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
IT'S A TRAP
Submitted 22 hours ago by fossilesque@mander.xyz to science_memes@mander.xyz
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Comments
BeatTakeshi@lemmy.world 2 hours ago
Schadrach@lemmy.sdf.org 23 minutes ago
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.
joucker29@lemmy.world 29 minutes ago
depends on what you mean by “smallest”
BilSabab@lemmy.world 4 hours ago
Is there a way to take both routes?
ours@lemmy.world 3 hours ago
Hit the hand brake and drift that sucker.
ICastFist@programming.dev 1 hour ago
BilSabab@lemmy.world 2 hours ago
with my knack for drifting i’ll miss both and hit something else entirely even within this imaginary scenario
AlteredEgo@lemmy.ml 2 hours ago
This hypothetical post is a thought crime!
ssfckdt@lemmy.blahaj.zone 7 hours ago
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.
aeternum@lemmy.blahaj.zone 7 hours ago
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.
filcuk@lemmy.zip 6 hours ago
Ah yes, I remember my eyes glazing over as things got too complicated to fit through my thick skull
tiredofsametab@fedia.io 10 hours ago
First, I start moving people to hotel rooms...
mumblerfish@lemmy.world 21 hours ago
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.
ivanafterall@lemmy.world 21 hours ago
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 21 hours ago
Too late! Now bend…
a_person@piefed.social 18 hours ago
So still sexually
HeyThisIsntTheYMCA@lemmy.world 11 hours ago
buffing_lecturer@leminal.space 21 hours ago
Limits still are not intuitive to me. Whats the distinction here?
NoneOfUrBusiness@fedia.io 20 hours ago
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.
mrmacduggan@lemmy.ml 21 hours ago
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.
turdcollector69@lemmy.world 15 hours ago
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.
PM_Your_Nudes_Please@lemmy.world 18 hours ago
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.
eleijeep@piefed.social 18 hours ago
The bottom one will kill an infinite amount of people in finite time.
instantaneously FTFY
chunes@lemmy.world 5 hours ago
Good to know there are roughly 6 real numbers for every integer
Knock_Knock_Lemmy_In@lemmy.world 4 hours ago
If there are child real numbers then you can fit more.
magic_lobster_party@fedia.io 21 hours ago
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
rooroo@feddit.org 21 hours ago
Wait until your league of super heroes is up against the axis of choice.
woodenghost@hexbear.net 6 hours ago
Also almost all real numbers are undefinable. (Unless you’re using a model, that makes them countable.)
So that means, if they are all different, than 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 where among them.
plinky@hexbear.net 20 hours ago
plus uncountable infinity implies there is uncountable supply of humans, which is nice.
madjo@feddit.nl 2 hours ago
Multilane drifting!
nathanjent@programming.dev 5 hours ago
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.
buttnugget@lemmy.world 2 hours ago
The mass of dead bodies is what replenishes the new living ones on the finite track.
answersplease77@lemmy.world 2 hours ago
Yes. The infamious theory of infinitly-expanding train track porportionally with train-travelled distence sequared by prof. buttnugget
answersplease77@lemmy.world 2 hours ago
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
sem@lemmy.blahaj.zone 2 hours ago
Desnt work when they’re different classes of infinity.
stupidcasey@lemmy.world 19 hours ago
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 18 hours ago
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 18 hours ago
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.
stupidcasey@lemmy.world 17 hours ago
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 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 no matter there condition but you would have to ask a philosopher about that one I’m paid to pull lever’s not philosophize.
socsa@piefed.social 17 hours ago
All the people tied to the track will die after a few days anyway.
Harvey656@lemmy.world 10 hours ago
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.
faythofdragons@slrpnk.net 7 hours ago
How do we know it’s an accurate illustration? They might have jacked up the trolley with monster truck wheels or something.
pruwybn@discuss.tchncs.de 22 hours ago
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 20 hours ago
Hey, maybe they're infinitely thin people, in which case you can have one for every real number.
helpImTrappedOnline@lemmy.world 15 hours ago
The second one. It’ll be a bit rough, but overall should be a smoother ride for the occupants.
OhNoMoreLemmy@lemmy.ml 21 hours ago
Bottom has infinite density and will collapse into a black hole killing everyone, and destroying the tram and lever.
niktemadur@lemmy.world 47 minutes ago
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.
narr1@lemmygrad.ml 3 hours ago
i asked myself: wwjd? and now i ask you because i have no idea
Sunsofold@lemmings.world 17 hours ago
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.
TeddE@lemmy.world 16 hours ago
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.
Sunsofold@lemmings.world 14 hours ago
Daft_ish@lemmy.dbzer0.com 10 hours ago
Getting killed by a train is apparently just an inevitably in this universe. Either choice is just the grand conductors plan.
Honytawk@lemmy.zip 16 hours ago
The top one, because time is still a factor.
Sure, infinite people will die either way, but that is only after infinite time.
Rednax@lemmy.world 12 hours ago
Yeah, but in the bottom one, the people are packed infinitely dense, which will probably cause the train to derail, saving infinitely more people.
HeyThisIsntTheYMCA@lemmy.world 11 hours ago
what if the trolleys got a cow catcher
davidagain@lemmy.world 8 hours ago
Tankies hate this one weird trick.
sgtlion@hexbear.net 11 hours ago
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.
rothaine@lemmy.zip 11 hours ago
What about the first guy
Daft_ish@lemmy.dbzer0.com 10 hours ago
He ded
MeowZedong@lemmygrad.ml 11 hours ago
They too lived a full (very short) life.
sgtlion@hexbear.net 10 hours ago
What real number is he? There’s infinity people before him too
Tiger_Man_@szmer.info 17 hours ago
Considering that there’s a small but non zero chance of surviving getting ran over by a train some of them are gonna survive this and since there are infinite people that will result in infinite train-proof people spawning machine
Wakmrow@hexbear.net 17 hours ago
I was actually told this is not how infinite sets work. But I didn’t get an actual explanation beyond that.
porous_grey_matter@lemmy.ml 17 hours ago
with the extra requirement that the probability applies to the whole set I think it checks out, intuitively anyway the expected ~0.0…01 * ∞ is still ∞
Daft_ish@lemmy.dbzer0.com 10 hours ago
Bottom. Train will stall faster.
InvalidName2@lemmy.zip 14 hours ago
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 13 hours ago
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.
for_some_delta@beehaw.org 10 hours ago
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.
prime_number_314159@lemmy.world 11 hours ago
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.
woodenghost@hexbear.net 6 hours ago
There are different ways to compare the “sizes” of infinite set. 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, 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 is to just take the integers and multiple each of them by two. 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 established 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.
mkwt@lemmy.world 13 hours ago
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 6 hours ago
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.
sgtlion@hexbear.net 12 hours ago
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.
The sizes of infinities are about set theory, and including more “dimensions” of number. Not really about which has “more” or “grows faster”. E.g. an infinite stack of one dollar bills and one of ten dollar bills are worth the same
Krudler@lemmy.world 11 hours ago
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.
BenLeMan@lemmy.world 14 hours ago
- I lay some extra track so the train will run over the perverts that come up with these “dilemmas” instead. Problem solved. 👍
_AutumnMoon_@lemmy.blahaj.zone 9 hours ago
either way infinite people die, just not getting involved
humanspiral@lemmy.ca 12 hours ago
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.
missfrizzle@discuss.tchncs.de 16 hours ago
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.
nuko147@lemmy.world 18 minutes ago
I thought that the correct answer to these was making a loop on the right, merging the lines.