I thought that the correct answer to these was making a loop on the right, merging the lines.
IT'S A TRAP
Submitted 5 months ago by fossilesque@mander.xyz to science_memes@mander.xyz
https://mander.xyz/pictrs/image/dd931720-08dc-4eea-9268-74fc635a1e79.png
Comments
nuko147@lemmy.world 5 months ago
Noodle07@lemmy.world 5 months ago
The answer is multi track drifting
Ceruleum@lemmy.wtf 5 months ago
No, we need a second trolley.
BeatTakeshi@lemmy.world 5 months ago
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
Schadrach@lemmy.sdf.org 5 months 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 5 months ago
depends on what you mean by “smallest”
AlteredEgo@lemmy.ml 5 months ago
This hypothetical post is a thought crime!
madjo@feddit.nl 5 months ago
Multilane drifting!
answersplease77@lemmy.world 5 months 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 5 months ago
Desnt work when they’re different classes of infinity.
narr1@lemmygrad.ml 5 months ago
i asked myself: wwjd? and now i ask you because i have no idea
BilSabab@lemmy.world 5 months ago
Is there a way to take both routes?
Adalast@lemmy.world 5 months ago
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.
BilSabab@lemmy.world 5 months ago
never doubt my ability to mess up the unmessable. i just might stumble into disabling clipping and end up falling forever.
ours@lemmy.world 5 months ago
Hit the hand brake and drift that sucker.
BilSabab@lemmy.world 5 months ago
with my knack for drifting i’ll miss both and hit something else entirely even within this imaginary scenario
chunes@lemmy.world 5 months ago
Good to know there are roughly 6 real numbers for every integer
Knock_Knock_Lemmy_In@lemmy.world 5 months ago
If there are child real numbers then you can fit more.
nathanjent@programming.dev 5 months 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 5 months ago
The mass of dead bodies is what replenishes the new living ones on the finite track.
answersplease77@lemmy.world 5 months ago
Yes. The infamious theory of infinitly-expanding train track porportionally with train-travelled distence sequared by prof. buttnugget
ssfckdt@lemmy.blahaj.zone 5 months 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 5 months 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 5 months ago
Ah yes, I remember my eyes glazing over as things got too complicated to fit through my thick skull
_AutumnMoon_@lemmy.blahaj.zone 5 months ago
either way infinite people die, just not getting involved
Harvey656@lemmy.world 5 months 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 5 months ago
How do we know it’s an accurate illustration? They might have jacked up the trolley with monster truck wheels or something.
Harvey656@lemmy.world 5 months ago
I mean, maybe, but I can only go off what I see here.
tiredofsametab@fedia.io 5 months ago
First, I start moving people to hotel rooms...
Daft_ish@lemmy.dbzer0.com 5 months ago
Getting killed by a train is apparently just an inevitably in this universe. Either choice is just the grand conductors plan.
Daft_ish@lemmy.dbzer0.com 5 months ago
Bottom. Train will stall faster.
Bronstein_Tardigrade@lemmygrad.ml 5 months ago
This is why it is important to only hire union trolley operators. They are trained to stop the trolley.
p3n@lemmy.world 5 months ago
I do what I always do: run to the trolley, then jump up and pull the emergency stop because I hate false dilemmas.
hakunawazo@lemmy.world 5 months ago
Correct, because if we ignore some important facts you could also have infinite time to stop the trolley. Checkmate, false dilemma creators.
_stranger_@lemmy.world 5 months ago
It’ll make it through maybe 3 infinities before derailing. Go bottom, end it faster.
sgtlion@hexbear.net 5 months 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 5 months ago
What about the first guy
sgtlion@hexbear.net 5 months ago
What real number is he? There’s infinity people before him too
Daft_ish@lemmy.dbzer0.com 5 months ago
He ded
MeowZedong@lemmygrad.ml 5 months ago
They too lived a full (very short) life.
humanspiral@lemmy.ca 5 months 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.
fossilesque@mander.xyz 5 months ago
BenLeMan@lemmy.world 5 months ago
- I lay some extra track so the train will run over the perverts that come up with these “dilemmas” instead. Problem solved. 👍
InvalidName2@lemmy.zip 5 months 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?
woodenghost@hexbear.net 5 months 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.
for_some_delta@beehaw.org 5 months 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.
Krudler@lemmy.world 5 months 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.
prime_number_314159@lemmy.world 5 months 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.
sgtlion@hexbear.net 5 months 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
humanspiral@lemmy.ca 5 months ago
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.
stevedice@sh.itjust.works 5 months ago
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.
calcopiritus@lemmy.world 5 months ago
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.
mkwt@lemmy.world 5 months 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 5 months 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.
umean2me@discuss.online 5 months 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.
Randelung@lemmy.world 5 months ago
What about a time loop where only one person dies, but infinite times?
helpImTrappedOnline@lemmy.world 5 months ago
The second one. It’ll be a bit rough, but overall should be a smoother ride for the occupants.
PhAzE@lemmy.ca 5 months ago
Geez, disconnect the trains so you can hit both lines at the same time, obviously.
missfrizzle@discuss.tchncs.de 5 months 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.
Honytawk@lemmy.zip 5 months ago
The top one, because time is still a factor.
Sure, infinite people will die either way, but that is only after infinite time.
davidagain@lemmy.world 5 months ago
Tankies hate this one weird trick.
Rednax@lemmy.world 5 months 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 5 months ago
what if the trolleys got a cow catcher
ryedaft@sh.itjust.works 5 months ago
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.
nairui@piefed.social 5 months ago
fossilesque you’re one of my fav posters
fossilesque@mander.xyz 5 months ago
ilu2 :)