Erica Minuz

”Twice upon a time there was a king…” The narrator tells a distorted fairy tale that seems absurd, but that is actually built on a mathematical structure. The king realizes that he has a double and his power falls apart, like a playing card castle. He then asks help from a magician (or a mathematician?). In order to solve the situation, the magician puts a spell on the kingdom (takes the quotient space) identifying every point with its reflection in the mirror. Now the king is one, but the kingdom has no more orientation: there’s no left nor right. ”What kind of kingdom is that?” the people ask themselves. The narrator will then show some examples of spaces where right and left do not make sense: Moebius Bands, Klein Bottles and Projective Spaces. These are examples of non-orientable spaces. What will happen to the king? What does it mean to be twice? And if the king was once two, why not three, four, five, or infinite?