Lecture 02 · Mathematics
What a shuffle actually does
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Meanwhile, read the outlineWhat you will learn
Distinguish identity, position and orientation, and compute cuts, reversals, deals, riffles and compositions on a labeled packet.
Before this lecture
Nothing. This lecture is a fine place to start.
In this lecture
An outline of the lecture, scene by scene, with the statements that appear on screen. It follows the draft script, so details may change in production.
Separate what changes from what identifies a card
- Identity: A, B, C, D
- Position: 1, 2, 3, 4
- Left to right = top to bottom
- Orientation: up or down
Define a cut and its inverse
- Cut 2: ABCD → CDAB
- Cut 1 four times = original order
- Cut 3: ABCD → DABC
Distinguish dealing from a cut
- Full deal: ABCD → DCBA
- Cut 2: ABCD → CDAB
- Deal 2, rest on top: ABCD → CDBA
Separate reversal of order from flipping faces
- Turn packet = reverse order + flip every face
- A↓ B↓ → B↑ A↑
- A↓ B↑ → B↓ A↑
Introduce permutations as position maps
- New deck order: B, C, D, A
- Old position → new position
- p=[4, 1, 2, 3]
- Inverse: reverse the arrows
Show that composition order matters
- Cut, then flip top ≠ flip top, then cut
- Undo in reverse order
Define riffle as interleaving without assuming randomness
- Left: ABC; right: DEF
- Choices: L, R, R, L, R, L
- Output: A, D, E, B, F, C
- Within-source order survives
Give a precise operation challenge and worked inverse
- ABCD → CDAB → ABDC
- Predict identity AND orientation
- Undo the last move first
Companion interactive
Planned
Predict complete states and construct valid inverse move sequences.
The interactive for this lecture is being built and will appear here.
Notes
Written notes for this lecture will appear here.
Sources
- Mathematical Card Magic, Convention Center, pp. 2–10, 14–24
How these sources were used
- Handling and permutation conventions; examples authored for this course.