inversz

Inversz is a fictional concept used in hypothetical discussions of symmetry and reversibility in mathematics, computer science, and philosophy. It denotes a generalized inverse operation that can be applied to systems where a true mathematical inverse may not exist, by selecting a contextual inverse that preserves essential structure or information.

In formal sketches within fiction and thought experiments, an inversz of a map f: X → Y is a relation or multi-valued function inv_f: Y → X that "undoes" f on a chosen subset Y0 ⊆ Y, while allowing some degrees of freedom on Y\Y0. When f is invertible, inv_f coincides with the usual inverse f^{-1}. The inversz is typically required to satisfy two guiding properties: reconstructivity on its domain (composing f with inv_f yields a projection onto a chosen subobject), and consistency with dualities or invariants that the system preserves.

In practice, inversz is used as a heuristic device in narratives about information preservation, reversible computation, and data interpretation. It helps explore questions like how much information must be retained to reverse a process, or how different choices of inversz affect outcomes in a system with noise or ambiguity.

See also: Inverse function, generalized inverse, pseudoinverse, duality, reversible computing.