The Enchantress of Numbers

Ada Lovelace’s parents were divorced soon after her birth and she never again saw her father, Lord Byron. She inherited some of his wildness, but from her mother, Anne Isabella Milbanke, she gained a fascination with mathematics. When, as a teenager, Lovelace attended a demonstration by Charles Babbage of his automatic calculator the Difference Engine (see Pioneers’ Page of January/February 2008), she was among the few observers who understood what it could do.

Augusta Ada King, Countess of Lovelace (1815–1852) — usually referred to simply as Ada Lovelace — was the daughter of the English poet Lord Byron. In answer to the question in last month’s Pioneers’ Page, it is she who forms the link between poetry, programming, and the computer patriarch Charles Babbage.

The Analytical Engine

Ada Lovelace became Babbage’s friend and collaborated in his work, especially with the advance on the Difference Engine: an all-purpose, programmable computer to be called the Analytical Engine, which he began to design around 1835.

Lovelace showed her wild streak in her fondness for gambling. And to help raise funds to develop the Analytical Engine, she and Babbage tried to create a mathematical formula for betting on horses. Unfortunately, it resulted in a large amount of gambling debts.

The Difference Engine could perform just one type of calculation. Rather than constructing different machines for each mathematical procedure, Babbage wanted to make a machine that could perform multiple tasks by changing the way each part interacted with another.

As in his first device, the central processing unit of the Analytical Engine was to be the “mill” to perform additions up to 50 decimal places. Up to one thousand 50-digit numbers could be kept in a “store”, or memory unit. Instructions (what we now call programs) could be given to the engine about storing calculations and what operations to carry out in what order. Punched cards were used for inputting these instructions, as well as for feeding in raw data. The card reader thus acted as a control unit. The output device was an automatic printer.

The idea of punched cards was adopted from the loom designed by Joseph Marie Jacquard (see Pioneers’ Page of December 2007), which could be programmed to weave very complex patterns. Babbage was highly impressed by this work and one of his prize possessions was an extremely intricate portrait of Jacquard woven in silk, which he bought in 1840 for the equivalent of several thousand US dollars today.

Also in 1840, Babbage gave a lecture in Turin, Italy, at which notes were taken and later published in Paris by Italian Federico Luigi, Count Menabrea. Lovelace translated these into English and Babbage urged her to also publish her own thoughts. Her “Sketch of the Analytical Engine”, issued in 1843, described how “we may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard loom weaves flowers and leaves”.

Lovelace also explained to the world at large that “the Analytical Engine does not occupy common ground with mere calculating machines. It holds a position wholly its own… In enabling mechanism to combine together general symbols, in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science. A new, a vast and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind”.

The first computer program

An example of how the Analytical Engine could be used was presented by Lovelace in an addendum to her essay. It was the first time ever that a computer program had been published, including such elements as subroutines and loops.

Lovelace described in detail an algorithm for generating Bernoulli numbers: a sequence of rational numbers with many mathematical applications. Babbage was clearly involved in this work, but also acknowledged Lovelace’s important role. “We discussed together the various illustrations that might be introduced (to Menabrea’s memoir)” he wrote. “I suggested several but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.”

A revolution delayed

Babbage’s Analytical Engine was never finished in his lifetime. He became increasingly eccentric and irascible, and lost his collaborator and publicist upon Lovelace’s early death in 1852. Had his machine been adopted, the information age might have started a century earlier than it did.

Disappointed with the lack of support for his efforts, Babbage wrote “forget this world and all its troubles and if possible its multitudinous charlatans — everything, in short, but the Enchantress of Numbers.” Was that enchantress his Analytical Engine? Perhaps it was none other than Ada Lovelace, child of a poet, friend of Babbage and publisher of the world’s first computer program.