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.
I've occasionally wondered at the origin of that image but never felt like looking into it. Thanks for the link, the whole thing is very funny! Really nails the Initial D parody!
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.
In any non-empty, finite interval on the real number line, there are uncountably infinitely many numbers = people in this thought experiment. If you think of physical space as continuous, we cross infinitely many points in any finite movement.
I'd like to see one of the numerous paradoxes you refer to.
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.
If there are infinite numbers, then there's 3 in there somewhere.
No, this is not true. Just because you have infinitely many numbers in some collection, doesn't mean one of the numbers in your collection has to be 3.
Look at the number line. There are infinitely many numbers on the number line between 1 and 2. For example 1+1/2, 1+1/4, 1+1/8, ... are in there (among many others). But all of the numbers between 1 and 2 are strictly smaller than 3, so none of them can be 3.
Alternatively, there are infinitely many numbers strictly smaller than 3, none of which are 3 either.
If 3 is not there then it's not infinite.
Well consider the set of numbers 3+1, 3+2, 3+3, 3+4, ... (the set of integer numbers strictly larger than 3). This set of numbers is also infinite and does not contain 3. So a set being infinite doesn't imply it must contain the number 3.
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.
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
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"
No. In any interval of the real numbers there's an uncountable infinity of real numbers. No matter how much you stretch the track any neighborhood, no matter how small, will need an infinite number of people in it.
There being a person for every real number doesn't mean there's a person at every real point on the track. If it did, then there would be people inside of each other, and we can visually see that the people are laid down next to one another.
No. If you put them in order one after another you are not talking about the real numbers. There is no "next" real number and no possible way to visit them all one at a time like with the rationals.
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.
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.
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 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.
I still would not be able to live with any action that caused people to die, whether it was my moral fault or not. And I wouldn't want to have to live with that either.
The difference is I didn't pull a lever or make a choice to help ensure that those people who die every day would die. And I disagree about ignoring things because I "have no reasonable influence" over them. I might not be able to change the fact that people die every day, but I sure as hell can act responsibly to help make sure I'm not part of the problem (i.e, I'm a safe driver, I don't drink, I don't own a gun, etc.). I do not think that anyone on earth is more non-ignorant of and conscientious about the plight of others on this planet, something I think about constantly.
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.
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.
Well, if each universe itself is infinite, then there are infinite planets, meaning the number of planets that are not earth is infinite. So, if there are infinite universes that are, themselves, infinite, then the infinity of universes that do not contain earth is infinitely larger than the infinity of universes that do.
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 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.
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.
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.
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.
Maybe we should talk about what "infinite" means. I'd like to propose the following idea: a sequence of things is infinite, if there is always "one more" object to consider. We could also say that for any number of finite steps, there is always another object of the series we haven't looked at yet.
As an example, the sequence of natural numbers would satisfy this: if I start considering the sequence 1, 2, 3 and so on, if I ever stop after finite time (say 1729 steps), I can always compute +1 to find another element of the sequence I haven't seen yet.
Also consider the following: the set of all numbers between 0 and 1 is in some sense bounded. However, I can find an infinite sequence of numbers in this set: consider
1/1, 1/2, 1/3, 1/4, ...
These numbers are always between 0 and 1, and are infinitely decreasing.
Perhaps the confusion comes from you talking about infinity as in a number which is larger than any real or natural number, while I'm talking about sizes of sets of infinite size. As I had demonstrated earlier, we can show the existence of uncountable infinite vs countably infinite sets, while such distinctions don't really come up in limit theory and calculus.
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.
My degree is in math. I feel pretty confident in saying that you are tossing around a whole bunch of words without actually knowing what they mean in a mathematical context.
If you disagree, try the following:
What is a function? What is an injective function? What is a surjective function? What is a bijection?
In mathematics, what does it mean for a set to be finite?
In mathematics, what does it mean for a set to be infinite?
I'm willing to continue this conversation if you can explain to me in reasonably rigorous terms what those words mean. I'll help you do it too. The link I sent you in my previous post that mentions cardinal numbers links you to a wikipedia page that links to articles explaining what finite and infinite sets are in the first paragraph.
To be clear here, your answer for 2 specifically should rely on your answer from 1 as the mathematical definition of a finite set is in terms of functions and bijections.
Here are some bonus questions for you to try also:
In mathematics, what does it mean for a set to be countable?
In mathematics, what does it mean for a set to be uncountable?
A finite universe, the one in which we live, can only produce finite objects. Those finite objects can only produce other finite objects. A finite object cannot create an infinite object, as the act of creation would be a starting point for the object, and if an object has a starting point or an end point, which are really the same thing, then the object is a finite object.
If a set of numbers originates from a starting point and moves away from that point in a seemingly infinite distance, and then you decide to traverse that set in the opposite direction towards the starting point, the starting point becomes an ending point, and if an object, in this case the set itself, has an ending point, it is a finite object. Finite objects cannot create infinite objects because the act of creation would negate their infinity. Infinity is neither created nor ends, nor does it have size, shape, or form.
None of this includes the correct answers to the questions I asked you. I'm not going to read anything else from you until you correctly answer the questions I asked.
I find it interesting that you have a degree in math, and apparently have never questioned a question. As I've demonstrated, in the posted problem, the statement "some Infinities are bigger than other infinities" is an illogical statement. The mere statement that there are multiple infinities, negates either objects identification as being infinite, and reduces both objects to finite objects, as the only way these objects can be determined to be seperate from each other is through a boundary that would impose a starting or ending point on each object, which in turn reduces them into finite objects.
I also find it interesting that you resort to gate keeping to try and control a situation that you are frustrated by. I was able to simply and clearly demonstrate my position. I also demonstrated the technique of: solving the problem by defeating its purpose. I've also demonstrated the difference in how a mathematician and an engineer attempt to solve a problem.
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.
Multi-axis drifting!?!?
Deja Vu!
For anyone who cares:
https://densha.org/
https://comick.io/comic/initial-d-densha-de-d-doujinshi
I've occasionally wondered at the origin of that image but never felt like looking into it. Thanks for the link, the whole thing is very funny! Really nails the Initial D parody!
This has everything:
This is one kaiju or sentai squad away from being peak Japan.
Aw, yeah, that's sick! I also choose this option.
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).
I'm pretty sure that leads to multi-track drifting, and so all the people die.
Source: https://i.kym-cdn.com/entries/icons/facebook/000/000/727/DenshaDeD_ch01p16-17.jpg
This is quintessential anime action. So ridiculous, yet so awesome.
🤣
Don't worry, the first body or two will take care of it!
I'm no expert, but I'd expect such a slow moving trolley to eventually derail itself anyway on account of all the corpses
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.
I think you just passed the Trolley version of the Kobayashi Maru. Well done.
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.
Way to stop the trolly problem dead in its tracks.
If the leading wheels are allowed to continue any interval down the original track, uncountably infinitely many people die.
Only if those people can also be infinitely packed into the distance the leading truck (the set of wheels) manages to travel.
Which, I guess is fair play in a thought experiment involving different sizes of infinities. :)
I think that wad the premise, yeah.
I would question the ability to line people up on a railroad track such that they have a 1:1 correspondence with the real numbers.
It's totally doable because they are real people.
Yeah, for any length of track, you would need to stack infinite people...
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.
It’s powered by screams.
The blood of the innocent also works
We have nuclear subs, why not nuclear trollies?
Nuclear lasts a long time, but it's nothing compared to infinity.
An infinity cube, of course
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.
just use a well ordering of the reals and you should be fine
Has anyone tried just asking the trolley to stop?
Or stopped the person who keeps tying all these people to the trolley tracks?
Or trying to understand its innate desire to kill?
It has tasted blood, it's too late to reason with it
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].
Found the Canadian!
It is my understanding that the trolley just wants to go forward. It doesn't care whether it kills people or not.
Therefore, make the trolley go in circles.
Or in reverse
Sorry, that's only an option of you have a Pro subscription.
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.
The straight ahead track actually kills an infinite number of people every interval of time.
The tram travels at light speed and so time no longer flows for you. You exist in a singular moment of splattergore.
But even light speed is finite for the people on the track. It's only the tram that stops experiencing time.
Also, you're not on the tram. You're standing at the switch.
All trolleys to date have been finite. A trolley which can kill an infinite number of people would truly be a marvel of engineering.
Every finite trolley passes infinitely many points when moves, if you accept space as infinitly divisible (structured as the real numbers).
The train tracks are linear time on Earth. It's basically the choice between letting people be killed or dying of old age.
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.
In any non-empty, finite interval on the real number line, there are uncountably infinitely many numbers = people in this thought experiment. If you think of physical space as continuous, we cross infinitely many points in any finite movement.
I'd like to see one of the numerous paradoxes you refer to.
Pulling the lever will kill people slower, therefore less deaths in the lifetime of the universe.
Fewer deaths
Gram
So I won't do it
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?
Pull the lever, thus killing -1/12th people.
Killing -1/12th? I didn't know it can revive people.
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!
but if the trolley moves at a faster pace than you so you will never catch up?
Just ride another trolley on the other track.
An infinite track has no end, just like a number line.
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.
That trolleys going to derail eventually. So the one with more people since they are tightly packed and it can't build momentum.
But isn't it more likely to derail if it gains momentum?
Depends
Not if the track is perfectly straight.
There are People lying on it, so it's probably pretty uneven and bumpy, no?
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.
Huh?
Any non-empty interval on the real number line holds uncountably infinitely many points.
Shit man if there's an infinite amount of people there must also be an infinite amount of track. So forget philosophy, I'm getting rich!
Fuck you Ayn Rand! I’m the railroad magnate now!
I come to an agreement with the person who has tied these people to the tracks to untie every 2nd person. I save an infinite number of people!
I tried to do a similar deal and ended up with negative one twelfth of a person dead.
The solution that gains us a person at the limit
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.
This feels like a Warhammer thing.
shouldn't there be at least one guy on the trolley?
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.
I don't think a black hole would have time to form before the entire universal collapse, though
that's infinite mass inside infinite volume right there, we aren't talking about only infinite density anymore
we need to get a theoretical physicist on this... track
I kill the trolley driver. The Dead Man button makes that the trolley stops.
Everybody dies, no matter what choice you make. It's just a matter of time.
There are infinite numbers between 1 and 2, none of which are 3.
Then wouldn't that make this statement false?
Which statement?
There are infinite numbers between 1 and 2, none of which are 3.
If there are infinite numbers, then there's 3 in there somewhere. If 3 is not there then it's not infinite.
Oh okay.
No, this is not true. Just because you have infinitely many numbers in some collection, doesn't mean one of the numbers in your collection has to be 3.
Look at the number line. There are infinitely many numbers on the number line between 1 and 2. For example 1+1/2, 1+1/4, 1+1/8, ... are in there (among many others). But all of the numbers between 1 and 2 are strictly smaller than 3, so none of them can be 3.
Alternatively, there are infinitely many numbers strictly smaller than 3, none of which are 3 either.
Well consider the set of numbers 3+1, 3+2, 3+3, 3+4, ... (the set of integer numbers strictly larger than 3). This set of numbers is also infinite and does not contain 3. So a set being infinite doesn't imply it must contain the number 3.
Ah, thank you for the explanation. That makes sense now.
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.
Reminds me of this: https://neal.fun/absurd-trolley-problems/
This is f'ing hilarious 🤣
This is awesome
I just tried to kill the most people every time and apparently a lot of people agree with me
People die faster if you do nothing, so doing nothing seems like the obvious choice
The trolley goes at infinite speed after the branch point. What's your outside the box answer now?
Halfway through the branch point pull the lever to derail the trolley?
it'll just do this
which size infinite speed we talkin’? if its faster than light then maybe we got ourselves a time travel trolley 😎
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!
resumes ranting
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.
That trolley is definitely stopping before it makes it through all those people on the bottom track.
Multi-track drifting, baby. Double infinite.
I'm just waiting for the black hole to form just from the mass of the infinite people between 0-1 on the Reals track.
Jump in front of the trolley, someone else's problem
Would suck being the last person on either track. It'd be a long and boring wait while tied up
Yeah, we actually have two natural sets here.
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
edit2: lmao I'm not the first
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"
Given infinite track, the reals could have enough space between them to avoid collapsing too
No. In any interval of the real numbers there's an uncountable infinity of real numbers. No matter how much you stretch the track any neighborhood, no matter how small, will need an infinite number of people in it.
There being a person for every real number doesn't mean there's a person at every real point on the track. If it did, then there would be people inside of each other, and we can visually see that the people are laid down next to one another.
No. If you put them in order one after another you are not talking about the real numbers. There is no "next" real number and no possible way to visit them all one at a time like with the rationals.
This comment section is politics in action! :-P
i love stirring the pot.
If you want to be a true masochist, you could re-run the experiment on Reddit - hurk 🤮.
The beauty of Lemmy is that here we can at least talk about such neat things:-).
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.
not an expert but the integer one is at the top i think
"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.
Thanks. Now I know I should avoid using LLM for anything related to maths.
I'm sure if I tried to rephrase the problem getting every detail wrong, I'd do a worse job than this.
But I'd change the number of tracks.
If we have infinite people, it wouldn't be such a bad thing to lose a couple.
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.
i'd ask for a second 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.
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 am sure even countably infinite people would violate some law of thermodynamics.
If you subscribe to the idea that the universe is infinite, there are possibly infinite people in it.
I want to unsubscribe, where do I click
Infinity people always die. Even if you don't make a decision.
I pull the lever and invoke Zeno's paradox to ensure the trolley's position remains < 1 for eternity.
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.
from the picture this is true but from the statement alone both options are identical
I leave it at whatever it was set at before I arrived. Why mess with destiny?
I quickly carry the people to the other side so they all can get run over.
Invent a new number system that provides aneven smaller infinity
I actually would like to choose the track where the number of people increases by one (so 1, 2, 3, 4...) and then the train will kill -1/12 people
PS Yes, I know this sum result is problematic, it's only a joke
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.
Except that the trolley is an Unstoppable Object.
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.
I don't agree to it. I think that making no choice, is not a choice. Therefore you are not responsible for it.
I still would not be able to live with any action that caused people to die, whether it was my moral fault or not. And I wouldn't want to have to live with that either.
ok then. you do you
i just wonder how you deal with the fact that people die every day, with no fault of yours.
sometimes you just have to ignore things that you have no reasonable influence over.
The difference is I didn't pull a lever or make a choice to help ensure that those people who die every day would die. And I disagree about ignoring things because I "have no reasonable influence" over them. I might not be able to change the fact that people die every day, but I sure as hell can act responsibly to help make sure I'm not part of the problem (i.e, I'm a safe driver, I don't drink, I don't own a gun, etc.). I do not think that anyone on earth is more non-ignorant of and conscientious about the plight of others on this planet, something I think about constantly.
Okay then, that makes sense.
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.
build new tracks to make the trolley run on (possibly in circles).
Do nothing - maximum destruction
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.
Are there more universes with earth or more without
Well, if each universe itself is infinite, then there are infinite planets, meaning the number of planets that are not earth is infinite. So, if there are infinite universes that are, themselves, infinite, then the infinity of universes that do not contain earth is infinitely larger than the infinity of universes that do.
String Theory
Slip the switch, like always
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.
Probably pull the leaver cuz then I can jump in front of the train.
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.
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.
@tedu @science_memes @fossilesque Can we space them out so the frequency is the same? 😂
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.
@EunieIsTheBus @science_memes It was half joke, half paradox. 😁
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.
Yes. Right under trolley. Will derail it.
Pull the switch as the trolley is on that rail so it gets stuck and the trolley kills nobody
Gödel posse represent!
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
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.
Maybe we should talk about what "infinite" means. I'd like to propose the following idea: a sequence of things is infinite, if there is always "one more" object to consider. We could also say that for any number of finite steps, there is always another object of the series we haven't looked at yet.
As an example, the sequence of natural numbers would satisfy this: if I start considering the sequence 1, 2, 3 and so on, if I ever stop after finite time (say 1729 steps), I can always compute +1 to find another element of the sequence I haven't seen yet.
Also consider the following: the set of all numbers between 0 and 1 is in some sense bounded. However, I can find an infinite sequence of numbers in this set: consider 1/1, 1/2, 1/3, 1/4, ...
These numbers are always between 0 and 1, and are infinitely decreasing.
Perhaps the confusion comes from you talking about infinity as in a number which is larger than any real or natural number, while I'm talking about sizes of sets of infinite size. As I had demonstrated earlier, we can show the existence of uncountable infinite vs countably infinite sets, while such distinctions don't really come up in limit theory and calculus.
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].
In the cardinality sense this is objectively untrue by Cantor's theorem or by considering Cantor's diagonal argument.
Edit: Realized the other commenter pointed out the diagonal argument to you very nicely also. Sorry for retreading the same stuff here.
Within other areas of math we occasionally deal positive and negative infinities that are distinct in certain extensions of the real numbers also.
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.
My degree is in math. I feel pretty confident in saying that you are tossing around a whole bunch of words without actually knowing what they mean in a mathematical context.
If you disagree, try the following:
What is a function? What is an injective function? What is a surjective function? What is a bijection?
In mathematics, what does it mean for a set to be finite?
In mathematics, what does it mean for a set to be infinite?
I'm willing to continue this conversation if you can explain to me in reasonably rigorous terms what those words mean. I'll help you do it too. The link I sent you in my previous post that mentions cardinal numbers links you to a wikipedia page that links to articles explaining what finite and infinite sets are in the first paragraph.
To be clear here, your answer for 2 specifically should rely on your answer from 1 as the mathematical definition of a finite set is in terms of functions and bijections.
Here are some bonus questions for you to try also:
In mathematics, what does it mean for a set to be countable?
In mathematics, what does it mean for a set to be uncountable?
A finite universe, the one in which we live, can only produce finite objects. Those finite objects can only produce other finite objects. A finite object cannot create an infinite object, as the act of creation would be a starting point for the object, and if an object has a starting point or an end point, which are really the same thing, then the object is a finite object.
If a set of numbers originates from a starting point and moves away from that point in a seemingly infinite distance, and then you decide to traverse that set in the opposite direction towards the starting point, the starting point becomes an ending point, and if an object, in this case the set itself, has an ending point, it is a finite object. Finite objects cannot create infinite objects because the act of creation would negate their infinity. Infinity is neither created nor ends, nor does it have size, shape, or form.
None of this includes the correct answers to the questions I asked you. I'm not going to read anything else from you until you correctly answer the questions I asked.
I find it interesting that you have a degree in math, and apparently have never questioned a question. As I've demonstrated, in the posted problem, the statement "some Infinities are bigger than other infinities" is an illogical statement. The mere statement that there are multiple infinities, negates either objects identification as being infinite, and reduces both objects to finite objects, as the only way these objects can be determined to be seperate from each other is through a boundary that would impose a starting or ending point on each object, which in turn reduces them into finite objects.
I also find it interesting that you resort to gate keeping to try and control a situation that you are frustrated by. I was able to simply and clearly demonstrate my position. I also demonstrated the technique of: solving the problem by defeating its purpose. I've also demonstrated the difference in how a mathematician and an engineer attempt to solve a problem.
To me you have demonstrated:
You don't know even the most basic definitions of the things you are trying to talk about.
You are possibly too willfully stupid to bother to learn said definitions.
You are capable of babbling incoherently about things you do not understand ad nauseum.