Our model captures first-order logical expressibility, which in the presence of arithmetic is known to coincide with constant-time parallel computability (uniform AC^0). This parallel-time/serial-space duality will be illustrated most beautifully by the example of binary addition, for which our main theorem constructively yields the carry look-ahead algorithm from the bit-serial (elementary school) algorithm. There also appear to be connections between space measurement in this model and quanta of information. This reinforces the notion that first-order logic is a machine-independent query language, and may also give possible insights into space-bounded quantum computation. Extensions to constant-depth threshold circuits (uniform TC^0) and ALOGTIME (uniform NC^1) will also be discussed.