Ada and Computation

Ada Lovelace (born 200 years ago) wrote presciently about digital numerical calculations. She expressed its features poetically: "We may say most aptly that [Babbage's] Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves." Ada explained the generality of digital computation, saying that "the engine can arrange and combine its numerical quantities exactly as if they were letters or any other general symbols." We will discuss some of the expected and unexpected consequences of alternate representations of computational data. On the other hand, Ada wrote that "the engine [is] the material expression of any indefinite function of any degree of generality and complexity." This we now know was overstating her case. We will discuss the formalization of the notion of effective computation and its consequences vis-a-vis computability and complexity of computation.