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and he in his early 40s. Babbage became, and remained, a close family friend until her death in
1852 at the age of 36. Young Ada Byron described Babbage at their first meeting as being ‘full
of animation—and talked about his wonderful machine’. Lovelace, who was tutored in math-
ematics by Augustus De Morgan, published her ‘Sketch of the Analytical Engine’ in 1843.^15
The Sketch consists of Lovelace’s translation from the French of the article on the Analytical
Engine by Luigi Menabrea, who was present at a convention in Turin in 1840 where he heard
Babbage speak about his engines, the only known occasion that he lectured in open forum
on his machines. Lovelace appended to her translation extensive notes of her own written in
close collaboration with Babbage.^16 To call it a ‘Sketch’ (translated from the French ‘notions’)
is misleading if this implies that its content is slight: the piece remains the most substantial
contemporary account of the capabilities and potential of the engine.
In her notes Lovelace described the mathematical capabilities of the engine, and moreover
emphasized the implications of machine computation outside mathematics:^17
[The Analytical Engine] might act upon other things besides number . . . Supposing, for instance,
that the fundamental relations of pitched sounds in the science of harmony and of musical com-
position were susceptible of such expression and adaptations, the engine might compose elabo-
rate and scientific pieces of music of any degree of complexity or extent.
Lovelace’s example takes a crucial step in signposting the representational power of number.
If meaning is assigned to number then results, arrived at by operating on number according
to rules, can say things about the world when they are mapped back onto the world using the
meanings assigned to them. The act of abstraction is in the assignment by us of such meanings.
Lovelace wrote that the machine could ‘arrange and combine its numerical quantities exactly as
if they were letters or any other general s y m b o l s ’.^18
The key transitional idea is that number could represent entity other than quantity and that
the potential of computing lay in the power of machines to manipulate, according to rules,
representations of the world contained in symbols. Nowhere, at least in his published work,
does Babbage speak in this way.
Babbage was much taken with Lovelace’s ideas, to the extent that he was reluctant at one
point to part with her manuscript. He wrote:^19
. . . the more I read your notes the more surprised I am at them and regret not having earlier
explored so rich a vein of the noblest metal.
If Babbage was true to character in this tribute then he was not dissembling, being patronising,
or falsely flattering. Yet if he was influenced by Lovelace’s ideas, he showed no sign of it. Towards
the end of his life he set out, finally, to write a general description of the Analytical Engine. Each
of his three separate attempts, none of which was finished, opened with a statement clarifying
the purpose of his engine. The third and last of these, dated 8 November 1869, some two years
before his death, opens:^20
The object of the Anal. Eng. Is two fold
1 st The complete manipulation of number
2 nd The complete manipulation of Algebraic Symbols
After half a century of deliberation and inspired design, Babbage in his most mature reflections
did not see the scope of the engine extending beyond algebra. And if he saw algebra having
a representational reach outside mathematics, he made no reference to it. The three separate