I think we take the machine analogy too far. Axiomatic systems are meant to provide a set of initial assumptions from which to construct the rest of the building. They are not algorithms, but logical propositions accepted by convention as true (so that all derived statements can be proven true). By themselves, they do not travel in time; our reasonings and explanations do, but only because our talking does. I'm getting lost. I thought you said you didn't want the ticks to represent numbers, since there is no way of telling the 5th from the 625th.