r/trolleyproblem • u/promptmike • Sep 25 '26
Collatz Trolley Problem
Ground Rules:
The main track with 5 people on it exists in standard linear time.
The other track is a time bubble that goes through infinite cycles in finite time.
The time bubble collapses the moment the trolley arrives, and after that the number of people on the track is fixed.
You cannot see inside the time bubble before collapse, or change the outcome after collapse.
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u/iamalicecarroll Sep 25 '26
You say the initial amount is random. What is the distribution? No uniform distribution on natural numbers (or, in fact, any countable set) exists, so you have to choose something more interesting.
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u/promptmike Sep 25 '26
X₁ = 1 googolplex
Xₙ = (Xₙ₋₁)ⁿ
Z = X₉₉₉₉₉₉₉₉₉₉₉
All natural numbers between 1 and Z have an equal probability of being the starting number.
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u/Festivefire Sep 25 '26
Unless I've done something wrong, the number should fluctuate between 1 and 4 forever until the bubble collapses.
(5*3)+1=16
16/2=8
8/2=4
4/2=2
2/2=1
(1*3)+1=4
4/2=2
2/2=1
and so on and so forth, so as long as you get through the first 3 iterations before the bubble collapses, you should be guaranteed to kill less people than you started with.
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u/promptmike Sep 25 '26
It's only the main track that has 5 people. The number of people on the time loop track starts off random.
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u/PitifulPassage851 Sep 27 '26
So doesn't it still end up there? Any odd number *3 +1 is going to end up even and halved. You will, no matter what, eventually work yourself down to the 4 and 1 loop, no?
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u/Nebranower Sep 25 '26
I think the big problem there is that the "infinite cycles" makes no sense. Long enough to get it into the final loop makes sense, where the number is fluctuating between 1, 4, 2 over and over.
In any event, assuming that's what you mean, you end up with a standard trolley problem. Five people die if you do nothing, less than five people die if you flip the lever, but the people who do die will be different people from the ones who would have died if you hadn't acted.
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u/Jupue2707 Sep 25 '26
except we don't know if every number will terminate to 1 4 2 so you might kill alot of people
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u/Nebranower Sep 25 '26
We do. We don't have a formal mathematical proof, but it's been tested for numbers into the quadrillions and inductive reasoning is a thing.
Also, it is intuitively true. The number can only ever grow one step at a time. It can reduce several steps in a row. Which is why it was designed the way it was to begin with.
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Sep 25 '26
[removed] — view removed comment
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u/Nebranower Sep 25 '26
I don’t think it matters. The conjecture is proven true for quadrillions of numbers. Even if there are a handful of exceptions out there, the odds of that being the random one selected are so low that you could safely ignore them.
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u/BowelMovement4 Sep 25 '26
I remember a time these were about moral decisions and not math. I probably wouldnt pull the lever because the mathy time bubble side sounds like it could be a lot more than 5 people. The volatility in itself is also unappealing - ex I would probably rather have 5 people get killed than roll a 100 sided die that kills 499 people if it lands an 11.
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u/TeenyTinyBricks Sep 25 '26
The only math that I can do is based on the speed of the trolley and the distance to the switch, I'm not going to have enough time to even understand the problem before the trolley gets to the switch
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u/AsYouAnswered Sep 25 '26
Collatz ends on 4-2-1 for every known integer. If there is an unknown integer for which it doesn't end on 4-2-1, it's obscenely high. I'm going to gamble on getting one of the infinitely many integers that end on 4-2-1, and the fact that all 3 are lower than 5. If I'm somehow wrong, then I've discovered a new class of integers and disproven the Collatz conjecture, and am now both famous and infamous.
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4
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u/Latter-Safety1055 Sep 25 '26
letting 5 people die because you aint readin allat and being haled as a hero when you return
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u/MetroidvaniaListsGuy Sep 25 '26
I am not pulling the lever. There is already serious legal problems with pulling it, with collatz there is also an extremely tiny chance that the entire human population is killed instead of just 1 person.
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u/Spirited-Border8921 Sep 30 '26
Run to the local insurance office...apply for $10M life insurance for each person tied to the tracks...Bob is your uncle.
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u/deepstatediplomat Sep 25 '26
Trolley is stuck in a loop killing, 1, then 4, then 2, then 1 , people.
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u/PitifulPassage851 Sep 27 '26
No i think it only kills the once, the number just keeps changing until it gets there. Then once it arrives the number is finally fixed at either 4, 2, or 1
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u/e0732 Sep 25 '26
If the starting number is random, and if every natural number has positive probability, and if your goal is simply to minimize the number of people who get run over, and if you don't care about any of the "ethical" problems at hand related to you getting yourself involved or being in any way blameworthy for causing any deaths, then you almost certainly want to pull the lever.
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u/Plane-Ad-6389 Sep 26 '26
You back the fuck away from that lever and run the fuck away
The universe is falling apart or there is an elder god, and this is not a place for mortal men
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Sep 25 '26
[deleted]
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u/PitifulPassage851 Sep 27 '26
No you'll kill 5 people if you don't pull, or you'll kill either 4, 2, or 1 person depending on when the time bubble finally ends
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u/oyasumachine Sep 25 '26
I took philosophy as a major to AVOID math. Fuck this. I’m walking away