Saturday June 5, 2021’s Smile of the Day: Ada Lovelace
On this Day:
In 1833, Ada Lovelace (future 1st computer programmer) met Charles Babbage, the inventor of the Analytical Engine.
The Analytical Engine was a proposed mechanical general-purpose computer designed by English mathematician and computer pioneer Charles Babbage. It was first described in 1837 as the successor to Babbage’s difference engine, which was a design for a simpler 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. In other words, the logical structure of the Analytical Engine was essentially the same as that which has dominated computer design in the electronic era. The Analytical Engine is one of the most successful achievements of Charles Babbage.
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 1941 that Konrad Zuse built the first general-purpose computer, Z3, more than a century after Babbage had proposed the pioneering Analytical Engine in 1837.
Babbage’s first attempt at a mechanical computing device, the Difference Engine, was a special-purpose machine designed to tabulate logarithms and trigonometric functions by evaluating finite differences to create approximating polynomials. Construction of this machine was never completed; Babbage had conflicts with his chief engineer, Joseph Clement, and ultimately the British government withdrew its funding for the project.
During this project, Babbage realised that a much more general design, the Analytical Engine, was possible. The work on the design of the Analytical Engine started in c. 1833.
The input, consisting of programs (“formulae”) 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. 16.6 kB). An arithmetic unit (the “mill”) would be able to perform all four arithmetic operations, plus comparisons and optionally square roots. Initially (1838) 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 (1858) depict a regularised 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. Babbage developed some two dozen programs for the Analytical Engine between 1837 and 1840, and one program later. These programs treat polynomials, iterative formulas, Gaussian elimination, and Bernoulli numbers.
In 1842, the Italian mathematician Luigi Federico Menabrea published a description of the engine based on a lecture by Babbage in French. In 1843, the description was translated into English and extensively annotated by Ada 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 (widely considered to be the first complete computer program), she has been described as the first computer programmer.
But back to Ada Lovelace!
From 1832, when she was seventeen, her mathematical abilities began to emerge, and her interest in mathematics dominated the majority of her adult life. Her mother’s obsession with rooting out any of the insanity of which she accused Byron was one of the reasons that Ada was taught mathematics from an early age. She was privately educated in mathematics and science by William Frend, William King, and Mary Somerville, the noted 19th-century researcher and scientific author. In the 1840s, the mathematician Augustus De Morgan extended her “much help in her mathematical studies” including study of advanced calculus topics including the “numbers of Bernoulli” (that formed her celebrated algorithm for Babbage’s Analytical Engine). In a letter to Lady Byron, De Morgan suggested that Ada’s skill in mathematics might lead her to become “an original mathematical investigator, perhaps of first-rate eminence.”
Lovelace often questioned basic assumptions through integrating poetry and science. Whilst 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, Lovelace was strongly interested in scientific developments and fads of the day, including phrenology and mesmerism. After her work with Babbage, Lovelace 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 pre-occupation, inherited from her mother, about her “potential” madness. As part of her research into this project, she visited the 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.
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 Number.” In 1843, he wrote to her:
Forget this world and all its troubles and if possible its multitudinous Charlatans—every thing in short but the Enchantress of Number.
During a nine-month period in 1842–43, Lovelace translated the Italian mathematician Luigi Menabrea’s article 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 many other scientists did not really grasp the concept and the British establishment had shown little interest in it. Lovelace’s notes even had to explain how the Analytical Engine differed from the original Difference Engine. Her work was well received at the time; the scientist Michael Faraday described himself as a supporter of her writing.
The notes are around three times longer than the article itself and include (in Note G), in complete detail, a method for calculating a sequence of Bernoulli numbers using the Analytical Engine, which might have run correctly had it ever been built (only Babbage’s Difference Engine has been built, completed in London in 2002). Based on this work, Lovelace is now considered by many to be the first computer programmer and her method has been called the world’s first computer program. Others dispute this because some of Charles Babbage’s earlier writings could be considered computer programs.
Note G also contains Lovelace’s 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 (criticising the government’s treatment of his Engine) as an unsigned preface, which could have been mistakenly interpreted as a joint declaration. When Taylor’s Scientific Memoirs ruled that the statement should be signed, Babbage wrote to Lovelace 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. The 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, Lovelace 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 Lovelace 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 the future Prime Minister of Italy, transcribed Babbage’s lecture into French, and this transcript was subsequently published in the Bibliothèque universelle de Genève in October 1842. Babbage’s friend Charles Wheatstone commissioned Ada Lovelace to translate Menabrea’s paper into English. She then augmented the paper with notes, which were added to the translation. Ada Lovelace 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 the September 1843 edition of Taylor’s Scientific Memoirs under the initialism AAL.
Ada Lovelace’s notes were labelled alphabetically from A to G. In note G, she describes an algorithm for the Analytical Engine to compute Bernoulli numbers. It is considered to be the first published algorithm ever specifically tailored for implementation on a computer, and Ada Lovelace has often been cited as the first computer programmer for this reason. The engine was never completed so her program was never tested.
In 1953, more than a century after her death, Ada Lovelace’s notes on Babbage’s Analytical Engine were republished as an appendix to B.V. Bowden’s Faster than Thought: A Symposium on Digital Computing Machines. The engine has now been recognised as an early model for a computer and her notes as a description of a computer and software.
In her notes, Ada Lovelace emphasised 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. In her notes, 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 an important development from previous ideas about the capabilities of computing devices and anticipated the implications of modern computing one hundred years before they were realised. Walter Isaacson ascribes Ada’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 the programmer John Graham-Cumming, whose project Plan 28 has the aim of constructing the first complete Analytical Engine.
According to the historian of computing and Babbage specialist Doron Swade:
Ada saw something that Babbage in some sense failed to see. In Babbage’s world his engines were bound by number…What Lovelace saw…was that number could represent entities other than quantity. So once you had a machine for manipulating numbers, if those numbers represented other things, letters, musical notes, then the machine could manipulate symbols of which number was one instance, according to rules. It is this fundamental transition from a machine which is a number cruncher to a machine for manipulating symbols according to rules that is the fundamental transition from calculation to computation—to general-purpose computation—and looking back from the present high ground of modern computing, if we are looking and sifting history for that transition, then that transition was made explicitly by Ada in that 1843 paper (per Wikipedia).
First, a Story:
Al Gore and Ada Lovelace started a band. They called it “The Al Gore Rhythms”
Second, a Song:
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Thought for the Day:
“Mathematical science shows what is. It is the language of unseen relations between things. But to use and apply that language, we must be able fully to appreciate, to feel, to seize the unseen, the unconscious.” – Ada Lovelace
Have a great day!
Dave & Colleen
© 2021 David J. Bilinsky and Colleen E. Bilinsky