And He took the five loaves and the two fish, and looking up to heaven, He blessed and broke and gave the loaves to the disciples; and the disciples gave to the multitudes. So they all ate and were filled, and they took up twelve baskets full of the fragments that remained. – Matthew 14.
The logician Willard Quine defined a paradox as an “absurd” statement backed up by an argument.
The famous result of Banach and Tarski definitely counts as a paradox by this definition. They proved that it is possible to take a unit sphere (a ball with radius 1), divide it into five pieces, then by rotations and translations reassemble it into two unit spheres.
View original post 1,604 more words