When 1+1+1 Equals 1
9 days ago
- #involution
- #logic
- #mathematics
- Mathematical operations that are involutions return to the original state when applied twice, such as taking the negative or reciprocal of a number.
- Near-involutions are operations where applying them three times is equivalent to applying them once, and four times is equivalent to twice, etc.
- Examples of near-involutions include orthocomplementation in linear algebra, intuitionistic negation in logic, and a network operation in graph theory.
- Orthocomplementation in geometry involves finding perpendicular lines, where applying the operation three times returns the same result as applying it once.
- Intuitionistic negation in constructivist logic behaves such that triple negation is equivalent to single negation, differing from classical logic.
- In social network analysis, an operation K(S) defines people who know everyone in set S, and applying K three times returns the original K(S).
- The article explores how these operations, though distinct, share the property of 'thrice equals once' and connects them to broader mathematical concepts.