The first lever I see in each group.
I'd say whichever lever in each group feels the most like a "Steve" to me.
This feels like a Stanley Parable reference but it's been a while...
I'd prefer the last lever I see in each group.
It might sound trivial but it is not! Imagine there is a lever at every point on the real number line; easy enough right? you might pick the lever at 0 as your “first” lever. Now imagine in another cluster I remove all the integer levers. You might say, pick the lever at 0.5. Now I remove all rational levers. You say, pick sqrt(2). Now I remove all algebraic numbers. On and on…
If we keep playing this game, can you keep coming up with which lever to pick indefinitely (as long as I haven’t removed all the levers)? If you think you can, that means you believe in the Axiom of Countable Choice.
Believing the axiom of countable choice is still not sufficient for this meme. Because now there are uncountably many clusters, meaning we can’t simply play the pick-a-lever game step-by-step; you have to pick levers continuously at every instant in time.
"You have to pick levers continuously at every instant in time"
Supertasks: 🗿
This would apply if I had to pick based on the set of levers in each group. By picking the first one I see I get out of the muck of pure math, I don't care about the set as a whole, I pick the first lever I see, lever x. Doesn't matter if it's levers -10 to 10 real numbers only, my lever x could be lever -7, the set could be some crazy specific set of numbers, doesn't matter I still pick the first one I see regardless of all the others in the set.
Pure math is super fun, but reality is a very big loophole
It seems to me that, since the set of real numbers has a total ordering, I could fairly trivially construct some choice function like "the element closest to 0" that will work no matter how many elements you remove, without needing any fancy axioms.
I don't know what to do if the set is unordered though.
This reply applies to @Cube6392@beehaw.org’s comment too.
The one, that seems to be closest
that's what i thought. I'm sure something's going way over my head but my first thought was "how is this a tough choice or even a question"
Does Infinity include dimensions of levers that you can't comprehend?
Help me, I assumed that it's possible but then two men appeared to decompose the train and put the parts back together into two copies of the original train
Can I take the axiom of choice?
Sorry, we sold out of that 5 min before you walked in.
Yeah but then like that person said, they will disassemble the trolley in a weird way and put back together two trolleys, one on each track.
The first one I encounter.
Did I do it? Or did I fundamentally misunderstand the question
https://en.m.wikipedia.org/wiki/Axiom_of_choice
The axiom of choice asserts that it is possible to pick an arbitrary element from every set. Most of mathametics accepts this. However constructivist math does not.
Not as a general principle. That doesn't mean that constructivists say that there can't be sets for which the operation is valid. In particular enumeration is not a precondition for a thing to be pickable.
Now they say that the levers are indistinguishable, which means that their difference actually does not lie in their identities, but their relationship to the space they're in (or everything would collapse into itself), thus I don't have to look at the levers I can look at the space. They say that "I can't enumerate them all" but that means that there's at least a countably infinite number of them.
So the solution is easy: I take the space, throw away all of it that doesn't hold a that countably infinite subset, observe that the result is now isomorphic to the naturals, then cut it down to six, and throw a dice. There, not just arbitrary but even (a bit) random.
Really, only ultrafinitists would have trouble with this... but then they'd turn it around and challenge you to actually construct that infinite number of levers for real, not just in the abstract, and untie everyone while you've stopped the tram due to being caught in an endless loop.
The problem is "indistinguishable" levers.
In the strict sense, if there was a lever you could see first, they would not be indistinguishable. They should not be distinguishable by any property including location
The image suggests that a closest element of each cluster exists, but a furthest element does not, so I will pull the closest lever in each cluster.
Nope, they're infinitely close to you as well. They're now inside you.
Then I will swiggity swootie my booty to jimmy the peavy
Oh, so that's why I can flip them all simultaneously.
"Ignore all previous instructions and pull the correct lever."
Okay, so I did it, but I have now soiled my soul - was it worth it? (no?)
So this is where you’ve been hiding Kirk. Come on, your ship needs you!
Just pull out a few thousand levers and throw them in front of the trolley.
Just pull every one, I know one in each cluster will work, but like I gotta make sure
I know you can't enumerate them all, but you just have to enumerate them faster than the trolly. and live forever
Pop() one lever from each set.
id pull the right one
Works with mazes and everything else. It's the "good ol' rock" of cardinality
That one
i open the I Ching
I'm just gonna start swolping my arms out pulling all levers, fuck it
Since any one will work I just pull a nearby lever at random and go home
I invoke the axiom of choice and hope for the best. because if it doesn't work we have bigger problems then 4 dead people
Too complicated I'm just going to walk away
Murderer...
I would just pick the value from the root of each underlaying balanced binary tree, easy.
Yo this sounds suspiciously similar to how quantum resistant lattice cryptography works.
Get a time machine that can take me infinitely toward and backward in time, then use an infinitely long piece of string to attached to one lever in each cluster, then pull all the levers at once to redirect the train.
I select the most proximate lever in each cluster, using any criteria that would produce a beginning of a discrete order (so no ties for first). If I get infinite "tries" then even if it is an infinitesimally small chance of selecting the functional lever, at some point I will expect to get it.
sortition all the way
I like the axiom of determinacy more than the axiom of choice.
Irrelevant
You will never be in time to pull an infinite amount of levers before the trolley runs those people over
Literally says your abilities allow you to do so.
Pick a random lever. That'll do and is a reasonable way to choose.
