The analytical engine, nicknamed the Clockwork Ouroboros by Ada Lovelace, was a self-reprogramming clockwork machine designed and built by Charles Babbage in the 1800s. It was notably used against Faction Paradox in the Clockwork Ouroboros affair.
Babbage developed the analytical engine as a more advanced version of his difference engine. However, he tried and failed to garner government funding for the project. (PROSE: The Book of the War) The Fourth Doctor believed that Babbage's engine ultimately "came to nothing." (AUDIO: The Enchantress of Numbers)
In 1834, the Star Chamber learned of Babbage's research and commissioned him to build the engine so it could run the Musical Offering and penetrate the Eleven-Day Empire. After it was completed, the machine was moved on 1 October to the physical Star Chamber beneath the Houses of Parliament. There it was activated, beginning the invasion of the Empire. (PROSE: The Book of the War)
Prior to first meeting her, the Fourth Doctor had read all of Ada Lovelace's notes on Babbage's analytical engine, and found them remarkable. Lovelace was surprised he had understood them. The Doctor noted that Lovelace had written the world's first computer program in her notes regarding the engine. (AUDIO: The Enchantress of Numbers)