A ≠ A: Identity, Reconstruction and the Limits of Sameness
When does a mathematically valid reconstruction cease to correspond to the the it claims to describe?
For centuries, science has excelled at describing the world through mathematics, measurement, and increasingly sophisticated models. But successful description is not necessarily the same thing as identity, and a successful reconstruction is not necessarily a unique one.
In this second edition of A ≠ A, Drew Farwell explores identity, reconstruction, recoverability, continuity, and physical admissibility through a series of thought experiments and physical examples. From apples and cloning to singularities, observation, information loss, and the limits of measurement, the book examines a possibility that is often overlooked:
Mathematical validity and physical realizability may not always be the same thing.
Rather than offering final answers, this work asks what happens when familiar assumptions are subjected to closer scrutiny. What survives division? What survives reconstruction? How much information must remain for identity to persist? And when does a mathematically valid description cease to correspond to the thing it claims to describe?
Part philosophy, part physics, and part investigation into the nature of knowledge itself, A ≠ A invites readers into a question that becomes increasingly difficult to ignore:
What remains recoverable (and why does that matter)?