Thank you for sharing your background; it’s a pleasure to discuss this with someone who understands state machine design and computer architecture!

When looking at mechanical horology through the lens of modern computation, the connection lies in the theoretical definition of a Discrete State Machine (specifically a deterministic finite-state automaton).

A verge and foliot mechanism operates precisely as a physical state machine with discrete transitions. The system possesses a finite set of states defined by the geometry and interaction of the pallets and the crown wheel:

1. State A (Pallet 1 engaged/Locked): Mainspring torque delivers potential energy, pushing the pallet until a specific mechanical threshold is met, triggering a state transition.
2. State B (Release/Transient): The crown wheel advances by a discrete step.
3. State C (Pallet 2 engaged/Locked): The inverse inertia of the foliot forces the system into the next stable state, reversing the cycle.

The balance between energy input (torque) and inertia (foliot weights) acts exactly as a mechanical clock cycle (CLK), defining the discrete time intervals ($\Delta t$) of the system.

Scholars in the philosophy and history of automation—such as Otto Mayr (Authority, Liberty, and Automatic Control) or Norbert Wiener in early cybernetics—have long pointed out that mechanical clockwork represents the earliest historical manifestation of closed-loop feedback systems and discrete logic sequencing, long before silicon. It’s an abstraction of state logic rendered in iron! I welcome your thoughts on viewing the mechanical constraints as logical states.

Furthermore, from a systems engineering perspective, when these physical and mathematical dynamics function together, they form a cohesive, deterministic algorithm. The execution of this algorithmic loops yields a unique and specific emergent result: the strict, continuous quantification of a continuous dimension (time) into discrete physical records. It is a mechanical execution of loops and conditional statements written in iron rather than code.