"A Matter of Choice" by Jim Holt. Lingua Franca, November 2001, page 68.
Holt describes the axiom of choice---its history, consequences, misuse, andstanding in modern mathematics. The latter third of the article deals with theBanach-Tarski paradox, which states that using the axiom of choice, one candissect a solid sphere and without stretching the pieces in any way, reassemblethose pieces to form two solid spheres each the same size as the original. Aconsequence of this is that a solid sphere the size of an orange could bedissected and reassembled into a sphere the size of the sun. Pieces ofarbitrarily fine detail are needed, so in practice such reassembly isimpossible. Holt relates an amusing tale regarding a bet between Princetonmathematicians and the late physicist Richard Feynman. Feynman challenged theabove claim about an orange and the sun saying, "...you said an orange, so Iassumed you meant a real orange."
--- Mike Breen