Physics, the science of change, has managed to discover and to explain a large number of qualitative and quantitative aspects of a large number of natural changes, but change itself remains unexplained since we first faced it, over twenty-seven centuries ago. This paper proves, in terms of transfinite arithmetic, that change is inconsistent within the infinitist framework of the spacetime continuum, were all solutions have been tried until now. It then proposes a consistent solution within the finitist framework of the discrete spacetimes of cellular automata like models, proving the factor that convert between continuum and discrete spacetimes has the algebraic form of the relativistic factor of Lorentz transformation, which could be reinterpreted as an operator to translate between a consistent discrete reality and an inconsistent continuous reality.