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Mathematical Digest


Short Summaries of Articles about Mathematics
in the Popular Press

"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