2014-08-11
Explanation
The Joke
A doctor tells a patient: "Well, the good news is that, according to Banach-Tarski, you now have THREE testicles." The patient sits on the examination table looking bewildered.
The Humor
The Banach-Tarski paradox is a theorem in set-theoretic geometry that states a solid ball can be decomposed into a finite number of pieces and reassembled into two identical copies of the original ball. In other words, you can theoretically take one sphere, break it apart, and create two spheres of the same size -- effectively duplicating matter through pure mathematics.
The comic applies this theorem to a medical context: the doctor is suggesting that through the Banach-Tarski paradox, a patient who presumably lost a testicle (or had some medical issue) now has three instead of two. The phrase "the good news" implies there is also bad news, and the absurdity of the "good news" makes the imagined bad news even more alarming.
The humor comes from the collision between abstract mathematics and practical reality. The Banach-Tarski paradox works only with non-measurable sets using the Axiom of Choice -- it has absolutely no applicability to physical objects. A doctor cheerfully citing an abstruse mathematical theorem as though it were a medical diagnosis is inherently absurd.
References
The Banach-Tarski paradox, formulated by Stefan Banach and Alfred Tarski in 1924, is a theorem in set theory that demonstrates that a solid ball in three-dimensional space can be split into a finite number of non-measurable pieces, which can then be reassembled using only rotations and translations into two identical copies of the original ball. The paradox relies on the Axiom of Choice and applies only to mathematical objects, not physical ones.