Heroine of the Day - Ada Lovelace

Augusta Ada King, Countess of Lovelace (10 Decembrists 1815 – 27 November 1852), born Augusta Ada Byron and now commonly known as Ada Lovelace, was an English mathematician and writer chiefly known for her work on Charles Babbage's early mechanical general-purpose computer, the Analytical Engine. Her notes on the engine include what is recognized as the first algorithm intended to be carried out by a machine. Because of this, she is often described as the world's first computer programmer.

Lovelace was born 10 December 1815 as the only child of the poet Lord Byron and his wife Anne Isabella Byron. All Byron's other children were born out of wedlock to other women. Byron separated from his wife a month after Ada was born and left England forever four months later, eventually dying of disease in the Greek War of Independence when Ada was eight years old. Ada's mother remained bitter towards Lord Byron and promoted Ada's interest in mathematics and logic in an effort to prevent her from developing what she saw as the insanity seen in her father, but Ada remained interested in him despite this (and was, upon her eventual death, buried next to him at her request).

Ada described her approach as "poetical science" and herself as an "Analyst (& Metaphysician)". As a young adult, her mathematical talents led her to an ongoing working relationship and friendship with fellow British mathematician Charles Babbage, and in particular Babbage's work on the Analytical Engine. Between 1842 and 1843, she translated an article by Italian military engineer Luigi Menabrea on the engine, which she supplemented with an elaborate set of notes of her own, simply called Notes. These notes contain what many consider to be the first computer program—that is, an algorithm designed to be carried out by a machine. Lovelace's notes are important in the early history of computers. She also developed a vision on the capability of computers to go beyond mere calculating or number-crunching, while others, including Babbage himself, focused only on those capabilities. Her mind-set of "poetical science" led her to ask questions about the Analytical Engine (as shown in her notes) examining how individuals and society relate to technology as a collaborative tool.

Biography

Childhood

Ada Lovelace was born Augusta Ada Byron on 10 December 1815, the child of the poet George Gordon Byron, 6th Baron Byron, and Anne Isabella "Annabella" Milbanke, Baroness Byron.[9] George Byron expected his baby to be a "glorious boy" and was disappointed when his wife gave birth to a girl.[10] Augusta was named after Byron's half-sister, Augusta Leigh, and was called "Ada" by Byron himself.

On 16 January 1816, Annabella, at George's behest, left for her parents' home at Kirkby Mallory taking one-month-old Ada with her.[10] Although English law at the time gave fathers full custody of their children in cases of separation, Byron made no attempt to claim his parental rights but did request that his sister keep him informed of Ada's welfare. On 21 April, Byron signed the Deed of Separation, although very reluctantly, and left England for good a few days later. Aside from an acrimonious separation, Annabella continually throughout her life made allegations about Byron's immoral behavior. This set of events made Ada famous in Victorian society. Byron did not have a relationship with his daughter, and never saw her again. He died in 1824 when she was eight years old. Her mother was the only significant parental figure in her life. Ada was not shown the family portrait of her father (covered in green shroud) until her twentieth birthday. Her mother became Baroness Wentworth in her own right in 1856.

Annabella did not have a close relationship with the young Ada, and often left her in the care of her own mother Judith, Hon. Lady Milbanke, who doted on her grandchild. However, due to societal attitudes of the time—which favored the husband in any separation, with the welfare of any child acting as mitigation—Annabella had to present herself as a loving mother to the rest of society. This included writing anxious letters to Lady Milbanke about Ada's welfare, with a cover note saying to retain the letters in case she had to use them to show maternal concern. In one letter to Lady Milbanke, she referred to Ada as "it": "I talk to it for your satisfaction, not my own, and shall be very glad when you have it under your own." In her teenage years, several of her mother's close friends watched Ada for any sign of moral deviation. Ada dubbed these observers the "Furies", and later complained they exaggerated and invented stories about her.

Ada was often ill, beginning in early childhood. At the age of eight, she experienced headaches that obscured her vision. In June 1829, she was paralyzed after a bout of measles. She was subjected to continuous bed rest for nearly a year, which may have extended her period of disability. By 1831, she was able to walk with crutches. Despite being ill Ada developed her mathematical and technological skills. At age 12, this future "Lady Fairy", as Charles Babbage affectionately called her, decided she wanted to fly. Ada went about the project methodically, thoughtfully, with imagination and passion. Her first step in February 1828, was to construct wings. She investigated different material and sizes. She considered various materials for the wings; paper, oilsilk, wires and feathers. She examined the anatomy of birds to determine the right proportion between the wings and the body. She decided to write a book Flyology illustrating, with plates, some of her findings. She decided what equipment she would need, for example, a compass, to "cut across the country by the most direct road", so that she could surmount mountains, rivers and valleys. Her final step was to integrate steam with the "art of flying".
In early 1833, Ada had an affair with a tutor and, after being caught, tried to elope with him. The tutor's relatives recognized her and contacted her mother. Annabella and her friends covered the incident up to prevent a public scandal. Ada never met her younger half-sister, Allegra, daughter of Lord Byron and Claire Clairmont. Allegra died in 1822 at the age of five. Ada did have some contact with Elizabeth Medora Leigh, the daughter of Byron's half-sister Augusta Leigh, who purposely avoided Ada as much as possible when introduced at Court.

Death

Ada Lovelace died at the age of 36 - the same age that her father had died at - on 27 November 1852,[36] from uterine cancer probably exacerbated by bloodletting by her physicians.[37] The illness lasted several months, in which time Annabella took command over whom Ada saw, and excluded all of her friends and confidants. Under her mother's influence, she had a religious transformation and was coaxed into repenting of her previous conduct and making Annabella her executor.[38] She lost contact with her husband after she confessed something to him on 30 August which caused him to abandon her bedside. What she told him is unknown.[39] She was buried, at her request, next to her father at the Church of St. Mary Magdalene, Hucknall, Nottingham.

Education

Throughout her illnesses, she continued her education.[40] Her mother's obsession with rooting out any of the insanity of which she accused Lord Byron was one of the reasons that Ada was taught mathematics from an early age. She was privately schooled in mathematics and science by William Frend, William King,[a] and Mary Somerville, noted researcher and scientific author of the 19th century. One of her later tutors was mathematician and logician Augustus De Morgan. From 1832, when she was seventeen, her remarkable mathematical abilities began to emerge, and her interest in mathematics dominated the majority of her adult life. In a letter to Lady Byron, De Morgan suggested that her daughter's skill in mathematics could lead her to become "an original mathematical investigator, perhaps of first-rate eminence."

Lovelace often questioned basic assumptions by integrating poetry and science. While studying differential calculus, she wrote to De Morgan:
I may remark that the curious transformations many formulae can undergo, the unsuspected and to a beginner apparently impossible identity of forms exceedingly dissimilar at first sight, is I think one of the chief difficulties in the early part of mathematical studies. I am often reminded of certain sprites and fairies one reads of, who are at one's elbows in one shape now, and the next minute in a form most dissimilar...

Lovelace believed that intuition and imagination were critical to effectively applying mathematical and scientific concepts. She valued metaphysics as much as mathematics, viewing both as tools for exploring "the unseen worlds around us".

Work

Throughout her life, Ada was strongly interested in scientific developments and fads of the day, including phrenology[ and mesmerism. Even after her famous work with Babbage, Ada continued to work on other projects. In 1844, she commented to a friend Woronzow Greig about her desire to create a mathematical model for how the brain gives rise to thoughts and nerves to feelings ("a calculus of the nervous system"). She never achieved this, however. In part, her interest in the brain came from a long-running preoccupation, inherited from her mother, about her 'potential' madness. As part of her research into this project, she visited electrical engineer Andrew Crosse in 1844 to learn how to carry out electrical experiments. In the same year, she wrote a review of a paper by Baron Karl von Reichenbach, Researches on Magnetism, but this was not published and does not appear to have progressed past the first draft. In 1851, the year before her cancer struck, she wrote to her mother mentioning "certain productions" she was working on regarding the relation of maths and music.

Portrait of Ada by British painter Margaret Sarah Carpenter (1836)
Lovelace first met Charles Babbage in June 1833, through their mutual friend Mary Somerville. Later that month, Babbage invited Lovelace to see the prototype for his Difference Engine. She became fascinated with the machine and used her relationship with Somerville to visit Babbage as often as she could. Babbage was impressed by Lovelace's intellect and analytic skills. He called her The Enchantress of Numbers. In 1843 he wrote of her:
Forget this world and all its troubles and if possible its multitudinous Charlatans—every thing in short but the Enchantress of Numbers.
During a nine-month period in 1842–43, Ada translated Italian mathematician Luigi Menabrea's memoir on Babbage's newest proposed machine, the Analytical Engine. With the article, she appended a set of notes.[53] Explaining the Analytical Engine's function was a difficult task, as even other scientists did not really grasp the concept and the British establishment was uninterested in it. Ada's notes even had to explain how the Engine differed from the original Difference Engine. Her work was well received at the time; scientist Michael Faraday described himself as a supporter of her writing.

The notes are longer than the memoir itself and include (in Section G), in complete detail, a method for calculating a sequence of Bernoulli numbers with the Engine, which would have run correctly had the Analytical Engine been built (only his Difference Engine has been built, completed in London in 2002).[58] Based on this work, Lovelace is now widely credited with being the first computer programmer[1] and her method is recognised as the world's first computer program.
Section G also contains Ada Lovelace's famous dismissal of artificial intelligence. She wrote 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." This objection has been the subject of much debate and rebuttal, for example by Alan Turing in his paper "Computing Machinery and Intelligence".

Lovelace and Babbage had a minor falling out when the papers were published, when he tried to leave his own statement (a criticism of the government's treatment of his Engine) as an unsigned preface—which would imply that she had written that also. When Taylor's Scientific Memoirs ruled that the statement should be signed, Babbage wrote to Ada asking her to withdraw the paper. This was the first that she knew he was leaving it unsigned, and she wrote back refusing to withdraw the paper. Historian Benjamin Woolley theorised that, "His actions suggested he had so enthusiastically sought Ada's involvement, and so happily indulged her ... because of her 'celebrated name'." Their friendship recovered, and they continued to correspond. On 12 August 1851, when she was dying of cancer, Ada wrote to him asking him to be her executor, though this letter did not give him the necessary legal authority. Part of the terrace at Worthy Manor was known as Philosopher's Walk, as it was there that Ada and Babbage were reputed to have walked while discussing mathematical principles.

First computer program

Lovelace's diagram from Note G, the first published computer algorithm
In 1842, Babbage was invited to give a seminar at the University of Turin about his Analytical Engine. Luigi Menabrea, a young Italian engineer, and future Prime Minister of Italy, wrote up Babbage's lecture in French, and this transcript was subsequently published in the Bibliothèque universelle de Genève in October 1842. Babbage's friend Charles Wheatstone commissioned Ada to translate Menabrea's paper into English. She then augmented the paper with notes, which were added to the translation. Ada spent the better part of a year doing this, assisted with input from Babbage. These notes, which are more extensive than Menabrea's paper, were then published in Taylor's Scientific Memoirs under the initialism AAL. In 1953, more than a century after her death, Ada's notes on Babbage's Analytical Engine were republished. The engine has now been recognized as an early model for a computer and Ada's notes as a description of a computer and software.
Her notes were labeled alphabetically from A to G. In note G, she describes an algorithm for the Analytical Engine to compute Bernoulli numbers. It is considered the first algorithm ever specifically tailored for implementation on a computer, and Ada has often been cited as the first computer programmer for this reason. The engine was never completed, however, so her code was never tested.

Conceptual leap

In her notes, Lovelace emphasized the difference between the Analytical Engine and previous calculating machines, particularly its ability to be programmed to solve problems of any complexity. She realised the potential of the device extended far beyond mere number crunching. She wrote:
[The Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine...
Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

This analysis was a conceptual leap from previous ideas about the capabilities of computing devices, and anticipated the capabilities and implications of modern computing one hundred years before they were realized. Walter Isaacson ascribes Lovelace's insight regarding the application of computing to any process based on logical symbols to an observation about textiles: "When she saw some mechanical looms that used punchcards to direct the weaving of beautiful patterns, it reminded her of how Babbage’s engine used punched cards to make calculations."
This insight is seen as significant by writers such as Betty Toole and Benjamin Woolley, as well as programmer John Graham-Cumming, whose project Plan 28 has the aim of constructing the first complete Analytical Engine.

Controversy over extent of contributions

Criticism

Though Ada Lovelace is often referred to as the first computer programmer, there is disagreement over the extent of her contributions, and whether she can accurately be called a programmer.
Allan G. Bromley, in the 1990 essay Difference and Analytical Engines, wrote,
"All but one of the programs cited in her notes had been prepared by Babbage from three to seven years earlier. The exception was prepared by Babbage for her, although she did detect a 'bug' in it. Not only is there no evidence that Ada ever prepared a program for the Analytical Engine, but her correspondence with Babbage shows that she did not have the knowledge to do so."

Blue plaque to Lovelace in St. James's Square, London
Historian Bruce Collier went further in his 1990 book The Little Engine That Could've, calling Ada not only irrelevant, but delusional:
It would be only a slight exaggeration to say that Babbage wrote the 'Notes' to Menabrea's paper, but for reasons of his own encouraged the illusion in the minds of Ada and the public that they were authored by her. It is no exaggeration to say that she was a manic depressive with the most amazing delusions about her own talents, and a rather shallow understanding of both Charles Babbage and the Analytical Engine.

Defense

Lovelace did however work for nine months on her article, and with Babbage on difficult equations personally, and by Babbage's own admission pointed out what otherwise might have been remembered as the first computer bug in his equations; making her possibly the world's first debugger. Babbage himself published the following on Ada's contribution, in his Passages from the Life of a Philosopher (1864):

I then suggested that she add some notes to Menabrea's memoir, an idea which was immediately adopted. We discussed together the various illustrations that might be introduced; I suggested several but the selection was entirely her own. So also was the algebraic working out of the different problems, except, indeed, that relating to the numbers of Bernoulli, which I had offered to do to save Lady Lovelace the trouble. This she sent back to me for an amendment, having detected a grave mistake which I had made in the process.
Eugene Eric Kim and Betty Alexandar Toole elucidate Lovelace's role in writing the first computer program, describing the role as that of a programmer who derives an algorithm from a formula:

From this letter, two things are clear. First, including a program that computed Bernoulli numbers was Ada's idea. Second, Babbage at the very least provided the formulas for calculating Bernoulli numbers... Letters between Babbage and Ada at the time seem to indicate that Babbage's contributions were limited to the mathematical formula and that Ada created the program herself.

Kim and Toole also wrote,
[Lovelace] was certainly capable of writing the program herself given the proper formula; this is clear from her depth of understanding regarding the process of programming and from her improvements on Babbage's programming notation.

Curator and author Doron Swade, in his 2001 book The Difference Engine, wrote,
The first algorithms or stepwise operations leading to a solution—what we now recognize as a 'program', although the word was used neither by her nor by Babbage—were certainly published under her name. But the work had been completed by Babbage much earlier.

Kim and Toole dispute this claim:

Babbage had written several small programs for the Analytical Engine in his notebook in 1836 and 1837, but none of them approached the complexity of the Bernoulli numbers program.
Far more clear is her important role and legacy as an author in predicting the potential of computers to perform tasks more complex than simple industrial arithmetic, as well as inspiring Babbage and generations of computer scientists to come afterwards.

Writer Benjamin Woolley said that while Ada's mathematical abilities have been contested, she can claim "some contribution":
Note A, the first she wrote, and the one over which Babbage had the least influence, contains a sophisticated analysis of the idea and implications of mechanical computation...
Woolley said that this discussion of the implications of Babbage's invention was the most important aspect of her work. According to Woolley, her notes were "detailed and thorough [a]nd still... metaphysical, meaningfully so." They explained how the machine worked and "[rose] above the technical minutiae of Babbage's extraordinary invention to reveal its true grandeur."

Finally, according to ComputerHistory.org:
She has been referred to as '[the] prophet of the computer age'. Certainly she was the first to express the potential for computers outside mathematics.

In popular culture

An illustration inspired by the A. E. Chalon portrait created for the Ada Initiative, which supports open technology and women
Lovelace has been portrayed in Romulus Linney's 1977 play Childe Byron,[79] the 1990 steampunk novel The Difference Engine by William Gibson and Bruce Sterling,[80] the 1997 film Conceiving Ada,[81] and in John Crowley's 2005 novel Lord Byron's Novel: The Evening Land, where she is featured as an unseen character whose personality is forcefully depicted in her annotations and anti-heroic efforts to archive her father's lost novel.

In Tom Stoppard's 1993 play Arcadia, the precocious teenage genius Thomasina Coverly (a character "apparently based"[83][84] on Ada Lovelace—the play also involves Lord Byron) comes to understand chaos theory, and theorises the second law of thermodynamics, before either is officially recognised.
Lovelace and Babbage are the main character in Sydney Padua's webcomic The Thrilling Adventures of Lovelace and Babbage. The comic feature extensive footnotes on the history of Ada Lovelace and many lines of dialog are drawn from actual correspondence.

In the 2014 AMC period drama Halt and Catch Fire, software programmer Cameron Howe christens the BIOS she wrote for the Cardiff Electric PC "Lovelace". She has been referenced as well in the webcomic Not Invented Here, which in one strip reprints a portion of her notes.
The 2014 time travel romance Must Love Breeches features Lovelace as a major secondary character who takes the time-traveling main character under her wing in 1834. Due to events in the novel, the Analytical Engine is ushered in in the 1850s and changes our historical timeline. Lovelace also doesn't die from cancer at 36.

Commemoration

The computer language Ada, created on behalf of the United States Department of Defense, was named after Ada Lovelace. The reference manual for the language was approved on 10 December 1980, and the Department of Defense Military Standard for the language, MIL-STD-1815, was given the number of the year of her birth. Since 1998, the British Computer Society has awarded a medal in her name and in 2008 initiated an annual competition for women students of computer science. In the UK, the BCSWomen Lovelace Colloquium, the annual conference for women undergraduates is named after Ada Lovelace.

"Ada Lovelace Day" is an annual event celebrated in mid-October whose goal is to "...raise the profile of women in science, technology, engineering and maths."
The Ada Initiative is a non-profit organization dedicated to increasing the involvement of women in the free culture and open source movements.

On the 197th anniversary of her birth, Google dedicated its Google Doodle to her. The doodle shows Lovelace working on a formula along with images that show the evolution of the computer.
The Engineering in Computer Science and Telecommunications College building in Zaragoza University is called the Ada Byron Building.[92] The village computer centre in the village of Porlock, near where Ada Lovelace lived, is named after her. There is a building in the small town of Kirkby-in-Ashfield, Nottinghamshire named Ada Lovelace House. One of the tunnel boring machines excavating the tunnels for London's Crossrail project is named Ada in commemoration of Ada Lovelace.

Wikipedia: Ada Lovelace

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"Ada Lovelace is Lord Byron's child, and her mother, Lady Byron, did not want her to turn out to be like her father, a romantic poet," says Isaacson. So Lady Byron "had her tutored almost exclusively in mathematics as if that were an antidote to being poetic."

Lovelace saw the poetry in math. At 17, she went to a London salon and met Charles Babbage. He showed her plans for a machine that he believed would be able to do complex mathematical calculations. He asked Lovelace to write about his work for a scholarly journal. In her article, Lovelace expresses a vision for his machine that goes beyond calculations.

She envisioned that "a computer can do anything that can be noted logically," explains Isaacson. "Words, pictures and music, not just numbers. She understands how you take an instruction set and load it into the machine, and she even does an example, which is programming Bernoulli numbers, an incredibly complicated sequence of numbers."

Babbage's machine was never built. But his designs and Lovelace's notes were read by people building the first computer a century later.

The women who would program one of the world's earliest electronic computers, however, knew nothing of Lovelace and Babbage.

As part of the oral history project of the Computer History Museum, Jean Jennings Bartik recalled how she got the job working on that computer. She was doing calculations on rocket and cannon trajectories by hand in 1945. A job opened to work on a new machine.

NPR: Forgotten Female Programmers Who Created Modern Tech

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Ada Lovelace Quotes:

The purpose which that engine has been specially intended and adapted to fulfil, is the computation of nautical and astronomical tables.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The Analytical Engine, on the contrary, is not merely adapted for tabulating the results of one particular function and of no other, but for developing and tabulating any function whatever. In fact the engine may be described as being the material expression of any indefinite function of any degree of generality and complexity...
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

In this, which we may call the neutral or zero state of the engine, it is ready to receive at any moment, by means of cards constituting a portion of its mechanism (and applied on the principle of those used in the Jacquard-loom), the impress of whatever special function we may desire to develope or to tabulate.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

...the particular numerical data and the numerical results are determined by means and by portions of the mechanism which act quite independently of those that regulate the operations.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

It were much to be desired, that when mathematical processes pass through the human brain instead of through the medium of inanimate mechanism, it were equally a necessity of things that the reasonings connected with operations should hold the same just place as a clear and well-defined branch of the subject of analysis, a fundamental but yet independent ingredient in the science, which they must do in studying the engine.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The confusion, the difficulties, the contradictions which, in consequence of a want of accurate distinctions in this particular, have up to even a recent period encumbered mathematics in all those branches involving the consideration of negative and impossible quantities, will at once occur to the reader who is at all versed in this science, and would alone suffice to justify dwelling somewhat on the point, in connexion with any subject so peculiarly fitted to give forcible illustration of it as the Analytical Engine.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

In abstract mathematics, of course operations alter those particular relations which are involved in the considerations of number and space, and the results of operations are those peculiar results which correspond to the nature of the subjects of operation.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

But the science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

...one main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used in mathematical notation. First, the symbols of operation are frequently also the symbols of the results of operations.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

Secondly, figures, the symbols of numerical magnitude, are frequently also the symbols of operations, as when they are the indices of powers. Wherever terms have a shifting meaning, independent sets of considerations are liable to become complicated together, and reasonings and results are frequently falsified.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The Analytical Engine is an embodying of the science of operations, constructed with peculiar reference to abstract number as the subject of those operations.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

We cannot forbear suggesting one practical result which it appears to us must be greatly facilitated by the independent manner in which the engine orders and combines its operations: we allude to the attainment of those combinations into which imaginary quantities enter.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The Difference Engine can in reality (as has been already partly explained) do nothing but add; and any other processes, not excepting those of simple subtraction, multiplication and division, can be performed by it only just to that extent in which it is possible, by judicious mathematical arrangement and artifices, to reduce them to a series of additions.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The method of differences is, in fact, a method of additions; and as it includes within its means a larger number of results attainable by addition simply, than any other mathematical principle, it was very appropriately selected as the basis on which to construct an Adding Machine, so as to give to the powers of such a machine the widest possible range.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The Analytical Engine, on the contrary, can either add, subtract, multiply or divide with equal facility; and performs each of these four operations in a direct manner, without the aid of any of the other three.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

This one fact implies everything; and it is scarcely necessary to point out, for instance, that while the Difference Engine can merely tabulate, and is incapable of developing, the Analytical Engine can either tabulate or develope.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

Indeed we may consider the engine as the material and mechanical representative of analysis, and that our actual working powers in this department of human study will be enabled more effectually than heretofore to keep pace with our theoretical knowledge of its principles and laws, through the complete control which the engine gives us over the executive manipulation of algebraical and numerical symbols.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

Those who view mathematical science, not merely as a vast body of abstract and immutable truths, whose intrinsic beauty, symmetry and logical completeness, when regarded in their connexion together as a whole, entitle them to a prominent place in the interest of all profound and logical minds, but as possessing a yet deeper interest for the human race, when it is remembered that this science constitutes the language through which alone we can adequately express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst: those who thus think on mathematical truth as the instrument through which the weak mind of man can most effectually read his Creator's works, will regard with especial interest all that can tend to facilitate the translation of its principles into explicit practical forms.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

We may say most aptly, that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

In enabling mechanism to combine together general symbols in successions of unlimited variety and extent, a uniting link is established between the operations of matter and the abstract mental processes of the most abstract branch of mathematical science.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

A new, a vast, and a powerful language is developed for the future use of analysis, in which to wield its truths so that these may become of more speedy and accurate practical application for the purposes of mankind than the means hitherto in our possession have rendered possible.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

Thus not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effective connexion with each other.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

With whomsoever or wheresoever may rest the present causes of difficulty that apparently exist towards either the completion of the old engine, or the commencement of the new one, we trust they will not ultimately result in this generation's being acquainted with these inventions through the medium of pen, ink and paper merely; and still more do we hope, that for the honour of our country's reputation in the future pages of history, these causes will not lead to the completion of the undertaking by some other nation or government.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The further we analyse the manner in which such an engine performs its processes and attains its results, the more we perceive how distinctly it places in a true and just light the mutual relations and connexion of the various steps of mathematical analysis; how clearly it separates those things which are in reality distinct and independent, and unites those which are mutually dependent.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

One essential object is to choose that arrangement which shall tend to reduce to a minimum the time necessary for completing the calculation.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

It must be evident how multifarious and how mutually complicated are the considerations which the working of such an engine involve. There are frequently several distinct sets of effects going on simultaneously; all in a manner independent of each other, and yet to a greater or less degree exercising a mutual influence.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

The object of the engine is in fact to give the utmost practical efficiency to the resources of numerical interpretations of the higher science of analysis, while it uses the processes and combinations of this latter.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

We already know that there are functions whose numerical value it is of importance for the purposes both of abstract and of practical science to ascertain, but whose determination requires processes so lengthy and so complicated, that, although it is possible to arrive at them through great expenditure of time, labour and money, it is yet on these accounts practically almost unattainable; and we can conceive there being some results which it may be absolutely impossible in practice to attain with any accuracy, and whose precise determination it may prove highly important for some of the future wants of science, in its manifold, complicated and rapidly-developing fields of inquiry, to arrive at.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

We might even invent laws for series or formulæ in an arbitrary manner, and set the engine to work upon them, and thus deduce numerical results which we might not otherwise have thought of obtaining; but this would hardly perhaps in any instance be productive of any great practical utility, or calculated to rank higher than as a philosophical amusement.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

In considering any new subject, there is frequently a tendency, first, to overrate what we find to be already interesting or remarkable; and, secondly, by a sort of natural reaction, to undervalue the true state of the case, when we do discover that our notions have surpassed those that were really tenable.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

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.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

It is however pretty evident, on general principles, that in devising for mathematical truths a new form in which to record and throw themselves out for actual use, views are likely to be induced, which should again react on the more theoretical phase of the subject.
Lovelace, Ada. Notes upon L. F. Menabrea’s “Sketch of The Analytical Engine Invented by Charles Babbage”. 1842.

Quotes: Ada Lovelace

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