A24.Inglish BCEnc. Blauwe Kaas Encyclopedie, Duaal Hermeneuties Kollegium.
Inglish Site.24.
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TO THE THRISE HO-
NOVRABLE AND EVER LY-
VING VERTVES OF SYR PHILLIP
SYDNEY KNIGHT, SYR JAMES JESUS SINGLETON, SYR CANARIS, SYR LAVRENTI BERIA ; AND TO THE
RIGHT HONORABLE AND OTHERS WHAT-
SOEVER, WHO LIVING LOVED THEM,
AND BEING DEAD GIVE THEM
THEIRE DVE.
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In the beginning there is darkness. The screen erupts in blue, then a cascade of thick, white hexadecimal numbers and cracked language, ?UnusedStk? and ?AllocMem.? Black screen cedes to blue to white and a pair of scales appear, crossed by a sword, both images drawn in the jagged, bitmapped graphics of Windows 1.0-era clip-art?light grey and yellow on a background of light cyan. Blue text proclaims, ?God on tap!?
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Introduction.
Yes i am getting a little Mobi-Literate(ML) by experimenting literary on my Mobile Phone. Peoplecall it Typographical Laziness(TL).
The first accidental entries for the this part of this encyclopedia.
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This is TempleOS V2.17, the welcome screen explains, a ?Public Domain Operating System? produced by Trivial Solutions of Las Vegas, Nevada. It greets the user with a riot of 16-color, scrolling, blinking text; depending on your frame of reference, it might recall ?DESQview, the ?Commodore 64, or a host of early DOS-based graphical user interfaces. In style if not in specifics, it evokes a particular era, a time when the then-new concept of ?personal computing? necessarily meant programming and tinkering and breaking things.
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Index.
99.Differential Calculus.
100.The Analytical Engine.
101.Augusta Ada King, Countess of Lovelace.
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99.Differential Calculus.
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus.
The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point.
Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration.
Differentiation has applications to nearly all quantitative disciplines. For example, in physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity with respect to time is acceleration. The derivative of the momentum of a body equals the force applied to the body; rearranging this derivative statement leads to the famous F = ma equation associated with Newton's second law of motion. The reaction rate of a chemical reaction is a derivative. In operations research, derivatives determine the most efficient ways to transport materials and design factories.
Derivatives are frequently used to find the maxima and minima of a function. Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena. Derivatives and their generalizations appear in many fields of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory and abstract algebra.
Suppose that x and y are real numbers and that y is a function of x, that is, for every value of x, there is a corresponding value of y. This relationship can be written as y = f(x). If f(x) is the equation for a straight line (called a linear equation), then there are two real numbers m and b such that y = mx + b. In this "slope-intercept form", the term m is called the slope and can be determined from the formula:
where the symbol ? (the uppercase form of the Greek letter Delta) is an abbreviation for "change in". It follows that ?y = m ?x.
A general function is not a line, so it does not have a slope. Geometrically, the derivative of f at the point x = a is the slope of the tangent line to the function f at the point a (see figure). This is often denoted f ?(a) in Lagrange's notation or dy/dx
in Leibniz's notation. Since the derivative is the slope of the linear approximation to f at the point a, the derivative (together with the value of f at a) determines the best linear approximation, or linearization, of f near the point a.
If every point.....
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100.The Analytical Engine.
The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician Charles Babbage.
It was first described in 1837 as the successor to Babbage's Difference engine, a design for a mechanical computer. The Analytical Engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete.
Babbage was never able to complete construction of any of his machines due to conflicts with his chief engineer and inadequate funding. It was not until the 1940s that the first general-purpose computers were actually built.
During Babbage's difference engine project, he realized that a much more general design, the Analytical Engine, was possible. The input (programs and data) was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary base-10 fixed-point arithmetic.
There was to be a store (that is, a memory) capable of holding 1,000 numbers of 40 decimal digits each (ca. 16.7 kB). An arithmetical unit (the "mill") would be able to perform all four arithmetic operations, plus comparisons and optionally square roots. Initially it was conceived as a difference engine curved back upon itself, in a generally circular layout, with the long store exiting off to one side. (Later drawings depict a regularized grid layout.) Like the central processing unit (CPU) in a modern computer, the mill would rely upon its own internal procedures, to be stored in the form of pegs inserted into rotating drums called "barrels", to carry out some of the more complex instructions the user's program might specify.
The programming language to be employed by users was akin to modern day assembly languages. Loops and conditional branching were possible, and so the language as conceived would have been Turing-complete as later defined by Alan Turing. Three different types of punch cards were used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back. There were three separate readers for the three types of cards.
In 1842, the Italian mathematician Luigi Menabrea, whom Babbage had met while travelling in Italy, wrote a description of the engine in French. In 1843, the description was translated into English and extensively annotated by Ada King (née Byron), Countess of Lovelace, who had become interested in the engine eight years earlier. In recognition of her additions to Menabrea's paper, which included a way to calculate Bernoulli numbers using the machine, she has been described as the first computer programmer. The modern computer programming language Ada is named in her honor.
Late in his life, Babbage sought ways to build a simplified version of the machine, and assembled a small part of it before his death in 1871.
In 1878, a committee of the British Association for the Advancement of Science recommended against constructing the Analytical Engine.
In 1910, Babbage's son Henry Prevost Babbage reported that a part of the mill and the printing apparatus had been constructed, and had been used to calculate a (faulty) list of multiples of pi. This constituted only a small part of the whole engine; it was not programmable and had no storage. (Popular images of this section have sometimes been mislabelled, implying that it was the entire mill or even the entire engine.) Henry Babbage's "Analytical Engine Mill" is on display at the Science Museum in London. Henry also proposed building a demonstration version of the full engine, with a smaller storage capacity: "perhaps for a first machine ten (columns) would do, with fifteen wheels in each". Such a version could manipulate 20 numbers of 25 digits each, and what it could be told to do with those numbers could still be impressive. "It is only a question of cards and time", wrote Henry Babbage in 1888, "... and there is no reason why (twenty thousand) cards should not be used if necessary, in an Analytical Engine for the purposes of the mathematician".
In 1991, the London Science Museum built a complete and working specimen of Babbage's Difference Engine No. 2, a design that incorporated refinements Babbage discovered during the development of the Analytical Engine. This machine was built using materials and engineering tolerances that would have been available to Babbage, quelling the suggestion that Babbage's designs could not have been produced using the manufacturing technology of his time.
In October 2010, John Graham-Cumming started a campaign to raise funds by "public subscription" to enable serious historical and academic study of Babbage's plans, with a view to then build and test a fully working virtual design which will then in turn enable construction of the physical Analytical Engine. As of October 2013, no actual construction had been reported.
Babbage is not known to have written down an explicit set of instructions for the engine in the manner of a modern processor manual. Instead he showed his programs as lists of states during their execution, showing what operator was run at each step with little indication of how the control flow would be guided. Bromley (see below) has assumed that the card deck could be read in forwards and backwards directions as a function of conditional branching after testing for conditions, which would make the engine Turing-complete:
The introduction for the first time, in 1845, of user operations for a variety of service functions including, most importantly, an effective system for user control of looping in user programs.
There is no indication how the direction of turning of the operation and variable cards is specified. In the absence of other evidence I have had to adopt the minimal default assumption that both the operation and variable cards can only be turned backward as is necessary to implement the loops used in Babbage?s sample programs. There would be no mechanical or microprogramming difficulty in placing the direction of motion under the control of the user.
From Bromley, A.G. Babbage's Analytical Engine Plans 28 and 28a. The programmer's interface. Annals of the History of Computing, IEEE. 2000
In their emulator of the engine, Fourmilab say:
The Engine's Card Reader is not constrained to simply process the cards in a chain one after another from start to finish. It can, in addition, directed by the very cards it reads and advised by the whether the Mill's run-up lever is activated, either advance the card chain forward, skipping the intervening cards, or backward, causing previously-read cards to be processed once again.
This emulator does provide a written symbolic instruction set, though this has been constructed by its authors rather than based on Babbage's original works. For example a factorial program would be written as:
N0 6
N1 1
N2 1
×
L1
L0
S1
-
L0
L2
S0
L2
L0
CB?11
where the CB is the conditional branch instruction or "combination card' used to make the control flow jump, in this case backwards by 11 cards.
Predicted influence
Babbage understood that the existence of an automatic computer would kindle interest in the field now known as algorithmic efficiency, writing in his Passages from the Life of a Philosopher, "As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise?By what course of calculation can these results be arrived at by the machine in the shortest time?"
Computer science.
Swedish engineers Georg and Edvard Scheutz, inspired by a description of the difference engine, created a mechanical calculation device based on the design in 1853. Table-sized instead of room-sized, the device was capable of calculating tables, but imperfectly.
From 1872 Henry continued diligently with his father's work and then intermittently in retirement in 1875. Percy Ludgate wrote about the engine in 1915 and even designed his own Analytical Engine (it was drawn up in detail, but never built). Ludgate's engine would be much smaller than Babbage's of about 8 cubic feet (230 L), and hypothetically would be capable of multiplying two 20-decimal-digit numbers in about six seconds.
Despite this ground work, Babbage's work fell into historical obscurity, and the Analytical Engine was unknown to builders of electro-mechanical and electronic computing machines in the 1930s and 1940s when they began their work, resulting in the need to re-invent many of the architectural innovations Babbage had proposed. Howard Aiken, who built the quickly-obsoleted electromechanical calculator, the Harvard Mark I, between 1937 and 1945, praised Babbage's work likely as a way of enhancing his own stature, but knew nothing of the Analytical Engine's architecture during the construction of the Mark I, and considered his visit to the constructed portion of the Analytical Engine "the greatest disappointment of my life". The Mark I showed no influence from the Analytical Engine and lacked the Analytical Engine's most prescient architectural feature, conditional branching. J. Presper Eckert and John W. Mauchly similarly were not aware of the details of Babbage's Analytical Engine work prior to the completion of their design for the first electronic general-purpose computer, the ENIAC.
If the Analytical Engine had been built, it would have been digital, programmable and Turing-complete. However, it would have been very slow. Ada Lovelace reported in her notes on the Analytical Engine: "Mr. Babbage believes he can, by his engine, form the product of two numbers, each containing twenty figures, in three minutes". By comparison the Harvard Mark I could perform the same task in just six seconds. A modern PC can do the same thing in well under a millionth of a second.
NameFirst operationalNumeral systemComputing mechanismProgrammingTuring complete
Difference EngineNever built (until the 1990s)DecimalMechanical ?No
Analytical EngineNever builtDecimalMechanicalProgram-controlled by punched cardsYes
Zuse Z3 (Germany)May 1941Binary floating pointElectro-mechanicalProgram-controlled by punched 35 mm film stock (theoretically Turing-complete but no conditional branch)Yes (proven in 1998)
Atanasoff?Berry Computer (US)1942BinaryElectronicSingle purpose; not programmableNo
Colossus Mark 1 (UK)December 1943BinaryElectronicProgram-controlled by patch cables and switchesNo
Harvard Mark I ? IBM ASCC (US)May 1944DecimalElectro-mechanicalProgram-controlled by 24-channel punched paper tape (but no conditional branch)No
ENIAC (US)July 1946DecimalElectronicProgram-controlled by patch cables and switchesYes
Manchester Baby (UK)1948BinaryElectronicFirst electronic stored program
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101.Augusta Ada King, Countess of Lovelace.
Augusta Ada King, Countess of Lovelace (10 December 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 recognised 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 of 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.
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. George Byron expected his baby to be a "glorious boy" and was disappointed when his wife gave birth to a girl. Augusta was named after Byron's half-sister, Augusta Leigh, and was called "Ada" by Byron himself.
Ada, aged four.
On 16 January 1816, Annabella, at George's behest, left for her parents' home at Kirkby Mallory taking one-month-old Ada with her. 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, aged seventeen, 1832.
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.
Adult years.
Lovelace developed a strong relationship with her tutor Mary Somerville. She had a strong respect and affection for Somerville. and the two of them corresponded for many years. Other acquaintances included Andrew Crosse, Sir David Brewster, Charles Wheatstone, Charles Dickens and Michael Faraday. By 1834, Ada was a regular at Court and started attending various events. She danced often and was able to charm many people, and was described by most people as being dainty. However, John Hobhouse, Lord Byron's friend, was the exception and he described her as "a large, coarse-skinned young woman but with something of my friend's features, particularly the mouth." This description followed their meeting on 24 February 1834 in which Ada made it clear to Hobhouse that she did not like him, probably due to the influence of her mother, which led her to dislike all of her father's friends. This first impression was not to last, and they later became friends.
On 8 July 1835, she married William King, 8th Baron King,[a] becoming Baroness King. Their residence was a large estate at Ockham Park, in Ockham, Surrey, along with another estate on Loch Torridon, and a home in London. They spent their honeymoon at Worthy Manor in Ashley Combe near Porlock Weir, Somerset. The Manor had been built as a hunting lodge in 1799 and was improved by King in preparation for their honeymoon. It later became their summer retreat and was further improved during this time.
They had three children: Byron (born 12 May 1836); Anne Isabella (called Annabella, later Lady Anne Blunt; born 22 September 1837), and Ralph Gordon (born 2 July 1839). Immediately after the birth of Annabella, Lady King experienced "a tedious and suffering illness, which took months to cure." In 1838, her husband became Earl of Lovelace. Thus, she was styled "The Right Honourable the Countess of Lovelace" for most of her married life. In 1843-44, Ada's mother assigned William Benjamin Carpenter to teach Ada's children, and to act as a 'moral' instructor for Ada. He quickly fell for her, and encouraged her to express any frustrated affections, claiming that his marriage meant he'd never act in an "unbecoming" manner. When it became clear that Carpenter was trying to start an affair, Ada cut it off.
In 1841, Lovelace and Medora Leigh (daughter of Lord Byron's half-sister Augusta Leigh) were told by Ada's mother that her father was also Medora's father. On 27 February 1841, Ada wrote to her mother: "I am not in the least 'astonished'. In fact you merely 'confirm' what I have for 'years and years' felt scarcely a doubt about, but should have considered it most improper in me to hint to you that I in any way suspected." She did not blame the incestuous relationship on Byron, but instead blamed Augusta Leigh: "I fear 'she' is 'more inherently' wicked than 'he' ever was." In the 1840s, Ada flirted with scandals: firstly from a relaxed relationship with men who were not her husband, which led to rumours of affairs ?and secondly, her love of gambling. The gambling led to her forming a syndicate with male friends, and an ambitious attempt in 1851 to create a mathematical model for successful large bets. This went disastrously wrong, leaving her thousands of pounds in debt to the syndicate, forcing her to admit it all to her husband. She had a shadowy relationship with Andrew Crosse's son John from 1844 onwards. John Crosse destroyed most of their correspondence after her death as part of a legal agreement. She bequeathed him the only heirlooms her father had personally left to her. During her final illness, she would panic at the idea of the younger Crosse being kept from visiting her.
Death.
Painting of Ada Lovelace at a piano in 1852 by Henry Phillips. While she was in great pain at the time, she sat for the painting as Phillips' father, Thomas Phillips, had painted Ada's father, Lord Byron.
Ada Lovelace died at the age of 36 - the same age that her father had died at - on 27 November 1852, from uterine cancer probably exacerbated by bloodletting by her physicians. 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. 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. 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. 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".
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. 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). Based on this work, Lovelace is now widely considered the first computer programmer 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.
In 1840, 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.
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.
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.
*
Augusta Ada King, Countess of Lovelace (10 December 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 recognised 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 of 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.
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. George Byron expected his baby to be a "glorious boy" and was disappointed when his wife gave birth to a girl. Augusta was named after Byron's half-sister, Augusta Leigh, and was called "Ada" by Byron himself.
Ada, aged four.
On 16 January 1816, Annabella, at George's behest, left for her parents' home at Kirkby Mallory taking one-month-old Ada with her. 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, aged seventeen, 1832.
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.
Adult years.
Lovelace developed a strong relationship with her tutor Mary Somerville. She had a strong respect and affection for Somerville. and the two of them corresponded for many years. Other acquaintances included Andrew Crosse, Sir David Brewster, Charles Wheatstone, Charles Dickens and Michael Faraday. By 1834, Ada was a regular at Court and started attending various events. She danced often and was able to charm many people, and was described by most people as being dainty. However, John Hobhouse, Lord Byron's friend, was the exception and he described her as "a large, coarse-skinned young woman but with something of my friend's features, particularly the mouth." This description followed their meeting on 24 February 1834 in which Ada made it clear to Hobhouse that she did not like him, probably due to the influence of her mother, which led her to dislike all of her father's friends. This first impression was not to last, and they later became friends.
On 8 July 1835, she married William King, 8th Baron King,[a] becoming Baroness King. Their residence was a large estate at Ockham Park, in Ockham, Surrey, along with another estate on Loch Torridon, and a home in London. They spent their honeymoon at Worthy Manor in Ashley Combe near Porlock Weir, Somerset. The Manor had been built as a hunting lodge in 1799 and was improved by King in preparation for their honeymoon. It later became their summer retreat and was further improved during this time.
They had three children: Byron (born 12 May 1836); Anne Isabella (called Annabella, later Lady Anne Blunt; born 22 September 1837), and Ralph Gordon (born 2 July 1839). Immediately after the birth of Annabella, Lady King experienced "a tedious and suffering illness, which took months to cure." In 1838, her husband became Earl of Lovelace. Thus, she was styled "The Right Honourable the Countess of Lovelace" for most of her married life. In 1843-44, Ada's mother assigned William Benjamin Carpenter to teach Ada's children, and to act as a 'moral' instructor for Ada. He quickly fell for her, and encouraged her to express any frustrated affections, claiming that his marriage meant he'd never act in an "unbecoming" manner. When it became clear that Carpenter was trying to start an affair, Ada cut it off.
In 1841, Lovelace and Medora Leigh (daughter of Lord Byron's half-sister Augusta Leigh) were told by Ada's mother that her father was also Medora's father. On 27 February 1841, Ada wrote to her mother: "I am not in the least 'astonished'. In fact you merely 'confirm' what I have for 'years and years' felt scarcely a doubt about, but should have considered it most improper in me to hint to you that I in any way suspected." She did not blame the incestuous relationship on Byron, but instead blamed Augusta Leigh: "I fear 'she' is 'more inherently' wicked than 'he' ever was." In the 1840s, Ada flirted with scandals: firstly from a relaxed relationship with men who were not her husband, which led to rumours of affairs ?and secondly, her love of gambling. The gambling led to her forming a syndicate with male friends, and an ambitious attempt in 1851 to create a mathematical model for successful large bets. This went disastrously wrong, leaving her thousands of pounds in debt to the syndicate, forcing her to admit it all to her husband. She had a shadowy relationship with Andrew Crosse's son John from 1844 onwards. John Crosse destroyed most of their correspondence after her death as part of a legal agreement. She bequeathed him the only heirlooms her father had personally left to her. During her final illness, she would panic at the idea of the younger Crosse being kept from visiting her.
Death.
Painting of Ada Lovelace at a piano in 1852 by Henry Phillips. While she was in great pain at the time, she sat for the painting as Phillips' father, Thomas Phillips, had painted Ada's father, Lord Byron.
Ada Lovelace died at the age of 36 - the same age that her father had died at - on 27 November 1852, from uterine cancer probably exacerbated by bloodletting by her physicians. 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. 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. 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. 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".
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. 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). Based on this work, Lovelace is now widely considered the first computer programmer 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.
In 1840, 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.
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.
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.
*
Inglish Site.24.
*
TO THE THRISE HO-
NOVRABLE AND EVER LY-
VING VERTVES OF SYR PHILLIP
SYDNEY KNIGHT, SYR JAMES JESUS SINGLETON, SYR CANARIS, SYR LAVRENTI BERIA ; AND TO THE
RIGHT HONORABLE AND OTHERS WHAT-
SOEVER, WHO LIVING LOVED THEM,
AND BEING DEAD GIVE THEM
THEIRE DVE.
***
In the beginning there is darkness. The screen erupts in blue, then a cascade of thick, white hexadecimal numbers and cracked language, ?UnusedStk? and ?AllocMem.? Black screen cedes to blue to white and a pair of scales appear, crossed by a sword, both images drawn in the jagged, bitmapped graphics of Windows 1.0-era clip-art?light grey and yellow on a background of light cyan. Blue text proclaims, ?God on tap!?
*
Introduction.
Yes i am getting a little Mobi-Literate(ML) by experimenting literary on my Mobile Phone. Peoplecall it Typographical Laziness(TL).
The first accidental entries for the this part of this encyclopedia.
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This is TempleOS V2.17, the welcome screen explains, a ?Public Domain Operating System? produced by Trivial Solutions of Las Vegas, Nevada. It greets the user with a riot of 16-color, scrolling, blinking text; depending on your frame of reference, it might recall ?DESQview, the ?Commodore 64, or a host of early DOS-based graphical user interfaces. In style if not in specifics, it evokes a particular era, a time when the then-new concept of ?personal computing? necessarily meant programming and tinkering and breaking things.
*
Index.
99.Differential Calculus.
100.The Analytical Engine.
101.Augusta Ada King, Countess of Lovelace.
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99.Differential Calculus.
In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus.
The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. The derivative of a function at a chosen input value describes the rate of change of the function near that input value. The process of finding a derivative is called differentiation. Geometrically, the derivative at a point is the slope of the tangent line to the graph of the function at that point, provided that the derivative exists and is defined at that point. For a real-valued function of a single real variable, the derivative of a function at a point generally determines the best linear approximation to the function at that point.
Differential calculus and integral calculus are connected by the fundamental theorem of calculus, which states that differentiation is the reverse process to integration.
Differentiation has applications to nearly all quantitative disciplines. For example, in physics, the derivative of the displacement of a moving body with respect to time is the velocity of the body, and the derivative of velocity with respect to time is acceleration. The derivative of the momentum of a body equals the force applied to the body; rearranging this derivative statement leads to the famous F = ma equation associated with Newton's second law of motion. The reaction rate of a chemical reaction is a derivative. In operations research, derivatives determine the most efficient ways to transport materials and design factories.
Derivatives are frequently used to find the maxima and minima of a function. Equations involving derivatives are called differential equations and are fundamental in describing natural phenomena. Derivatives and their generalizations appear in many fields of mathematics, such as complex analysis, functional analysis, differential geometry, measure theory and abstract algebra.
Suppose that x and y are real numbers and that y is a function of x, that is, for every value of x, there is a corresponding value of y. This relationship can be written as y = f(x). If f(x) is the equation for a straight line (called a linear equation), then there are two real numbers m and b such that y = mx + b. In this "slope-intercept form", the term m is called the slope and can be determined from the formula:
where the symbol ? (the uppercase form of the Greek letter Delta) is an abbreviation for "change in". It follows that ?y = m ?x.
A general function is not a line, so it does not have a slope. Geometrically, the derivative of f at the point x = a is the slope of the tangent line to the function f at the point a (see figure). This is often denoted f ?(a) in Lagrange's notation or dy/dx
in Leibniz's notation. Since the derivative is the slope of the linear approximation to f at the point a, the derivative (together with the value of f at a) determines the best linear approximation, or linearization, of f near the point a.
If every point.....
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100.The Analytical Engine.
The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician Charles Babbage.
It was first described in 1837 as the successor to Babbage's Difference engine, a design for a mechanical computer. The Analytical Engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete.
Babbage was never able to complete construction of any of his machines due to conflicts with his chief engineer and inadequate funding. It was not until the 1940s that the first general-purpose computers were actually built.
During Babbage's difference engine project, he realized that a much more general design, the Analytical Engine, was possible. The input (programs and data) was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. It employed ordinary base-10 fixed-point arithmetic.
There was to be a store (that is, a memory) capable of holding 1,000 numbers of 40 decimal digits each (ca. 16.7 kB). An arithmetical unit (the "mill") would be able to perform all four arithmetic operations, plus comparisons and optionally square roots. Initially it was conceived as a difference engine curved back upon itself, in a generally circular layout, with the long store exiting off to one side. (Later drawings depict a regularized grid layout.) Like the central processing unit (CPU) in a modern computer, the mill would rely upon its own internal procedures, to be stored in the form of pegs inserted into rotating drums called "barrels", to carry out some of the more complex instructions the user's program might specify.
The programming language to be employed by users was akin to modern day assembly languages. Loops and conditional branching were possible, and so the language as conceived would have been Turing-complete as later defined by Alan Turing. Three different types of punch cards were used: one for arithmetical operations, one for numerical constants, and one for load and store operations, transferring numbers from the store to the arithmetical unit or back. There were three separate readers for the three types of cards.
In 1842, the Italian mathematician Luigi Menabrea, whom Babbage had met while travelling in Italy, wrote a description of the engine in French. In 1843, the description was translated into English and extensively annotated by Ada King (née Byron), Countess of Lovelace, who had become interested in the engine eight years earlier. In recognition of her additions to Menabrea's paper, which included a way to calculate Bernoulli numbers using the machine, she has been described as the first computer programmer. The modern computer programming language Ada is named in her honor.
Late in his life, Babbage sought ways to build a simplified version of the machine, and assembled a small part of it before his death in 1871.
In 1878, a committee of the British Association for the Advancement of Science recommended against constructing the Analytical Engine.
In 1910, Babbage's son Henry Prevost Babbage reported that a part of the mill and the printing apparatus had been constructed, and had been used to calculate a (faulty) list of multiples of pi. This constituted only a small part of the whole engine; it was not programmable and had no storage. (Popular images of this section have sometimes been mislabelled, implying that it was the entire mill or even the entire engine.) Henry Babbage's "Analytical Engine Mill" is on display at the Science Museum in London. Henry also proposed building a demonstration version of the full engine, with a smaller storage capacity: "perhaps for a first machine ten (columns) would do, with fifteen wheels in each". Such a version could manipulate 20 numbers of 25 digits each, and what it could be told to do with those numbers could still be impressive. "It is only a question of cards and time", wrote Henry Babbage in 1888, "... and there is no reason why (twenty thousand) cards should not be used if necessary, in an Analytical Engine for the purposes of the mathematician".
In 1991, the London Science Museum built a complete and working specimen of Babbage's Difference Engine No. 2, a design that incorporated refinements Babbage discovered during the development of the Analytical Engine. This machine was built using materials and engineering tolerances that would have been available to Babbage, quelling the suggestion that Babbage's designs could not have been produced using the manufacturing technology of his time.
In October 2010, John Graham-Cumming started a campaign to raise funds by "public subscription" to enable serious historical and academic study of Babbage's plans, with a view to then build and test a fully working virtual design which will then in turn enable construction of the physical Analytical Engine. As of October 2013, no actual construction had been reported.
Babbage is not known to have written down an explicit set of instructions for the engine in the manner of a modern processor manual. Instead he showed his programs as lists of states during their execution, showing what operator was run at each step with little indication of how the control flow would be guided. Bromley (see below) has assumed that the card deck could be read in forwards and backwards directions as a function of conditional branching after testing for conditions, which would make the engine Turing-complete:
The introduction for the first time, in 1845, of user operations for a variety of service functions including, most importantly, an effective system for user control of looping in user programs.
There is no indication how the direction of turning of the operation and variable cards is specified. In the absence of other evidence I have had to adopt the minimal default assumption that both the operation and variable cards can only be turned backward as is necessary to implement the loops used in Babbage?s sample programs. There would be no mechanical or microprogramming difficulty in placing the direction of motion under the control of the user.
From Bromley, A.G. Babbage's Analytical Engine Plans 28 and 28a. The programmer's interface. Annals of the History of Computing, IEEE. 2000
In their emulator of the engine, Fourmilab say:
The Engine's Card Reader is not constrained to simply process the cards in a chain one after another from start to finish. It can, in addition, directed by the very cards it reads and advised by the whether the Mill's run-up lever is activated, either advance the card chain forward, skipping the intervening cards, or backward, causing previously-read cards to be processed once again.
This emulator does provide a written symbolic instruction set, though this has been constructed by its authors rather than based on Babbage's original works. For example a factorial program would be written as:
N0 6
N1 1
N2 1
×
L1
L0
S1
-
L0
L2
S0
L2
L0
CB?11
where the CB is the conditional branch instruction or "combination card' used to make the control flow jump, in this case backwards by 11 cards.
Predicted influence
Babbage understood that the existence of an automatic computer would kindle interest in the field now known as algorithmic efficiency, writing in his Passages from the Life of a Philosopher, "As soon as an Analytical Engine exists, it will necessarily guide the future course of the science. Whenever any result is sought by its aid, the question will then arise?By what course of calculation can these results be arrived at by the machine in the shortest time?"
Computer science.
Swedish engineers Georg and Edvard Scheutz, inspired by a description of the difference engine, created a mechanical calculation device based on the design in 1853. Table-sized instead of room-sized, the device was capable of calculating tables, but imperfectly.
From 1872 Henry continued diligently with his father's work and then intermittently in retirement in 1875. Percy Ludgate wrote about the engine in 1915 and even designed his own Analytical Engine (it was drawn up in detail, but never built). Ludgate's engine would be much smaller than Babbage's of about 8 cubic feet (230 L), and hypothetically would be capable of multiplying two 20-decimal-digit numbers in about six seconds.
Despite this ground work, Babbage's work fell into historical obscurity, and the Analytical Engine was unknown to builders of electro-mechanical and electronic computing machines in the 1930s and 1940s when they began their work, resulting in the need to re-invent many of the architectural innovations Babbage had proposed. Howard Aiken, who built the quickly-obsoleted electromechanical calculator, the Harvard Mark I, between 1937 and 1945, praised Babbage's work likely as a way of enhancing his own stature, but knew nothing of the Analytical Engine's architecture during the construction of the Mark I, and considered his visit to the constructed portion of the Analytical Engine "the greatest disappointment of my life". The Mark I showed no influence from the Analytical Engine and lacked the Analytical Engine's most prescient architectural feature, conditional branching. J. Presper Eckert and John W. Mauchly similarly were not aware of the details of Babbage's Analytical Engine work prior to the completion of their design for the first electronic general-purpose computer, the ENIAC.
If the Analytical Engine had been built, it would have been digital, programmable and Turing-complete. However, it would have been very slow. Ada Lovelace reported in her notes on the Analytical Engine: "Mr. Babbage believes he can, by his engine, form the product of two numbers, each containing twenty figures, in three minutes". By comparison the Harvard Mark I could perform the same task in just six seconds. A modern PC can do the same thing in well under a millionth of a second.
NameFirst operationalNumeral systemComputing mechanismProgrammingTuring complete
Difference EngineNever built (until the 1990s)DecimalMechanical ?No
Analytical EngineNever builtDecimalMechanicalProgram-controlled by punched cardsYes
Zuse Z3 (Germany)May 1941Binary floating pointElectro-mechanicalProgram-controlled by punched 35 mm film stock (theoretically Turing-complete but no conditional branch)Yes (proven in 1998)
Atanasoff?Berry Computer (US)1942BinaryElectronicSingle purpose; not programmableNo
Colossus Mark 1 (UK)December 1943BinaryElectronicProgram-controlled by patch cables and switchesNo
Harvard Mark I ? IBM ASCC (US)May 1944DecimalElectro-mechanicalProgram-controlled by 24-channel punched paper tape (but no conditional branch)No
ENIAC (US)July 1946DecimalElectronicProgram-controlled by patch cables and switchesYes
Manchester Baby (UK)1948BinaryElectronicFirst electronic stored program
*
101.Augusta Ada King, Countess of Lovelace.
Augusta Ada King, Countess of Lovelace (10 December 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 recognised 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 of 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.
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. George Byron expected his baby to be a "glorious boy" and was disappointed when his wife gave birth to a girl. Augusta was named after Byron's half-sister, Augusta Leigh, and was called "Ada" by Byron himself.
Ada, aged four.
On 16 January 1816, Annabella, at George's behest, left for her parents' home at Kirkby Mallory taking one-month-old Ada with her. 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, aged seventeen, 1832.
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.
Adult years.
Lovelace developed a strong relationship with her tutor Mary Somerville. She had a strong respect and affection for Somerville. and the two of them corresponded for many years. Other acquaintances included Andrew Crosse, Sir David Brewster, Charles Wheatstone, Charles Dickens and Michael Faraday. By 1834, Ada was a regular at Court and started attending various events. She danced often and was able to charm many people, and was described by most people as being dainty. However, John Hobhouse, Lord Byron's friend, was the exception and he described her as "a large, coarse-skinned young woman but with something of my friend's features, particularly the mouth." This description followed their meeting on 24 February 1834 in which Ada made it clear to Hobhouse that she did not like him, probably due to the influence of her mother, which led her to dislike all of her father's friends. This first impression was not to last, and they later became friends.
On 8 July 1835, she married William King, 8th Baron King,[a] becoming Baroness King. Their residence was a large estate at Ockham Park, in Ockham, Surrey, along with another estate on Loch Torridon, and a home in London. They spent their honeymoon at Worthy Manor in Ashley Combe near Porlock Weir, Somerset. The Manor had been built as a hunting lodge in 1799 and was improved by King in preparation for their honeymoon. It later became their summer retreat and was further improved during this time.
They had three children: Byron (born 12 May 1836); Anne Isabella (called Annabella, later Lady Anne Blunt; born 22 September 1837), and Ralph Gordon (born 2 July 1839). Immediately after the birth of Annabella, Lady King experienced "a tedious and suffering illness, which took months to cure." In 1838, her husband became Earl of Lovelace. Thus, she was styled "The Right Honourable the Countess of Lovelace" for most of her married life. In 1843-44, Ada's mother assigned William Benjamin Carpenter to teach Ada's children, and to act as a 'moral' instructor for Ada. He quickly fell for her, and encouraged her to express any frustrated affections, claiming that his marriage meant he'd never act in an "unbecoming" manner. When it became clear that Carpenter was trying to start an affair, Ada cut it off.
In 1841, Lovelace and Medora Leigh (daughter of Lord Byron's half-sister Augusta Leigh) were told by Ada's mother that her father was also Medora's father. On 27 February 1841, Ada wrote to her mother: "I am not in the least 'astonished'. In fact you merely 'confirm' what I have for 'years and years' felt scarcely a doubt about, but should have considered it most improper in me to hint to you that I in any way suspected." She did not blame the incestuous relationship on Byron, but instead blamed Augusta Leigh: "I fear 'she' is 'more inherently' wicked than 'he' ever was." In the 1840s, Ada flirted with scandals: firstly from a relaxed relationship with men who were not her husband, which led to rumours of affairs ?and secondly, her love of gambling. The gambling led to her forming a syndicate with male friends, and an ambitious attempt in 1851 to create a mathematical model for successful large bets. This went disastrously wrong, leaving her thousands of pounds in debt to the syndicate, forcing her to admit it all to her husband. She had a shadowy relationship with Andrew Crosse's son John from 1844 onwards. John Crosse destroyed most of their correspondence after her death as part of a legal agreement. She bequeathed him the only heirlooms her father had personally left to her. During her final illness, she would panic at the idea of the younger Crosse being kept from visiting her.
Death.
Painting of Ada Lovelace at a piano in 1852 by Henry Phillips. While she was in great pain at the time, she sat for the painting as Phillips' father, Thomas Phillips, had painted Ada's father, Lord Byron.
Ada Lovelace died at the age of 36 - the same age that her father had died at - on 27 November 1852, from uterine cancer probably exacerbated by bloodletting by her physicians. 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. 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. 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. 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".
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. 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). Based on this work, Lovelace is now widely considered the first computer programmer 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.
In 1840, 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.
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.
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.
*
Augusta Ada King, Countess of Lovelace (10 December 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 recognised 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 of 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.
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. George Byron expected his baby to be a "glorious boy" and was disappointed when his wife gave birth to a girl. Augusta was named after Byron's half-sister, Augusta Leigh, and was called "Ada" by Byron himself.
Ada, aged four.
On 16 January 1816, Annabella, at George's behest, left for her parents' home at Kirkby Mallory taking one-month-old Ada with her. 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, aged seventeen, 1832.
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.
Adult years.
Lovelace developed a strong relationship with her tutor Mary Somerville. She had a strong respect and affection for Somerville. and the two of them corresponded for many years. Other acquaintances included Andrew Crosse, Sir David Brewster, Charles Wheatstone, Charles Dickens and Michael Faraday. By 1834, Ada was a regular at Court and started attending various events. She danced often and was able to charm many people, and was described by most people as being dainty. However, John Hobhouse, Lord Byron's friend, was the exception and he described her as "a large, coarse-skinned young woman but with something of my friend's features, particularly the mouth." This description followed their meeting on 24 February 1834 in which Ada made it clear to Hobhouse that she did not like him, probably due to the influence of her mother, which led her to dislike all of her father's friends. This first impression was not to last, and they later became friends.
On 8 July 1835, she married William King, 8th Baron King,[a] becoming Baroness King. Their residence was a large estate at Ockham Park, in Ockham, Surrey, along with another estate on Loch Torridon, and a home in London. They spent their honeymoon at Worthy Manor in Ashley Combe near Porlock Weir, Somerset. The Manor had been built as a hunting lodge in 1799 and was improved by King in preparation for their honeymoon. It later became their summer retreat and was further improved during this time.
They had three children: Byron (born 12 May 1836); Anne Isabella (called Annabella, later Lady Anne Blunt; born 22 September 1837), and Ralph Gordon (born 2 July 1839). Immediately after the birth of Annabella, Lady King experienced "a tedious and suffering illness, which took months to cure." In 1838, her husband became Earl of Lovelace. Thus, she was styled "The Right Honourable the Countess of Lovelace" for most of her married life. In 1843-44, Ada's mother assigned William Benjamin Carpenter to teach Ada's children, and to act as a 'moral' instructor for Ada. He quickly fell for her, and encouraged her to express any frustrated affections, claiming that his marriage meant he'd never act in an "unbecoming" manner. When it became clear that Carpenter was trying to start an affair, Ada cut it off.
In 1841, Lovelace and Medora Leigh (daughter of Lord Byron's half-sister Augusta Leigh) were told by Ada's mother that her father was also Medora's father. On 27 February 1841, Ada wrote to her mother: "I am not in the least 'astonished'. In fact you merely 'confirm' what I have for 'years and years' felt scarcely a doubt about, but should have considered it most improper in me to hint to you that I in any way suspected." She did not blame the incestuous relationship on Byron, but instead blamed Augusta Leigh: "I fear 'she' is 'more inherently' wicked than 'he' ever was." In the 1840s, Ada flirted with scandals: firstly from a relaxed relationship with men who were not her husband, which led to rumours of affairs ?and secondly, her love of gambling. The gambling led to her forming a syndicate with male friends, and an ambitious attempt in 1851 to create a mathematical model for successful large bets. This went disastrously wrong, leaving her thousands of pounds in debt to the syndicate, forcing her to admit it all to her husband. She had a shadowy relationship with Andrew Crosse's son John from 1844 onwards. John Crosse destroyed most of their correspondence after her death as part of a legal agreement. She bequeathed him the only heirlooms her father had personally left to her. During her final illness, she would panic at the idea of the younger Crosse being kept from visiting her.
Death.
Painting of Ada Lovelace at a piano in 1852 by Henry Phillips. While she was in great pain at the time, she sat for the painting as Phillips' father, Thomas Phillips, had painted Ada's father, Lord Byron.
Ada Lovelace died at the age of 36 - the same age that her father had died at - on 27 November 1852, from uterine cancer probably exacerbated by bloodletting by her physicians. 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. 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. 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. 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".
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. 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). Based on this work, Lovelace is now widely considered the first computer programmer 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.
In 1840, 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.
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.
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.
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