Explain xkcd: It's 'cause you're dumb.
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|| This explanation may be incomplete or incorrect: More on the match, especially the title text.|
Miss Lenhart is back teaching a math class. She begins a proof when one of her students (Cueball) interrupts her asking if this is one of those Dark Magic proofs. She says no, but it soon turns out that it is; Cueball exclaims that he just knew it would be.
If this actually refers to the proof being magical, or just to the fact that many students often feel like the resulting proof just appeared without any reason, i.e. either the teacher did not do it clearly, or the student is not up to the task of understanding proofs of that complexity, is not clear.
The proof she starts setting up resembles a proof by contradiction. These often involve making an assumption that there exists some formula or figure that fulfills the requirements given and plucking that answer out of abstract mathematics, much like summoning of demons is associated with black magic. This is usually done by relying on knowledge of the constraints of the form (for example, having the square root of 2 be a/b where a and b are both integers and have no common factors when proving that the square root of 2 is irrational). This common usage is then shown to be not the case in the comic as the proof then goes to claim that the answer will be written in a specific place (though this could be taken as indicating that the result is finite or has a simple algorithm for continuing it). This may also be a reference to proof by induction, which can be thought of as a proof of the existence of an infinite number of more specific proofs.
In the title text the decision of whether to take the axiom of choice is made by a deterministic process. The axiom of determinacy is incompatible with the axiom of choice, which is the continuation of the joke of these dark magic proofs. The axiom of choice was mentioned earlier in 804: Pumpkin Carving.
Although Miss Lenhart did retire a year ago after 1519: Venus, she seems to have returned here for a math course at university level, but continues the trend she finished with in the her undergraduate class...
- [Miss Lenhart is standing facing left in front of a whiteboard writing on it. Eleven left aligned lines of writing is shown as unreadable scribbles. A voice interrupts her from off-panel right.]
- Miss Lenhart: ... Let's assume there exists some function F(a,b,c...) which produces the correct answer-
- Cueball (off-panel): Hang on.
- [In a frame-less panel Cueball is sitting on a chair at a desk with a pen in his hand taking notes.]
- Cueball: This is going to be one of those weird, dark magic proofs, isn't it? I can tell.
- [Miss Lenhart has turned right towards Cueball, who is again speaking off-panel. The white board is also off-panel.]
- Miss Lenhart: What? No, no, it's a perfectly sensible chain of reasoning.
- Cueball (off-panel): All right...
- [Miss Lenhart is facing the whiteboard again writing more scribbles behind some of the lines from before (the first line has disappeared). The lines that have more text added are now number three and five (four and six before). Cueball again speaks off-panel.]
- Miss Lenhart: Now, let's assume that the correct answer will eventually be written on the board at the coordinates (x, y). If we—
- Cueball (off-panel): I knew it!
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