Review of “Reckoning with Matter: Calculating Machines, Innovation, and Thinking about Thinking from Pascal to Babbage”
Matthew L. Jones is the James R. Barker Professor of Contemporary Civilization in the Department of History at Columbia University. He obtained his BA and PhD from Harvard, and his masters from Cambridge. His focus is on the history of science and technology in early modern Europe, as well as the development of information technology.
In Reckoning, Jones traces the development of mechanical devices capable of automating basic arithmetic operations, beginning in the mid-17th century. He structures the book as a chronologically ordered series of profiles of the key “inventors” in the field, and the skilled artisanal collaborators they worked with over centuries of attempts. Between each profile, he delivers an episodic saga of Charles Babbage’s attempts to realize his Difference Engine. He closes the book with a meditation on how human perceptions of the limits to machine “creativity” have evolved over the last four centuries.
In chapters one and two, Jones describes the essential problems requiring solutions in the construction of such a device. First, it must “mechanize carry” — it must somehow apply sufficient force so as to propagate the carrying of successive digits across the various columns in addition or subtraction. Second, it must “keep things digital” — in other words, it must track and express whole numbers, despite being constructed from analog mechanical components which possess continuous, rather than discrete, state. Third, it must match the excellence of manual instruments in simplicity, compactness, and ease of use. To these ends, device designs relied upon discs and gears, precise division of those discs and gears, and an internal mechanism to drive them. These components the skills of craftsmen experienced in striking coinage, precision engraving, and clockmaking. As a pioneer in 1646, Pascal found himself in the position of having to make the case for the utility of such a device. Pascal pointed to the error-prone and boring process of compiling a long series of sums, common in accounting and bookkeeping. At that time, numeracy was concentrated in the commercial centers, and an increasing sophistication and density of commercial transactions was creating plausible demand for automation. Meanwhile, “computation” was seen as a mechanical activity of lower intellectual status, distinct from logic and reasoning (then perceived as not reducible to arithmetic operations).
Pascal’s machine attempted to automate the cascade of carries, and the necessary force propagation, by means of progressively heavier weights in each column of numbers. As a result, it was not reversible (incapable of subtraction), and required a level surface for operation. Jones’ ability to explain intricate and arcane engineering design principles shines through; in an analogical example typical of his explanations throughout the book, he explicates what happens inside a modern mechanical odometer when it turns over one million miles! Pascal made more than fifty attempts to ruggedize his device, but it never caught on. Meanwhile, across the Channel in 1669, Morland produced a less ambitious, more portable device that relied upon manual carries. It automated John Napier’s “bones” method for multiplication. In a feat of sourcing typical of his extensive primary bibliography, Jones details an itemized invoice for a prototype to Lennox, Morland’s patron, for a sum equivalent to a month’s wages for the entire Lennox household. Here Jones also introduces an ongoing exploration of the interplay between inventors and artisans, praising Morland’s “knowledge of his limits and taste in collaborators”. Morland perceived two “classes” — inventors and copiers; Pascal thought artisans lacked theory and weren’t inventors, but acknowledged a symbiotic relationship, where his need for artisan skill was matched by their inability to execute without his theories. Furthermore, Pascal thought that theory-guided exploration was more efficient than trial-and-error.
Chapter two also relies upon the extensive correspondence between Leibniz and his collaborator Ollivier concerning the four-decade quest to construct Leibniz’s design. In 1672, Leibniz presented a model of a device capable of multiplication via repeated addition to the Royal Society in London. After a favorable reception, he embarked on a search in Paris for someone whose fascination with machines exceeded his self-interest, and found Ollivier. Leibniz was impressed by Colbert’s policy of attracting artisans and then stealing their secrets. Leibniz awarded Ollivier a three-year fixed price contract for a project that ultimately consumed forty years of effort. Here Jones emphasizes that the custom of presenting a model enabled an inventor to claim priority, while allowing others to assist the acknowledged inventor. Since Leibniz was based in Hanover, and Ollivier remained in Paris, almost the entirety of their collaboration is preserved in letters, which are a fascinating dialogue between vague qualitative descriptions by Leibniz, requiring Ollivier’s skilled and discretionary interpretation, and Ollivier’s frustrations with the limits of written communications: “I cannot explain, the machine would need to be present for you to understand.” This depiction strengthens Jones’ argument that “technology transfer” in the 17th century was chiefly a matter of moving artisans between geographic locales. Jones uncovers an unexecuted contract dated 1679 which lays bear Leibniz’s frustrations with his engineer. It specifies an almost absurd degree of micromanagement that belies the considerable autonomy conveyed in Leibniz’s letters. Here Jones also admits the limitations imposed by his sources — eventually the Ollivier correspondence falls silent, and Jones is unable to prove that this was due to a move by Ollivier to Hanover. This seems unlikely, given that Ollivier’s frustrations had grown to a point where he threatened to “melt down everything” on account of Leibniz’s failure to recognize him as more than just a journeyman technician.
Chapter three examines nascent concepts of intellectual property, beginning with an exploration of the 17th century concept of “privilege” as distinct from the modern conception of a “patent”. Privilege protected an already extant manufacturing process and required “reduction to practice”. It other words, privilege was seldom awarded to a mere idea on paper. In this regard, Pascal received special treatment: a perpetual monopoly for what was then largely a thought experiment. The reasons for this appear to be a unique confluence of the Pascal family’s relationships in the French court, an ongoing Colbertist process of state primacy exertion over the cities and regions, and the fact that privilege was more a symbolic gift than any actual mechanism for enhanced commercial renumeration. Across the Channel, Morland ran aground on a general suspicion of patents following the Glorious Revolution; patents were seen as examples of royal overreach and corruption in the pre-Cromwell era. Leibniz also failed to procure protection, since the typical “window” for successful reduction to practice was only six months.
Chapter four’s title is the splendid “Productivity of Ignorance”. Leibniz’s ultimate failure was legendary, and this “ignorance” and struggle inspired others to attempt and persist. After all, if the great Leibniz couldn’t achieve a solution, the problem must be truly worthy. Jones explores the prevalence of imitation as a virtue — “challenge alone can force the improvement of a talent”, whereas mere copying lacks the same rigor. This burst of innovation by many competitors produced the first well-working machine, a cylindrical approach which bore an inscription assigning nearly equal credit: “Braun invented it, Vayringe made it”.
Chapter five chronicles the effort of the Earl of Stanhope, beginning in 1777. Stanhope was brought up in the middle of the Geneva clockmaking ferment and served a technical apprenticeship in the construction of marine chronometers. He was a habitual sketcher, tacking between “paper and metal”, but he was ultimately unable to recreate the constellation of talent he’d encountered in Geneva at his Chevening workshop, with the exception of his engineer Varley, to whom he bequeathed its entire contents. Stanhope and Varley did not publish or patent their designs. However, it seems that Stanhope’s prototypes exerted great influence on Charles Babbage, and Babbage was scrupulous about dividing credit for his ideas, meeting with Stanhope’s son and heir and procuring Stanhope’s prototypes when the Royal Society requested a “literature review” of sorts, detailing prior attempts and why they had failed. Jones again acknowledges the limitations of his sources, noting that it is impossible to determine if any of Stanhope’s innovations made their way into Babbage’s designs.
Jones’ interwoven description of Babbage’s quest to build his Difference Engine is a clever structural conceit, but at times the reader struggles to hold the plot thread across the span of the entire book — not unlike the mental persistence required to perform arithmetic. Babbage conceived of the Difference Engine as a means of automating the production of numerical tables by the method of adding differences, and then automatic typesetting and printing of the resulting value series. He constructed his first model in 1822, and abandoned the pursuit in 1833 with only a conceptual demonstration of the calculating component. Jones details Babbage’s iterative relationship with Clement, a “draftsman of the highest order to economize the labor of my [Babbage’s] own head, and a workman to execute the experimental machinery to which I am obliged constantly to have recourse”, as well as his constant struggle to extract sufficient research and development funding from the British government. Periodically, British officials requested that the Royal Society effectively audit Babbage’s project, a position of considerable discomfort for the Royal Society, given that it had no mandate for the endorsement or rejection of national scientific investments. Eventually Peel became Prime Minister, and as a longtime opponent of the project, ended Babbage’s patronage. During Babbage’s meeting with Peel, he cited the opportunity cost of the Difference Engine and its exclusion of other efforts, as well as the government’s irresponsibility in “stringing him along”, leading him to believe that there was a firm commitment to the realization of a functioning device. In reports on the project, the Royal Society cited the spinoffs from Babbage’s efforts — tools for large-scale draftsmanship, as well as precision toolmaking, which eventually paid dividends for British industry. In fact, such were the quality of Clement’s drawings that the British Science Museum was able to construct a functioning prototype of the Difference Engine in 1991. During that project, the museum uncovered a flaw that Babbage would have doubtless encountered and corrected, if he’d had the resources to build it. Eventually, a Swedish father/son duo, the Scheutzes, build a working machine in 1853 with Babbage’s blessing, and dedicated the first printing of their numerical tables to him.
Chapter six considers the position of arithmetic in the early modern conception of reasoning. In 1843 Ada Lovelace, Babbage’s longtime collaborator and the daughter of Lord Byron, cautioned that their engines could “only do whatever we know how to order them to perform”. Calculating machines were seen as simply the wrong sort of matter to think with, since arithmetic was perceived as a small slice of human reasoning. However, Stanhope had mused that reasoning is merely the “arrangement of signs”, which is reducible to mechanism, implying that reasoning itself is reducible to mechanism. Leibniz’ view was that the human mind can “transplant itself, such that it gives matter the power of doing more than it could by itself”. Babbage, grappling with the problem of runtime efficiency, endowed his design with a prediction capability of sorts — “teaching the machine to foresee and then act on that foresight — performing carries before the additions that cause them”.
This anticipatory calculation aspect is highly analogous to branch prediction in modern microprocessors, and shows that the earliest hardware and software designer was operating at an extremely high level of conceptual sophistication by modern standards. Indeed, Jones points out that, even today, the performance characteristics of a state-of-the-art chip are not known until the chip is physically produced. Almost four hundred years later, “rational design” remains a goal rather than a reality, and that is the central message of Jones’ book: a design on paper seldom survives contact with the physical world, and his work restores a long-neglected balance between the marquee “idea guys” and their engineering collaborators, who actually brought their designs into the physical world. Jones also shows that the current Information Age, far from a modern phenomenon, is the result of a slow-burn process that began when data was becoming large, if not yet “big”.
