S0 Unit: Two-State Opposition
S0 is the smallest finite layer in the book: two states and a flip between them.
Unit Goal
Learn the idea of opposition before learning full circular motion. S0 prepares the vocabulary for signs, paired states, poles, antipodes, and later sphere scaffolds.
The Idea
With only two points, there is not much room for motion. But there is one important action: switch to the opposite point.
Definition In Words
An S0 opposition system has two states. Applying the flip once moves to the other state; applying it twice returns to the starting state.
flip(flip(x)) = x
This is useful because many later ideas have a paired form: positive/negative, north/south, a point and its antipode, or a sign ambiguity in a rotation representation.
Checkpoint
Why is S0 useful even though it has only two points?