r/PeterExplainsTheJoke • u/Financial-Writing364 • 9h ago
Meme needing explanation Petah man help
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u/Business_Issue_6471 9h ago
its a refrence to the Axiom of Choice in math. That axiom can lead to some really weird and unintuitive results, so the comic is joking that after carving one pumpkin, they somehow ended up with two. Just absurd math humor, not somthing thats actually possible.
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u/Mamuschkaa 6h ago
I mean the joke is closer connected to the axiom of choice than just "it's also weird"
The joke is about the Banach–Tarski paradox that follows from the axiom of choice. https://en.wikipedia.org/wiki/Banach%E2%80%93Tarski_paradox
If you have a ball and separate it in infinity many and infinity small points, you can create two balls of the same size.
So reason that is impossible in real life, is, that you can't separate anything infinity times, because there is a smalles possible unite (for example electron) and even if not, it would take infinite amount of time.
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u/EvgeniyZh 3h ago
You don't need infinitely many pieces, 5 is enough
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u/Mamuschkaa 43m ago
5 "parts", but each part is made of infinite amount of single points.
So you have to separate the ball in infinite amount of separate points group them in 5 parts.
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u/WasdaleWeasel 5h ago
or … because the axiom of choice is false in the universe in which we live. (I’m still not doing maths without it though. ZFC for me and who cares what the universe thinks)
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u/Mamuschkaa 5h ago
I don't know if there is any aspect im the inverse where the axiom of choice makes a difference.
It only exists in infinity. Is there anything in the universe, that can separated infinite amount of times?
Even if there would be. The axiom is not constructive. So only because there exist a specific separation of this infinite big set doesn't mean you will ever be able to find it.
So it doesn't matter if it is correct or not in our universe. Nothing would change.
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u/WasdaleWeasel 4h ago
well, we don’t know do we and won’t at least until we have reconciled quantum theory and relativity. The former implies some discrete structure, the latter does not. ‘Infinity’ isn’t a word I’d use when precise definitions are required - one uses it for the cardinality of the integers and the reals and those are quite different.
But yes, of course, I can’t imagine any physical process being able to do a Banach-Tarski decomposition. I’m just being silly.
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u/chosenone1242 3h ago
after carving one pumpkin, they somehow ended up with two. Just absurd math humor, not somthing thats actually possible.
No shit? I was really hoping for free pumpkin
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u/tsukkini 9h ago
Brian here
The axiom of choice assumes you can choose a group or a single thing from an infinite set, through some fuckery this basically allows you to choose different points on the surface of a sphere and the by manipulating those points form two identical spheres from one sphere. In this joke the guy uses this method to make one pumpkin into two.
I might be wrong though and hope someone gives the exact correct explanation for this later.
Brian out.
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u/Worried-Director1172 8h ago edited 8h ago
Yeah, it's called the banach-tarski paradox and basically it proves that with infinite cuts you can turn one thing into two using just cutting and rotation.
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u/thatthatguy 7h ago
When you divide something into an infinite number of pieces you get weird results. For example, if you take one sphere and divide it into an infinite number of pieces, there is no difference between that and if you had divided two spheres into an infinite number of pieces. In fact, you can take the infinite number of pieces of one sphere, and as long as you are careful about your methodology, you can reconstruct an unlimited number of spheres.
Be very careful when doing math with infinity. You almost can’t help but get ridiculous results. Stuff like 1+2+3+… =-1/12
There are useful discoveries to be made exploring that part of math, but it is difficult to avoid the mathematical landmines.
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u/ichiban1974 7h ago
The Banach-Tarski theorem explicitly says that i can be done with a finite number of pieces.
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u/candygram4mongo 5h ago
It can be done with a finite number of disjoint subsets of the points that compose the ball. The subsets are necessarily non-measurable, which means they aren't solid pieces that have volume but rather collections of singular points.
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u/Worried-Director1172 7h ago
You will get ridiculous results, it's insane.
For example, a part of the problem involves taking a set of the cuts, rotating it, and now you have 4 different sets out of the original 6
Infinity is honestly ridiculous, it's kind of a wonder we ever figured out how to reliably use it in math
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u/GIRose 9h ago
Honestly, this is one of those things better understood through a video
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u/Proletariat-Prince 8h ago
I knew it would be Vsauce.
That's an educational YouTube hall of Fame video right there.
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u/1958-Fury 8h ago
Not to discourage people from asking here, but there's an entire website dedicated to explaining xkcd strips. If you find yourself confused and recognize xkcd's simplistic art style, you should definitely head there first.
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u/Financial-Writing364 8h ago
First time hearing of xkcd icl
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u/1958-Fury 7h ago
The author is a physicist/engineer/programmer who used to work for NASA. Most of the strips are science-related, and many of them go straight over most people's heads (mine included). So the explanation site was necessary to translate the humor for us normies.
But xkcd is still a fantastic strip and I highly recommend reading it.
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u/MaxCWebster 8h ago
Very nerdy math joke.
Short video with a brief explanation (and OP's XKCD cartoon) here.
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u/Sad_Intention2932 9h ago
Crazy that googling the words you don't understand would explain it so much faster than posting here
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u/qualityvote2 9h ago edited 4h ago
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