804: Pumpkin Carving
Title text: The Banach-Tarski theorem was actually first developed by King Solomon, but his gruesome attempts to apply it set back set theory for centuries.
This comic is a reference to the American custom of carving pumpkins to set out on porches and front steps for the American holiday of Halloween, which occurs on October 31. The pumpkin has the inside emptied out and a face or design carved in the side. Then a light in placed inside (usually a candle). These are called "Jack-O'-Lanterns". The Jack-O'-Lantern in the 3rd frame is the typical and standard design for a carved pumpkin.
Beret Guy, naturally, stays oddly on-topic by carving a pumpkin in his pumpkin.
In the 2nd frame, Black Hat is putting Nitroglycerin (an explosive) into his carved pumpkin in the hopes that someone will attempt to smash it and it will explode. His note would most likely only serve to encourage the intended targets (teenage vandals). His chest pain reference is because Nitroglycerin is used to open blood vessels to quickly improve blood flow when someone has chest pains.
In the 3rd frame, Megan is our typical emotional xkcd comic character. She is projecting herself onto the jack-o'-lantern as she tries to distract herself with holiday traditions that won't work to distract her.
In the 4th frame, Cueball is referencing the Banach-Tarski paradox, a theorem which states that if you carve up a 3-dimensional ball, in this case a pumpkin, into a finite number of pieces, you can then reassemble the pieces into two different balls identical to the original. This paradox has been proven for just about anything... except objects made of atoms, which our universe is comprised of. The person off-screen in that frame references the Axiom of choice which is a mathematical axiom that says that given a set of buckets or bins (each that contain one or more object(s)) it is possible to select exactly one object from each bucket. The Banach-Tarski rests on several axioms which are fairly well respected, but also requires the Axiom of Choice to work correctly. So a person who does not believe in the Axiom of Choice would not have been able to do what Cueball managed to do.
The title text says that King Solomon developed the Banach-Tarski theorem first. This is a reference to the story of two women being brought before him. Both were arguing that a particular child was their own. Solomon said that the solution was to cut the child in half and give each woman one of the halves. One of the two women said that the other should have the baby whole. Solomon then knew she was the true mother, and gave her the child. The joke is that Solomon, may not have intended to kill the child, but knowing that two whole children could be made from the one, intended give a baby to each woman, and the Banach-Tarski paradox states that, were the baby not made of atoms, it should be possible.
- [Beret guy stands next to a pumpkin with a picture of a pumpkin carved into it.]
- Interlocutor: So what did you-
- Beret Guy: I carved a pumpkin!
- Interlocutor: ...
- [Black Hat stands next to a pumpkin and a box labeled "Nitro-glycerin. Do not shake."]
- Interlocutor: Taking on teen vandals, I see.
- Black Hat: Heavens, No. My pumpkin simply has chest pains. In fact, I'll leave a note warning them not to smash it.
- [Megan stands next to a jack-o' lantern.]
- Megan: My pumpkin's name is Harold. He just realized that all the time he used to spend daydreaming, he now spends worrying. He'll try to distract himself later with holiday traditions, but it won't work.
- [Cueball stands next to two pumpkins and a knife.]
- Cueball: I carved and carved, and the next thing I knew I had two pumpkins.
- Interlocutor: I told you not to take the axiom of choice.