Editing 804: Pumpkin Carving
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In the third frame, [[Megan]] is our typical emotional xkcd comic character. She is the only one out of the four who actually carved a typical jack-o'-lantern; however, she is projecting herself onto it, and has named it Harold. Her dialogue suggests it (or he) is suffering from typical holiday depression, with symptoms such as using a lot of time daydreaming, worrying, and trying to distract herself with holiday traditions, but she already knows that it won't work. Some have speculated that this is a possible reference to the classic {{w|Internet meme|meme}} [http://knowyourmeme.com/memes/hide-the-pain-harold Hide The Pain Harold], but this is highly unlikely; the meme [https://knowyourmeme.com/memes/hide-the-pain-harold only surfaced in 2011], a year after the comic was published. | In the third frame, [[Megan]] is our typical emotional xkcd comic character. She is the only one out of the four who actually carved a typical jack-o'-lantern; however, she is projecting herself onto it, and has named it Harold. Her dialogue suggests it (or he) is suffering from typical holiday depression, with symptoms such as using a lot of time daydreaming, worrying, and trying to distract herself with holiday traditions, but she already knows that it won't work. Some have speculated that this is a possible reference to the classic {{w|Internet meme|meme}} [http://knowyourmeme.com/memes/hide-the-pain-harold Hide The Pain Harold], but this is highly unlikely; the meme [https://knowyourmeme.com/memes/hide-the-pain-harold only surfaced in 2011], a year after the comic was published. | ||
| − | In the fourth frame, [[Cueball]] is shown in front of two un-carved pumpkins | + | In the fourth frame, [[Cueball]] is shown in front of two un-carved pumpkins exclaming that this is the result of carving one pumpkin. He is referencing the {{w|Banach-Tarski paradox}} (which is made clear in the title text), a theorem which states that it is possible to split a three-dimensional ball, in this case a pumpkin, into a finite number of "pieces," and then reassemble these "pieces" into two distinct balls both identical to the original. This paradox has been proven for theoretical shapes, but requires infinitely complicated pieces which are impossible for anything made of physical {{w|atomic theory|atoms}} rather than mathematical {{w|point (geometry)|points}}. |
The off-screen interviewer in that frame references the {{w|Axiom of Choice}}. This axiom is the foundation for many theorems (including the Banach–Tarski paradox) and is extremely influential to modern mathematics; however, it has been historically controversial precisely because it enables this kind of weirdness. It is called an "axiom" because it is a statement that is not meant to be proven or disproven—only accepted or rejected depending on the theoretical framework one wishes to work with. Rejecting the Axiom of Choice results in a perfectly coherent alternate form of set theory. Since the proof for the Banach–Tarski paradox relies on accepting the axiom of choice, the interviewer is suggesting Cueball's unexpected result would not have happened without using the axiom. | The off-screen interviewer in that frame references the {{w|Axiom of Choice}}. This axiom is the foundation for many theorems (including the Banach–Tarski paradox) and is extremely influential to modern mathematics; however, it has been historically controversial precisely because it enables this kind of weirdness. It is called an "axiom" because it is a statement that is not meant to be proven or disproven—only accepted or rejected depending on the theoretical framework one wishes to work with. Rejecting the Axiom of Choice results in a perfectly coherent alternate form of set theory. Since the proof for the Banach–Tarski paradox relies on accepting the axiom of choice, the interviewer is suggesting Cueball's unexpected result would not have happened without using the axiom. | ||
