Are you suggesting Ada Lovelace isn't capable of reasoning about a problem?

You can come up with an algorithm or system without knowing programming. Presumably we can agree the opposite, that being a programmer doesn't give you mystical insight into every programming problem.

Ultimately this isn't even a programming problem.

Timmy writes homework, Jimmy writes homework. They can name the homework however they want. Both go in the same pigeon hole. How can the teacher tell who did which homework?