Banach-Tarski and the Paradox of Infinite Cloning
One of the strangest results in mathematics explains how it’s possible to turn one sphere into two identical copies, simply by rearranging its pieces. The post Banach-Tarski and the Paradox of Infinite Cloning first appeared on Quanta Magazine
Imagine two friends hiking in the woods. They grow hungry and decide to split an apple, but half an apple feels meager. Then one of them remembers one of the strangest ideas she’s ever encountered. It’s a mathematical theorem involving infinity that makes it possible, at least in principle, to turn one apple into two. That argument is called the Banach-Tarski paradox...
Originally published in Quanta Abstractions.
