## Ada Lovelace and Charles Babbage

Born in 1815 Ada Byron was the only legitimate offspring of Lord Byron, although he had countless illegitimate children with multiple partners. Her mother left Byron 8 weeks after Ada’s birth and he left England when she was a few months old. Determined that her daughter would not grow up in the same path as her father, Lady Byron set out a strict regime of mathematics alongside the usual music and language lessons for a young lady of the time. She was a sickly child and was housebound by frailty from the ages of 11 to 13, but she kept herself busy with her mathematics and other studies.

Just a little aside about Byron himself; while he was an undergraduate at Cambridge he had a pet bear which he kept in his room. When summoned to the Proctors, they exclaimed that of course you couldn’t keep a tame bear in your room. Byron infamously retorted, I assure you sir that it is entirely wild.

Ada grew up into a dainty young woman and apart from an unsuccessful attempt to elope with one of her tutors when she was 17, she grew up titled enough and controversy free enough to be presented onto the marriage market. Marrying William King, the 8th Baron King, (who would become the Count of Lovelace three years later) and providing him with three children, Ada, Countess of Lovelace wasn’t living the typical life of a mathematical great. It was only when the boredom of married life set in after having her third child that she returned to her childhood hobby of mathematics. She sent letters out and was in regular correspondence with several mathematicians and logicians. Augustus de Morgan was suggested as a suitable mathematics tutor for her and as usual with these sort of deals her wealth propped up his funding problems for research into his field, which was logic.

It was in this period that Lovelace also had contact by post with Charles Babbage who she had first met as a late teenager when he had displayed some of his machines to the aristocracy. Babbage was born in 1791 and so was significantly older than Lovelace. He born into a banking family and worked as a mathematics lecturer and then later a mechanical inventor. He saw how laborious calculating logarithmic tables could be, but they were frequently being used in every scientific field and had applications in war and finance.

Recognising the potential of automating the process Babbage sought to create a differential engine that could calculate these values. His first engine was designed in 1823 with £1700 funding from the British government and could calculate the coefficients of polynomials using the method of differences. These polynomials could be used to approximate other functions to any degree of accuracy in theory, although only to the seventh order each with 31 decimal places for each coefficient in Babbage’s designs.

However Babbage was more interested in expanding the theory than actually getting a prototype up and running. By the time the government had finally lost confidence that this was an efficient way of getting log tables, 19 years had passed and they had sunken £17,000 of investment into the design. Every time a workable design had drawn up he would move on to designing one with more capability for accuracy (i.e. one which could deal with more decimal places).

Ada Lovelace was only 8 when the first designs came out but by the 1840s she and Babbage had been in regular correspondence about his ideas. Both were fascinated by the Jacquard Loom which revolutionised the textiles industry around 1800. The loom worked by taking in various punch cards as instructions for whether to stitch or not and so it could make complex patterns in a mass produced way. Here’s a portrait of the inventor Joseph-Marie Jacquard that would be made out of silk to order for buyers and was the result of 24,000 punched cards: Babbage owned a copy.

This idea was developed by Babbage in 1840 (which finally crushed the government’s hope that he would finally get the difference engine up and running) into make the analytical machine. This would be capable of taking in much more general instructions by punch cards and computing the results: it was programmable.

That year Babbage gave a talk at a conference in Turin (auto-correct corrected that to Turing, I think it has caught on to what I am typing about) where Luigi Menabrea, a professor of mechanics and later the Prime minister of Italy took interest. In 1942 Menabrea wrote up his thoughts on how to encode the punch cards to produce many mathematical ideas. Babbage asked Lovelace to translate the article from Italian and she added her own thoughts. Her extra notes were three times longer than the original article.

As well as coming up with an iterative way of implementing the Bernoulli numbers, she also pointed out that the analytical machine had the capability to make a copy of any punch cards it read which would be feed back into the machine, therefore repeating instructions. This was the first example of what we now call a loop. I thought this description from Lovelace was great: "The Analytical Engine weaves algebraic patterns just as The Jacquard Loom weaves flowers and leaves."

In describing the loop for finding the Bernoulli numbers she wrote: "My Dear Babbage, I have worked incessantly, & most successfully, all day. You will admire the Table & Diagram extremely. They have been made out with extreme care, & all the indices most minutely & scrupulously attended to. Lord L [her husband] is at this moment kindly inking it all over for me. I had to do it in pencil..."

Further Lovelace speculated that the engine "might act upon other things beside number... the Engine might compose elaborate and scientific pieces of music of any degree of complexity or extent."

None of the full Difference or Analytical Engines were built in Babbage's lifetime, but using his plans a team has put together a working Difference Engine and part of the Analytical Engine. They are both on display in the London Science Museum.

At the age of 25 Lovelace contracted uterine cancer and later died of it at the age of 37 in 1852 having spent the latter part of her life on heavy drugs for the pain. She was in heavy debt by the end of her life after a failed mathematical approach to gambling. Her notes on the Analytical Engine went mostly unnoticed until Alan Turing spook of her highly at the advent of the electronic computer.

Babbage died at the age of 79 in 1871 and was a known name in mechanical circles by the end of his life. Despite never finishing a working Difference or Analytical Engine, he was considered a success. He never did pay back the British Government.