Ada! Sole daughter of my house and heart?
When last I saw thy young blue eyes they smiled,
And then we parted …

So said Lord Byron, English aristocrat and romantic poet, in the third canto of a work that made him famous and also made him a fortune. Byron was a terrible father, abandoning wife, Anne Isabella Noel Byron, the eleventh Baroness Wentworth, and child Ada when the girl was three months old. He was never to see either of them again.²⁰³

Like her mother, Ada had mathematical inclinations. Byron had dismissively called his wife “Princess of Parallelograms.” Also like her mother, Augusta Ada Byron was to marry within the English aristocracy, though to a man more settled and less unsettling than her father, and supportive of his wife’s mathematical studies. Augusta Ada King-Noel, Countess of Lovelace, she was thenceforth to be known, or Ada Lovelace.

Ada and her mother first met Charles Babbage one evening in June 1833, before she married. She was eighteen, and Babbage twenty-four years her senior. He had studied at Cambridge University at about the same time as both her father and future husband, and was a leading light in the Analytical Society, devoted to replacing Newton’s notation for the calculus with Leibniz’s.^§1.3.2d A famed inventor, Babbage held regular soirées at his home, attended by thinkers and dignitaries from engineer Isambard Kingdom Brunel§2a to novelist Charles Dickens, to natural scientist Charles Darwin, to Queen Victoria’s consort, Prince Albert. This was one of those soirées.

On display in the house was Babbage’s “Difference Engine,” an elaborate mechanical calculator.* It was designed to mechanize the labor-intensive process of manually creating logarithmic tables, used for the multiplication of large numbers.²⁰⁴ A friend of her mother said that while most visitors stared at the machine in perplexed awe, “Miss Byron, young as she was, understood its working, and saw great beauty in the machine.”²⁰⁵

Pursuing her interest in things mechanical and analytical, in the following year Ada Byron and her mother toured English factories, including cloth factories using punched cards to manufacture elaborate patterns in fabric and lace.²⁰⁶ The mechanical loom had also been an interest of her father’s, though of a different kind. In his maiden speech to the house of Lords in 1812, three years before Ada was born, Lord Byron had taken the opportunity to protest a bill that would have made the wave of machine-breaking a capital crime.²⁰⁷

“By the adoption” of such machines, he said, “one man performed the work of many, and the superfluous labourers were thrown out of employment, [being] … left in consequence to starve.” It would seem that “the maintenance and well doing of the industrious poor, were objects of greater consequence than the enrichment of a few individuals,” the owners of the mechanical looms. The protestors were left “liable to conviction, on the clearest evidence, of the capital crime of poverty.”²⁰⁸

Ada, now married to the Earl of Lovelace, pursued her mathematical studies over the decade following her first meeting with Babbage, met him frequently, and corresponded with him at length.²⁰⁹ By 1842, his work was at a crossroads. Despite substantial government funding, he had failed to produce a complete Difference Engine. To the annoyance of his sponsors his plans had moved on to a seemingly more fanciful and never-to-be-built Analytical Engine. Babbage even met British Prime Minister Sir Robert Peel in person in a failed attempt to appeal for further funding.²¹⁰ “What shall we do to get rid of Mr. Babbage and his calculating Machine?” Peel asked in desperation.²¹¹

Hopes dashed in England, Babbage visited Italy. There his proposed Analytical Engine attracted the attention of Luigi Menabrea, Professor of Mechanics in the Military Academy of the University of Turin, later to be Prime Minister of Italy. Menabrea was sufficiently impressed with Babbage’s plan for the Analytical Engine to write an article about it in French.

Upset and annoyed by Babbage’s partly self-inflicted failures to secure support for the project – when he met Prime Minister Peel, instead of showing gratitude for past support, he complained that his work had been unappreciated – Lovelace offered to translate Menebrea’s article, and add some explanatory notes. Perhaps this would breathe life back into the project.

The translated article, “Sketch of The Analytical Engine Invented by Charles Babbage, By L. F. Menabrea, with Notes upon the Memoir by the Translator,” was published in 1843. The translated part is just over 10,000 words; Lovelace’s notes, simply signed A.L.L., run to over 22,000 words.²¹²

In the notes, Lovelace goes far beyond Babbage in addressing what is for us a critical question, the transposability of meanings by machines of calculation. Today we call such machines “computers.” Where Babbage saw his machines as primarily mathematical, Lovelace saw broader potentials.

Lovelace makes a distinction between what would today be called software and data: “In studying the action of the Analytical Engine, we find that the peculiar and independent nature of the considerations which in all mathematical analysis belong to operations, as distinguished from the objects operated upon and from the results of the operations performed upon those objects, is very strikingly defined and separated.”²¹³

However, Lovelace casts the net of “operation” far wider than mathematics in the abstract, to any calculable meanings in the world: “It may be desirable to explain, that by the word operation, we mean any process which alters the mutual relation of two or more things, be this relation of what kind it may. This is the most general definition, and would include all subjects in the universe.” By mathematical representation and calculation, it may be possible to “express the great facts of the natural world, and those unceasing changes of mutual relationship which, visibly or invisibly, consciously or unconsciously to our immediate physical perceptions, are interminably going on in the agencies of the creation we live amidst.”²¹⁴

The model for such mechanical possibility, Lovelace went on, was “the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs.” The Analytical Engine was also designed to run on the same kinds of punched cards she and her mother had seen at work in the factories they had toured. “[T]he Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.” In these ways, “not only the mental and the material, but the theoretical and the practical in the mathematical world, are brought into more intimate and effective connexion with each other.”²¹⁵

However, Lovelace adds an important proviso: “to guard against the possibility of exaggerated ideas that might arise as to the powers of the Analytical Engine … It can follow analysis; but it has no power of anticipating any analytical relations or truths. Its province is to assist us in making available what we are already acquainted with.” Any such machine’s capacity is limited to “devising for mathematical truths a new form in which to record and throw themselves out for actual use.” To this extent and no more its contribution is “extensions of human power, or additions to human knowledge.”²¹⁶

We rephrase: the limits of calculated meaning were to be the limits of calculability, its affordances in terms of the constraints as well as the potentials for transposing other meaning functions (such as instances, concepts, qualities) into quantities, and quantities into other meaning functions.

A.L.L.’s translation and its notes were received to great acclaim, and congratulations poured in. Babbage signed off a letter of appreciation to her, “Ever my fair Interpretess, Your faithful slave.”²¹⁷

Then the paper was forgotten for the best part of a century.

• Cope, Bill and Mary Kalantzis, 2020, Making Sense: Reference, Agency and Structure in a Grammar of Multimodal Meaning, Cambridge UK: Cambridge University Press, pp. 156-9. [In-text numbers in this post are footnotes in the book. § markers are cross-references to other sections.]