What is quantum superposition?

A superposition is a state that carries an amplitude for each answer to a question at once, numbers whose squares are the odds and which can cancel where odds never can. An atom that a sideways magnet sent left carries one amplitude for up and one for down, and asked up or down, half such atoms go each way. A beam secretly made of half up atoms and half down atoms gives the same fifty-fifty on every up-or-down question. Write each beam as a two-by-two table of numbers and the tables agree everywhere except the corners, which hold the whole difference. Bring the split paths back together and the superposition rebuilds the original beam, while the secret mixture cancels nowhere. Dark bands in an interference pattern are places where amplitudes of opposite sign met and left nothing.