This article proposes a methodological approach to the historiography of computing in terms of information hiding--that is, the introduction of levels of abstraction (LoAs) between the human being and the computing machine. This approach applies the LoAs, in terms of the epistemological levelism proposed within the philosophy of information, to the transition from ancient to modern computing. In particular, the black-box metaphor and von Neumann's architectures are discussed. Also, the authors propose a formal LoAs method as a mathematical counterpart. Information itself is then treated as structure-preserving functions so that a LoA can distinguish what kind of information gets hidden when human beings interact with computing machines.