The problem of causality in the system of gears reminds me of this comment, comparing a control system model of the stepwise algorithm "measure, compute correction, apply correction, repeat" versus the continuous reality of a centrifugal governor for a steam engine. I didn't fully understand the discussion there, but perhaps there is some relation. (I think of arguing that the governor can be seen as the limit of increasing the update rate of the algorithmic solution; and that limit is merely best analyzed by different tools than the algorithm, not fundamentally different — but as I said, I haven't studied the discussion, and the limit still has a cycle in it so this isn't directly relevant to your problem.)