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Ada’s Algorithm

Ada Lovelace

Augusta Ada King, Countess of Lovelace

Maybe you know about Ada Lovelace, Lord Byron’s daughter, a very bright young mathematician who worked with the older scientist, Charles Babbage, when he was developing the first programmable computing machine — a precursor of the contemporary computer. If you know a bit more, you know that the machine, which was never actually built, was to be programmed by punched cards, similar to the punched cards that were used a hundred and more years later in the early computers of the 20th century. And if you’re like most people who know about Ada, that’s about all you know of her.

Ada’s life has the elements of a good gossipy story, and that’s the way it’s treated in James Essinger’s biography, Ada’s Algorithm. Or, as the book’s subtitle says, How Lord Byron’s Daughter Ada Lovelace Launched The Digital Age. Ada’s father was as notorious for his bad-boy behavior as he was famous for his poetry, and Ada wasn’t able to escape the celebrity of his name. Probably the most decisive effect of having Byron for a father was that Ada’s mother constructed an educational program for Ada that was designed to stamp out any fanciful or imaginative tendencies the girl might have inherited from dreadful dad. Lady Byron gave birth to Ada on December 10, 1815, and thirty-five days later she folded back the covers from her side of the bed, slipped from her sleeping husband’s side, then bundled herself and her daughter in warm clothes and, with a maidservant, left their London house.

Ada never saw her father after that. George Gordon, Lord Byron, was a great poet but he wasn’t cut out to be a husband or father.

James Essinger’s light and chatty biography provides brief sketches of Ada’s parents and grandparents and, what’s more to the point, it gives the reader a good sense of how mother and daughter behaved in regard to each other. Lady Byron’s plan to protect Ada from whatever imaginative tendencies she might have inherited from her father included a good dose of mathematics. As it happened, Ada did very well in mathematics. Indeed, she excelled in that field and eventually directed her own studies and became a fine mathematician — not an easy feat for a woman in the early 19th century. She had a lively interest in science and technology, too. In 1833 Ada turned 18 and, following the custom of her class, she was formally introduced to society as a marriageable young woman. Young women of high social status were often presented at court and so it was with Ada who, wearing white satin and tulle, and accompanied by her mother, curtsied to the king and queen, and hobnobbed with the dignitaries there on that day in May.

The following month, mother and daughter were at a different social gathering. In a letter about it, Lady Byron wrote approvingly that “Ada was more pleased with a party she was at on Wednesday than with any of the assemblage in the grand monde. She met there a few scientific people — amongst them Babbage with whom she was delighted.” Charles Babbage was forty-four, a socially prominent polymath, an intellectual celebrity who was just eccentric enough to be made fun of. As Lady Byron said in that same letter, “Babbage was full of animation and talked of his wonderful machine(which he is to shew us) as a child does of its plaything.”

Charles Babbage’s machine was his Difference Engine, a mechanical calculator that would be the first ever to work, if he completed it. When Ada met Babbage he had not yet built a complete machine, but he had assembled a one-seventh section of it that he used as a demonstration model. Babbage never did produce a complete Difference Engine. Indeed, it wasn’t until the advent of the contemporary computer that curiosity in Babbage’s invention revived. In 2002 a complete working Difference Engine was made from Babbage’s original designs; it has 8,000 parts, weighs 5 tons, is 11 feet long and 7 feet tall.

Ada was delighted by Babbage and his machine, but at this point in her life she and Lady Byron were far more interested in finding a well-to-do aristocrat appropriate for Ada to marry. In the spring of 1835, through the proper stratagems of that time and place, nineteen-year-old Ada, daughter or Lord and Lady Byron, was introduced to William, Lord King, age thirty, and they were married that summer. Their first child, a son, was born ten months later, and was soon followed by a daughter and another son. Ada King became Countess of Lovelace and nowadays is known simply as Ada Lovelace.

A couple of times in this biography, Essinger raises the question of whether or not Ada Lovelace and Charles Babbage had a romantic interest in each other. It’s an odd question. There’s no evidence that suggests such an interest and the biographer prudently dismisses the thought each time.

Charles Babbage was the Lucasian Professor of Mathematics at the University of Cambridge, probably the most prestigious professorship in all of academia. Other professors who have held that position include Isaac Newton, Paul Dirac, and the current holder, Stephen Hawking. Professor Babbage admired young Ada’s growing mathematical ability, and – what certainly must have counted equally with him — she understood the importance his Analytical Engine. The surviving correspondence between Ada and Babbage shows that she not only understood the workings of those machines, she understood the frustrated, irritable and sometimes semi-paranoid workings of the inventor.

When Ada met Charles Babbage his focus had already shifted from his partially assembled Difference Engine to his unbuilt Analytical Engine. His beloved wife had died five years earlier, and to work his way out from despair he had thrown himself into composing plans for a machine that would go far beyond his Difference Engine.

Babbage had seen a Jacquard loom weave patterned cloth, and had seen that instructions on how to weave the pattern were transmitted to the mechanical loom by a chain of cards with holes punched in them. To weave a design on a loom the weaver must insert colored threads, back and forth, over and under, fixed threads. The fixed threads are called the warp; the shuttling threads are the weft. By raising or lowering the warp, the shuttle will pass over or under the fixed threads and the colored thread will show or be hidden. Until Joseph-Marie Jacquard invented his revolutionary loom, weaving a design into a fabric had been done by hand, following written instructions, a very slow and terribly labor-intensive task.

Unfortunately, Essinger’s biography doesn’t explain how the punched cards worked on the Jacquard loom or on Babbage’s machine. In principle, if you have a group of small diameter rods, each of which can connect to the machine to perform a single different task — such as pressing this, or hooking that — and if you want to select from that group a series of certain rods, you can make that selection by using a series of cards with carefully placed holes in them. The holes will permit certain rods to pass through while blocking the passage of all the others. Charles Babbage saw the use of punched cards in a Jacquard loom, and realized that the same principle could be used to manipulate a machine that carried out mathematical operations.

Ada Lovelace is remembered and celebrated nowadays because she worked with Charles Babbage on his Analytical Engine. Specifically, Ada translated for publication an article about the Engine. The piece, in French, was written by Luigi Federico Menabrea, an Italian mathematician, military general and statesman, an important figure in Italy’s emergence as a nation. In his autobiography, Babbage says that when Ada informed him that she had translated the article, he asked her why she had not herself written an original article, since she was so knowledgeable about the machine. She said the thought had not occurred to her, and Babbage then suggested that she should add some notes to the article. Those “notes” range far beyond Menabrea’s description of the Analytical Engine; indeed, they are more than twice as long as the translation itself. And in them is Ada Lovelace’s claim to fame.

James Essinger’s sprightly biography omits the technical explanations and mathematical material in Ada’s notes, but for readers interested in learning more, Ada’s translation of Menabrea’s article and her notes are available online. Early in the course of writing the Notes, Ada points out certain distinctions that are, in her words, “perhaps too little kept in view in the study of mathematical science in general.” What she’s writing about is the difference between operations performed on numbers (adding, squaring, dividing and so forth), the numbers operatized upon, and the results.

Ada emphasizes this because it’s central to the concept of the Analytical Engine and crucial to the distinction between Babbage’s Difference Engine and his Analytical Engine. James Essinger believes that in this passage Ada is “seeking to do nothing less than invent the science of computing, and separate it from the science of mathematics.” Well, maybe. But readers may choose to think Ada is simply clarifying what we do when we do mathematics, rather than inventing a new science.

Ada wrote seven Notes, listed as A through G, and her place in history is secured in Note G. She begins by saying that “It is desirable to guard against the possibility of exaggerated ideas that might arise as to the powers of the Analytical Engine.” And she assures us that “The Analytical Engine has no pretensions whatever to originate anything. It can do whatever we know how to order it to perform. It can follow analysis; but it has no power of anticipating any analytical relations or truths. Its province is to assist us in making available what we are already acquainted with.” But Ada had a penetrating mind and, despite the limitations of the Analytical Engine, she saw what we, living in an age of computers, have surely discovered  —“There are in all extensions of human power, or additions to human knowledge, various collateral influences, besides the main and primary object attained.”

She goes on to say, “We will terminate these Notes by following up in detail the steps through which the engine could compute the Numbers of Bernoulli, this being (in the form in which we shall deduce it) a rather complicated example of its powers.” James Essinger limits himself to a one-sentence explanation of what a Bernoulli number is, and in this brief review it’s enough to say that they’re named after Jakob Bernoulli (1654-1705) who noticed that they arose during the calculation of sums of powers of consecutive integers. Bernoulli numbers are important in various areas of mathematics and they’re remarkably tedious to calculate.

Next, Ada shows the reader some different ways of calculating Bernoulli numbers, but dismisses them and chooses a more difficult method, because, she says “our object is not simplicity or facility of computation, but the illustration of the powers of the engine.” She then concludes Note G by listing twenty-three cards in detail which, when fed into the Analytical Engine, will instruct the Engine to produce Bernoulli numbers. All of which is to say that Ada Lovelace wrote out an algorithm, a menu for a machine, the world’s first computer program.

James Essinger’s entitled the penultimate chapter of this biography of Ada A Horrible Death. She died of uterine cancer, a slow and painful passage from this life, and this biography has a selection of details to illustrate just how slow and how painful it was. Augusta Ada King, Countess of Lovelace, died young, age 36, the same age as her father.

Ada’s Algorithm is a well researched and engaging biography. It’s an easy read and provides a very accessible non-mathematical understanding of Ada’s ancestry and birth, her relation to Babbage and the Analytical Engine, her death and burial. Probably it would have been better to have omitted some of the gossipy passages about grandfather Byron and to have added material about Ada’s growing addiction to gambling — there’s nothing about it this book — and perhaps to have explored whether her gambling was related to her knowledge of mathematics. Maybe Essinger’s admiration for her achievements causes him to overstate the case when he writes “She was also, beyond doubt, a genius,” and the subtitle of his book goes too far, way too far, when it asserts that she “Launched The Digital Age.” Within the pages of the book itself, the author is more balanced in his assessment and points out that not everyone considers Ada’s work in Note D the equivalent of a computer program. Ada’s translation and her Notes are at www.fourmilab.ch/babbage/sketch.html for all to see and judge. Ada was a remarkable woman, a fine mathematician, the equal of all but the greatest around her, and for sure she wrote the first computer program.

More Notes

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