"If you can't give me poetry, can't you give me poetical science?" — in a letter to her mother
"The Analytical Engine weaves algebraical patterns, just as the Jacquard-loom weaves flowers and leaves." — from her Notes on the Analytical Engine
When Charles Babbage built a calculating machine, Ada Lovelace (1815-1852) looked at it and saw a whole universe. That contrast gets to the heart of her type. Where Babbage saw a tool for producing arithmetical results, Lovelace saw the abstract principle latent inside it — the leap from "this machine computes numbers" to "hey, this machine could compute anything." This is typical of the ILE inner workings: grasping general possibility hidden in a particular thing.
The actual code in Note G — the Bernoulli-number algorithm — leaned heavily on Babbage, who had drafted earlier, albeit simpler, programs and was the better technician with more experience in these matters. If her fame rested solely on writing the procedure, it would be contestable. But Babbage (plausibly some sort of ST type, although I haven't investigated him furhter) conceived his engine as a number-cruncher, a thing for producing arithmetical results. Lovelace's insight was epistemological. She saw that a machine which manipulates symbols according to rules is not bound to numbers at all: that if relationships in music, or letters, or any domain could be represented symbolically, the engine could operate on them — that it was, in her own careful phrase, "an embodying of the science of operations," constructed with reference to abstract number as merely one of the operations' possible subjects. That is the ILE move in its typical form: seeing past the concrete instance to the abstract, generative principle that makes it a special case of something far larger. Babbage probably deserves the title of the first programmer, but Lovelace should rightfully be called the first computer scientist.
She reasoned by analogy and pattern across domains that, seemingly, had no business being connected, which is exactly how the "NeTi" mind finds its way to hidden general structure. Her most famous line, that the Analytical Engine "weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves" was her comparative method. She perceived that the punched cards controlling a textile loom and the operations of a mathematical engine were instances of one underlying pattern, the abstract idea of a mechanism following encoded instructions, and she reached that perception by leaping the gap between weaving and algebra.
"Again, it might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine. Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent."
This is intuition hunting resemblance beneath surface difference: the common principle that unites unlike things. This is also what she meant by "poetical science" — the fusion of imaginative leap with formal rigor, using her innate gift for analogy as an instrument of abstract discovery.
Left to herself, Lovelace was a seeker of possibilities, showing her generally "irrational" nature: as a child, she embarked on what she called "Flyology," studying the anatomy of birds and experimenting with materials in order to fashion a set of wings for herself. As an adult, she continued to be enamored with ILE-ish schemes, including even an attempt to figure out how mathematics could be used to win at the horse races, and historians of her collaboration with Babbage see her as the one with the "fail-forward" attitude while Babbage was the perfectionist. This is the intuitive who generates a hundred possibilities and needs a steadier partner to ground them — which is precisely the relationship the work records.
Her mother, terrified that Ada had inherited her father's (EIE with both Ne and Se increased) volatile imagination, imposed a regimen of mathematics and logic specifically to stamp these tendencies out — even forcing the child to lie still for long periods to instill "self-control." But the mathematics her mother forced on her did not replace or stamp out the "perceiving" visionary mind, but turned out actually hepful in the sense it gave it an instrument. The discipline became the rigor that the "poetical science" needed. Such was woman the legend remembers as the poet's daughter who brought feeling to the machine. Her work has been continued by many other computer science pioneers, notably, Alan Turing, as this extremely interesting review points out.
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