Mechanisms follow sequences

How can hidden state and ordered physical events create observable behavior?

Frequency analysis inferred hidden symbols from statistical regularity; programmable automata encoded changing behavior into cams, floats, valves, and timed releases. Both reveal state through consequences.

A system becomes computationally legible when we can name its state, transition rule, input, and output.

Reconstruct the mechanism

1. Choose an observable alphabet or physical state
2. Measure an input event or distribution
3. Apply a transition encoded in rules or mechanism
4. Observe output and use it to infer or continue state

Break a substitution cipher, then model al-Jazarī’s elephant clock as a finite-state machine with events, state, and outputs.

Evidence and uncertainty

Do not call every automaton a computer. Make the specific control analogy and its expressive limits explicit.

• Elephant Clock folio — The Metropolitan Museum of Art · public domain
• Arabic cryptology — King Saud University manuscript project