December 10 is named Programmer's Day in honor of the first representative of this not too ancient profession, who was also born on this day.
Augusta Ada Lovelace was born on December 10, 1815. She was the only daughter of the great English poet George Gordon Byron (1788 - 1824) and Annabella Byron, née Milbank (1792 - 1860). “She is an extraordinary woman, a poet, a mathematician, a philosopher,” Byron wrote about his future wife in 1813. Her parents separated when the girl was two months old, and she never saw her father again.
Ada inherited her mother’s love of mathematics and many of her father’s traits, including a similar emotional character.
Byron dedicated several touching lines to his daughter in Childe Harold’s Pilgrimage, but at the same time, in a letter to his cousin, he was worried in advance: “I hope that God will reward her with anything, but not a poetic gift...
Ada had an excellent upbringing. The study of mathematics occupied an important place in him, to a large extent under the influence of his mother. Her teacher was the famous English mathematician and logician Augustus de Morgan. Her first acquaintance with the outstanding mathematician and inventor Charles Babage, the creator of the first program-controlled digital computer, which he called “analytical,” dates back to 1834. Babbage, who knew Lady Byron, encouraged young Ada's passion for mathematics. Babbage constantly monitored Ada's scientific pursuits; he selected and sent her articles and books, primarily on mathematical issues. Ada's studies were encouraged by her family's friends - Augustus de Morgan and his wife, the Sommervilles and others. Ada attends D. Lardner's public lectures on the machine. Together with Sommerville and others, she visits Babbage for the first time and inspects his workshop. After her first visit, Ada began to visit Babbage often, sometimes accompanied by Mrs. de Morgan. In her memoirs, de Morgan described one of her first visits as follows: “While some of the guests looked in amazement at this amazing device with such a feeling, as they say, savages see a mirror for the first time or hear a shot from a gun, Miss Byron, still very young, was able to understand operation of the machine and appreciated the great merit of the invention.”
Augusta Ada's family life was happy. In 1835, Ada Byron, aged nineteen, married 29-year-old Lord King, who later became Earl of Lovelace. The husband had nothing against his wife’s scientific pursuits and even encouraged her in them. True, highly appreciating her mental abilities, he lamented: “What an excellent general you could become!” The Lovelace couple led a social lifestyle, regularly hosting receptions and evenings at their London home and the Oakhut Park country estate. Ada's marriage did not alienate her from Babbage; their relationship became even more cordial. At the beginning of their acquaintance, Babbage was attracted by the girl’s mathematical abilities. Subsequently, Babbage found in her a person who supported all his bold endeavors. Ada was almost the same age as his daughter who died early. All this led to a warm and sincere attitude towards Ada for many years.
Ada was short, and Babbage, when mentioning her, often called her a fairy. The editor of Examiner magazine once described her as follows: “She was amazing, and her genius (and she had genius) was not poetic, but mathematical and metaphysical, her mind was in constant motion, which was combined with great exactingness. Along with such masculine qualities as firmness and determination, Lady Lovelace was characterized by delicacy and refinement of the most refined nature. Her manners, her tastes, her education... were feminine in the good sense of the word, and a superficial observer could never have guessed the power and knowledge that lay hidden beneath her feminine attractiveness. As much as she disliked frivolity and banality, she loved to enjoy real intellectual society.
The Lovelace couple had a son in 1836, a daughter in 1838 and a son in 1839. Naturally, this took Ada away from mathematics for a while. But soon after the birth of her third child, she turns to Babbage with a request to find her a mathematics teacher. At the same time, she writes that she has the strength to go as far in achieving her goals as she wishes. Babbage, in a letter dated November 29, 1839, responds to Lovelace: “I think that your mathematical abilities are so obvious that they do not need testing. I made inquiries, but at present I have not been able to find a person whom I could recommend to you as a teacher. I will continue searching"
From the beginning of 1841, Lovelace began seriously studying Babbage's machines. In one of her letters to Babbage, Ada writes: “You must tell me basic information regarding your machine. I have good reason for wanting this." In a letter dated January 12, 1841, she outlines her plans: “...For some time in the future (maybe within 3 or 4, or perhaps even many years) my head may serve you for your purposes and plans... Exactly I want to have a serious conversation with you on this issue." This offer was gratefully accepted by Babbage. Since that time, their cooperation has not been interrupted and has produced brilliant results.
In October 1842, Menabrea's article was published, and Ada began translating it. They developed the plan and structure of the notes together. Having finished each note, Ada sent it to Babbage, who edited it, made various comments and sent it on. The work was transferred to the printing house on July 6, 1843.
The central point of Lovelace's work was the compilation of a program (numbers) for calculating Bernoulli numbers. Lovelace's comments included three of the world's first computer programs that she compiled for Babbage's machine. The simplest of them and the most detailed is a program for solving a system of two linear algebraic equations with two unknowns. When analyzing this program, the concept of work cells (work variables) was first introduced and the idea of sequentially changing their content was used. From this idea there is one step left to the assignment operator - one of the fundamental operations of all programming languages, including machine ones. The second program was compiled to calculate the values of the trigonometric function with repeated repetition of a given sequence of computational operations; For this procedure, Lovelace introduced the concept of a loop, one of the fundamental constructs of structured programming. The third program, designed to calculate Bernoulli numbers, already used recurrent nested loops. In her comments, Lovelace also expressed an excellent guess that computational operations could be performed not only with numbers, but also with other objects, without which computers would remain just powerful, high-speed calculators.
Since 1844, Ada Lovelace became more and more interested in racing, especially since she herself rode well and loved horses. Both Babbage and William Lovelace played at the races, and Babbage, who was interested in applied questions of probability theory, looked at the game at the races from these positions and looked for the optimal gaming system. However, both Babbage and Ada's husband relatively soon abandoned participation in the game. But Ada, passionate and stubborn, continued to play. Moreover, Lady Ada became close to a certain John Cross, who blackmailed her. She spent almost all her funds and by 1848 had incurred large debts. Then her mother had to pay off these debts, and at the same time buy the incriminating letters from John Cross. In the early 50s, the first signs of the disease that claimed the life of Ada Lovelace appeared. In November 1850 he wrote to Babbage: “My health... is so bad that I want to accept your offer and appear to your medical friends upon arrival in London.” Despite the measures taken, the disease progressed and was accompanied by severe suffering. On November 27, 1852, Ada Lovelace died before the age of 37. Along with her outstanding intellect, her father also passed on to her this terrible heredity - early death - the poet died at the same age... She was buried next to her father in the Byron family crypt.
Success came to her with great stress and not without damage to her health. Augusta Ada Lovelace accomplished little in her short life. But the little that came from her pen inscribed her name in the history of computational mathematics and computer technology as the first programmer. The ADA language, developed in 1980, is one of the universal programming languages, named in memory of Ada Lovelace. This language was widely used in the United States, and the US Department of Defense even approved the name “Ada” as the name of a unified programming language for the American military, and later for the entire NATO.
Two small cities in America are also named after Ada Lovelace - in the states of Alabama and Oklahoma. There is also a college named after her in Oklahoma.
(George Gordon Byron) - was 27 years old, and at this age he gained great popularity in England thanks to his poetry. Her mother, Annabella Milbank, a 23-year-old progressive, inherited the title of Baroness Wentworth. Her father said he named her Ada because the name was short, ancient and melodious.
Ada's parents are a kind of study of opposites. Byron led a tumultuous life, and perhaps became the most colorful "top bad boy" of the 19th century - with dark episodes from his childhood and adolescence and a large number of romantic and other stories. In addition to writing poetry and flouting the social norms of his time, he often did something unusual: keeping a tame bear in his room while studying at Cambridge, for example, or living with poets in Italy and “five peacocks on the main staircase” (quote from one of his acquaintances) Byron), wrote a textbook on Armenian grammar, and, if he had not died so early, would have led troops in the Greek War of Independence (as commemorated by the large statue in Athens), despite his complete lack of military training.
Annabella Milbank was an educated, religious and very correct woman, passionate about reforms and good deeds, whom Byron nicknamed the “Princess of Parallelograms.” Her marriage to Byron did not last long, and fell apart when Ada was only 5 weeks old; Ada never saw her father again (even though he kept a photograph of her on his desk and mentioned her in his poetry). He died aged 36 at the height of his fame, when Ada was 8. There was a huge fuss about him, spawning hundreds of books and a “holy war” between sympathizers of Lady Byron (as Ada’s mother imagined herself) and Byron himself, which lasted a century, if not more.
Ada spent her childhood isolated on her mother's rented estate, with governesses, teachers and her cat, Mrs. Puff. Her mother was often absent for various (rather stupid) reasons related to health activities, providing Ada with a rich education system with many hours of classes and self-control exercises. Ada studied history, literature, languages, geography, music, chemistry, sewing, cursive writing and mathematics (taught partly with an empirical approach) to the level of elementary geometry and algebra. When Ada was 11, she went with her mother and entourage on a year-long trip to Europe. When she returned, she was quite enthusiastic about learning what she called flyology, thinking about how the flight of a bird could be reproduced using steam engines.
Ada then contracted measles (and possibly encephalitis), ending up bedridden and in poor health for 3 years. She managed to fully recover by the time when, according to the customs of society of that time, girls should join society: closer to 17, she left for London. On June 5, 1833, 26 days after she was "presented at Court" (i.e., met the king), she was received by 41-year-old Charles Babbage (whose eldest son was the same age as Ada). She apparently charmed the owner, and he invited her and her mother to a demonstration of his newly created difference engine: a 60-centimeter tall, manually operated contraption with two thousand brass components, which can now be seen in the Science Museum in London:
Ada's mother called her a "thinking machine," and then said that she could find the roots of quadratic equations, as well as raise some numbers to the second and third powers. This event changed Ada's life.
Charles Babbage
What is the story of Charles Babbage? His father was a successful and enterprising jeweler and banker. After various schools and private tutors, Babbage went to Cambridge, where he studied mathematics, but soon became inspired by the idea of modernizing the approaches to mathematics adopted there, and together with his lifelong friends John Herschel (son of the discoverer of Uranus) and George Peacock ( who later became a pioneer in abstract algebra), founded the Analytical Society (which later became the Cambridge Philosophical Society) to promote reforms such as, say, replacing Newton's dot notation (British) in calculations with Leibnizian (Continental) based on functions.
Babbage graduated from Cambridge in 1814 (a year before the birth of Ada Lovelace) and went with his wife to live in London, where he realized himself on the scientific and social scene. He did not have a job as such, but he lectured on astronomy and wrote several well-received papers in various mathematical fields (functional equations, infinite products, number theory, etc.), and was supported by his father and his wife's family.
In 1819, Babbage visited France and learned of a large-scale government project to create tables of logarithms and trigonometric functions. Mathematical tables in those days were of great importance in the military and commercial fields, and were used in science, finance, engineering calculations, and navigation. It has often been said that errors in tables can ground ships and destroy bridges.
Returning to England, Babbage founded a project with Herschel to create tables for their new astronomical community, and in attempting to test these tables, Babbage is said to have exclaimed: " I pray to God that these tables will be obtained by the power of steam!", which marked the beginning of his lifelong work in an attempt to mechanize the creation of these tables.
Level of development of this area
There were mechanical calculators long before Babbage. Pascal made one in 1642, and now we know that there was at least one in ancient times. But in Babbage's time, such machines were very rare and not reliable enough for regular use. Tables were created by human calculators (that was a profession), work was distributed across teams, and the most low-level calculations were based on estimating polynomials (say, series expansion) using the difference method.Babbage thought that there might be such a device - difference machine- which will be able to calculate any polynomial to a certain extent using the difference method, which will then automatically produce the result, thereby reducing the human factor to zero.
(Museum of the History of Science)
By early 1822, the 30-year-old Babbage was studying different types of mechanisms, creating prototypes and thinking about what a difference engine might be. The astronomical society, of which he was a co-founder, awarded him a medal for his idea, and in 1823 the British government agreed to provide funding for a similar machine.
In 1824, Babbage went slightly off topic with his idea for a life insurance company, for which he made many calculation tables. However, he set up a workshop in his stable (his "garage") and continued to develop ideas on how to implement a difference engine using the components and tools of his time.
In 1827, a table of logarithms, compiled by hand, was finally completed, after which it was reprinted for approximately a hundred years. Babbage printed these tables on yellow paper, with the idea that this would reduce the number of errors when using them. (When I was in elementary school, logarithm tables were still the fastest way to calculate products.)
In addition, Babbage's father died in 1827, leaving him an inheritance of about one hundred thousand pounds sterling, which is approximately $14,000,000 in today's dollars, and this money supported Babbage for the rest of his life. That same year, however, his wife also died. She left him with eight children, of whom only three lived to adulthood.
Depressed by the death of his wife, Babbage went on a trip to continental Europe, and, impressed by the scientific achievements he saw, wrote a book - Reflections on the decline of science in England- which gave rise to sharp criticism of the Royal Society (of which he was a member).
Although often distracted, Babbage continued to work on the difference engine, producing thousands of pages of notes and design drawings. He was quite good at creating blueprints and experimenting with mechanisms. But he was not very good at managing the engineers he hired, nor was he very good at managing finances. However, by 1832, a small working prototype of a difference engine (without a printing device) was successfully completed. And this was exactly what Ada Lovelace saw in June 1833.
(Science Museum/Science and Society Image Library)
Back to Ada
Perhaps it was after Ada saw the difference machine that her interest in mathematics awoke. She met Mary Somerville, a translator of Laplace and a renowned expositor of science, and, partly under her influence, soon became an enthusiastic student of the works of Euclid. In 1834, Ada took part in a charity tour of factories in northern England organized by her mother, as a result of which she was impressed by the high-tech equipment they had by the standards of those times.
Upon her return, Ada taught mathematics to some of her mother's friends' daughters. She continued to teach classes by mail, noting that it could be " the beginning of a mathematical correspondence for many years between two ladies of the highest rank, which, no doubt, may hereafter be published as an instruction to mankind (mankind) or the feminine part of it (womankind - a play on words; man both as a man and as a man)“Ada’s letters did not contain complex mathematics, but she expressed it very clearly, accompanying the letters with instructions like “you should never limit yourself to indirect evidence if possible direct." (Much of Ada’s correspondence was underlined here in italics.)
Babbage, perhaps, initially underestimated Ada, trying to interest her in a toy, which was a mechanical doll ( Silver Lady automaton toy), which he demonstrated at his receptions. But Ada continued to communicate with Babbage and Somerville, both separately and together. And Babbage soon introduced her to many topics, including the problem of government financing of his project to create a difference engine.
In the spring of 1835, when Ada was 19, she met 30-year-old William King (or Lord William King to be precise). He was a friend of Mary Somerville's son, educated at Eton (the same school I went to 150 years later) and Cambridge, and then a civil servant, later at an outpost of the British Empire in the Greek Isles. William appears to have been an accurate, conscientious and decent man; maybe a little tough. But, in any case, Ada quickly got involved with him, and on July 8, 1835, they got married without announcing it until the last minute, fearing publicity and excessive press attention.
The next few years of Ada's life seem to be devoted to raising three children and running a large household, although she devoted some time to horse riding, learning to play the harp, and mathematics (including topics such as spherical trigonometry). In 1837, Queen Victoria (then 18) ascended the throne and, as a member of high society, Ada met her. In 1838, in connection with his public service, William was created an earldom and Ada became Countess of Lovelace.
(Powerhouse Museum in Sydney)
A few months after the birth of her third child in 1839, Ada returned to mathematics with a serious attitude. She told Babbage that she wanted to find a mathematics tutor in London, asking that her name not be used, probably for fear of publicity.
In correspondence with Babbage, Ada showed an interest in discrete mathematics and was surprised, for example, that solitaire " can be combined with mathematical formulas and solved"But in accordance with the traditions of mathematical education of that time (which extend to our time), de Morgan taught Ada mathematical analysis.
(British Library)
Her letters to De Morgan regarding calculus were not particularly different from those of calculus students today, but were quite unusual in Victorian England. Even many of the misconceptions are the same, although Ada was hurt more than usual by unfortunate notations in calculations (“ why can't you multiply by dx?", etc.). Ada was a persistent student, and seemed to enjoy plunging into the depths of mathematics. She was glad to discover her mathematical abilities and de Morgan's high assessment of them. She kept in touch with Babbage, and in one of his visits (in January 1841, when she was 25 years old), she charmingly told the then 49-year-old Babbage, “If you ice skating, promise to bring skates to Occam; it’s the hottest place right now and a must-visit.”
Ada's relationship with her mother was very difficult. From the outside it seemed that Ada treated her mother with great respect. But she seemed to constantly struggle with her mother's attempts to control and manipulate her. Ada's mother often complained about her health, lamenting that she was about to die (but in fact she lived to be 64 years old). She often criticized Ada on issues of raising children, housekeeping, and behavior in society. But on February 6, 1841, Ada had enough confidence in herself and her mathematics studies to write a very detailed letter to her mother about her thoughts and aspirations.
She wrote: " I consider myself to have a very rare combination of qualities ideally suited to make me a discoverer of the hidden realities of nature" She talked about her ambitions to create something great, about her "restless and restless energy", which, in her opinion, she found an application for. And she said that after 25 years she became less "secretive and suspicious" in relation to her.
But three weeks later, her mother revealed that Byron and his half-sister had a baby before Ada was born, and this news unsettled her. Incest was not illegal in England at the time, but it was a scandal. Ada found this difficult to accept, and for some time she distanced herself from mathematics.
Ada periodically had health problems, and in 1841, apparently, the situation worsened, and she began to systematically take opiates. She really wanted to succeed at something, and began to think that perhaps she should devote herself to music and literature. But her husband William seems to have dissuaded her from this idea, and at the end of 1842 she returned to mathematics.
Returning to Babbage
What was Babbage doing all this time? With a variety of things and with varying degrees of success.After several attempts, he was able to secure a position as Lucasian Professor of Mathematics at Cambridge, but subsequently he did not visit there much. Nevertheless, he wrote, as it later turned out, a very important book - Economics of technology and production(On the Economy of Machinery and Manufactures), which dealt with how to allocate production tasks (a question that actually arose in connection with mathematical table calculations).
In 1837 he studied natural theology, popular at that time, adding his Bridgewater's Ninth Treatise into a series of treatises written by other people. The central question sounded something like this: " Are some observable features of nature and the environment evidence of the existence of God?"Babbage's book is quite difficult to read (and translate!); take, for example, the quote: “ The concepts we derive from ideas and plans are born from comparing our observations of the creation of other beings with the aspirations in which we see our own endeavors.” (“The notions we acquire of contrivance and design arise from comparing our observations on the works of other beings with the intentions of which we are conscious in our own undertakings.”)
Clearly resonating with some of my work, published 150 years later, he discusses the relationships between mechanical processes, natural laws, and free will. In his book he states that " complex calculations can be carried out using mechanical means", but then goes on to claim (with very weak examples) that a mechanical engine can produce sequences of numbers that exhibit unexpected changes, comparing it to a miracle.
Babbage tried his hand at politics, running for parliament twice on a pro-industrial agenda, but failed to win the election, partly due to claims of mishandling of public money allocated for the difference engine.
Babbage continued to host high-class parties at his home in London, attracting such luminaries as Charles Dickens, Charles Darwin, Florence Nightingale, Michael Faraday and the Duke of Wellington, who was often accompanied by his elderly mother. But even with the number of titles and honors that were listed in the six lines after his name, he was greatly upset, as he believed, by the lack of recognition.
At the center of all this was the fate of the difference engine. Babbage hired the best engineers of his time to build the machine. But, for some reason, despite ten years of work and many high-precision machines and tools, the machine was never built. Let's go back to 1833; Shortly after meeting Ada, Babbage tried to take full control of the project, but as a result the chief engineer withdrew from the project and insisted that he was entitled to all the drawings of the difference engine, even those made by Babbage himself.
But at the time, Babbage believed that he probably had a better idea about the future of this machine. Instead of a machine that would simply calculate differences, he imagined " analytical engine", which would support many different operations that could be specified in some programmed sequence. At first he imagined a machine that calculated some specific formulas, but later he added new features, such as conditions, and explained , often suggesting very elegant ways to implement this or that functionality using mechanisms. But, most importantly, he understood how to control the steps of calculations using punched cards, similar to those invented in 1801 by Jacquard to set sewing patterns on looms.
(Museum of the History of Science)
Babbage created some very complex designs, and it now appears that they could work just fine. But let's go back to 1826, when Babbage invented what he called " Mechanical notation"Its purpose was to symbolically represent the operations of mechanisms in the same way that mathematical notation describes operations in mathematics.
By 1826, Babbage was very depressed that people did not appreciate his invention. No doubt people did not understand him, since even now it is not clear how his inventions worked. But, apparently, this was his greatest invention, the design and operating principles of which he was able to describe in great detail.
Babbage's project to create a difference engine cost the British crown £17,500, which in today's money is about $2,000,000. This was a very modest amount compared to other government expenditures, but the project, due to its unusual nature, was widely discussed. Babbage liked to point out that, unlike many of his contemporaries, he did not receive money from the government for his work (except for payments to upgrade his workshop to a fireproof one, etc.). He also claimed to have spent £20,000 of his own money - the majority of his fortune (I'm not entirely sure where that number comes from) - on his various projects. And he continued to try to obtain additional government support, outlining a plan for his No. 2 difference engine, which required only 8,000 parts instead of 25,000.
By 1842, the government had changed, and Babbage insisted on meeting the new Prime Minister (Robert Peel), but this did not work out, which made him very angry. In parliament, the idea of funding the difference engine eventually sank under the weight of jokes about its use. (The transcripts of the debate about the difference engine are quite fascinating, especially when it comes to discussions of its possible applications for government statistics, which have a surprising resonance with today's computing capabilities of Wolfram|Alpha.)
Ada's article
Despite the lack of support in England, Babbage's ideas gained some popularity elsewhere, and in 1840 Babbage was invited to lecture on the Analytical Engine in Turin, where he was honored by the Italian government.Babbage never published any detailed review of the Difference Engine, and wrote nothing at all about the Analytical Engine. But he was talking about the Analytical Engine in Turin to a certain Luigi Menabrea, a 30-year-old military engineer who 27 years later became Prime Minister of Italy (and also contributed to the development of structural analysis in mathematics).
In October 1842, Menabrea published an article in French based on his notes. When Ada saw his article, she decided to translate it into English and submit it to a British publication. Many years later, Babbage said that he suggested to Ada that she write her own paper on the Analytical Engine, to which she replied that the idea had not occurred to her. However, in February 1843, Ada decided to make a translation and add extensive notes to it.
Over the following months, she worked very hard on this topic, conducting an almost daily exchange of letters with Babbage (despite the presence of other “urgent and unavoidable meetings”). And although in those days letters were sent by mail (which arrived 6 times a day in London in those days), or sent by messenger (Ada lived about a mile from Babbage when she lived in London), they were quite similar to modern e -mail exchanged between project participants, except for the fact that this took place in Victorian England. Ada asks Babbage questions; he answers; she explains something; he comments on this. Obviously she was submissive, but it was felt that she became quite annoyed when Babbage, for example, tried to make his own changes to her manuscripts.
It is very fascinating to read Ada's letters about how she is working on debugging her system for calculating Bernoulli numbers: " My dear Babbage. I'm pretty confused when faced with these numbers, so I don't have a chance to sort it all out today... So I'm getting back to riding. Tant mieux (the better - French)."Later she wrote to Babbage: " I worked non-stop all day, and quite successfully. You will be extremely fascinated by the resulting tables and charts. They were made with extreme precision, and all the signs were collected in great detail and scrupulously."She then added that William (or 'Lord L.' as she called him)" very kindly outlined everything in ink for me. I had to do everything in pencil first..."
View illustrations...
It appears that it was William who suggested that she sign the translation and notes. As she wrote to Babbage: " It wasn't mine desire– sign, at the same time I wanted to add something that would help identify me, connect this text with future works signed as A.A.L." (Ada Augusta Lovelace).
By the end of July 1843, Ada had almost completed her notes. She was proud of them, just as Babbage spoke very flatteringly of them. But Babbage wanted something else: to add an anonymous preface (written by him) that talks about how the British government failed to support the project. Ada thought this was a bad idea. Babbage insisted, saying that without a preface the publication should be withdrawn. Ada was furious and told Babbage about it. Eventually, Ada's translation appeared, signed "A.A.L." and without preface, containing her notes in the chapter “Translator's Notes.”
Ada, with great joy, sent her mother a copy of the article, explaining that " no one can estimate the scale of the problem and endless labor that requires double-checking everyone mathematical formulas for printing. This is a joyful prospect, because it turns out that many hundreds and thousands of similar formulas will, to one degree or another, come from my pen". She said that her husband William enthusiastically distributed copies to his friends, and also wrote that " William introduces me to this righteous light that no one else could compare with him in this. He also told me that my work had a good impact on his reputation."
For several days, the entire community discussed Ada's publication. She explained to her mother that she and William " did not at all strive to do this in secret, but at the same time did not want importance this event was exaggerated and overrated"She saw herself as a successful interpreter and interpreter of Babbage's works, presenting them in a clearer light.
And although Babbage’s foreword was not a good idea, it was precisely this that prompted Ada to write him a very exciting and very frank 16-page letter on August 14, 1843. (Unlike her usual letters on small folded pages, this one was placed on large sheets.) In it, she explains that while he is often "implicit" in his speeches, she herself is "always an explicit function of x." She says that “Your affairs have deeply occupied and occupied both me and Lord Lovelace... And it so happens that I have plans for you...” Then she moves on to the question: “If I introduce you to one or two year is a very worthy offer for creating your car... will there be any chance of allowing me ... to manage this business; this will allow you to fully concentrate on your work..."
In other words, she proposed to take on the role of manager and Babbage to become technical director. This was not easy, especially given Babbage's personality. But she skillfully did her job, and as part of this she talked about the structure of her motives. Ada wrote: “My own immutable principle is the desire to love truth and God more than glory and honor...", while your "love for truth and God... is eclipsed desire for fame and recognition." But she further explained: “I wouldn’t be myself if I denied the influence of ambition and thirst for fame on myself. No living soul was more imbued with this than I was... and I, of course, would not deceive myself or others by pretending that this is not at all an important motive and component of my character and nature.”
And she ended the letter like this: “I wonder if you will continue working with your lady-fairy?”
The next day at noon she wrote to Babbage again asking for help on "final edition." Then she added: “You received my long letter this morning. You may no longer want to deal with me. But I hope for the best..."
(New York Public Library)
At 5 pm that same day, Ada was in London and wrote to her mother: “I do not understand how the matter with Babbage will turn out ... I wrote to him ... very specifically, presenting to him my own conditions... He is so convinced of the advantage of his supremacy that he will certainly refuse; although I demanded that he make strong concessions. If If he accepts my offer, then I may need to take care of his situation and get his car completed (however, based on what I have seen of him and his habits in the last three months, it seems to me that this is unlikely to happen , at least, unless someone greatly influences him and forces him). Sometimes he is extremely disorganized and unsystematic. I’m ready to do it for the next three years if I see decent chances of success.”
On a copy of Ada's letter to Babbage, he wrote: "Saw AAL this morning and refused all her offers."
However, on August 18, Babbage wrote to Ada that he would bring notes and drawings the next time he visited her. The following week, Ada wrote to Babbage: “We are very pleased with your (somewhat unexpected) proposal” (after a long visit to Ada and her husband). Afterwards, Ada wrote to her mother: “Babbage and I, I believe, are on better terms now than ever. I have never seen him so sweet, so sensible and in such a good spirit! „
Then, on September 9, Babbage wrote to Ada, expressing his admiration for her and (flatteringly) calling her “the number charmer” and “my dear and delightful interpreter.” (Yes, he is often misquoted; he wrote “numbers”, not “numbers”).
The next day, Ada replied to Babbage: “You are a brave man for allowing your sorceress to lead you!”, and Babbage signed his name in the next letter as “Your humble servant.” And in her letter to her mother, Ada described herself as " High Priestess of Babbage's Difference Engine".
After the article
But, unfortunately, everything did not work out as expected. For a time, Ada took care of family and household affairs, neglected during the period when she was concentrated on her notes. But after that, her health deteriorated greatly, and she spent many months on doctors and various “healers” (her mother suggested her “mesmerism,” that is, hypnosis).However, she still admired science. Ada communicated with Michael Faraday, who nicknamed her " rising star of science." She spoke of her first publication as " his firstborn“, “in colors and with implications (very implicitly expressed) about her very general and extensive metaphysical ideas.” She wrote: “It (her work; she calls it “He” - approx.) will become (as I hope) a wonderful chapter a large family with many brothers and sisters."
When her notes were published, Babbage said: “You should write your own paper. However, if you wait a little, you can make it even more beautiful.” But in October 1844, David Brewster (inventor of the kaleidoscope, among other things) decided to write about the Analytical Engine, and Ada asked that perhaps Brewster could suggest another topic for her, saying: " I think that some topics from the field of physiology might suit me; however, like any other."
Indeed, in the same year she wrote to her friend (who was also her lawyer and the son of Maria Somerville): “I do not believe that the structures of the brain are less subject to mathematicians than the movements and properties stars And planets; quite, if you choose to consider them the right point of view. I would like to leave it to future generations computational model of the nervous system." An impressive vision, and this is 10 years before, for example, George Boole raised the question of such things.
Both Babbage and Mary Somerville began their scientific careers with translations, and she saw a similar path for herself, saying that perhaps her next work would be reviews of Whewell and Ohm, and that she might eventually become " prophet of science".
Of course, she also had obstacles. Such as the fact that women at that time did not have access to the library of the Royal Society in London, although her husband, partly thanks to her efforts, was a member of the society. But the most serious problem remained Ada's health. She had many problems, although in 1846 she still spoke with optimism: “All that is needed is another year or two of patience and taking care of your health.»
There were also problems with money. William had a never-ending range of complex and often quite innovative building projects (he seems to have been particularly interested in towers and tunnels). And with a request for funding, they were forced to turn to Ada’s mother, who was often difficult to deal with. Ada's children were already entering adolescence, and she had to devote a lot of time to them.
Meanwhile, she had a good relationship with Babbage and began to see him more often, although in her letters she talks about dogs and pet parrots more often than about the Analytical Engine. In 1848, Babbage had the reckless idea of building a tic-tac-toe machine to tour the country to raise money for his projects. Ada dissuaded him. Babbage's idea centered on a meeting with Prince Albert to discuss his machines, but this never happened.
William also published. He already had short works with titles such as “a method of growing beans and cabbage on the same land” and “On Chard beets.” But in 1848 he wrote another article comparing the agricultural productivity of France and England, based on detailed statistics, with remarks like " It is easy to show that the French are not only much worse than the English, but that they now eat even worse than in the worst times of the empire."
1850 was an important year for Ada. She and William moved to a new house in London, increasing their presence on the London scientific scene as a result. She was deeply impressed after visiting her father's family home in the north of England for the first time, which led to an argument between her and her mother. Then she became interested in betting on horse races and lost some money on it. (Not to say that it was her or Babbage's style to develop some kind of mathematical scheme for betting, but there is no evidence that they did this.)
In May 1851, the World Exhibition opened at the Crystal Palace in London. (When Ada decided to visit her in January, Babbage wrote to her: " Please wear woolen stockings, cork-soled shoes and any other things that will keep you warm.") The exhibition showcased the cutting-edge of Victorian science and technology, and Ada, Babbage and their scientific circle were impressed (though Babbage expected more). Babbage distributed leaflets on his mechanical notation in large quantities. William received a prize for his manufacturing solution bricks.
However, this year Ada’s health situation has become very difficult. For a while, her doctors simply advised her to spend more time at sea. But eventually they found she had cancer (based on what we know now, it was most likely cervical cancer). Opium no longer suppressed pain; she began experimenting with marijuana. By August 1852 she wrote: " I begin to understand death; it creeps up imperceptibly and gradually every minute, and it will never be the work of any specific moment.“And on August 19, she asked Babbage’s friend, Charles Dickens, to come to her and read a story about death from one of his books.
Her mother moved into her house, keeping other people away from her, and on September 1, Ada made some unknown confession that clearly upset William. She seemed close to death, but, overcoming the pain, she held on for another three months, and finally died on November 27, 1852, at the age of 36. Florence Nightingale, who looked after Ada and was her friend, wrote: " They say that she could not have lived so long if it were not for the enormous vitality of her brain, which did not want to die."
Ada chose Babbage to be the executor of her will. And, to the chagrin of her mother, she was buried in the Byron family crypt next to her father, who, like her, died at the age of 36 (Ada lived 266 days longer). Her mother built a memorial that contained a sonnet written by Ada called "The Rainbow".
After Ada's death
Ada's funeral was very modest; neither her mother nor Babbage were present. But the obituaries were friendly, in the spirit of the Victorian era:
William survived her by 41 years, eventually remarrying. Her eldest son, with whom Ada had many difficulties, joined the Navy a few years before her death, but then deserted. Ada thought he might have gone to America (apparently he was in San Francisco in 1851), but he actually died at 26 while working in a shipyard in England. Ada's daughter married a very eccentric poet, spent many years in the Middle East and became the world's largest breeder of Arabian horses. Ada's youngest son inherited the family title and spent most of his life on the family estate.
Ada's mother died in 1860, but even then gossip about her and Byron continued to appear in articles and books, including Lady Byron acquitted 1870 by Harriet Beecher Stowe. In 1905, a year before his death, Ada's youngest son, raised largely by his grandmother (Ada's mother), published a book about all this, with a basic agenda in the style of " there is nothing interesting in the life of Lord Byron, except for what has already been discussed many times".
When Ada died, her personality was surrounded by a whole tangle of gossip and rumors. Did she have any affairs? Did she have huge gambling debts? Arguments and evidence were very scarce. Perhaps this was a reflection of the idea of her father as a “bad guy”. But long before that there were rumors that she had pawned (twice!) her family jewels, and lost what some said was £20,000, maybe even £40,000 (equivalent to about $7,000,000 in today's money) on horse bets .
It seemed that Ada's mother and her youngest son were against her. On September 1, 1852 - the day of her confession to William - Ada wrote: " My earnest dying message to all my friends who have letters from me: give them to my mother Lady Noel Byron after my death." Babbage refused. The rest agreed. But later, when her son systematized them, he decided to destroy some of them.
True, many thousands of pages from Ada’s letters are still scattered all over the world. Letters and responses to them are similar to modern correspondence - arrangements for meetings, conversations about health and illness. Charles Babbage complains about the postal service. Three Greek sisters ask Ada for money because their dead brother was Lord Byron's page. Charles Dickens talks about chamomile tea. Courtesy notes from a man Ada met at Paddington Station. And household calculations, diluted with notes, inserts of musical parts, recipes for various sweets. And then, mixed in with all of the above, serious intellectual discussions about the Analytical Engine and many other things.
What happened to Babbage?
So what happened to Babbage? He lived another 18 years after Ada's death and died in 1871. He tried to continue work on the Analytical Engine in 1856, but did not achieve much success. He wrote articles like " Beacon statistics", "Table of relative frequencies for the causes of destruction of glass windows", "About ancient artifacts of human art mixed with bones of extinct animal species".Then, in 1864, he published his autobiography - Excerpts from the life of a philosopher- a very strange and bitter creation. The chapter on the Analytical Engine opens with a quote from Byron's poem - " If they make a mistake, then time takes revenge for it" (“Man wrongs, and Time avenges”; Chyumina O. in 1905 translated as follows: " Injustice is in the world, but vengeance is in the future"), and continues in the same vein. There are chapters on theatre, travel tips (including advice on how to organize transportation in Europe in some kind of modern caravan), and, perhaps most strangely, on troubles on the street. For some reason, Babbage waged a campaign against buskers, who he claimed woke him up at 6 a.m., causing him to lose a quarter of his productive time. It is unknown why he did not develop some kind of soundproofing solution , but his campaign was so prominent, and so strange, that when he died, it was the main message.
Babbage never remarried after his wife's death, and his last years seem to have been rather lonely. The gossip column of the time wrote the following about him:
Apparently he liked to say that he would gladly give up the rest of his life for three days spent 500 years in the future. When he died, his brain was preserved and it is still on display...
And even though Babbage never built his difference engine, a Swedish company did it for him, even demonstrating part of it at the world exhibition. When Babbage died, many of the documents and components of his Difference Engine project passed to his son, Major General Henry Babbage, who published some of these documents, and privately assembled several devices and some components of the computational part of the Analytical Engine. Meanwhile, a fragment of the difference engine, built in Babbage's time, was exhibited at the Science Museum in London.
Reopening
After Babbage's death, his life's work - the work on creating computers 1 - was forgotten by everyone (although, for example, they were mentioned in). However, mechanical computers continued to develop, gradually giving way to electromechanical ones, which in turn gave way to electronic ones. And when people began to delve into programming in the 1940s, Babbage’s work and Ada’s notes were remembered again.People knew that "AAL" was Ada Augusta Lovelace, and that she was Byron's daughter. Alan Turing read her notes and coined the term " Lady Lovelace's objection" (about the inability of AI to create and create) in his 1950 paper on the Turing test. But Ada herself was represented in it only as a footnote.
There was one Bertram Bowden, a British nuclear physicist who went into work in the computer industry and eventually became Secretary of State for Education and Science, and who "rediscovered" Ada. In his book Faster than thoughts from 1953 (yes, about computers) he writes that he contacted Ada's granddaughter Lady Wentworth (daughter of Ada's daughter), who told him about the family knowledge about Ada, both accurate and not so accurate, and allowed him to study her work . It's interesting how Bowden notes that in the book Ada's granddaughter “About purebred racing breeds and their pedigrees» uses the binary system in pedigree calculations. Ada, like the Analytical Engine, of course, used the decimal system, without considering the binary system in any way.
But even in the 1960s, Babbage and Ada were not particularly well known. The prototype of Babbage's difference engine was given to the Science Museum in London, but although I visited there many times as a child in the 60s, I am sure I never saw it there. However, in the 1980s, especially after the US Department of Defense named its ill-fated programming language after Ada, awareness of Ada Lovelace and Charles Babbage began to increase, and their biographies, sometimes full of idiotic errors, began to appear (my favorite is where is the mention " three body problem", in a letter from Babbage is interpreted as a romantic triangle between Babbage, Ada and William, although it was about the three-body problem from celestial mechanics!).
As interest in Babbage and Ada grew, so did curiosity about whether the difference engine would work if built according to Babbage's designs. The project was started, and in 1991, after herculean efforts, a completed version of the difference engine was built (and the printer was added in 2000) with only one correction in the drawings. Surprisingly, the machine worked. Construction cost about the same (adjusted for inflation) as Babbage asked for from the British government back in 1823.
As for the Analytical Engine, no version of it has ever been created, not even a model simulating it.
What did Ada actually write about?
So now that I've talked (in great detail) about the life of Ada Lovelace, what exactly was in her notes on the Analytical Engine?She begins without introduction: " the function whose integral the difference engine must calculate is..." She then explains that the difference engine can calculate the values of any sixth-degree polynomials, but the analytical engine is different in that it can perform the operations in any order. Or, to quote: " The Analytical Engine is reflection of the science of operations , constructed in such a way that abstract numbers are the subjects of these operations. The difference engine embodies only one specific, and, moreover, very limited set of operations..."
Quite fascinating, at least for me, considering how many years I spent on Mathematica; a little later she writes: " We can consider the car as material and mechanical embodiment of analysis, and that our actual capabilities in this branch of human knowledge will be used more effectively than before. This is necessary in order to keep up with our theoretical knowledge of these principles and laws. And this is realized through gaining complete control over the handling of algebraic and numerical symbols, which the machine gives us."
A little later she explains how punch cards are used to control the analytical engine, and then quotes the now classic phrase: " analytical engine weaves algebraic patterns like a jacquard loom weaving flowers and leaves."
Ada then breaks down how the Analytical Engine would carry out a sequence of separate types of calculations with " transaction cards" which define the sequence of operations, and " variable maps", by which values are specified. Ada talks about loops, and loops of loops, etc., now known as loops and nested loops, defining a mathematical notation for them:
Ada's recordings contain much that seems very contemporary. She writes that “ there is a beautiful woven Jacquard portrait that required 24,000 cards to produce" She then discusses the idea of using loops to reduce the number of cards, and the value of reordering operations to optimize their execution for the analytical engine, ultimately showing that with just three cards it is possible to do what would require 330 without loops.
Ada discusses how far the Analytical Engine can go, making things computable (at least with some accuracy) that previously seemed impossible. And as an example she cites the three-body problem, and the fact that at one time " in calculation of 295 coefficients of lunar disturbances“Many calculations didn’t add up.
Finally, in my Note G(can be translated as note G, or as note G - a play on words) she writes: " The Analytical Engine cannot create something new. She can do anything we ourselves know how to do it... its purpose is only to help us carry out what we are already familiar with".
Ada seemed to be very clear about the traditional view of programming: we create a program that does the things we want. But then she notes that the performance " facts and formulas of analysis"in a form suitable for the machine, " will reveal many areas of knowledge in a new light, making them more deeply developed"In other words, as I have often noted, if we program something, we will learn something new about it; it will open up new horizons of understanding for us.
She says that " in bringing mathematical truths into a new form in which they will be used will give us a new vision, which, in turn, will influence the theoretical component of this field of knowledge". In other words, as I have often said (see post on Habré "Computable Knowledge and the Future of Pure Mathematics") - presenting mathematical truths in computable form is likely to allow them to be better understood.
Ada seemed to understand that " operations science" performed by a machine can be used for more than just traditional mathematical calculations. For example, she notes that if " The fundamental relationships between sounds in the science of harmony would be amenable to abstract operations, then the machine could use them to scientifically write musical works of any complexity". Not a bad level of understanding for 1843.
Calculating Bernoulli numbers
Ada's most famous piece of writing was the calculation of Bernoulli numbers in Note G. This topic seems to be a development of her letter to Babbage in July 1843. The letter begins like this: " I work hard like the devil himself; (which I may be)". She then asks a few background questions and then writes: " I want to talk about Bernoulli numbers in one of my notes as an example of how an implicit function can be calculated by a machine without occupying human minds and hands... Please provide me with the necessary data and formulas".Ada's choice of Bernoulli numbers to demonstrate the Analytical Engine was quite interesting. In the 17th century, say, some people spent their entire lives developing tables of sums of powers of integers, in other words, tabulating values for various m And n. But Jacob Bernoulli discovered that all such sums can be expressed as polynomials in m, with coefficients that are now called Bernoulli numbers. And in 1713, Bernoulli proudly declared that he had calculated the first 10 Bernoulli numbers “in a quarter of an hour,” reproducing many years of work by other people.
These days, of course, they can be instantaneously calculated in, say, the Wolfram Language:
And it just so happens that a few years ago, as part of a demonstration of new algorithms, we calculated 10 million of them.
Okay, but how did Ada plan to do this? She began with the fact that Bernoulli numbers appear when expanded in a series:
Then, rearranging the components of this expression and sorting by powers X, she obtained a sequence of equations for the Bernoulli numbers Bn, which she guessed to represent in recurrent form:
Ada then explained how to calculate this on the Analytical Engine. First, she used the fact that all odd Bernoulli numbers other than B 1 ) are equal to zero, then calculated B n, which is our modern B 2n(or BernoulliB in Wolfram Language). Then she started with B 0 , calculating then B n for large n, while storing each value obtained. Here's what the algorithm she used looked like (in modern form):
The idea of analytical engine computing was to implement a sequence of operations (which are specified by "operation cards") by means of " number crushers" (Mill), with operands coming from " store" (with addresses listed on " variable map"). (In the store, each number was represented by a sequence of wheels, each of which had to be scrolled to the required number.) To calculate Bernoulli numbers, Ada wanted to use two nested loops of operations. With the analytical engine model available at that time, Ada had to unroll these loops. But in the end she successfully described how to calculate B 8 (which she called B 7 ):
Essentially, this is a trace of a program on an analytical engine, which is executed in 25 steps (plus a loop). Each trace step shows which operation is performed on which variable map, and which variable map the result is written to. Having no symbolic designation for cycles, Ada simply put them in brackets and explained that these fragments should be repeated.
In the end, the final result of the calculation is written to position 24:
As you can see, Ada has an error in line 4, causing the fraction to be upside down. But if you fix this, you can easily get a modern version of what Ada did:
And here is what the same scheme will produce for the two subsequent (non-zero) Bernoulli numbers. Ada found that to calculate subsequent numbers, it would not require more memory (which is implemented by variable maps), but only more operations.
The Analytical Engine, developed in 1843, was supposed to store a thousand 40-digit numbers, which would allow calculations up to perhaps B 50 (=495057205241079648212477525/66). And this would happen very quickly; The analytical engine was designed for a performance of 7 operations per second. So the calculation B 8 would take 5 seconds, but B 50 - about a minute.
Interestingly, even the record-breaking performance calculations of Bernoulli numbers a few years ago used basically the same algorithm that Ada used, although there are now slightly faster ones that effectively calculate the moduli of the numerators of Bernoulli numbers as a sequence of primes, and then restore them to of a complete number using the Chinese remainder theorem.
Babbage vs. Hell?
The Analytical Engine and its creation were Babbage's life's work. So what did Ada bring? Ada saw herself primarily as an interpreter of his work. Babbage showed her many plans and examples of the Analytical Engine. She wanted to present a big picture vision of it, how everything is connected; as she put it: " bring a general, large-scale, metaphysical vision".The surviving archive of Babbage's papers (years later found in the leather suitcase of their family's lawyer) contains a large number of descriptions of the principles of the Analytical Engine - from 1830 onwards through the decades, with headings like “ Analytical Engine" And " The Science of Numbers Reduces to Mechanisms" Why Babbage did not publish any of them is not clear. They present very detailed descriptions of the basic principles of the machine, although they certainly seem decidedly less interesting than Ada's work.
Babbage died while working on " History of the Analytical Engine", which was then completed by his son. It contains a dated list of " 446 remarks about the analytical engine", each of which tells how some operation - say division - can be implemented on it. The dates begin in the 1830s, continuing into the 1840s, but with almost no entries in the summer of 1843.
Meanwhile, in the collection of Babbage's papers on display at the Science Museum, there are some sketches of high-level operations for the Analytical Engine. For example, an entry from 1837: " difference between two first degree equations", which is the essence of the assessment of a rational function:
There are some very simple recurrence relations:
Then, in an entry from 1838, the calculation of the coefficients of the product of two polynomials is described:
But there is nothing in his notes comparable in complexity and clarity to Ada's calculations of Bernoulli numbers. Babbage certainly helped Ada in her work, but she was definitely at the head of this work.
So, what did Babbage say about this? In his autobiography, written 26 years later, he wrote few good things about anyone or anything. Here's what he writes about Ada's recordings: " Together we discussed various illustrations that could be submitted for publication; I suggested several, but the choice was entirely hers. There was also work on various algebraic problems, except, of course, those related to Bernoulli numbers, which I volunteered to solve on my own in order to protect Lady Lovelace from unnecessary trouble. She then forwarded the corrected version to me, having discovered the blunder I had made."
When I first read this, it was as if Babbage was saying that he was the literary negro of all Ada's notes. But re-reading, I realized that he was only saying that he offered Ada various options that she could accept or refuse them.
To me, there is no doubt about how it went: Ada had an idea about what the Analytical Engine could do, and asked Babbage how it could be implemented. In my personal experience working with hardware designers, their answers were often quite detailed. Ada's achievement was to connect these parts into a clear representation of the principles of the machine - something Babbage never did. (In his autobiography, he often simply refers to Ada’s notes.)
Babbage's Secret Ingredient
For all his shortcomings, the fact that Babbage figured out how to build a (functioning) difference engine, let alone an Analytical Engine, is quite impressive. So how did he do it? I think the key was in its mechanical notation. He first wrote about it in 1826 in an article entitled " Methods for designating machine operations using signs"His idea was to take the detailed structure of a machine and represent it using symbolic diagrams of how the components should interact with each other. As a first example, he gives a hydraulic device:
He then gives the example of a watch, showing in a sort of "execution trace" on the left how the parameters of the watch's components change, and on the right what appears to be a flowchart of their interconnections:
This is a pretty good way of representing how a system works, similar in some respects to modern timing diagrams, but still different in some ways. And over the years that Babbage spent working on the Analytical Engine, his notes began to contain increasingly complex diagrams. It's not entirely clear what the following means:
However, one can notice a surprising similarity with modern representations in the Modelica language, such as, say, in Wolfram SystemModeler. (One of the differences with modern representations is that nowadays subsystems are represented much more hierarchically, and also that all representations are now computable, and from them the actual behavior of the system can be modeled.)
Babbage made extensive use of his various diagrams in his writings, but never published anything about them. Indeed, his only other printed work on mechanical notation is a booklet distributed at the 1851 World's Fair - apparently as a step towards standardizing drawings of mechanical components (and notations like the above appear periodically on Babbage's diagrams ).
I'm not sure why Babbage didn't write more about his mechanical notation and diagrams. Perhaps he was bitter that people in 1826 failed to recognize the value of these ideas. Or perhaps he saw them as " secret ingredient", allowing him to create his own projects. And even though engineering systems have come a long way since the days of Babbage, his ideas can still serve as a source of inspiration.
On a larger scale
So what does what happened with Ada, Babbage and the Analytical Engine look like on a larger scale?Charles Babbage was an energetic man who had many ideas, some of them very good. In his 30s, he wanted to create mathematical tables using a machine, and he never gave up his idea for the next 49 years, while inventing the Analytical Engine to achieve this goal. He was excellent, perhaps even gifted, when it came to engineering. But he was very bad in choosing a trajectory for the project, in its management.
Ada Lovelace was an intelligent woman who became friends with Babbage (there is no evidence they ever had anything romantic). Thanks to Babbage, she described the working principles of the Analytical Engine, and in doing so brought a more abstract vision of it than Babbage's, as well as an idea of the incredibly powerful idea of universal computing.
The difference engine and similar devices are special-purpose computers, the hardware of which is designed only to do one specific thing. It would seem that in order to do many different things, you would need a large number of different computers. But that's not true. Instead, we are faced with the fundamental fact that it is possible to make general-purpose computers where a single, fixed piece of hardware can be programmed to perform any computation. And it was this idea of universal computing that enabled software to exist, which launched the computer revolution of the 20th century.
Babbage's basic concept for the Analytical Engine was to automatically create mathematical tables and then print them or display them as graphs. He envisioned these tables being used by humans, plus he was developing the idea of some pre-computed map libraries that would be machine-readable versions.
Nowadays, in, say, the Wolfram Language, there is no need to store mathematical tables; you can simply figure out what you need and when you need it. But in the time of Babbage, with his idea of a huge analytical engine, this was simply unthinkable.
Okay, but would the Analytical Engine be used for anything other than calculating mathematical tables? I think yes. If Ada had lived as long as Babbage, she would have seen the 1890s, the time when Herman Hollerith was developing a map-based electromechanical device for the census (who, incidentally, was one of the founders of what would become IBM ). The Analytical Engine could provide much more.
Perhaps Ada would realize her idea of using the Analytical Engine to automatically create algorithmic music. Perhaps the machine would be used to solve the three-body problem; maybe even through simulation. If they had thought of using a binary system, perhaps they would have implemented systems like cellular automata.
Neither Babbage nor Ada ever made money from commerce (and, as Babbage was at pains to emphasize, his government contracts served only to pay his engineers, and he himself received nothing). If they developed an analytics engine, could they find a business model to implement it? Surely they would sell several versions to various government agencies. Perhaps they would create some kind of remote computing service in the service of Victorian science, technology, finance and other things.
But none of this actually happened, and instead Ada died young, the Analytical Engine was never completed, and the potential of computing was only rediscovered in the 20th century.
What were they like?
If you met Babbage, what would he seem like? He was, it seems to me, a good conversationalist. At the beginning of his life he was an idealist (" do my best to leave the world wiser than the one I came into"); later he became an almost Dickensian caricature of a bitter old man. He gave wonderful parties and attached great importance to connections with the intellectual elite. But, especially in recent years, he spent most of his time alone in his large house, filled with books, articles and unfinished projects.Babbage had little understanding of people, and even in his eighties he was like a child in his polemics. He also had problems focusing on any one problem - he was constantly distracted by his new ideas. There was only one big exception - his almost 50 years of work in trying to automate the computing process.
I myself have been pursuing similar goals (more precisely, their modern versions) in my life (..., Mathematica, Wolfram|Alpha, Wolfram Language, ...), but so far only for forty years. I'm fortunate to live in a time when technology makes this much easier to achieve, but every major project I've undertaken has required a tremendous amount of dedication, tenacity, and leadership to see it through to completion.
So what can we say about Hell? First and foremost, he is a articulate and clear-thinking individual. She came from an upper class background, but did not wear particularly fashionable clothes, and was much less a stereotypical countess than an intellectual. She was an adult and emotionally mature person; probably more mature than Babbage, and seems to have had a good applied understanding of people and the world around them.
Like Babbage, she was rich and did not have to work to support her life. But she was ambitious and wanted to do something herself. I guess behind the mask of a high-society Victorian lady was a kind of nerd with math jokes and other trappings. She was also very focused and persistent, spending several months writing her notes, for example.
In mathematics, she successfully reached the level of knowledge of those times; perhaps equaling Babbage. However, we do not know, unlike the situation with Babbage, what exactly she did in mathematics, so it is difficult to judge her level; Babbage was respected, although unremarkable.
When you read Ada's letters, you seem to be an intelligent, complex person with clear logical thinking. Her speeches are often cloaked in Victorian pleasantries, but underneath are clear and often powerful ideas.
Ada was clearly aware of her position in society, and that she was “Lord Byron’s daughter.” In a way, her success story is based on her ambition and desire to try something new. (I can't stop comparing her as the lead engineer in creating the Analytical Engine and Lord Byron leading the Greek army). But I also suspect that his problems affected her. For many years, partly due to her mother's influence, she shied away from such things as poetry. Her gaze was turned to abstract things, and not only to mathematics and science, but also to more metaphysical areas.
And she seems to have concluded that her best application would be to work in the unification of the scientific and the metaphysical - perhaps that is what she called " poetic science"Perhaps her self-perception was correct. After all, in a sense, this is exactly what she was doing: taking the engineering part developed by Babbage, she created an abstract, “metaphysical” concept, which later gave us our first idea of the idea of universal computing .
Conclusion
The story of Ada and Babbage has many interesting aspects. This is a story about the meeting of technical mastery and broad abstract vision. This is a story about friendship between an old and a young man. This is a story of people who had the courage to be original and creative.It's also a tragedy. A tragedy for Babbage, who lost so many people in his life, and whose personality alienated others and prevented him from realizing his ambitions. It’s a tragedy for Ada, who had just found her life’s work when her health deteriorated.
We will never know what Ada could have done. Another Mary Somerville - a famous interpreter of Victorian science? A kind of Steve Jobs shaping the vision of the Analytical Engine? Or Alan Turing understanding the abstract idea of universal computing?
That Ada touched what would become the defining idea of our time was a great stroke of luck. Babbage did not understand what he was dealing with; Ada saw glimpses and successfully described them.
For some people, particularly me, the story of Ada and Babbage has a special resonance. Like Babbage, I spent most of my life pursuing specific goals, although, unlike Babbage, I was able to realize some of them. And I suspect that, like Ada, I was given the opportunity to see glimpses of some significant ideas of the future.
But the problem is that sufficiently " be Ada"to understand what awaits us, or at least" find that Ada", who understands. At least now, I think I have an understanding of what the same Ada was like, born 200 years ago: a worthy person on the path to universal computing, present and future achievements in the field of computational thinking.
It was very nice to meet you, Ada. Acknowledgments
Many organizations and people helped me obtain information and materials for this post. I would like to thank the British Library, the History of Science Museum, Oxford, the Science Museum, London, the Bodleian Library, Oxford (by permission of the Earl of Lytton, Ada's great-great-grandson, one of her 10 living descendants), the New York Public Library, St. Mary Magdalene (in Hucknall, Nottinghamshire - burial place of Ada), Betty Toole (author Add tags
Augusta Ada Byron-King, whose birthday is 201 on December 10, went down in history not only as the daughter of the poet Lord Byron, but also as the first computer programmer. The mathematician countess described a computer and wrote the first program at a time when computers did not yet exist.
A. E. Shalon. Watercolor portrait of Ada King, Countess of Lovelace. Fragment
The programming language Ada is named after her, and the terminology introduced by Lady Byron is still used today. The Countess was so smart and attractive that her contemporaries accused her of having connections with the devil, but she did not deny this.
Ada Byron as a child
Ada's father Lord Byron
The famous father saw his daughter only once, at the age of one month. She was born in December 1815, and in April 1816 George Gordon Byron divorced his wife and left England. The girl was named Augusta in honor of Byron's sister, but after the divorce in her mother's house no one spoke this name; everyone called her Ada. And all her father’s books were removed from the family library.
Ada's mother Annabella Milbank
Ada's parents: George Gordon Byron and Annabella Milbank
The girl inherited her love for exact sciences from her mother, Annabella Milbank-Byron, who was called the “queen of parallelograms.” Noticing her daughter’s abilities, the mother invited her former teacher, Scottish mathematician A. de Morgan, and his wife M. Somerville to study with her. At the age of 13, Ada was already drawing drawings of aircraft in her album.
A. de Morgan and M. Somerville
From her mentor, Ada first heard the name of Charles Babbage, a professor of mathematics at Cambridge University, and soon met him personally. At that time, he was developing a design for a calculating machine that could perform calculations with an accuracy of up to the twentieth digit. The project was never implemented, but Ada took part in the development. While translating the work of the Italian scientist L. Menebrea, she provided the text with such detailed comments and observations that she surpassed the author himself.
Charles Babbage and his difference engine
She managed to discern in the machine being described something that even the inventor did not suspect: “The essence and purpose of the machine will change depending on what information we put into it. The machine will be able to write music, draw pictures and show science ways that we have never seen anywhere.” Ada foresaw the possibilities of the computer even before it was created. She described an algorithm for calculating Bernoulli numbers on the Analytical Engine. It was the first program written for a computer, and although Babbage's machine was never built during his lifetime, Ada is considered the first programmer.
Augusta Ada Byron at age 17
In secular society, Countess Lovelace made a splash. She had not only a remarkable mind, but also stunning beauty. Because of this, contemporaries suspected her of conspiring with the devil. Ada not only did not deny these rumors, but also added fuel to the fire with her statements. So, in a letter to Babbage, she declared, not without coquetry: “I am a devil or an angel. I work like the devil for you, Charles Babbage; I’m sifting through Bernoulli’s numbers for you.” And another time she self-confidently asserted: “I swear to the devil, not even ten years will pass and I will suck enough life juice from the secrets of the universe. In a way that ordinary mortal minds and lips cannot do. No one knows what monstrous power lies still untapped in my little flexible creature.”
Margaret Sarah Carpenter. Portrait of Ada Lovelace, 1836
Ada did not give up her studies even after marriage and the birth of three children. Her husband was Baron King, who soon inherited the title of Lord Lovelace. He did not interfere with his wife’s hobbies and provided her with significant financial support. She herself tried to earn money, and in a very unusual way. Together with Babbage, they began to develop a win-win betting system on horse races - Countess Lovelace was a gambler. Having lost an impressive amount, she did not stop and continued to play. Secretly from her loved ones, Ada spent all her personal money on the races. Once she even became a victim of blackmailers who threatened to reveal her secret.
Unknown artist. Portrait of Ada Lovelace, c. 1840
Ada Lovelace
They say that only the sudden death of Ada saved the Lovelace family from complete ruin. The Countess died in 1852 from cancer, a few days short of turning 37, just like her father. She was buried in the Byron family crypt, next to her father, whom she had never seen. The ideas of Ada Lovelace and Charles Babbage were developed only a century later: in 1991, a mechanical computing machine was built based on Babbage’s drawings, and although its speed was incomparable with modern computers, it was this machine that gave impetus to their creation.
A computer created according to Babbage's drawings
The name of one of the smartest women of the early 19th century became known only decades after her death. Until now, she remains in the shadow of her male colleagues. In most specialized textbooks there is not a single word about it. Meanwhile, the contribution of Ada Lovelace, née Byron, to the development of programming can rightfully be considered enormous.
Augusta Ada Byron was born on December 10, 1815, the only legitimate child of the English poet George Gordon Byron and his wife Anna Isabella Byron (Anabella). However, she was never destined to meet her famous father: the first and last time Byron saw his daughter was a month after birth. And on April 21, 1816, he signed an official divorce and left England forever.
The girl received her first name Augusta in honor of Byron's half-sister, with whom he was rumored to have had an affair. After the divorce, the mother and mother's parents never called the girl by this name, but called her Ada. Moreover, all of her father’s books were removed from the family library.
Bo More than anything else, Ada’s mother was worried that her daughter would inherit her father’s passion for writing and grow up to be just as eccentric and hot-tempered. Therefore, from an early age, she did not welcome the girl’s passion for reading prose and poetry. Fortunately, her daughter inherited an interest in exact sciences from her mother - after all, Byron called Anabella herself the “Queen of Parallelograms.”
To teach her daughter, ex-Mrs. Byron invited her teacher, the mathematician Augustus de Morgan. As a result, at the age of 13, Ada had already created several drawings of aircraft. Another mentor of the girl was Mary Somerville, who at one time translated from French “Treatise on Celestial Mechanics” by mathematician and astronomer Pierre-Simon Laplace. It was Mary who became a role model for her pupil.
In 1833, 16-year-old Ada met Charles Babbage, a professor of mathematics at Cambridge University. This meeting determined her life path. A few years earlier, Babbage had completed a description of a calculating machine that could perform calculations accurate to the twentieth digit. A drawing with numerous rollers and gears, which were driven by a lever, lay on the Prime Minister’s desk. In 1823, the first subsidy was paid to build what is now known as Babbage's Large Difference Engine and is considered to be the first computer on Earth! Construction lasted ten years, the design of the machine became more and more complicated, but in 1833 funding was stopped.
Ada became a close friend, assistant and the only like-minded person of the scientist. Moreover, even the fact that at the age of 19 she married Lord Lovelace did not prevent her from seriously pursuing science. Whether it was love or whether it was guided by precise calculation and pragmatism, one can only guess. However, the marriage turned out to be very successful in all respects. The husband did not interfere with his wife’s hobbies and even financed them from the Lovelaces’ rich treasury. Even three children of the same age could not extinguish the flame of passion for science that raged inside Ada.
The basis for calling Ada Lovelace the world's first programmer comes from the work she created, consisting of a translation into English of an article describing Babbage's invention. However, this was not just a translation. Ada supplemented the text with detailed comments, increasing its volume more than three times. They, in particular, discussed the development of an operational plan for the analytical engine. This was the first programming! Its “operations,” according to the creator herself, endowed the computer with the amazing ability to weave algebraic formulas, like a Jacquard loom that creates leaves, flowers, and patterns from yarn.
For example, in one of his comments, Ada describes an algorithm for calculating Bernoulli numbers on the Analytical Engine. It was recognized that this was the first program specifically implemented for playback on a computer!
Nature generously endowed Ada with not only beauty and intelligence, but also insight. Another passion of the Countess was music. One day she boldly suggested that the time would come when a computing machine would become so advanced that it would be able to create amazing pieces of music. Well, today we are able to assess the accuracy of its forecasts. It is no coincidence that Ada’s mind was highly valued by the outstanding personalities of the era with whom she was familiar: Michael Faraday, David Brewster, Charles Wheatstone, Charles Dickens and others.
Unfortunately, medicine in those years could not boast of scientists who were ahead of their time, like Ada Lovelace. On November 27, 1852, at the age of 36, Ada Lovelace died from bloodletting while attempting to treat uterine cancer.
