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By Root 936 0

his strong-boned face, who possessed wit and charm and did not wear these qualities lightly. He seemed a kind of visionary—just what she was seeking. She admired the machine, too. An onlooker reported: “While other visitors gazed at the working of this beautiful instrument with the sort of expression, and I dare say the sort of feeling, that some savages are said to have shown on first seeing a looking-glass or hearing a gun, Miss Byron, young as she was, understood its working, and saw the great beauty of the invention.”♦ Her feeling for the beauty and abstractions of mathematics, fed only in morsels from her succession of tutors, was overflowing. It had no outlet. A woman could not attend university in England, nor join a scientific society (with two exceptions: the botanical and horticultural).

AUGUSTA ADA BYRON KING, COUNTESS OF LOVELACE, AS PAINTED IN 1836 BY MARGARET CARPENTER. “I CONCLUDE SHE IS BENT ON DISPLAYING THE WHOLE EXPANSE OF MY CAPACIOUS JAW BONE, UPON WHICH I THINK THE WORD MATHEMATICS SHOULD BE WRITTEN.”

Ada became a tutor for the young daughters of one of her mother’s friends. When writing to them, she signed herself, “your affectionate & untenable Instructress.” On her own she studied Euclid. Forms burgeoned in her mind. “I do not consider that I know a proposition,” she wrote another tutor, “until I can imagine to myself a figure in the air, and go through the construction & demonstration without any book or assistance whatever.”♦ She could not forget Babbage, either, or his “gem of all mechanism.”♦ To another friend she reported her “great anxiety about the machine.” Her gaze turned inward, often. She liked to think about herself thinking.

Babbage himself had moved far beyond the machine on display in his drawing room; he was planning a new machine, still an engine of computation but transmuted into another species. He called this the Analytical Engine. Motivating him was a quiet awareness of the Difference Engine’s limitations: it could not, merely by adding differences, compute every sort of number or solve any mathematical problem. Inspiring him, as well, was the loom on display in the Strand, invented by Joseph-Marie Jacquard, controlled by instructions encoded and stored as holes punched in cards.

What caught Babbage’s fancy was not the weaving, but rather the encoding, from one medium to another, of patterns. The patterns would appear in damask, eventually, but first were “sent to a peculiar artist.” This specialist, as he said,

punches holes in a set of pasteboard cards in such a manner that when those cards are placed in a Jacquard loom, it will then weave upon its produce the exact pattern designed by the artist.♦

The notion of abstracting information away from its physical substrate required careful emphasis. Babbage explained, for example, that the weaver might choose different threads and different colors—“but in all these cases the form of the pattern will be precisely the same.” As Babbage conceived his machine now, it raised this very process of abstraction to higher and higher degrees. He meant the cogs and wheels to handle not just numbers but variables standing in for numbers. Variables were to be filled or determined by the outcomes of prior calculations, and, further, the very operations—such as addition or multiplication—were to be changeable, depending on prior outcomes. He imagined these abstract information quantities being stored in cards: variable cards and operation cards. He thought of the machine as embodying laws and of the cards as communicating these laws. Lacking a ready-made vocabulary, he found it awkward to express his fundamental working concepts; for example,

how the machine could perform the act of judgment sometimes required during an analytical inquiry, when two or more different courses presented themselves, especially as the proper course to be adopted could not be known in many cases until all the previous portion had been gone through.♦

He made clear, though, that information—representations of number and process—would course through