Counting is constructed using two sets, the uncounted set and the counted set. For each distinct object being counted, one unit is subtracted from the uncounted set and one unit is added to the counted set until all of the distinct objects have been counted. The uncounted and counted sets exchange 1 and 0 for each object counted.
Chiralkine treats an object as a mirror symmetric relationship between what it is and what it is not. Counting works just like the clearing of offers and wants by users in an exchange of goods and services, but where the offers and wants are 1s and 0s.
For each distinct object being counted, the uncounted set offers 1 and wants 0 and the counted set offers 0 and wants 1. Counting is complete only when all 1s and 0s have been exchanged between the uncounted and counted sets.
For example, three distinct objects x, y and z are counted as follows.
Object x offer is paired with object y want.
Object x want is paired with object z offer.
Object y offer is paired with object z want.
This completes a ring. All 1s and 0s can now be exchanged between the uncounted and counted sets. The offers and wants associated with x, y and z can be paired in any order, but they must all be paired to form a ring to complete the count. This treats what each object is and what each object is not mirror symmetrically.
For example, if the offers start out as 0101 and the wants as 1010, counting is complete when all the 1s and 0s have been exchanged, so the offers end up as 1010 and the wants as 0101. The distinction between offers and wants has been cleared.
Instead of there being two absolute arithmetic steps (subtraction and addition), there are three coupled relational steps:
0101 → 0110 → 0011 → 1010
1010 → 1001 → 1100 → 0101.