Population expansion is exponential but the tram moves at constant velocity, so by the time it reaches the end of the track of 8bn people there will be an exponentially increasing number of people further down the track.
pruwybn@discuss.tchncs.de
on 02 Oct 15:48
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Use the fact that a set people corresponding to the real numbers are laying in a single line to prove that the real numbers are countable, thus throwing the mathematics community into chaos, and using this as a distraction to sabotage the trolley and save everybody.
NoneOfUrBusiness@fedia.io
on 02 Oct 17:17
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Hey, maybe they're infinitely thin people, in which case you can (and necessarily must, continuum hypothesis moment) have one for every real number.
mumblerfish@lemmy.world
on 02 Oct 16:03
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In the top one you will never actually kill an infinite number of people, just approach it linearly. The bottom one will kill an infinite amount of people in finite time.
Edit: assuming constant speed of the train.
ivanafterall@lemmy.world
on 02 Oct 16:07
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I’m going bottom.
NOT LIKE THAT. Not like sexually. I just mean I want to kill all the people on the bottom with my train.
ConstantPain@lemmy.world
on 02 Oct 16:19
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For every integer, there are an infinite number of real numbers until the next integer. So you can’t make a 1:1 correspondence. They’re both infinite, but this shows that the reals are more infinite.
(and yeah, as other people mentioned, it’s the 1:1 correspondence, countability, that matters more than the infinite quantity of the Real numbers)
buffing_lecturer@leminal.space
on 02 Oct 16:35
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There are infinitely many rational numbers between any two integers (or any two rationals), yet the rationals are still countable, so this reasoning doesn’t hold.
The only simple intuition for the uncountability of the reals I know of is Cantor’s diagonal argument.
You can assign each rational number a single unique integer though if you use a simple algorithm. So the 1:1 correspondence holds up (though both are still infinite)
There are also an infinite number of rationale between two integers, but the rationals are still countable and therefore have the same cardinality as the naturals and integers.
NoneOfUrBusiness@fedia.io
on 02 Oct 17:22
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If people on the top rail are equally spaced at a distance d from each other, then you'd need to go a distance nd to kill the nth person. For any number n, nd is just a number, so it'll never be infinity. Meanwhile the number of real numbers between 0 and 1 is infinite (for example you have 0.1, 0.01, 0.001, etc), so running a distance d will kill an infinite number of people. Think of it like this: The people on the top are blocks, so walking a finite distance you only step on a finite number of blocks. Meanwhile the people on the bottom are infinitely thin sheets. To even have a thickness you need an infinite number of them.
PM_Your_Nudes_Please@lemmy.world
on 02 Oct 19:30
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There are an infinite amount of real numbers between 0 and 1. On the top track, when you reach 1, you would only kill 1 person. But on the bottom track you would’ve already killed infinite people by the time you reached 1. And you would continue to kill infinite people every time you reached a new whole number.
On the top track. You would tend towards infinity, meaning the train would never actually kill infinite people; There would always be more people to kill, and the train would always be moving forwards. Those two constants are what make it tend towards infinity, but the train can never actually reach infinity as there is no end to the tracks.
But on the bottom track. The train can reach infinity multiple times, and will do so every time it reaches a whole number. Basically, by the time you’ve reached 1, the bottom track has already killed more people than the top track ever will.
That’s still not doing it justice. If there were one person for every rational number there would be infinitely many in any finite interval (but still actually no more than the top track, go figure) but the real numbers are a whole other kind of infinite!
What I still don’t understand is where time comes into play. Is it defined somewhere? Wouldn’t everything still happen instantly even if there are infinite steps inbetween?
I guess it could be implied by it being a trolley on a track, but then the whole mixing of reality and infinity would also kind of fall apart.
Is every person tied to the track by default? If so, wouldn’t it be more humane to just kill them?
There aren’t infinite trams. There’s one tram that has to step over (roll through) one person at a time. Good luck to it making any progress, it will never get to the person numbered 1
turdcollector69@lemmy.world
on 02 Oct 22:33
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Different slopes.
On top you kill one person per whole number increment. 0 -> 1 kills one person
On bottom you kill infinity people per whole number increment. 0 -> 1 kills infinity people
You can basically think of it like the entirety of the top rail happens for each step of the bottom rail.
eleijeep@piefed.social
on 02 Oct 19:36
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The bottom one will kill an infinite amount of people in finite time.
instantaneously FTFY
HeyThisIsntTheYMCA@lemmy.world
on 03 Oct 02:33
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Practically no one dies on either path, since a tram is a real thing it can’t traverse infinities of people (which notably have among their mandatory elements mass and volume) very well. It would hardly get far. Its automatic braking would stop it in any case.
Whatever happens infinities of people still remain which exceeds the carrying capacity of our observable universe
dontbelievethis@sh.itjust.works
on 02 Oct 16:17
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Bottom. Greater probability that it gets stuck in the corpses.
TomMasz@piefed.social
on 02 Oct 16:30
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I remember seeing a science show on PBS where the presenter explained how there are different infinities by using set theory and the integers/reals. That was mind-blowing at the time.
magic_lobster_party@fedia.io
on 02 Oct 16:41
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Bottom.
Killing one person for every real number implies there’s a way to count all real numbers one by one. This is a contradiction, because real numbers are uncountable. By principle of explosion, I’m Superman, which means I can stop the train by my super powers. QED
plus uncountable infinity implies there is uncountable supply of humans, which is nice.
woodenghost@hexbear.net
on 03 Oct 07:20
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Also, almost all real numbers are undefinable. (Unless you’re using a model, that makes them countable.)
So that means, that almost all the “humans” on the bottom track are something we can not even imagine in principle. Wouldn’t be surprised, if infinite Superman’s were among them.
Either that or the humans are so “infinitely packed” that they’re probably already dead squashed into each other.
Now, if you put infinite people in a chamber, and then compress the chamber and then put an infinite amount of compressed chambers inside a chamber…
Will we have Real People?
OhNoMoreLemmy@lemmy.ml
on 02 Oct 16:42
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Bottom has infinite density and will collapse into a black hole killing everyone, and destroying the tram and lever.
Ah, so now Schwarzschild is driving the trolley!
Or maybe he’s coming to stop the trolley!
Or maybe Feynman is coming, to renormalize the infinities!
I really don’t know anymore! Aleph nought, Aleph omega…
go away, come again some other… perhaps infinite… day.
ThermonuclearEgg@hexbear.net
on 02 Oct 22:27
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The image actually says this
LadyAutumn@lemmy.blahaj.zone
on 02 Oct 16:46
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In the top case has it been arbitrarily decided to include space in between the would-be victims? Or is the top a like number line comparison to the bottom? Because if thats the case it becomes relevant if there is one body for every real number unit of distance. (One body at 0.1 meter, and at 0.01 meter, at 0.001, etc)
If so then there’s an infinite amount of victims on the first planck length of the bottom track. An infinite number of victims would contain every possible victim. Every single possible person on the first plank length. So on the next planck length would be every possible person again.
Which would mean that the bottom track is actually choosing a universe of perpetual endless suffering and death for every single possible person. The top track would eventually cause infinite suffering but it would take infinite time to get there. The bottom track starts at infinite suffering and extends infinitely in this manner. Every possible version of every possible person dying, forever.
CommissarVulpin@lemmy.world
on 02 Oct 16:48
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Okay, so what’s the point of “proving” that there some “infinities” are “bigger” than others? What’s the practical application here? Because an infinite hotel with an infinite number of guests is physically impossible, so I don’t see the point.
NoneOfUrBusiness@fedia.io
on 02 Oct 17:13
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Practical application in math tends to be like three degrees of separation and half a century removed from the math at play. In this case, all of modern mathematics is based on set theory, so it's more that this stuff allows us to do other, more practically useful math while knowing what we're talking about.
The practical consequence of this example is that the integers die regardless of what you choose.
However infinitely many people will survive if you choose the first option.
CommissarVulpin@lemmy.world
on 02 Oct 17:46
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And yet there can never, and will never, be a situation where an infinite number of people are tied to a railroad track. So this thought experiment is meaningless.
It’s more about set theory than the actual numbers.
Let’s say you have 100 people with everyone tied up across both tracks. Heads on one track and legs on the other. Let’s assume they die if the train touches any part of them, but you still need to choose between running over heads or legs.
The best choice is then legs, because there’s a probability of some of them being handicapped and not having legs.
A practical application is for example in probability theory (or anywhere that deals with measures) such as this question:
If we generate a random real number from 0 to 1, what is the probability that it is rational?
Because we know that the continuum is so much larger in a sense than the set of rationals, we can answer this confidently and say the probability is zero, even though it is theoretically possible for us to get a rational number.
Statistics deals with similar scenarios quite frequently, and without it we wouldn’t have the modern scientific method.
I’ve never been a fan of just saying “some infinities are bigger than others,” to be honest. Way too easy to misunderstand and it’s also kind of meaningless by itself.
wildncrazyguy138@fedia.io
on 02 Oct 16:55
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Like everything else in this holographic universe we live in, I’d just close my eyes and believe the bodies I’m trampling are imaginary.
Matriks404@lemmy.world
on 02 Oct 17:04
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Imagine being the first one being killed on any of these tracks.
The probability of that is…?
Mathematicians tell me, please, because my mind is breaking.
NoneOfUrBusiness@fedia.io
on 02 Oct 17:07
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It's 0. I mean someone has to be the first, but betting on any particular person to be the first will necessarily be a losing bet.
silasmariner@programming.dev
on 02 Oct 20:42
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But what if I know Steve’s first and bet it’s Steve?
NoneOfUrBusiness@fedia.io
on 02 Oct 21:04
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Then you're legally obligated to give me half your earnings.
I think on the bottom you have to be the zeroth, but typically the first person tied to the track would be the first, so if the first is at 1 they’re safe since there’s an infinity (a large infinity even) before them and there’s only one tram that can hit one person at a time
It’ll take infinite time just to start hitting
IAmNorRealTakeYourMeds@lemmy.world
on 02 Oct 17:07
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sort them so you kill one person first, then 2, then 3, then 4…
bizarroland@lemmy.world
on 02 Oct 17:50
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I would pull the lever and then steal a bus and knock the trolley off of the track, killing the least amount of people possible.
I take the square root of all the negative real numbers and kill in an entirely new dimension.
stupidcasey@lemmy.world
on 02 Oct 18:37
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I pull the lever, if the cart goes over the real numbers it will instantly kill an infinite amount of people and continue killing an infinite amount of people for every moment for the rest of existence.
If I pull the lever a finite amount of people will die instantly and slowly over time tending twords infinity but due to the linear nature of movement it would never actually reach Infinity even if there are an infinite number of people tied to the track a finite amount is all that could ever die.
dharmacurious@slrpnk.net
on 02 Oct 18:58
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So you’re going to let those infinite people on top stay tied to the track and starve to death slowly‽
PM_Your_Nudes_Please@lemmy.world
on 02 Oct 19:25
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I mean, in that case it’s not really a matter of the trolley killing them, per se. The number will tend towards infinity, until it suddenly spikes to real infinity as people starve.
Probably better than an infinite number of people waiting an infinite amount of time for there impending doom and then also an infinite number of people starving to death.
you have to remember ℵ^0 in this case is included in ℵ^1 or at least the numerical value is, which is the only information given.
I guess technically you could value one human soul above the other and technically this is philosophy? So I guess technically you should? but anyway everything that happens on ℵ^0 will also happen on ℵ^1 except more will always happen on ℵ^1 than ℵ^0 so whether there is unintended consequences or not doesn’t really matter. it’s always safer to pick the countable infinities.
Unless there is something innately good about physically having more people exist no matter there condition. but you would have to ask a philosopher about that one, I’m paid to pull lever’s not philosophize.
All the people tied to the track will die after a few days anyway.
krooklochurm@lemmy.ca
on 02 Oct 19:09
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I masturbate until I forget about the decision I have to make and then put off cleaning my apartment until I finally just run out, randomly pull the lever, and never think of the consequences again.
Of course by that point everyone has already starved to death which is the worst possible outcome.
Sunsofold@lemmings.world
on 02 Oct 20:11
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I ignore the question and go to the IT and maintenance teams to put a series of blocks, physical and communication-system-based, between the maths and philosophy departments. Attempts to breach containment will be met with deadly force.
Math is the philosophy department in that math is an extension of logic, which is in turn an extension of philosophy. You’d have a better chance of divorcing math from applied math (engineering/physics) than separating math from philosophy.
missfrizzle@discuss.tchncs.de
on 02 Oct 21:13
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you know, I’m not sure you can have an uncountably infinite number of people. so whatever that abomination is I’ll send the trolley down its way. it’s probably an SCP.
Geez, disconnect the trains so you can hit both lines at the same time, obviously.
helpImTrappedOnline@lemmy.world
on 02 Oct 21:55
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The second one.
It’ll be a bit rough, but overall should be a smoother ride for the occupants.
Randelung@lemmy.world
on 02 Oct 23:29
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What about a time loop where only one person dies, but infinite times?
InvalidName2@lemmy.zip
on 02 Oct 23:30
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Some infinities are bigger than other infinities
Is this actually true?
Many eons ago when I was in college, I worked with a guy who was a math major. He was a bit of a show boat know it all and I honestly think he believed that he was never wrong. This post reminded me of him because he and I had a debate / discussion on this topic and I came away from that feeling like he he was right and I was too dumb to understand why he was right.
He was arguing that if two sets are both infinite, then they are the same size (i.e. infinity, infinite). From a strictly logical perspective, it seemed to me that even if two sets were infinite, it seems like one could still be larger than the other (or maybe the better way of phrasing it was that one grew faster than the other) and I used the example of even integers versus all integers. He called me an idiot and honestly, I’ve always just assumed I was wrong – he was a math major at a mid-ranked state school after all, how could he be wrong?
Thoughts?
umean2me@discuss.online
on 03 Oct 00:20
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It is true! Someone much more studied on this than me could provide a better explanation, but instead of “size” it’s called cardinality. From what I understand your example of even integers versus all integers would still be the same size, since they can both be mapped to the natural numbers and are therefore countable, but something like real numbers would have a higher cardinality than integers, as real numbers are uncountable and infinite. I think you can have different cardinalities within uncountable infinities too, but that’s where my knowledge stops.
It’s pretty well settled mathematics that infinities are “the same size” if you can draw any kind of 1-to-1 mapping function between the two sets. If it’s 1-to-1, then every member of set A is paired off with a member of B, and there are no elements left over on either side.
In the example with even integers y versus all integers x, you can define the relation x <–> y = 2*x. So the two sets “have the same size”.
But the real numbers are provably larger than any of the integer sets. Meaning every possible mapping function leaves some reals leftover.
stevedice@sh.itjust.works
on 03 Oct 06:53
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Weeeell… not really. It’s pretty well settled mathematics that “cardinality” and “amount” happen to coinciden when it comes to finite sets and we use it interchangeably but that’s because we know they’re not the same thing. When speaking with the regular folk, saying “some infinities are bigger than others” is kinda misleading. Would be like saying “Did you know squares are circles?” and then constructing a metric space with the taxi metric. Sure it’s “true” but it’s still bullshit.
I side with you, though the experts call me stupid for it too.
if for all n < infinity, one set is double the size of another then it is still double the size at n = infinity.
calcopiritus@lemmy.world
on 03 Oct 04:34
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You’re not stupid for it. Since it makes sense.
However, due to the way we “calculate” the sizes of infinite sets, you are wrong.
Even integers and all integers are the same infinity.
But reals are “bigger” than integers.
stevedice@sh.itjust.works
on 03 Oct 06:45
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I know it seems intuitive but assuming that a property holds for n=infinity because it holds for all n<infinity would literally break math and it really doesn’t make much sense when you think about it more than a minute. Here’s an easy counterexample: n is finite.
In the end it depends on your definition of “bigger”. Traditionally, we use “bigger” to just refer to who has the highest number or count, but neither apply here.
Imagine we have a straight line of skittles. Lines with more are defined as “bigger”. Now imagine the line is expanded into another dimension, a square. Is it still “bigger”? Each line has the same count, so it’s traditional “bigness” value is unchanged…
prime_number_314159@lemmy.world
on 03 Oct 02:27
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Two sets with infinitely many things are the same size when you can describe a one to one mapping from one set to the other.
For example, the counting numbers are the same size as the counting numbers except for 7. To go from the former set to the latter set, we can map 1-6 to themselves, and then for every counting number 7 or larger, add one. To reverse, just do the opposite.
Likewise, we can map the counting numbers to only the even counting numbers by doubling the value or each one as our mapping. There is a first even number, and a 73rd even number, and a 123,456,789,012th even number.
By contrast, imagine I claim to have a map from the counting numbers to all the real numbers between 0 and 1 (including 0 but not 1). You can find a number that isn’t in my mapping. Line all the numbers in my mapping up in the order they map from the counting numbers, so there’s a first real number, a second, a third, and so on. To find a number that doesn’t appear in my mapping anywhere, take the first digit to the right of the decimal from the first number, the second digit from the second number, the third digit from the third number, and so on. Once you have assembled this new (infinitely long) number, change every single digit to something different. You could add 1 to each digit, or change them at random, or anything else.
This new number can’t be the first number in my mapping because the first digit won’t match anymore. Nor can it be the second number, because the second digit doesn’t match the second number. It can’t be the third or the fourth, or any of them, because it is always different somewhere. You may also notice that this isn’t just one number you’ve constructed that isn’t anywhere in the mapping - in fact it’s a whole infinite family of numbers that are still missing, no matter what order I put any of the numbers in, and no matter how clever my mapping seems.
The set of real numbers between 0 and 1 truly is bigger than the set of counting numbers, and it isn’t close, despite both being infinitely large.
Change the numbers to rubber balls with pictures of ducks or trains and different iconography. You can now intuit that both sets are the same size.
for_some_delta@beehaw.org
on 03 Oct 03:16
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Hilbert’s Paradox of the Grand Hotel seems to be the thought experiment with which you were engaged with your math associate. There are countable and uncountable infinities. Integers and skip counted integers are both countable and infinite. Real numbers are uncountable and infinite. There are sets that are more uncountable than others. That uncountability is denoted by aleph number. Uncountable means can’t be mapped to the natural numbers (1, 2, 3…). Infinite means a list with all the elements can’t be created.
There are different ways to compare the “sizes” of infinite sets. So you could both be right in different contexts and for different sets. But the one concept people mostly mean, when they say, that some infinities are larger than other, is one to one correspondence (also called “cardinality”):
If you have a set and you can describe how you would choose one element of a second set for each element of the first and end up with every element chosen, than that’s called a one to one correspondence. In that case, people say the two sets have the same cardinality which is one way to define their size (and a very common and useful one).
For example there is a one to one correspondence between the integers and the even integers. The procedure of choosing is to just take the integers and multiple each of them by two. You always get an even number and take that one to correspond to the integer you started with. So these two sets have the same cardinality and in that sense, the same size.
There is even a procedures that proofs, that the set of the rational numbers has the same cardinality as the natural numbers.
But Cantor proved, that there can never be such a procedure, that establishes a one to one correspondence between the natural numbers and the reals. So it’s in that sense, that people say the reals form the larger set.
like the infinite monkeys with typewritters, universal limits to the rescue. Trolley’s are slow. Each bump makes them slower. Some of the people in the discrete line will have long lives until an excruciatingly painful death from dehydration.
Bottom. No matter what your “real” number assignation in the queue is, theres an infinite number of people before the train gets to you. Therefore every single person will live a full life before the train reaches them.
The illustration can’t be accurate - you can’t picture an infinite number of people between each pair of people, but the description is clear. The trolly can’t progress because it can’t get from the first person to the second due to the infinite people between them, and the infinite people between each of those between them, etc.
Like in the second infinity you can’t count to one, you can’t count from 0 to 1*10^(-1000)
_AutumnMoon_@lemmy.blahaj.zone
on 03 Oct 04:12
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either way infinite people die, just not getting involved
You’ve misunderstood “some infinities are bigger than others.” Both of these infinities are the same size. You can show this since each person on the bottom track can be assigned a person from the top track at 1 to 1 ratio. An example of infinities that are different sizes are all whole numbers and all decimal numbers. You cannot assign a whole number to every decimal number.
Matt parker does a good video on this. I can’t remember the exact title but if you search “is infinite $20 notes worth more than infinite $1 notes” you should find it.
sniggleboots@europe.pub
on 03 Oct 06:00
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There are more reals than naturals, they do not match up 1 to 1, for exactly the reason you mentioned. Maybe you misread the meme?
stevedice@sh.itjust.works
on 03 Oct 06:24
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Yeah, but if you can line up the elements of a set as shown in the bottom track, then they’re, at most, aleph 0.
Ah I see why they worded it the way they did. I would argue that’s just the limitation of the illustration, considering the text words the premise correctly, but fair!
But you actually can assign a unique person to every number, you just need an infinite number of people. You literally mathematically can’t do that for uncountable infinities.
Really? Isn’t the point that when you assign a natural number to every real number you can always generate a “new” real number you haven’t “counted” yet, meaning the set of real numbers is larger which is also is the point of the image.
No, thats not what I mean and that’s not the case. Even though there are infinite natural numbers, you can count them all. More accurately you can define a process that eventually will count them all. This is entirely different from decimal numbers which there is no process you can define that will exhaust all decimals. In this way the decimals are uncountable.
When talking about infinities this makes the infinity that contains all decimals larger than the infinity that contains only whole numbers.
My disagreement with the meme is that assigning an individual to each decimal is essentially a process of counting and this is a fundamental contradiction. As such the comparison to the set of natural numbers is nonsensical and the implication that there are less people assigned to the smaller infinity is incoherent.
By assigning a person to a decimal value and implying that every decimal has an assigned person the meme is essentially counting all the decimals. This is impossible, the decimals are an uncountable infinity. It’s like saying. Would you rather the number of people the trolley hits to be 7 or be dog.
What the meme has done is define the decimals to be a countable infinity bigger than another countable infinity. They’re both the same infinity.
Okay, to clarify, I mean the “is partial set of” instead of “is smaller than”.
Your saying it would be correct for “whole numbers” and “decimal numbers”. But that’s exactly what OP said “natural” and “real”
themagzuz@lemmy.blahaj.zone
on 03 Oct 07:29
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actually you can show that the naturals, integers and rationals all have the the same size.
for example, to show that there are as many naturals as integers (which you do by making a 1-to-1 mapping (more specifically a bijection, i.e. every natural maps to a unique integer and every integer maps to a unique natural) between them), you can say that every natural, n, maps to (n+1)/2 if it is odd and -n/2 if it is even. so 0 and 1 map to themselves, 2 maps to -1, 3 maps to 2, 4 maps to -2, and so on. this maps every natural number to an integer, and vice-versa. therefore, the cardinality (size) of the naturals and the integers are the same.
you can do something similar for the rationals (if you want to try your hand at proving this yourself, it can be made a lot easier by noting that if you can find a function that maps every natural to a unique rational (an injection), and another function that maps every rational to a unique natural, you can use those construct a bijection between the naturals and rationals. this is called the schröder-bernstein theorem).
it turns out that you cannot do this kind of mapping between the naturals (or any other set of that cardinality) and the reals. i won’t recite it here, but cantor’s diagonal argument is a quite elegant proof of this fact.
now, this raises a question: is there anything between the naturals (and friends) and the reals? it turns out that we don’t actually know. this is called the continuum hypothesis
You can’t count the decimals, op is counting the decimals and insisting that they are more of those counted decimals than in the integers. This inherently doesn’t make sense and is improper use of what infinities are and what they can represent.
BlackRoseAmongThorns@slrpnk.net
on 03 Oct 07:05
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The bottom rail represents the real numbers, which are “every decimal number”.
By assigning people to it it becomes countable. You can’t assign uncountable numbers like that. It’s both in the text of the meme and in the illustration
BlackRoseAmongThorns@slrpnk.net
on 03 Oct 15:26
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i don’t know why you’re trying so hard to away explain why the meme doesn’t work, but sure.
mathemachristian@lemmy.blahaj.zone
on 03 Oct 11:28
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An example of infinities that are different sizes are all whole numbers and all decimal numbers.
not sure what you mean by this, if you mean fractions you are wrong. Rational numbers and natural numbers can have a 1 on 1 assignment, look up cantors diagonalization. If you meant real numbers then you are right.
Decimals are how you represent numbers, not the numbers themselves.
Ah yes, I remember my eyes glazing over as things got too complicated to fit through my thick skull
ssfckdt@lemmy.blahaj.zone
on 03 Oct 06:47
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The first one, because people will die at a slower rate.
The second one, because the density will cause the trolley to slow down sooner, versus the first one where it will be able to pick up speed again between each person. Also, more time to save people down the rail with my handy rope cutting knife.
nathanjent@programming.dev
on 03 Oct 08:28
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An infinite amount of people on the track implies that the track is infinitely long. If that is not the case and the track is a normal length then the sudden addition of all that bio-mass in a finite space will cause a gravitational collapse. But will the collapse start on the first track or the second? Either way I hope you saved your game because you might lose your progress.
You dont have to since the set of all positive integers belongs to the set of all real numbers, you actually hit both tracks by just taking the lower track.
The set of all primes is the same size infinity as the set of all positive integers because you could create a way to map one to the other aka you can count to the nth prime. Reals are different in that there are an infinite number of real between any two reals which means there’s no possible way to map them.
Unfortunately it’s hard to join the tag end of one infinity to the tag end of another infinity to allow traversing both completely
I don’t really think it’s even sensible to talk about the tag end of an infinity. The bitten/bitter end is at 1, the tag end at infinity in this mental model. I feel that is the correct way to use rope terms for imagined embodied infinities as the small end is clearly bitten to (tied to) zero while the other end is free
I don’t think we want a world where there are any sort of infinity of people, and I don’t think a tram is the solution to revert a world from having its infinities to having a finite number
I also see practicality problems in tying even a small infinity of people to railway tracks, as that requires yet another infinity of people to hold people down, and another infinity of people people to do the tying (as well as the infinities of people to do the tying and holding on the other track) and all of those people will have to be fed and watered with infinite amounts of food and water (some infinities of people for infinite time), the infinities of people tying people down would need some education, implying infinite teachers
threaded - newest
Doesn’t matter, there are not enough people to try this anyway
Not with that attitude
Depends on the speed of the trolley.
Population expansion is exponential but the tram moves at constant velocity, so by the time it reaches the end of the track of 8bn people there will be an exponentially increasing number of people further down the track.
Use the fact that a set people corresponding to the real numbers are laying in a single line to prove that the real numbers are countable, thus throwing the mathematics community into chaos, and using this as a distraction to sabotage the trolley and save everybody.
Hey, maybe they're infinitely thin people, in which case you can (and necessarily must, continuum hypothesis moment) have one for every real number.
“smallest”?
.
In the top one you will never actually kill an infinite number of people, just approach it linearly. The bottom one will kill an infinite amount of people in finite time.
Edit: assuming constant speed of the train.
I’m going bottom.
NOT LIKE THAT. Not like sexually. I just mean I want to kill all the people on the bottom with my train.
Too late! Now bend…
So still sexually
Limits still are not intuitive to me. Whats the distinction here?
For every integer, there are an infinite number of real numbers until the next integer. So you can’t make a 1:1 correspondence. They’re both infinite, but this shows that the reals are more infinite. (and yeah, as other people mentioned, it’s the 1:1 correspondence, countability, that matters more than the infinite quantity of the Real numbers)
Makes sense, thanks!
There are infinitely many rational numbers between any two integers (or any two rationals), yet the rationals are still countable, so this reasoning doesn’t hold.
The only simple intuition for the uncountability of the reals I know of is Cantor’s diagonal argument.
You can assign each rational number a single unique integer though if you use a simple algorithm. So the 1:1 correspondence holds up (though both are still infinite)
There are also an infinite number of rationale between two integers, but the rationals are still countable and therefore have the same cardinality as the naturals and integers.
If people on the top rail are equally spaced at a distance d from each other, then you'd need to go a distance nd to kill the nth person. For any number n, nd is just a number, so it'll never be infinity. Meanwhile the number of real numbers between 0 and 1 is infinite (for example you have 0.1, 0.01, 0.001, etc), so running a distance d will kill an infinite number of people. Think of it like this: The people on the top are blocks, so walking a finite distance you only step on a finite number of blocks. Meanwhile the people on the bottom are infinitely thin sheets. To even have a thickness you need an infinite number of them.
There are an infinite amount of real numbers between 0 and 1. On the top track, when you reach 1, you would only kill 1 person. But on the bottom track you would’ve already killed infinite people by the time you reached 1. And you would continue to kill infinite people every time you reached a new whole number.
On the top track. You would tend towards infinity, meaning the train would never actually kill infinite people; There would always be more people to kill, and the train would always be moving forwards. Those two constants are what make it tend towards infinity, but the train can never actually reach infinity as there is no end to the tracks.
But on the bottom track. The train can reach infinity multiple times, and will do so every time it reaches a whole number. Basically, by the time you’ve reached 1, the bottom track has already killed more people than the top track ever will.
Worse. It will kill an infinity every time it will move any distance no matter how small.
Great explanation, I’d just like to add to this bit because I think it’s fun and important
Or any new number at all. Between 0 and 0.0…01 there are already infinite people. And between 0.001 and 0.002.
That’s still not doing it justice. If there were one person for every rational number there would be infinitely many in any finite interval (but still actually no more than the top track, go figure) but the real numbers are a whole other kind of infinite!
What I still don’t understand is where time comes into play. Is it defined somewhere? Wouldn’t everything still happen instantly even if there are infinite steps inbetween?
I guess it could be implied by it being a trolley on a track, but then the whole mixing of reality and infinity would also kind of fall apart.
Is every person tied to the track by default? If so, wouldn’t it be more humane to just kill them?
There aren’t infinite trams. There’s one tram that has to step over (roll through) one person at a time. Good luck to it making any progress, it will never get to the person numbered 1
Different slopes.
On top you kill one person per whole number increment. 0 -> 1 kills one person
On bottom you kill infinity people per whole number increment. 0 -> 1 kills infinity people
You can basically think of it like the entirety of the top rail happens for each step of the bottom rail.
instantaneously FTFY
<img alt="" src="https://lemmy.world/pictrs/image/d1da6980-a83d-47dd-bb43-60e455e007fb.jpeg">
Hold the lever halfway so the trolley picks both rails at the same time, to ensure highest possible kill comboq
That’s effectively just the bottom track, where an uncountable number of people (literally) will die as soon as the train reaches position (0.
Not with that attitude :3
Practically no one dies on either path, since a tram is a real thing it can’t traverse infinities of people (which notably have among their mandatory elements mass and volume) very well. It would hardly get far. Its automatic braking would stop it in any case.
Whatever happens infinities of people still remain which exceeds the carrying capacity of our observable universe
Bottom. Greater probability that it gets stuck in the corpses.
I remember seeing a science show on PBS where the presenter explained how there are different infinities by using set theory and the integers/reals. That was mind-blowing at the time.
Bottom.
Killing one person for every real number implies there’s a way to count all real numbers one by one. This is a contradiction, because real numbers are uncountable. By principle of explosion, I’m Superman, which means I can stop the train by my super powers. QED
Wait until your league of super heroes is up against the axis of choice.
plus uncountable infinity implies there is uncountable supply of humans, which is nice.
Also, almost all real numbers are undefinable. (Unless you’re using a model, that makes them countable.)
So that means, that almost all the “humans” on the bottom track are something we can not even imagine in principle. Wouldn’t be surprised, if infinite Superman’s were among them.
Either that or the humans are so “infinitely packed” that they’re probably already dead squashed into each other.
Now, if you put infinite people in a chamber, and then compress the chamber and then put an infinite amount of compressed chambers inside a chamber… Will we have Real People?
Bottom has infinite density and will collapse into a black hole killing everyone, and destroying the tram and lever.
Ah, so now Schwarzschild is driving the trolley!
Or maybe he’s coming to stop the trolley!
Or maybe Feynman is coming, to renormalize the infinities!
I really don’t know anymore! Aleph nought, Aleph omega…
go away, come again some other… perhaps infinite… day.
there are more real numbers than integers though
The image actually says this
In the top case has it been arbitrarily decided to include space in between the would-be victims? Or is the top a like number line comparison to the bottom? Because if thats the case it becomes relevant if there is one body for every real number unit of distance. (One body at 0.1 meter, and at 0.01 meter, at 0.001, etc)
If so then there’s an infinite amount of victims on the first planck length of the bottom track. An infinite number of victims would contain every possible victim. Every single possible person on the first plank length. So on the next planck length would be every possible person again.
Which would mean that the bottom track is actually choosing a universe of perpetual endless suffering and death for every single possible person. The top track would eventually cause infinite suffering but it would take infinite time to get there. The bottom track starts at infinite suffering and extends infinitely in this manner. Every possible version of every possible person dying, forever.
Okay, so what’s the point of “proving” that there some “infinities” are “bigger” than others? What’s the practical application here? Because an infinite hotel with an infinite number of guests is physically impossible, so I don’t see the point.
Practical application in math tends to be like three degrees of separation and half a century removed from the math at play. In this case, all of modern mathematics is based on set theory, so it's more that this stuff allows us to do other, more practically useful math while knowing what we're talking about.
The real numbers also includes the integers.
The practical consequence of this example is that the integers die regardless of what you choose.
However infinitely many people will survive if you choose the first option.
And yet there can never, and will never, be a situation where an infinite number of people are tied to a railroad track. So this thought experiment is meaningless.
It’s more about set theory than the actual numbers.
Let’s say you have 100 people with everyone tied up across both tracks. Heads on one track and legs on the other. Let’s assume they die if the train touches any part of them, but you still need to choose between running over heads or legs.
The best choice is then legs, because there’s a probability of some of them being handicapped and not having legs.
A practical application is for example in probability theory (or anywhere that deals with measures) such as this question:
If we generate a random real number from 0 to 1, what is the probability that it is rational?
Because we know that the continuum is so much larger in a sense than the set of rationals, we can answer this confidently and say the probability is zero, even though it is theoretically possible for us to get a rational number.
Statistics deals with similar scenarios quite frequently, and without it we wouldn’t have the modern scientific method.
I’ve never been a fan of just saying “some infinities are bigger than others,” to be honest. Way too easy to misunderstand and it’s also kind of meaningless by itself.
Like everything else in this holographic universe we live in, I’d just close my eyes and believe the bodies I’m trampling are imaginary.
Imagine being the first one being killed on any of these tracks.
The probability of that is…?
Mathematicians tell me, please, because my mind is breaking.
It's 0. I mean someone has to be the first, but betting on any particular person to be the first will necessarily be a losing bet.
But what if I know Steve’s first and bet it’s Steve?
Then you're legally obligated to give me half your earnings.
.
I think on the bottom you have to be the zeroth, but typically the first person tied to the track would be the first, so if the first is at 1 they’re safe since there’s an infinity (a large infinity even) before them and there’s only one tram that can hit one person at a time
It’ll take infinite time just to start hitting
sort them so you kill one person first, then 2, then 3, then 4…
I would pull the lever and then steal a bus and knock the trolley off of the track, killing the least amount of people possible.
I take the square root of all the negative real numbers and kill in an entirely new dimension.
I pull the lever, if the cart goes over the real numbers it will instantly kill an infinite amount of people and continue killing an infinite amount of people for every moment for the rest of existence.
If I pull the lever a finite amount of people will die instantly and slowly over time tending twords infinity but due to the linear nature of movement it would never actually reach Infinity even if there are an infinite number of people tied to the track a finite amount is all that could ever die.
So you’re going to let those infinite people on top stay tied to the track and starve to death slowly‽
I mean, in that case it’s not really a matter of the trolley killing them, per se. The number will tend towards infinity, until it suddenly spikes to real infinity as people starve.
I assume the people spawn into existence as the render distance comes into frame.
<img alt="" src="https://i.imgur.com/qChp5dE.gif">
Probably better than an infinite number of people waiting an infinite amount of time for there impending doom and then also an infinite number of people starving to death.
you have to remember ℵ^0 in this case is included in ℵ^1 or at least the numerical value is, which is the only information given.
I guess technically you could value one human soul above the other and technically this is philosophy? So I guess technically you should? but anyway everything that happens on ℵ^0 will also happen on ℵ^1 except more will always happen on ℵ^1 than ℵ^0 so whether there is unintended consequences or not doesn’t really matter. it’s always safer to pick the countable infinities.
Unless there is something innately good about physically having more people exist no matter there condition. but you would have to ask a philosopher about that one, I’m paid to pull lever’s not philosophize.
All the people tied to the track will die after a few days anyway.
I masturbate until I forget about the decision I have to make and then put off cleaning my apartment until I finally just run out, randomly pull the lever, and never think of the consequences again.
Of course by that point everyone has already starved to death which is the worst possible outcome.
Ah, procrasturbation.
I use the lever to kill the train driver.
I ignore the question and go to the IT and maintenance teams to put a series of blocks, physical and communication-system-based, between the maths and philosophy departments. Attempts to breach containment will be met with deadly force.
Math is the philosophy department in that math is an extension of logic, which is in turn an extension of philosophy. You’d have a better chance of divorcing math from applied math (engineering/physics) than separating math from philosophy.
That’s like just your axiom man
<img alt="" src="https://lemmy.world/pictrs/image/580c0783-7e8e-43d2-ba7e-8589422f23d9.jpeg">
That sounds an awful lot like someone looking to arrange a containment breach. <img alt="" src="https://i.giphy.com/3o6ZtiXDMx3RX4o7VS.webp">
Can I group the people into groups of 1, then 2, then 3 and so forth? When the trolley is done with the killing, it will have killed -1/12 people.
I reject the premise since there will only ever exist a finite number of people. They will all die. One day the last human will die.
The top one, because time is still a factor.
Sure, infinite people will die either way, but that is only after infinite time.
Yeah, but in the bottom one, the people are packed infinitely dense, which will probably cause the train to derail, saving infinitely more people.
what if the trolleys got a cow catcher
Tankies hate this one weird trick.
you know, I’m not sure you can have an uncountably infinite number of people. so whatever that abomination is I’ll send the trolley down its way. it’s probably an SCP.
Geez, disconnect the trains so you can hit both lines at the same time, obviously.
The second one. It’ll be a bit rough, but overall should be a smoother ride for the occupants.
What about a time loop where only one person dies, but infinite times?
Is this actually true?
Many eons ago when I was in college, I worked with a guy who was a math major. He was a bit of a show boat know it all and I honestly think he believed that he was never wrong. This post reminded me of him because he and I had a debate / discussion on this topic and I came away from that feeling like he he was right and I was too dumb to understand why he was right.
He was arguing that if two sets are both infinite, then they are the same size (i.e. infinity, infinite). From a strictly logical perspective, it seemed to me that even if two sets were infinite, it seems like one could still be larger than the other (or maybe the better way of phrasing it was that one grew faster than the other) and I used the example of even integers versus all integers. He called me an idiot and honestly, I’ve always just assumed I was wrong – he was a math major at a mid-ranked state school after all, how could he be wrong?
Thoughts?
It is true! Someone much more studied on this than me could provide a better explanation, but instead of “size” it’s called cardinality. From what I understand your example of even integers versus all integers would still be the same size, since they can both be mapped to the natural numbers and are therefore countable, but something like real numbers would have a higher cardinality than integers, as real numbers are uncountable and infinite. I think you can have different cardinalities within uncountable infinities too, but that’s where my knowledge stops.
It’s pretty well settled mathematics that infinities are “the same size” if you can draw any kind of 1-to-1 mapping function between the two sets. If it’s 1-to-1, then every member of set A is paired off with a member of B, and there are no elements left over on either side.
In the example with even integers y versus all integers x, you can define the relation x <–> y = 2*x. So the two sets “have the same size”.
But the real numbers are provably larger than any of the integer sets. Meaning every possible mapping function leaves some reals leftover.
Weeeell… not really. It’s pretty well settled mathematics that “cardinality” and “amount” happen to coinciden when it comes to finite sets and we use it interchangeably but that’s because we know they’re not the same thing. When speaking with the regular folk, saying “some infinities are bigger than others” is kinda misleading. Would be like saying “Did you know squares are circles?” and then constructing a metric space with the taxi metric. Sure it’s “true” but it’s still bullshit.
I side with you, though the experts call me stupid for it too.
if for all n < infinity, one set is double the size of another then it is still double the size at n = infinity.
You’re not stupid for it. Since it makes sense.
However, due to the way we “calculate” the sizes of infinite sets, you are wrong.
Even integers and all integers are the same infinity.
But reals are “bigger” than integers.
I know it seems intuitive but assuming that a property holds for n=infinity because it holds for all n<infinity would literally break math and it really doesn’t make much sense when you think about it more than a minute. Here’s an easy counterexample: n is finite.
In the end it depends on your definition of “bigger”. Traditionally, we use “bigger” to just refer to who has the highest number or count, but neither apply here.
Imagine we have a straight line of skittles. Lines with more are defined as “bigger”. Now imagine the line is expanded into another dimension, a square. Is it still “bigger”? Each line has the same count, so it’s traditional “bigness” value is unchanged…
The sizes of infinities are about set theory, and including more “dimensions” of number. Not really about which has “more” or “grows faster”. Your even v all integers is actually a classic example of two same-size infinities E.g. an infinite stack of one dollar bills and one of ten dollar bills are worth the same
Two sets with infinitely many things are the same size when you can describe a one to one mapping from one set to the other.
For example, the counting numbers are the same size as the counting numbers except for 7. To go from the former set to the latter set, we can map 1-6 to themselves, and then for every counting number 7 or larger, add one. To reverse, just do the opposite.
Likewise, we can map the counting numbers to only the even counting numbers by doubling the value or each one as our mapping. There is a first even number, and a 73rd even number, and a 123,456,789,012th even number.
By contrast, imagine I claim to have a map from the counting numbers to all the real numbers between 0 and 1 (including 0 but not 1). You can find a number that isn’t in my mapping. Line all the numbers in my mapping up in the order they map from the counting numbers, so there’s a first real number, a second, a third, and so on. To find a number that doesn’t appear in my mapping anywhere, take the first digit to the right of the decimal from the first number, the second digit from the second number, the third digit from the third number, and so on. Once you have assembled this new (infinitely long) number, change every single digit to something different. You could add 1 to each digit, or change them at random, or anything else.
This new number can’t be the first number in my mapping because the first digit won’t match anymore. Nor can it be the second number, because the second digit doesn’t match the second number. It can’t be the third or the fourth, or any of them, because it is always different somewhere. You may also notice that this isn’t just one number you’ve constructed that isn’t anywhere in the mapping - in fact it’s a whole infinite family of numbers that are still missing, no matter what order I put any of the numbers in, and no matter how clever my mapping seems.
The set of real numbers between 0 and 1 truly is bigger than the set of counting numbers, and it isn’t close, despite both being infinitely large.
Change the numbers to rubber balls with pictures of ducks or trains and different iconography. You can now intuit that both sets are the same size.
Hilbert’s Paradox of the Grand Hotel seems to be the thought experiment with which you were engaged with your math associate. There are countable and uncountable infinities. Integers and skip counted integers are both countable and infinite. Real numbers are uncountable and infinite. There are sets that are more uncountable than others. That uncountability is denoted by aleph number. Uncountable means can’t be mapped to the natural numbers (1, 2, 3…). Infinite means a list with all the elements can’t be created.
There are different ways to compare the “sizes” of infinite sets. So you could both be right in different contexts and for different sets. But the one concept people mostly mean, when they say, that some infinities are larger than other, is one to one correspondence (also called “cardinality”):
If you have a set and you can describe how you would choose one element of a second set for each element of the first and end up with every element chosen, than that’s called a one to one correspondence. In that case, people say the two sets have the same cardinality which is one way to define their size (and a very common and useful one).
For example there is a one to one correspondence between the integers and the even integers. The procedure of choosing is to just take the integers and multiple each of them by two. You always get an even number and take that one to correspond to the integer you started with. So these two sets have the same cardinality and in that sense, the same size.
There is even a procedures that proofs, that the set of the rational numbers has the same cardinality as the natural numbers.
But Cantor proved, that there can never be such a procedure, that establishes a one to one correspondence between the natural numbers and the reals. So it’s in that sense, that people say the reals form the larger set.
like the infinite monkeys with typewritters, universal limits to the rescue. Trolley’s are slow. Each bump makes them slower. Some of the people in the discrete line will have long lives until an excruciatingly painful death from dehydration.
monkeys.zip
Bottom. No matter what your “real” number assignation in the queue is, theres an infinite number of people before the train gets to you. Therefore every single person will live a full life before the train reaches them.
What about the first guy
They too lived a full (very short) life.
He ded
What real number is he? There’s infinity people before him too
This some Zeno shit, man
The zeroth person is dead. I don’t know how the trolly finds the next one because there’s always a smaller one than whatever it chooses
It’ll make it through maybe 3 infinities before derailing. Go bottom, end it faster.
I do what I always do: run to the trolley, then jump up and pull the emergency stop because I hate false dilemmas.
Correct, because if we ignore some important facts you could also have infinite time to stop the trolley. Checkmate, false dilemma creators.
This is why it is important to only hire union trolley operators. They are trained to stop the trolley.
Bottom. Train will stall/derail faster.
Getting killed by a train is apparently just an inevitability in this universe. Either choice is just the grand conductors plan.
First, I start moving people to hotel rooms...
I mean, the bottom. The trolley simply would stop, get gunked up by all the guts and the sheer amount of bodies so close together. Checkmate tolley.
How do we know it’s an accurate illustration? They might have jacked up the trolley with monster truck wheels or something.
I mean, maybe, but I can only go off what I see here.
The illustration can’t be accurate - you can’t picture an infinite number of people between each pair of people, but the description is clear. The trolly can’t progress because it can’t get from the first person to the second due to the infinite people between them, and the infinite people between each of those between them, etc.
Like in the second infinity you can’t count to one, you can’t count from 0 to 1*10^(-1000)
either way infinite people die, just not getting involved
You’ve misunderstood “some infinities are bigger than others.” Both of these infinities are the same size. You can show this since each person on the bottom track can be assigned a person from the top track at 1 to 1 ratio. An example of infinities that are different sizes are all whole numbers and all decimal numbers. You cannot assign a whole number to every decimal number.
Matt parker does a good video on this. I can’t remember the exact title but if you search “is infinite $20 notes worth more than infinite $1 notes” you should find it.
There are more reals than naturals, they do not match up 1 to 1, for exactly the reason you mentioned. Maybe you misread the meme?
Yeah, but if you can line up the elements of a set as shown in the bottom track, then they’re, at most, aleph 0.
It’s just an illustration… how else would you draw it?
Diagonally
My argument applies to the text of the post too. You literally can’t assign people (count) the decimals.
I don’t think we should take the visuals of the hypothetical shit post literally.
If they say there’s one guy for every real number, let them
Ah I see why they worded it the way they did. I would argue that’s just the limitation of the illustration, considering the text words the premise correctly, but fair!
One person for every decimal isn’t possible even with infinite people. That is the point I’m making.
Neither is assigning a person to every natural number, so I’m not sure what point you’re trying to make?
But you actually can assign a unique person to every number, you just need an infinite number of people. You literally mathematically can’t do that for uncountable infinities.
Really? Isn’t the point that when you assign a natural number to every real number you can always generate a “new” real number you haven’t “counted” yet, meaning the set of real numbers is larger which is also is the point of the image.
No, thats not what I mean and that’s not the case. Even though there are infinite natural numbers, you can count them all. More accurately you can define a process that eventually will count them all. This is entirely different from decimal numbers which there is no process you can define that will exhaust all decimals. In this way the decimals are uncountable.
When talking about infinities this makes the infinity that contains all decimals larger than the infinity that contains only whole numbers.
My disagreement with the meme is that assigning an individual to each decimal is essentially a process of counting and this is a fundamental contradiction. As such the comparison to the set of natural numbers is nonsensical and the implication that there are less people assigned to the smaller infinity is incoherent.
By assigning a person to a decimal value and implying that every decimal has an assigned person the meme is essentially counting all the decimals. This is impossible, the decimals are an uncountable infinity. It’s like saying. Would you rather the number of people the trolley hits to be 7 or be dog.
What the meme has done is define the decimals to be a countable infinity bigger than another countable infinity. They’re both the same infinity.
Natural numbers < whole numbers < rational numbers < real numbers
Okay, to clarify, I mean the “is partial set of” instead of “is smaller than”.
Your saying it would be correct for “whole numbers” and “decimal numbers”. But that’s exactly what OP said “natural” and “real”
actually you can show that the naturals, integers and rationals all have the the same size.
for example, to show that there are as many naturals as integers (which you do by making a 1-to-1 mapping (more specifically a bijection, i.e. every natural maps to a unique integer and every integer maps to a unique natural) between them), you can say that every natural, n, maps to (n+1)/2 if it is odd and -n/2 if it is even. so 0 and 1 map to themselves, 2 maps to -1, 3 maps to 2, 4 maps to -2, and so on. this maps every natural number to an integer, and vice-versa. therefore, the cardinality (size) of the naturals and the integers are the same.
you can do something similar for the rationals (if you want to try your hand at proving this yourself, it can be made a lot easier by noting that if you can find a function that maps every natural to a unique rational (an injection), and another function that maps every rational to a unique natural, you can use those construct a bijection between the naturals and rationals. this is called the schröder-bernstein theorem).
it turns out that you cannot do this kind of mapping between the naturals (or any other set of that cardinality) and the reals. i won’t recite it here, but cantor’s diagonal argument is a quite elegant proof of this fact.
now, this raises a question: is there anything between the naturals (and friends) and the reals? it turns out that we don’t actually know. this is called the continuum hypothesis
I clarified my above comment
You can’t count the decimals, op is counting the decimals and insisting that they are more of those counted decimals than in the integers. This inherently doesn’t make sense and is improper use of what infinities are and what they can represent.
The bottom rail represents the real numbers, which are “every decimal number”.
No it’s doesn’t because the bottom rail is a countable infinity, the decimals are an uncountable infinity. Go watch the video it explains it.
the real numbers on the bottom rail include all decimals, no?
I know it is drawn countably infinite, but it represents the reals, also wise guy, i studied basic logic in university, it covers this topic.
By assigning people to it it becomes countable. You can’t assign uncountable numbers like that. It’s both in the text of the meme and in the illustration
i don’t know why you’re trying so hard to away explain why the meme doesn’t work, but sure.
not sure what you mean by this, if you mean fractions you are wrong. Rational numbers and natural numbers can have a 1 on 1 assignment, look up cantors diagonalization. If you meant real numbers then you are right.
Decimals are how you represent numbers, not the numbers themselves.
I’m not talking about fractions, I’m talking about the reals because that it what op referred to
I think it was numberphile, or maybe vsauce, who did a video on infinities. It was really interesting. I learnt a lot, then forgot it all.
Ah yes, I remember my eyes glazing over as things got too complicated to fit through my thick skull
The first one, because people will die at a slower rate.
The second one, because the density will cause the trolley to slow down sooner, versus the first one where it will be able to pick up speed again between each person. Also, more time to save people down the rail with my handy rope cutting knife.
An infinite amount of people on the track implies that the track is infinitely long. If that is not the case and the track is a normal length then the sudden addition of all that bio-mass in a finite space will cause a gravitational collapse. But will the collapse start on the first track or the second? Either way I hope you saved your game because you might lose your progress.
The mass of dead bodies is what replenishes the new living ones on the finite track.
The infamious theory of infinitly-expanding train track in porportion with train-travelled distence sequared by prof. buttnugget
Q.E.D.
Good to know there are roughly 6 real numbers for every integer
If there are child real numbers then you can fit more.
Is there a way to take both routes?
Hit the hand brake and drift that sucker.
with my knack for drifting i’ll miss both and hit something else entirely even within this imaginary scenario
<img alt="" src="https://static.tvtropes.org/pmwiki/pub/images/MultiTrackDrifting.jpg">
Running in the 90s intensifies
You dont have to since the set of all positive integers belongs to the set of all real numbers, you actually hit both tracks by just taking the lower track.
never doubt my ability to mess up the unmessable. i just might stumble into disabling clipping and end up falling forever.
i asked myself: wwjd? and now i ask you because i have no idea
Actually… this means there are infinite people so:
Let X be the number of people killed = (-infinity)
As infity is defined :
infinity + X = infinity
infinity + (-infinity) =
infinity - infinity = infinty
So no people would have died black guy pointing at his head meme
Desnt work when they’re different classes of infinity.
Multilane drifting!
This hypothetical post is a thought crime!
Top case is not the smallest infinite; going for prime number would save a lot of time for a lot of people before they die
depends on what you mean by “smallest”
The set of all primes is the same size infinity as the set of all positive integers because you could create a way to map one to the other aka you can count to the nth prime. Reals are different in that there are an infinite number of real between any two reals which means there’s no possible way to map them.
I thought that the correct answer to these was making a loop on the right, merging the lines.
No, we need a second trolley.
The answer is multi track drifting
Unfortunately it’s hard to join the tag end of one infinity to the tag end of another infinity to allow traversing both completely
I don’t really think it’s even sensible to talk about the tag end of an infinity. The bitten/bitter end is at 1, the tag end at infinity in this mental model. I feel that is the correct way to use rope terms for imagined embodied infinities as the small end is clearly bitten to (tied to) zero while the other end is free
I don’t think we want a world where there are any sort of infinity of people, and I don’t think a tram is the solution to revert a world from having its infinities to having a finite number
I also see practicality problems in tying even a small infinity of people to railway tracks, as that requires yet another infinity of people to hold people down, and another infinity of people people to do the tying (as well as the infinities of people to do the tying and holding on the other track) and all of those people will have to be fed and watered with infinite amounts of food and water (some infinities of people for infinite time), the infinities of people tying people down would need some education, implying infinite teachers
It’s a logistic nightmare
If the next person getting tied down holds down the person currently being tied down then this could work. I’m sure they’d be game so that’s fine.
fossilesque you’re one of my fav posters
ilu2 :)