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I don’t quite remember how I came to first know about Lady Lovelace, but I suspect that it was at the Science museum in London, where a working differential engine is displayed in the computing exhibit. Until then I thought that Alan Turing had been the father of computer science, the first person not only to imagine how to use machines to do complex calculations, but also the person who first imagined a science of information. Turns out that he was not the first to think about either of those two things, they were first imagined by Charles Babbage and Lady Lovelace, respectively, more than a century earlier.

Analytical Engine at the Science Museum in London

Charles Babbage was an accomplished 19th century scientist and inventor, who had already conceived and partly build the Difference Engine by the time he met 17 year old Ada. The Difference Engine was the first mechanical machine conceived to tabulate values of functions (e.g. logarithms) for mathematical tables, it used the method of divided differences (hence the name), which was commonly used at the time by computers, people who did these calculations by hand. Human error was common in these calculations and it could have dire consequences, since these mathematical tables were a crucial tool in engineering at the time. In the era of the industrial revolution, Charles Babbage set out to substitute this manual process by a mechanical one that could run without human error.

Sketch of Difference Engine

At the time they met in London, Augusta Ada had already received an incredibly advanced education in science and math for a teenager at the time, and a woman for that matter! She was the only legitimate child of Lord Byron, the famous poet, but had been raised by her mother, also incredibly well educated in science and maths (nicknamed by Byron the princess of paralellograms), away from the influences of her famous father. Lady Byron had hoped an intense education in science and math would tame the creative drive she foresaw in her daughter, and while she didn’t manage to extinguish it (as she seemed to have hoped), she gave Ada the tools to focus her creativity on something constructive. Ada was a passionate child with great interest in technology, for a few of her formative years she was passionate about inventing a steam machine to be able to fly and there are numerous letters to her mother with design ideas.

Augusta Ada King, Countess of Lovelace

Babbage’s engine captivated Ada’s imagination and they soon became lifelong friends and collaborators. In the collaboration with Babbage, and the study and understanding of the mathematics governing the functioning of Babbage’s engines (first differential, then analytical), Ada found a stimulating topic that she could make her own, and had nothing to do with her father’s fame or her mother’s bitterness towards him, which had darkened her childhood. As an adult, she sought to continue her education to understand the matters related to the machine better, and self-imposed a study regiment for herself, despite her social and familial obligations as a member of the aristocracy and a mother. I believe that Ada had more luck than most, she had a mother with appreciation for maths and science education, as well as a husband who encouraged her to pursue her passion. Their unwavering support allowed her to follow her interests, despite other influences to the contrary such as that of her tutor Augustus De Morgan, a famous mathematician and logistician. We know his opinion of her through some of his letters to Lady Byron and Lord Lovelace, where he warned them that studying mathematics would not be good for Ada’s constitution and temperament. Despite acknowledging that her intelligence in the matter was extraordinary for a beginner in the study, he believed that women could not make the intelectual effort required to advanced science, and tried to convince them Ada should not continue her studies. Fortunately, they didn’t paid any attention to these warnings.

Ada Lovelace illustration by Rachel Ignotofsky.

After Babbage had partially built his difference engine, he conceived of a second engine, the analytical engine, which was a mechanical general-purpose computer. The structure of the analytical engine had a striking resemblance to the functional structure of computers from over a century afterwards, having a processor and memory, and having the ability to process multiple different programs by using a system of punched cards. What is fascinating to learn, however, is that these concepts did not appear first in a computational engine and in fact, information processing borrowed these concepts from the first process of digitization of everyday life: the Jacquard loom machine. In 1804, Joseph Maria Jacquard invented a machine that could easily loom extremely complex and detailed patterns using a special machine that made use of punched cards, where the presence or absence of a hole in the card would determine whether a thread would or would not be included in the pattern. The processor and memory concepts were also inspired by the separation between the factory floor (processor) and the store room (memory).

Jacquard loom machine

The analytical engine was never built during their lifetime due to Babbage’s inability to convince those in power of its utility, as he needed help to raise funds to build it, and his rejection of Ada’s offer to help. However, it is possible that the true impediment to the construction was that the precision engineering required to manufacture the dented cogs of the machine, of which thousands were required, did not exist yet. Regardless, Babbage’s efforts were known in Europe’s scientific circles, and in 1842, an Italian mathematician, Luigi Federico Menabrea, published a description of the engine based on one of Babbage’s lectures. It is this lecture that lady Lovelace translated to English, much to Babbage’s surprise, as he thought that she was such an expert in the subject that she should write a treatise herself. Maybe it was that she was a woman of her time, at least in customs, or the influence of the many tutors she had had who had considered her less able because of her condition as female, but Ada never saw herself has possessing an equal intelligence to the male scientists. It’s interesting to see the dichotomy in her letters, on one hand she is aware of her own capacities and how much further she can push them, but at the same time she’d never thought of publishing her own treatise of the machine, and in fact had not even thought of signing her work until her husband suggested it. Babbage, in contrast, had a very high opinion of her abilities, in a letter to Michael Faraday he described her as “Enchantress who has thrown her magical spell around the most abstract of Sciences and has grasped it with a force which few masculine intellects could have exerted over it“.

Structure of the Analytical Engine

The work that Lady Lovelace finally published was a translation of Menabrea’s work, along side several Notes of the translator, which are much more detailed and more than double the size of the original text. Note G is of particular interest, it is deemed the first computer program, and it describes an algorithm to calculate Bernoulli numbers using the Analytical Engine. This algorithm was developed together with Babbage, as evidenced in their letter exchanges.

Diagram of computation of Bernoulli numbers

Lady Lovelace died young, after a long and painful battle with cancer. Her trailblazing contributions would be almost forgotten for the next 100 years, but we have evidence that Alan Turing knew of her work. What sets Ada Lovelace apart was the fact that from the design of the Analytical Engine, she went beyond Babbage’s use of the machine and she was able to abstract a new uses for the machine(”the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent”) and a completely new type of science, computer science, which she called the science of operations. Here is the visionary passage of the Notes:

”It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this reaction of what kind it may. This is the most general definition, and would include all subjects in the universe. […] But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and values, independently of the subjects to which we may apply its reasonings and processes”

Today’s post is commemorates Ada Lovelace Day, a day to celebrate the achievements of women in science, technology, engineering and maths (STEM). A couple of years ago I wrote a post about my favorite mathematician, Emmy Noether, and this year I decided to spend some time learning more about Lady Lovelace.

I obtained most of the biographical material for this blogpost from the book Ada’s Algorithms, by James Essinger and the original “Notes“. Other engaging sources are:

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