Section 1 of 7
Basic Concepts
A shuffle can scramble positions while leaving a count untouched.
The course opens with Miraskill, a trick in which a deck the spectator shuffles still keeps a promise. The two lectures that follow set up the language for everything after: what a shuffle does to positions, identities and faces, and how to ask what cannot change.
Lectures in this section
Performance lecture, with a trick to play Mathematics lecture
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Lecture 1, performance: Miraskill: order hidden inside a shuffled deck
Deal a shuffled deck in pairs. The red–red pile and the black–black pile always tie. Play Miraskill -
Lecture 2, mathematics: What a shuffle actually does
Distinguish identity, position and orientation, and compute cuts, reversals, deals, riffles and compositions on a labeled packet. -
Lecture 3, mathematics: The magician’s question: what cannot change?
Formulate an invariant with an initial condition and legal moves, and distinguish proof, testing and counterexamples.