The Banach-Tarski Miracle

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Today’s Spiked Math comic is:

Joke Explanation:

The joke lies in combining the Banach-Tarski paradox with a miracle that Jesus performed:

1. The Banach-Tarski paradox is a theorem that basically says a solid ball (in 3-dimensions) can be split into a finite number of non-overlapping pieces, which can then be put back together in a different way to yield TWO identical copies of the original ball. It doesn’t work in 1 or 2-dimensions though. Wikipedia has a great picture of this:

banach tarski paradox

2. One of the miracles of Jesus was feeding the multitude. Basically the story has Jesus taking five (or seven) loaves and two fish and feeding thousands of people. Jesus took the five loaves and the two fish and looking up to heaven, “he gave thanks and broke the loaves. Then he gave them to the disciples, and the disciples gave them to the people. They all ate and were satisfied, and the disciples picked up twelve basketfuls of broken pieces that were left over. The number of those who ate was about five thousand men, besides women and children.”