the second book of Euclid.

Ada’s enthusiasm appeared to be boundless. Returning to his orderly home on Regency Square in Brighton from an exhausting April fortnight in the company of Miss Byron and her mother at the spa town of Tunbridge Wells, poor Dr King was thankful to escape his protégée’s endless interrogations and demands. ‘You must trammel your mind . . .’ he warned, while urging her to calm herself with soothing readings from William Whewell. If Ada ignored the worthy Dr King’s advice, her excitement was understandable. By the time of her visit to Tunbridge, she had met Charles Babbage twice and been introduced to his remarkable, albeit unfinished, machine.

The second and more significant introduction to Babbage had been brought about by Mary Montgomery. Miss Montgomery deserves more credit than she has received for the formative role she played in Ada Byron’s life. An invalid herself, she understood better than most the hunger Ada felt for all the experiences of which three semi-bedridden years had deprived her. An alert, clever and empathetic woman, Mary was on friendly terms with many of the giants of London’s leading intellectual circles. It was she who provided Ada with her entrée to the world that opened her eyes to an imaginable future.

The word ‘scientist’ was first coined by William Whewell for his anonymous and laudatory review of Mary Somerville’s On the Connexion of the Physical Sciences in April 1834. The study of science was already in the air and Ada, guided by Mary Montgomery, was escorted to the lecture rooms of London at which the latest inventions and ideas were being displayed and discussed. At the Royal Institution, Ada attended the thrillingly eloquent and vivid lectures of Michael Faraday. Beneath the domed roof of the Surrey Institution at Blackfriars, she listened to talks about geology, chemistry and natural philosophy. Respectably chaperoned by the indefatigable Miss Montgomery (an 18-year-old with the notorious surname of Byron could never have gone alone), she entered the wonderful circus of scientific entertainments on the Strand that had recently been named in honour of William IV’s royal spouse (despite the fact that Queen Adelaide never passed its doors).

Ada must have adored her visits to the Adelaide. Here, shortly after it first opened its doors in 1832, visitors could watch a Jacquard loom weaving intricate designs by the use of hole-punched cards, before admiring the acrobatic dances of Thalia, an infant prodigy, who performed beneath the floating bulk of a tethered gas balloon. Electrical displays involving Leyden jars and numerous magnets dazzled the gallery-goers with showers of fiery sparks. A central canal – broad enough for Thomas Telford to conduct experiments with his new steamboat paddles – bestowed an unexpected touch of serenity on this palace of educational delights.

But the ever-helpful Miss Montgomery had further tricks up her sleeve. Some of the most interesting scientific discussions in London at that time took place within the drawing rooms of private houses. In the same month as Ada’s introduction to Mrs Somerville, Mary took her into the home of Roderick Murchison, where fireside debates about geology were raising questions about the divine versus the natural order of the world. (Lady Murchison’s interest in fossils had led to her husband’s identification – while walking in Wales – of an ancient and largely aquatic period of the earth’s history that Sir Roderick named the Silurian Age.) But the introduction through which Mary Montgomery made her biggest contribution to Ada’s life came a month later.

On 19 March 1834, Miss Montgomery took Ada to dine with the Murchisons before conducting her to a house on Dorset Street, just off Manchester Square. It was here, in his private London home, that Charles Babbage held his famous Saturday soirées. While excited and doubtless intrigued (Mr Babbage’s parties were celebrated for the extraordinary range of guests that they attracted), Ada had no idea that she was about to encounter a mind that was every bit as enquiring, lively and playfully capricious as her own.

Born into wealth, Charles Babbage was one year older than Ada’s mother. Like Ada, he had suffered from a long period of illness during his youth. Like her again, he had early discovered himself to be both inventive and ambitious. Ada had wanted to use a steam-powered Pegasus for her proposed flights about the world. Babbage had attempted to walk on water (using home-made paddleboards to cross Devon’s River Dart). Further signs that Babbage would follow no conventionally charted path emerged during university. At Cambridge, he was punished for defending a supposedly blasphemous thesis. Forbidden to sit a formal exam, the brilliant young mathematician graduated without honours.

Aged twenty-one when he married in 1812 and settled in Marylebone, Babbage suffered bitter disappointment when he was refused a mathematics chair at Edinburgh in 1819 (it went instead to a Scotsman, William Wallace). Instead, Babbage spent part of the following year in helping his friend John Herschel to found the Royal Astronomical Society. It was while working with Herschel on various mathematical tables that Babbage dreamed up the idea of a steam-powered computing machine. If his contraption worked, it would simplify the process – and reduce the chances of error – in a core aspect of what was needed for the nation’s military and industrial success.

This was where Babbage’s travails as an inventor had begun. By 1823, the British government had been persuaded to invest in the ingenious new calculating engine.* Ten years later, an official fireproof room had been expensively constructed within government-owned property to house a machine that remained incomplete. ‘The logarithmetical Frankenstein’ was one journalist’s sneering put-down for the creator of a half-finished monster.

The construction of Babbage’s ambitious device had offered the inventor welcome distraction during a bleak period in his life. In 1827, Babbage lost a son, a daughter, his father and his wife. Leaving his surviving children in the care of his mother, the widower set off for Europe, to discuss his project with such eminent figures as Laplace and von Humboldt. Interest

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