FACTUAL / CONCEPTUAL NOTE
CONTROL VS CALCULATION

Two machines can look equally complicated while doing fundamentally different
things.

CONTROL MACHINE
Coordinates a sequence of actions.
Example abstraction: lift arm, turn head, strike bell, reset.

CALCULATING MACHINE
Transforms numerical state according to mathematical operations.
Example abstraction: add column A to column B, propagate carry, advance cycle.

PROGRAMMABLE MACHINE
Allows the sequence of operations to be altered by an instruction representation.

These categories overlap but should not be collapsed. An automaton can be an
extraordinary controller without being a general-purpose calculator. A calculator
can be mathematically powerful without looking lifelike.

The history of computing becomes clearer when we ask what the machine actually
controls, stores, transforms, and exposes to the operator.