you mean in terms of senses of distances between points, in the previous link involving the extended reals, there is a section pointing out that the extended reals are metrizable, informally this means we can define a function (called a metric) that measures distances between points in the extended reals that works roughly as we'd expect (such a function is necessarily well defined if either one or both points are positive or negative infinity).
If infinity can be measured, by either size, shape, distance, timespan or lifecycle, then the object being considered infinite is a finite object. Infinity, nothing, and everything follow these same rules. If there are two multiple infinite objects side by side to each other, which means there is a measurable boundry that seperates them, then those objects aren't infinite, they are finite objects, within an infinite space that contains them. Only the space that contains these objects is infinite. Any infinite numbers that are generated within this infinite space, regardless of where they originated within this space, belong to this single infinity. There is no infinityA or infinityB there is just infinity itself.