Brock Algebra introduces a unique system where each number is paired with a history component that tracks operations affecting it over time. This history allows for reversible operations and provides additional structure for algebraic manipulation. With k-valued Brock Algebra, we track the history of the negatives and can think of a negative one times a negative one as a double negative one.

Light intro into Brock Algebra where the history of a number is as important as the number itself! Brock Algebra augments numbers with a history component, enabling reversibility by preserving information that standard arithmetic discards. Brock Algebra is an informal term for an algebraic framework where numbers carry history about their operations. The key idea is that the history of a number can be as important as the number's current value . For example, in Brock Algebra one might say a negative one times a negative one is a "double negative one" (i.e. 1 with a k-value of 2) meaning the result remembers that it came from multiplying two negatives, instead of simply collapsing to +1 as in ordinary arithmetic. The goal is to augment numbers with minimal extra information so that operations become invertible (reversible) even when they would normally lose information.