[JohnMakin]

Programmable looms (which used a type of punchcard) such as the Jacquard Loom had existed for a little while - if I recall she specifically referenced this as inspiration for some of her ideas. Not trying to diminish how impressive her work was, but I do believe some form of primitive mechanical computation had already been done for a little while.

[int_19h]

Jacquard loom was indeed well-known, and one of the sources of inspiration for Babbage, but it is still fundamentally about designing a system around a specific task - the cards directly encode operations on hooks.

What Ada is saying here is that, once you have a machine that let you do generic operations on numbers, you can use it to do all kinds of non-math stuff so long as you can come up with ways to encode other things as numbers (= finite sets of symbols). This was not at all obvious to other people who worked on the Engine, including Babbage himself.

[layer8]

Given that the looms’ punched cards already represented non-math stuff, the thought wasn’t entirely far-fetched.