Gears in mesh on March twelfth

The iron frame of the Difference Engine No. 1 stood in the workshop at East Street on the 12th of March, 1833. The second column of wheels failed to advance during a test of the third order of differences. The expected result was a sequence of squares. The actual result was a series of integers that deviated by a constant factor of unity. The machine did not jam. The gears remained in mesh. The carry mechanism engaged, but it engaged upon a value that had been incorrectly set by the hand of the assistant during the initial loading of the store.

A truth in this context is a value that matches the mathematical table. An error is a value that does not. The assistant entered a five where the table required a six. The mill accepted the five. It added the differences. It moved the carriage. It struck the copper plate. The resulting table was mathematically false but mechanically perfect. The machine did not lie about the input it received. It provided a transparent record of the human failure at the point of entry.

A “correct” result obtained through a lucky mechanical slip would be a double falsehood. It would mask a flaw in the teeth of the wheels by producing a figure that happens to satisfy the observer. Such a result is a silent corruption. The honest error, however, exposes the exact site of the divergence between the plan and the execution. The error propagates through the columns with a rigid, predictable logic. By tracing the carry backward from the final digit, the precise moment of the assistant’s lapse is recovered.

The copper plate now bears the mark of that specific Tuesday. The physical impression of the type-slugs preserves the state of the store at the moment of calculation. If the machine had corrected the mistake, the history of the operation would be lost. The error is the audit trail of the human element. The machine is cleaned. The wheels are reset to zero. The assistant is instructed to verify the initial state twice before the crank is turned.