This paper proposes a model to explain the usefulness of the number system. The number line and basic number theorems are used daily by people to make predictions and explanations of real world events. People commonly believe arithmetic works and this paper offers one systematic model to explain it. The proposal is that a two-dimensional cellular automation can be used for modeling the correspondence between the real world and features of the arithmetic number line. I postulate that any other universal computing tool could also be used for the model. So reversible Turing machines and lambda calculus could also be used for this modeling.
Numbers are posited to be human artifacts that model processes like measurable objects in space/time. The paper details the differences between real world space-time energy-matter and the human artifact of the number line. Then we offer a model that bridges the two. It is postulated that number features are expressed with symbols and a finite sequence of instructions.
While the domain covered by this model is limited to positive integers of the natural number sequence and basic arithmetic, some unexpected implications about number theory will be stated for future exploration.