FACTUAL REFERENCE
BABBAGE DIFFERENCE ENGINE

Charles Babbage began work on Difference Engine No. 1 in 1821. The design aimed
to automatically calculate and tabulate polynomial functions using the method of
finite differences.

Why finite differences mattered mechanically:
Repeated addition is much easier to implement with gearwheels than a general
mechanical multiplication/division system. By arranging columns of number wheels
and carrying mechanisms, a difference engine can generate table values through a
sequence of additions.

Babbage's first engine project was not completed in his lifetime. He later designed
Difference Engine No. 2. A full-size working construction of that later design was
completed by the Science Museum project, demonstrating that the design could work.

The crucial archive connection is automatic calculation plus state sequencing.
This is no longer merely a moving figure. The mechanism exists to transform
numbers according to a mathematical method.