Charles Babbage’s Analytical Engine | The Computers that Made the World

Here is a taste of the latest book published by Raspberry Pi Press. The Computers that Made the World by Tim Danton tells the story of the birth of the technological world we now live in. It chronicles how computers reshaped World War II through the origins of 12 influential machines built between 1939 and 1950. In this first chapter, we learn about the Analytical Engine designed by Charles Babbage, whose name lives on in our official mascot, Babbage Bear. If you’d like to read the book in its entirety, you can order it online from Raspberry Pi Press.

Groucho Marx was very nearly right when he said there are two certainties in life. There are indeed two, but they aren’t death and taxes: they’re that humans have an innate need to count and that we all make mistakes.

The trouble is that mistakes cost lives. Anyone working in the fields of engineering or navigation in the 1800s relied on printed mathematical tables that contained pre-calculated answers to equations. This meant they didn’t need to work out the results by hand, and theoretically the answers would be far more accurate than someone attempting to work them out on demand. Theoretically: in reality, the tables contained errors almost impossible to spot that could cost lives and livelihoods.

Charles Babbage, 1860 (Image: Public Domain)

Not that Charles Babbage needed to worry about putting his own life at risk or poverty. With a generous inheritance and formidable intellect, he was an enfant terrible of the academic world, scorned by some, admired by others. By the time 1821 rolled around, when he had just turned 30, he had many achievements to his name: co-founder of the Analytical Society to promote continental advances in mathematics in England, Fellow of the Royal Society for his contributions to science and maths, and a founding member of the Royal Astronomical Society.

He and his friend John Herschel had taken on the job of preparing a set of star tables for the new society the previous year. “My friend Herschel, calling upon me, brought with him the calculations of the (human) computers, and we commenced the tedious process of verification,” Babbage is quoted as saying in one account. “After a time many discrepancies occurred, and at one point these discordances were so numerous that I exclaimed ‘I wish to God these calculations had been executed by steam’.”

From this exclamation – so the story goes – came the idea of creating a machine that could do exactly that. Specifically, to create complex logarithm ‘star tables’ to aid navigation. 

He called the machine the Difference Engine because, rather than attempt to perform a complex equation for each value, the machine would build upon the previous result and add the difference. It was an idea that Babbage borrowed from a visit to Paris in 1819, where they were remaking their tables on an unprecedented scale after Napoleon decreed that France should move from imperial measurements (pounds and ounces, inches and feet) to metric.

By creating a machine to perform this work, Babbage would also bypass the errors inevitably made when transcribing results. Now all he had to do was design and build it. The design was the far simpler affair of the two, with Babbage designing a complex web of pinions, gears, and cogged wheels that would complete the task. His paper on the subject, ‘On the Theoretical Principles of the Machinery for Calculating Tables’, won the Royal Society’s first ever Gold Medal – its highest accolade.

He had the design, he had the backing of the Royal Society. Now all Babbage needed was the money. Here, he turned to the British government, who awarded him £1500 (which conveniently translates into roughly £150,000 today) towards the project. In tandem with so many stories of computers in the rest of this book, that rough costing turned out to be woefully low. 

The Difference Engine was a precision instrument even by today’s standards, and Babbage had high ambitions: to calculate results up to 20 digits rather than the then standard six digits, and there needed to be somewhere to store calculations. A basic mechanical calculator had been invented before, but this was several orders of magnitude more complicated. Take its size alone: the Difference Engine would be big enough to fill a room.

Despite the work of one of Britain’s most talented machinists, Joseph Clement, the challenge proved too much. After ten years of effort and with nothing to show for their investment other than a collection of completed parts and pleas for more money, the government said enough: no more funds. Clement also walked away from the project, taking Babbage’s plans with him as hostage until Babbage gave him money he was still owed.

This enforced break from the project may have been a piece of great fortune. It gave Babbage time and space away from the Difference Engine, and when he was eventually reunited with his plans – having finally agreed a settlement with Clement after 16 months – and started looking through them, he came up with an even better idea. 

The idea would become known as the Analytical Engine, and it was a piece of thinking a century before its time. This wouldn’t be a single-purpose machine like the Difference Engine. You could change its function – reprogram it, in modern parlance – to perform any task you liked. 

To describe the Analytical Engine’s main elements is to echo what makes up a modern-day computer. Babbage conceived of four key components: a mill, store, reader, and printer. The mill was where calculations took place, like today’s CPU or the accumulators in early digital computers. The store is where information would be held before it was processed. And the reader and printer hardly need any introduction, being equivalent to the input and output devices that we are all accustomed to.

Again, Babbage didn’t hold back when it came to ambition: his store would hold a thousand numbers up to 50 digits long. To put that into perspective, even Alan Turing wasn’t that optimistic when setting out his plans for the ACE. Babbage would also create an automatic printer to avoid any possibility of human mistakes. For a reader, he would use punched cards, building upon technology already created by Joseph-Marie Jacquard for the loom. But rather than use these to weave multicoloured patterns on fabric, they would hold instructions and data.

Here, we shall introduce Ada Lovelace (née Augusta Ada Byron) for the first time. Famously, she was the daughter of Lord Byron, poet and lothario. Ada’s mother, Annabella Milbanke Byron, legally separated from her husband when Ada was only two months old over concerns about Byron’s mental health, his relationship with his half-sister, and rumours over his sexuality; Byron left the country, never to return and never to see his daughter again.

Annabella was a leading advocate for education, eventually establishing a school in London for the underprivileged, and she gave her intelligent daughter every chance to thrive through private tutors. Tutors who she largely outgrew, eventually resorting to teaching herself through books. 

Ada married Baron William King in July 1835 at the age of 19, becoming Countess of Lovelace three years later when he was created an Earl. By this point, she had already met Babbage and become intrigued by his machines. The two became firm friends, and it was Babbage she turned to when seeking guidance for a tutor who could help guide her. He suggested Augustus De Morgan, a mathematician and logician best known for De Morgan’s laws, who would also have given her insights into the workings of Babbage’s Analytical Engine.

Despite being a prolific writer, Babbage never set down his own description of the Analytical Engine on paper. The first printed account came in 1842, when Italian mathematician Luigi Menabrea published ‘Notions sur la machine analytique de M. Charles Babbage’ in a Swiss journal. Menabrea had attended a presentation by Babbage in Turin, introducing the assembled scientists to radical concepts such as conditional branching, and it took Menabrea almost two years to complete his 23-page article.

Ada took on the task of not only translating this article into English but adding her own copious notes. The end result was published in London a year later under the title ‘Sketch of the Analytical Engine invented by Charles Babbage Esq.’ with an additional 41 pages simply titled ‘Notes by the translator’. The only hint of the translator’s identity being an ‘A.L.L.’ at the end; a typesetter’s error, as those are not Augusta Ada Lovelace’s initials.

There is one particular section that brings the Analytical Engine to life: “We may say most aptly that the Analytical Engine weaves algebraic patterns just as the Jacquard-loom weaves flowers and leaves,” wrote Ada. There is a hint of poetry there, as we might expect from Lord Byron’s daughter, but also the crucial point that Babbage’s invention was far more than an accumulator of numbers. 

The translation was collaborative, with much correspondence between Babbage and Lovelace during its creation. Ada’s crowning glory, which earns her the title of ‘world’s first programmer’ in many people’s eyes, is her sequence of mathematical operations that could be performed on the Analytical Engine to calculate Bernoulli numbers. Even today, it resembles code.

She also looked beyond mathematics: “Suppose, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations,” Ada wrote, “the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.” Tragically, this was to be her last big contribution: she died at the age of 36, probably from cancer; she was buried next to Lord Byron, at her request.

Despite all the positive coverage for the Analytical Engine, it was destined to never be built. The machine was even more complicated than the Difference Engine and the British government simply wasn’t interested in spending any more money on Babbage’s hare-brained schemes. 

Could it have been built using technology from that era? In his 22-page article that explores the Analytical Engine in great detail, Allan Bromley concluded that the answer was yes. “Analyses such as these [on machining accuracy and weights] lead me to believe that the Analytical Engine could have been built with the technology at Babbage’s disposal, although the work would undoubtedly have been demanding and expensive,” he wrote. 

What’s certainly true is that things were much easier for Howard Aiken, creator of the Harvard Mark I, who once joked that, “if Babbage had lived 75 years later I would have been out of a job.” It’s hard to argue with that conclusion (although Babbage may have got distracted by a new invention instead). After all, electricity is a much friendlier supplier of power than steam, and despite Bromley’s optimism it’s worth noting that even the failed attempt at creating the Difference Engine pushed the boundaries of machining at the time.

Babbage eventually gave up on the idea of the Analytical Engine, deciding instead to design a simplified version of the Difference Engine. Again, he never made this machine, but a real-size replica of the Difference Engine No. 2 based on Babbage’s designs can be found on display at the Science Museum, London. You’ll also find another Difference Engine there, but this one was created in Babbage’s lifetime and based on his first design. It was made by a Swedish inventor and his son: Georg and Edvard Scheutz. Babbage even saw his creation when they brought it to London, where it went on display at the Royal Society. It was used to generate and print mathematical tables, but sadly proved temperamental.

The tragic side effect on the Scheutz family and Babbage was that building mathematical engines brought neither happiness nor wealth. The Swedish pair would die bankrupt, while Babbage grew gradually more bitter about the government’s failure to back his machines and his failure to bring his inventions to life. Although – and those of a squeamish nature should look away now – Michael Williams, editor-in-chief of the IEEE Annals of the History of Computing, gives context to Babbage’s reported irascible nature in later life by the string of medical conditions he was suffering from: “Who would not be ‘crusty’ with kidneys and urinary tracts and arteries such as these?” Williams wrote.

Nor should we simply write off Charles Babbage as simply a man before his time. He achieved incredible things during his life, with accomplishments covering everything from the invention of the ophthalmoscope to a ‘black box’ to help detect the reason for train accidents to proposing a scientific method for using ring dating to determine the age of trees. 

There is one other factor to consider, one that is driven home by the stories of the computers elsewhere in this book. Ultimately, you can argue, it wasn’t the lack of technology that halted the creation of the Analytical Engine. You also need a driving force. Money, almost without limit. These conditions are rarely found in peacetime: it took war to drive the development of the ENIAC, and Colossus, and without this how long might we have had to wait for truly electronic computers?

The Computers that Made the World on sale now!

The story of computing in World War II takes us through Germany, the UK, and the US, before covering the explosive post-war years when anything seemed possible.

Discover the fascinating stories behind the Manchester Baby, EDSAC, EDVAC, UNIVAC, Princeton IAS, and Alan Turing’s Pilot ACE and the birth of artificial intelligence. This new title is now available at our online store — and in the offline store — for £19.99. You can also find it on Amazon UK or Amazon US. In The Computers that Made the World, you’ll not only learn about the computers that shaped the world we live in, but what happened behind the scenes.

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