2015-02-18
Explanation
The Joke
A woman presents a mathematical argument to a man using set theory. She considers the series {dog, dog, dog...} and calls it D_1. Since D_1 contains infinite dogs, and you can subtract D_1 from D_1, by simple algebra you can "prove" that you can get a dog from nothing (D_1 - D_1 = 0, but since D_1 contains dogs, the difference somehow also yields a dog). The next panel shows "FLASH!" and then the Earth from space, followed by a city being overrun, and finally people running from what appear to be dogs everywhere, with someone saying "We must use this discovery carefully."
The Humor
The comic parodies mathematical proofs that exploit the properties of infinity to reach absurd conclusions. The woman's "proof" is a version of the classic fallacy where subtracting infinite sets from each other can yield seemingly paradoxical results (similar to Hilbert's Hotel or the Banach-Tarski paradox). The joke escalates by treating this flawed mathematical reasoning as if it actually works in reality -- the "proof" somehow conjures dogs from nothing, leading to an apocalyptic scenario where the world is overrun with dogs. The final deadpan line about using the discovery carefully is funny because the catastrophe has clearly already happened. The humor also works because dogs are an inherently charming and non-threatening thing to accidentally summon in infinite quantities.
References
- Set theory and infinity paradoxes: The comic references real mathematical puzzles about infinite sets, where subtraction and other operations can produce counterintuitive results.
- Banach-Tarski Paradox: A theorem in set-theoretic geometry that shows a solid ball can be decomposed and reassembled into two balls identical to the original -- getting something from nothing, in a sense.