Idea Makers: Personal Perspectives on the Lives & Ideas of Some Notable People

by Stephen Wolfram

Ada seems to have understood with some clarity the traditional view of programming: that we engineer programs to do things we know how to do. But she also notes that in actually putting “the truths and the formulae of analysis” into a form amenable to the engine, “the nature of many subjects in that science are necessarily thrown into new lights, and more profoundly investigated.” In other words—as I often point out—actually programming something inevitably lets one do more exploration of it. She goes on to say that “in devising for mathematical truths a new form in which to record and throw themselves out for actual use, views are likely to be induced, which should again react on the more theoretical phase of the subject”, or in other words—as I have also often said—representing mathematical truths in a computable form is likely to help one understand those truths themselves better. Ada seems to have understood, though, that the “science of operations” implemented by the engine would not only apply to traditional mathematical operations. For example, she notes that if “the fundamental relations of pitched sounds in the science of harmony” were amenable to abstract operations, then the engine could use them to “compose elaborate and scientific pieces of music of any degree of complexity or extent.” Not a bad level of understanding for 1843.