Two-Point Flip
The S0 chapter records the finite two-point opposition model. It is intentionally small: a two-point type and an operation that swaps its two points.
Lesson Goal
Understand the simplest possible closed action: flip once to leave, flip twice to return.
The Idea
The two-point flip is the smallest example of a reversible finite action. It does not yet have the richer structure of a circle with many addresses, but it gives the book a clean way to talk about paired states.
If the two states are left and right, then:
flip(left) = right
flip(right) = left
flip(flip(left)) = leftWhy It Comes Before S1
S1 rotations can have many steps before returning. S0 returns after exactly two flips. That makes it the first closed finite behavior a reader can hold in mind before learning modular addresses.
Checkpoint
What is similar between a two-point flip and a stride on a finite circle? What is missing from S0 that appears in S1?