Week 1 (3/25,27): Arithmetic-Accelerated

[jamesallenevans]

Numbers form the basis of computation, and this week we focus on the emergence of early machines intended to augment or replace human computing capacities for tasks ranging from bookkeeping and finance to astronomical and nautical measurements promoting the interests of business, science and empire. Here, we specifically focus on the emergence of machine designs from Blaise Pascal to Gottfried Leibniz and beyond. What were the key challenges associated with large-scale arithmetic problems, put to machines? What were social and technical challenges associated with designing and constructing novel devices never built before? What are the implications for skilling and de-skilling human workers/thinkers?

Post your response as a Comment in reply to this message!

[Gio-Choi]

Students are to prepare and post an up to 500-word response memo every week (except a foreshortened one when a digital museum project is due) by 10am on Thursday in response to the appropriately labeled assignment on the Canvas website (linked from the appropriate weekly page). These “responses” will respond to questions posted the prior Tuesday. They should not be summaries of the readings but develop theoretical or empirical arguments, ideally drawing on information across the readings and lectures (both convergences and contrasts) and possibly raising questions for further investigation. Quote and unambiguously cite (e.g., with a relevant page number) relevant passages from the readings as you draw upon them, but only as it assists you in furthering your argument. An additional small paragraph of this response (in addition to the 500-word memo) should be headed “Discovery.” In this paragraph, you will be expected to note something you “discovered” about computation through the historical exploration or field trip, whether or not related to the question, and to briefly speculate on its significance for (or absence from) computation, artificial intelligence and society today. Please be specific and locate the discovery through citation (and, if helpful, quotation) of the relevant explored passage or experienced historical artifact.

Note that these are NOT “quizzes.” They will be evaluated based on the depth of your analysis from 3 to 0, with: 3 (superb); 2 (good); 1 (adequate); 0 (nothing turned in), which roughly translate to the following emojis (grades): 😃(~A), 😐(~B+), 😕 (~B-), 💩 (~F). At least three of your memos should have the tag “” at the top to signify that this exploration assignment involved sensory interaction with original materials (e.g., not digital materials). This could include artifacts from one of our “field trips.” I want these memos to be well crafted and edited, but please paste them as text in response to the appropriate thread (not as a separate PDF document). Include optional photos, pictures, screenshots or diagrams as attached files, separate from but referenced in the text of your response memo.

[cavanbgon]

The posing of these questions, though they avoid the word “computation”, was not sufficient for me to be able to ignore some complications from attempting to define a computational task. Most urgently, we are asked to consider as a unified collection the arithmetic devices of on the one hand Pascal and (putatively) on the other hand Morland. Though it can be said that both devices assist with the performance of “arithmetic tasks”, this elides a deep qualitative distinction. Jacqueline Pascal’s attribution of a crude “reasoning” to her brother’s invention seems essentially misguided yet stating that the invention is a “new thing in nature” seems essentially justified (Jones, 43). Allowing for such a distinction, how can Morland’s device be included among any collection of relevantly novel devices? More to the point, how can Morland’s device, which requires the operator to perform a specified task for “carrying the one”, sharply be distinguished from previous arithmetic aids like the abacus (Jones, 23)? The challenge of isolating an intermediary between an abacus and Pascal’s machine nearly necessitates some remarks on a theory of computation – more than would fill the 500-word limit.

It seems far easier to clarify the development of arithmetic aids as a kind of developmental economic phenomenon. In this sense, the devices lose a clear sense of having been members of a linear progression – at least one indexed by engineering sophistication (note the “sufficient-force” and “keeping it digital” problems). Whatever his technical innovations were, Insofar as Pascal sought to relieve the previously “fatigued”, he failed (Pascal, 2). Pascal developed a machine whose convenience for solving arithmetic came at the expense of massive inconvenience for those who had to produce the machine (Jones, 15). In other words, the necessary capital investment for the operation the device far exceeded what demand for arithmetic aid could justify and thus could not address what demand did exist. Rather, arithmetic aids can be viewed as having been strictly successful where they could produce some marginal increase in the ratio between the investment of capital and the investment of labor. Successful aids like the abacus and slide rule, though they couldn’t perform independent of a diligent operator, made the operator’s task much easier - without giving artisans so many headaches.  It would only be much later, the broad dissemination of technical knowledge begun by the encyclopédistes having advanced and (not unrelated) pure demand for arithmetic aid having increased, that the value of Pascal’s project could become clear.

Discovery:
I knew that Pascal had made some attempts to develop early machines but had no concept of the full story. I was especially surprised to find that there had been early concerns over the emergence of sentience within man-made objects. These are, as was noted in class, pervasive, featuring in both Greek myth and Jewish folklore, among many other such traditions. But that they would manifest so early among such serious people represents a remarkable connection to the past.

[mhmanek]

The pioneering efforts at building early computers involved many technical engineering challenges, such as design and choice of materials. For example, in his dedicatory letter, Blaise Pascal writes "I took the patience to make up to more than fifty models, all different, some of wood, others of ivory and ebony, and others of copper, before I came to the accomplishment of the machine which I am now bringing forth". This is reminiscent of Edison, who would fidget with all sorts of materials to empirically, pragmatically ascertain which material may be optimal for a given use case.

There were social challenges too, such as -

1. Constructing such a device required the collaboration of a theoretician and an engineer, and there could be a metaphorical 'frictional' loss of information in this process of communication (e.g., Pascal writes "it was not in my power, with all the theory imaginable, to execute my own design alone without the aid of a workman"; the book Reckoning With Matter calls this "the coordination of mind and hand", which proved to be one of the "chief culprits" in the failure to produce machines). How much of this challenge consisted in the challenge of integrating these two skillsets into a single human, versus the challenge of correspondence between two or more different humans who specialized in different aspects?

2. Faulty prototypes constructed by people without the requisite knowledge posed the threat of ruining the reputation of the genuine device (quoting Pascal, "a false execution of my thought made by a worker from the city of Rouen..."). To overcome this challenge, Monsignor the Chancellor granted Pascal "a privilege which is not ordinary", namely his exclusive rights to building the device. In terms of social and political influence, what enabled Pascal to receive such privileges and not someone else? Is the granting of such exclusivity a good strategy for a government seeking to optimize for innovation, technological progress and economic growth?

An additional barrier to widespread adoption was the prerequisite knowledge of arithmetic necessary to use the computing device. Skills needed to be acquired in order to even use the machine (let alone devising/creating it). In a modern context, this is reminiscent of the expensive and elaborate Bloomberg terminals, whereby analysts at financial firms often need to undergo training from Bloomberg support staff to understand how to use it. This acts as a constraint to the number of people who can use it.

As Reckoning With Matter writes, "it is easy to disregard the skills necessary to use calculators and computers", and in today's age, one might add AI. One need not be proficient in the computer science behind LLMs, but surely the ability to use the LLMs is itself a potent skill that can make or break the career of a modern day knowledge worker.

Discovery
I had never heard of people like Walter Pitts, Warren McCulloch, Edsger Djikstra etc., and it was fascinating to read about them - e.g., how Walter Pitts attended Bertrand Russell's lectures at UChicago as a homeless student.

[eeengland1]

It’s clear that inventors like Pascal, Morland had to contemplate a fair share of problems in constructing their arithmetic machines— a great number of these challenges are related to the context of the time period and uniqueness of their invention stifling effective production of these machines. One clear case of this is the (perceived) inability of artisans and producers of these machines to accurately make them to the degree of faithfulness necessary for the machine to work, or at least so claims Pascal. Pascal himself seems to have failed to recognize the artisanal skill in making these machines or ignored the role of said artisans to a certain extent, whereas Morland seems to have acknowledged the work of his manufacturers.

On this note, the lack of manufacturers for making these unique machines played a role in preventing arithmetic machines from becoming mainstream for a while, as there was both a lack of willing and qualified manufacturers, and also an information disconnect existed between the artisans, mathematicians, and engineers that slowed production— an individual with an understanding of all of these fields of study would be able to complete the creation of these machines on their own, but very few existed. Indeed, Pascal tried to undertake creating his arithmetic machine by himself, considering himself qualified to perform all steps of the creation process.

Pascal also needed to deal with the issue of finding suitable materials to build his device with— the machine needed to be fairly intricate but also very stable to withstand all sorts of journeys, and a comprehensive knowledge of materials science and manufacturing to the degree of the modern era had yet to exist. Pascal went through over 50 iterations of his device to come up with a suitable design, which cost an extraordinary amount of time and effort on his part, as all of these had to be manufactured and tested physically (we have simulations to do most of this work now).

Perhaps one of the most important reasons these arithmetic machines didn’t gain significant recognition and use is due to the fact that the device still did not automate enough of the hyperoperation process for people to use them with no needed knowledge of arithmetic themselves; buyers still needed to understand the processes behind arithmetic, in addition to (and more importantly )how the machine functioned, to be able to use the device correctly. Beyond all of this, the pricing of these hyperoperation (1-3) machines was still not suitable for the masses, and so its immediate use in society was limited to a smaller number of individuals.

Discovery: I was very unaware of the extent of the difficulty individuals like Pascal needed to overcome to create these machines, especially the technical challenge of building one capable of carrying digits in all scenarios. The philosophical discussion on computing machines, the human mind, the importance of mathematics to understanding the physical sciences, the call to unify theory and physical skill, and the attempts of certain philosophers to gain the trust of the existing governments (p.19, Reckoning with Matter) also caught my attention.

[Alex7692]

Response

One significnt challenge associated to the mechanization of large-scale arithmetic operations is the problem of carrying. To carry forward a digit to the next order of ten is an action that a trained, "numerate" human can mentally perform at ease. But the procedure complicates when devising a mechanism that can both reliably and efficiently carry tens over for a computational machine. The "computer" must be able to discern when the carry should happen, and then add it up to the current digit on the place value. Moreover, the function must also be easily repeatable such that large-scale arithmetic operations may be executed. As Jones illustrates with the example of adding 1 to 999999 (p.26), the sophistication with reiterating the carries is much of an issue.

Samuel Morland's solution is to record whenever carrying would happen and hand over the task of adding everything toegher to the user. Pascal was dissatisfied with the lack of automation and went on to design special components ("sautoirs") to the generate the "sufficient force" to perform a series of carries.

This exemplifies a more general concern for creating novel devices never built before in a way that refute the "hylomorphic" conception of invention, which dictates the separation between "design" and "construction". On the one hand, one would have to first possess the relevant theoretical knowledge (or the underlying principles; "carry", in the case of arithmetic operations) to articulate the procedure the device seeks to automate / realize. On the other, one would have be adequately familiar with the technical skills, as well as restraints, to be able to design an operable machine. As it is rare for one to possess both the theoretical and technical skills, collaborative efforts between designers and artisans are required to construct the machinery.

It therefore becomes a social problem as "success" is measured, and indeed materialized by the network of productive relations an inventor could employ. One would have to mediate and secure the necessary, quality-assuring sources of material for each component of the blueprinted device. At the same time, the distribution of specialized labor makes it more difficult to claim the authorship of a particular invention. A question of legitimacy (as well as its institution) concurrently arises. In the case of Pascal, he resorted to official support (King Louis XIV's grant of exclusive right) in order to monopolize the design and production of his model of calculating machines against "flawed imitations". Nonetheless, Pascal was unable to sustain this monopoly as large amount of efforts at improvement by other technicians (e.g. de Roberval and Grillet) have ensued.

Pascal has firmly denounced the counterfeiters, as he believed the coordination of theoretical and engineering knowledge is among one of his "distinctive competencies", and that regular craftspeople, whom are deemed as mere instruments by Pascal during the constructive process (p.33). While Diderot's encyclopedia entry of his machine has basically "open-sourced" the mechanism of Pascal's machine, it has also "deskilled" the observation-based learning of human workers in the process of recreating and perfecting previous models. It substantiates what Marx would come to observe as an ideologization of theory at the cost of neglecting the real, material human activities, the economic forces and relations that have antecedently shaped the production of knowledge.

Discovery

It is thought-provoking to note the historical efforts at "open-sourcing" Pascal's calculating machine, which is really reminiscent of the recent episodes of DeepSeek open-sourcing its model in competition with ChatGPT. I've also been pondering over the distinction between "science" and "technology" that the introductory remarks to this book criticizes... As the narrative goes, East Asian civilizations have never developed a mature system of scientific theories, but only that of works on the practical construction of technologies. I wonder how the invention of abacus would fit under this archaeological scheme...

[ardimascio]

Discussion:

I think it is prudent to thinking about deskilling through the last line of Jones’s piece: “The nonhuman stuff of the world, animals and calculating machines included, are simply machines: we ought not to mistake their effect” (Jones, 43). Essentially, just because machines can produce an output that has typically been thought of as an exclusive product of a reasoning beings does not mean that these machines are themselves can reason. But what does it mean, socially and/or phenomenologically, to produce a machine that is capable of imitating rationality? Pascal seemed very concerned with this question. Beyond concerns of plagiarism among artisans who might seek to create technically inferior copies of his machines, “Pascal lumped all artisans together into the noninventive class, at least for complicated machines. Any invention requiring theory remained beyond the capacities of artisans” (Jones, 34). Beyond Pascal’s more self-interested reasons for doing so, namely, “…to aid his quest for a royal privilege to grant him a monopoly on calculating machines…” (Jones, 34), his ardent imposition of rigid professional boundaries around the epistemic category of “invention” seems to suggest a fascinating labor-centric reproduction of the dynamic that Jones articulates at the end of his piece. Those who actualize the desires of the designers of the machines are, economically speaking, essentially tantamount to machines themselves, at least with respect to their creative capacity. These artisans merely reproduce the outputs of traditionally understood creative behavior, rather than engaging in creativity themselves. The economic implication here seems to be that, if these artisans are not themselves engaging in creative (or, phrased another way, unique) behavior, they are essentially as interchangeable with one another as the parts of the machines they produce, thus resulting in a substantial decrease in the perceived value of their labor when compared to the “true inventors” like Pascal. However, beyond this point, I think it would be worthwhile (perhaps as a point for future discussion, if nothing else) to begin exploring the connections between these economic ideas and the theological ideas that are mentioned toward the end of the piece as well. When articulating the connections between inventors and Gods, Jones notes how, “Forgetting the skills necessary to make the machine perform its arithmetical behaviors and to correct its sometime defects, [observers] saw [the machine] as a proxy for a reasoning being, not a tool to be used by one” (Jones, 42). One might argue that this perception results in a set of social conditions where inventors are understood, in a roundabout way, the new caste of human gods of the burgeoning Enlightenment. Inventors, especially those who create mechanisms that produce outputs classically understood as products of reasoning beings, are themselves creating reasoning beings, a capability that, previously, had been ascribed to God alone within the Western paradigm. Not only does this make their value virtually impossible to tabulate within an economic context, but provides an interesting theoretical precursor to later Enlightenment-era ideas that place primacy on human reasoning over a fidelity to divine law.

Discovery:

Man, internally accounting for rounding is really hard! Even when doing it manually with the abacus (which I am almost certain that I did completely incorrectly), this exercise really helped me internalize just how impressive of an engineering feat it was for Pascal to design something that could internally account for this. I think that, at least for me, the biggest takeaway from this exercise is the fact that it is a mistake to treat tools, no matter how advanced, as reasoning and purposive agents in the same ways that humans are. When we are taught to add and multiply as children, we develop such an intuition about what it means to carry digits that we do it almost naturally and without any significant forethought when we perform calculations longhand. No tool can develop this capability without explicit human engineering. As such, they cannot be said to “reason” as humans do, and labels that would imply this seem (at least through the first week of the course) to be little more than category errors, albeit with significant implications that we will likely discuss more in depth later, especially when one considers the links between reason, economic value, and knowledge production, as alluded to in my previous response.

[Laurelli7]

Early mechanical calculators faced significant challenges in handling large-scale arithmetic problems. Multi-digit addition and subtraction required machines to carry and borrow numbers across columns, which was difficult to automate. Multiplication and division were even harder to implement mechanically. Despite these challenges, early inventors developed machines to perform arithmetic operations.
Pascal’s Pascaline was one of the first mechanical calculators designed to automate addition and subtraction, successfully managing carrying and borrowing. Leibniz improved on Pascal’s design by creating the Stepped Reckoner, which could perform all four basic arithmetic operations. Later, Babbage designed the Difference Engine to automate mathematical table calculations for fields like navigation and astronomy. It relied on gears and levers and used the method of finite differences, eliminating the need for multiplication and division. However, it was never fully built due to funding and engineering limitations. These inventions showed that machines were capable of performing arithmetic, but the real challenge was scaling their capabilities.
Scaling posed two main challenges. The first was the ability to handle larger numbers and higher precision. Fields like accounting and astronomy required computations with very large numbers, but early machines, while functional for smaller calculations, could not maintain accuracy on a larger scale. Simply increasing a machine’s size and complexity was not a reliable solution, as most artisans at the time lacked the technical knowledge to manage the increased complexity. Additionally, the manufacturing techniques available were not precise enough to ensure error-free operation in complex designs.
The second challenge was mass production. Early mechanical calculators were expensive and difficult to produce in large numbers. Each prototype required significant time and money to build, and training artisans to construct these machines was a slow process. Scaling production also raised concerns about quality control. If machines were poorly made, it could damage the inventor’s reputation. Pascal, for example, sought intellectual property protection for his Pascaline to prevent low-quality imitations. However, as discussed in Reckoning with Matter by Jones, restricting access to new technology could slow further innovation. Many breakthroughs built upon earlier inventions, as seen when Leibniz was influenced by Pascal and Babbage by both of them.
Beyond technical and production challenges, there were also social concerns. Skilled human "computers" feared they would lose their jobs to machines (deskilling), while workers in fields like accounting and astronomy had to learn how to use mechanical calculators (skilling). Philosophers and intellectuals debated whether machines replacing human thinking in arithmetic would have broader consequences. Similar concerns exist today with artificial intelligence, raising questions about how automation impacts human work and knowledge.

Discovery：After getting to analyze the technical challenges of inventing mechanical calculators in scale, I discovered that the challenges of scaling have always been a pattern. We see it here in the development of mechanical calculators; we witnessed it in personal computers, in the Internet and now in LLMs. I believe the scaling challenge can shed light on a more general technical innovation framework.

[malongo03]

You might think that Pascal inventing a mechanical calculator in the 17th century would usher in an age where merchants and natural philosophers would increasingly rely on such tools to assist them, in the same way the invention of the crane ushered in an age where buildings are increasingly built using cranes or the horse-drawn plow ushered in an age of increasingly mechanized agriculture. These evolutions were slow but define, but mechanical calculators never seemed to "catch on" in the same way.
The abacus reading mentioned that the simple slide rule was still used into the 1970s to perform calculations.

The reading attributes this to the "carry" problem and the "keep-it-digit" problem frustrating efforts to make simple machines and the poor cooperation between theorists like Pascal and the artisans he employed. His machine was difficult to use, as were many future machine. But frankly, I'm unconvinced. Europe had a community of watchmakers confronting and surpassing similar problems. and I know the conclusion of the story: easy to use mechanical calculators like the Curta that could be held in one hand or incredibly fast machines like the Millionaire that could perform one-step multiplication. These problem have elegant solutions, and I think the watchmakers of Europe would have been able to solve them if they had put their minds to it, as they were

Instead, I believe there were many false starts like Pascal's machine because there was no market for a mechanical calculator. Accurate pocket-clocks benefit anyone as compared to an inaccurate sundial, but a mechanical calculator requires a profession with heavy use of arithmetic and has to compete with far cheaper devices like the pen and paper, abacus, and eventually the slide rule. It has to be so much easier and quicker to use compared to these devices that it makes up for the horribly increased cost, and that was always going to be a small niche even as manufacturing improvements allowed the machines to become cheaper and cheaper. This is exactly what Pascal's contemporaries pointed out, noting Pascal's machines ended up as curiosities that sat in vaults rather than becoming highly sought after luxury items.

Discovery:
It is also funny to discover a parallel to modern topic in historical ones: after Pascal produces his machine, you have people philosophizing that it imitates human reason while Pascal tries to temper their expectations by reminding them that the machine possess no will (Reckoning, pg 42). I found the discovery humorous because I have had similar experiences arguing against the anthropomorphization of the outputs of LLMs, particularly from those who assert it has some form of sentience or self-awareness. It seems that this might always be a controversial topic: is intelligence defined by reasoning or willful reasoning?

[benkim04]

The very key issue with building a machine for large-scale arithmetic problems was the issue of carrying the 1. As written, “Mechanizing the carrying of tens was a profound technical challenge” (Jones, 5). It is easy to observe that carrying the one when counting is not a difficult task. We have small mechanical clicking counters that quite accurately and easily carry the one. I have used such counters in the past. The difficulty quite clearly arises during arithmetic.
The challenges associated with designing and constructing novel devices are similar to those constraints that impact us today: the freedom and ability to invest capital, in the forms of labor, time, and material costs, to hopefully/maybe/perhaps build something that is worthy of its time. This is overcome by “institutions that seek to promote creativity [and] codified into legal systems protecting intellectual property” (Jones, 6). That is to say, very similar to the methods of the modern age. The institutions, which may have been royal courts as shown by Pascal’s Ad, involve the willing investment of those with capital to spare. In the modern era, that is commonly represented by government grants, university grants, and winnings from competitions. Still, it is evident that much like the modern day, it was difficult to motivate or convince those with capital that any one individual was deserving of such capital. This discrepancy arises due to the separation between intellectual genius and material existence, in that intellectual genius alone was and is not sufficient to convince those with capital to invest. Rather, it is the physical manifestation and products that are capable of convincing institutions. We see further the issue of “early adoption” within the example of arithmetic machines. Because Pascal’s machine contained many gears and springs that only a skilled watchmaker could make and the difficulty of use such that only a skilled mathematician could operate, it was relegated to “cabinets and great libraries” rather than “government bureaus and trading houses” like Pascal had hoped (jones, 13). We can still observe this phenomenon today. The very first iteration of an invention is most often the worst iteration. For example, Samsung’s first folding phone was a disaster, in which now it is often seen as an important stepping stone, yet largely an incomplete product. This is true of the arithmetic machine as well. Although it was a product of genius and one of the first of its kind, its utility in the form then was low. Thus, the pattern of invention shown by the arithmetic machine is still a pattern that manifests itself today, and can be seen as a sort of inevitability on the path to invention.

Discovery:
I thought that the mechanisms for the abacus were particularly interesting. Firstly, the different versions of the abacus allowed either decimal calculations or even hexadecimal calculations, which were possible using the Chinese abacus, as well as our simulation. Still, the Chinese abacus allows us to perform decimal calculations by simply ignoring the very top line of beads. I discovered that the hexadecimal system, which in my mind has been ingrained solely in computer architectural contexts, has been used in different contexts, and very real contexts outside of a computer system. It was so prevalent, in fact, that there was a mechanism to count solely in hexadecimal systems! That provided me greater context as to how numerical methods differed and developed in the past. Video of Performing 9233*144 on the abacus

[suryachinnappa]

Response:
Many of the problems faced in the development of the earliest computing machines were in their optimization for applicability and commercial viability, such that they could be sold and distributed as useful instruments. The texts made repeated reference to the fact that many iterations of these machines may very well sit idly as curiosities in the menageries of collectors, but as emphasized by Pascal in his letter, the aim of these inventions was not merely to show that mechanical arithmetic could be done, but for practical purposes, including bookkeeping, pedagogy, and other tasks; this sentiment was evidently echoed by many of the early inventors, including Morland.

If these machines were to be practical, inventors had to carefully balance a number of factors. Immediately obvious is size: large, complex machines may easily be able to mechanize many arithmetic operations, but these would never be viable, as their intended use demanded that they be portable. As a result, tiny, intricate designs were required, which demanded very particular skill sets. This naturally leads to the social factors crucial to the development of these machines; namely, that their construction required collaboration of experts of various kinds. While engineers had the right combination of theoretical and physical expertise to devise designs for these novel instruments, only artisans possessed the embodied knowledge crucial to actually construct the parts required. Each element of the device might be made by a different artisan, specializing in specific parts in accordance with their respective expertise; after all, in constructing these machines, they were creating something never built before, and as a result, would have to generalize from their previous experience with other projects. Given the tiny, intricate nature of the parts needed, oftentimes the artisans with the necessary skills were watchmakers. Collaboration between the artisans and engineers was instrumental in bringing these designs to fruition.

The mechanical element itself proved to pose a significant challenge to the development of these machines. As they were primarily dial-operated, and used the energy of the human turning these dials, engineers ran into many mechanical constraints that proved to be difficult problems to solve, prompting rounds of innovation and re-innovation. It became evident that addition engines were substantially simpler to construct than multiplication engines, and the complexity of the latter group reflected in their price; in fact, the particular logic employed in constructing the multiplication engine itself necessitated addition, requiring an addition engine to be built-in. A clever innovation was the development of the sautoir in order to address the tricky issue of carrying in addition; creating an addition engine with automated carrying required that the single turn of an input dial update an entire chain of output dials in the case of repeated carries. This could easily become a mechanical limitation due to the sheer heaviness of the dial which scales with increasing numbers of repeated carries in a single computation, a problem which the sautoir solved using clever manipulations of potential energy.

Discovery:
From this historical exploration it seems even more clear to me how intertwined our understandings of computation and intelligence are. Our sources this week dealt with events happening hundreds of years before the cognitive revolution, and yet it seems that the inventors of these mechanical arithmetic engines had the intuitive sense that the devices they were constructing had some level of parallel or affinity to human cognition and reasoning. In the history of cognitive science, I’ve often seen the mind-computer metaphor presented as a more recent development, coinciding with that of digital computers, but from the words of Pascal and Morland I see that a certain epistemology surrounding computational devices as “mind-like” was beginning to form even with respect to their (relatively) ancient ancestors.

[TonyYZ]

Response:
The failure of Pascal’s machine in its first appearance made it stay “in cabinets and great libraries,” which is counterintuitive at first glance, as the race for better computational power pervades the contemporary computer market (Jones 13). While Pascal’s machine possesses greater computational power than Morland’s machine as it automates carrying and digital transformation, Morland’s machine gained more popularity among common users. Taking account of the broader context of these machines, we may explain the differences in usage popularity among such machines using (1) the transmission of information about the machine and (2) the intuitiveness of the machine. This analysis highlights the agents’ ability to interpret and interact with the machines.

The tension between the opaqueness and transparency of the machines emerged from the inventors’ different approaches to designing and marketing them. Pascal’s machine requires greater precision in its various components, complicating the manufacturing process. The opaqueness of the machinery is aggravated by being encapsulated in a box. It is difficult to understand for replication or even modification - “it is impossible for all simple artisans...to perfect a new part...without the help of a person who...gives them the measurements and proportions” (Pascal 5). On the other hand, despite requiring manual addition, Morland's machine is easier to manufacture with fewer components, reducing the costs for artisans to interpret and spread the machine. The information interpretation and propagation is further facilitated through Morland’s instruction manual, The Description and Use of Two Arithmetick Instruments, and marketing strategies as in Moore’s advertisement about Morland’s machine in his mathematical compendium (Jones 25, 21). The accessibility to information about Morland’s machine compensates for its unfledged design, which involves social roles from artisans to merchants.

Intuitiveness directly maps the user’s knowledge and the machine’s mechanism. The machine does not work independently from its user, who provides the essential input and feedback for the machine to work properly through the computational procedure. Although Pascal’s machine has more automation, it does not become a persuasive advantage over Morland’s more basic design for its users since it does not make use of the user’s knowledge of basic addition. In contrast, Morland’s machine serves as a “[tool] to aid someone performing calculation” whose mechanism intuitively makes the user recall the manual practice of addition (Jones 36). Diderot’s encyclopedia, which leads to the “hylomorphic model” of the creative process, demonstrates the machine’s composition and procedure through the “descriptive and pictorial” medium and frees the mind from the details of the material (Jones 39, 40). This medium makes the use procedure more abstract and thus easier to map to the user’s mathematical concepts. In this way, Diderot’s attempt allows the users to interpret machines more intuitively while still taking into account machines with higher complexity, such as Pascal's.

Discovery:
Pascal’s oversimplified view of artisans as “instruments for implementing designs” reminded me of the contemporary attitude of AI algorithms like GPT (Jones 33). People generally distrust their creative potential and instead assign them with repetitive work. This analogy is surprising as artisans somehow become “part” of the machines, where only the inventor’s ingenious mind has the right to specify and control the movements of their machine, including the artisans. As I am doubtful about this dualist stance, I feel the need to explore an alternative to machines’ creativity. Just like Morland, who gave artisans the freedom to decide the specific parameters of material, should we try to take the risk of letting algorithms make their choices when crafting a precise object?

[akivah]

An interesting difference in the social sentiment towards machination of thinking, is how it relates the human mind. Hobbes' opinion: effectively reducing the human mind to computation, was clearly unpopular in his time, but surprisingly is now widely accepted in the era of neural networks. This early public opinion though, seems to have set back the development of computing for wider uses as it was not even fathomable for most to attempt to design a computer to do certain tasks of more human scope than just arithmetic. Even creating a machine that can do arithmetic proved challenging though, with carrying proving to be challenging until the 1850s.

Jones discusses how lack of interactions with artisans are partially responsible for this delay. The people envisioning computational machines seemed to be more focused on the hypotheticals and philosophy of the matter rather than the implementation; a problem we still see today at the interface of engineering and envisioning. Jones describes this as the interplay between "Mind, Hand, and Material." (Jones 8) Pascal brings up this important interplay in his response, calling out philosophers and artisans who failed to bridge the gaps. For example, Pascal insults the mechanical familiarity of those who may claim his machine could be "less composed." (Pascal 3) Social acceptance of the mechanical complexity necessary to approach these problems was clearly an issue. While the basis of the ethical considerations is starkly different, it seems analogous to resistance to large data centers today.

Jones also makes the interesting point that there are two tracks to the history of the modern computer: the track of the logical backdrop (software), and the track of the electronic technology (hardware.) Mechanical calculation has a direct lineage in the software. Examining the history of carrying tens allows us to study this lineage and avoid getting caught up in the idealistic conception of a general-purpose computer. At first, machines capable of carrying were reserved only as spectacle pieces for the wealthy, as they cost "50 pistols." (Jones 13) It was not an easy to replicate machine, Jones describes a necessary level of creativity and improvisation. We now know today from an assembly-line perspective that those are hugely expensive involvements in the manufacturing process.

While they were clearly cost prohibitive, people like Morland "did not charge" (Jones 19) for their time, indicating some degree of altruistic love for the development. Morland also developed an addition machine, and a fairly cost/size effective one at that. However, many consider it to be little more than a curiosity as it "hardly makes things easier." (Jones 21) In the case of Morland's machine, the mechanism by which one had to deal with carries seems almost as complicated as pen and paper. Carries were a very important gauge of both the usefulness and mechanical complexity of these early mechanical computers. The "sufficient-force problem" seemed to create the most problems for a direct toothed gear approach (Jones 26.) Despite his frustrations, many other artisans began attempting to perfect Pascal's machine like enabling subtraction by optimizing the weights and orientation (Jones 35.) This event mirrors the modern collective approach to innovation, and is in contrast with the solo approach mentioned previously in the book.

Discovery:

I found the physical processes behind the manufacturing particularly interesting. From a supply chain point of view, many of the challenges that faced these early inventors seem to still apply today. When you are on the forefront of a technological development, sourcing funding and expertise is very challenging. Silicon lithography for example: TSMC has a monopoly as they are the only “artisan” capable of producing at the highest level; and yet, they need the architecture designs of GPU/CPU corporations to make use of this production capability. As resources become more scarce, I.E water/energy when running LLMs, the "Mind, Hand, and Material." (Jones 8) are becoming increasingly clear to be directly relevant to the development of more advanced computing today. The modern relevance of this theme even today is fascinating to me.

[ciara-kinney]

Disdain for artisans is explicit in Blaise Pascal’s Dedicatory letter to Chancellor Séguier. He repeatedly points to what he perceives as their presumption, ignorance, and the “groping” manner in which they stumble through their development process (Pascal, 5). Pascal maintains that artisans are incapable of producing functional replicas of his model without the guiding force of theory, which, he implies, cannot be sourced from the artisans employed in the model’s construction, but must rather come from Pascal himself (or, presumably, others adequately equipped with theory). His rhetoric evidences a common attitude of his contemporaries that artisans existed as simple tools to be utilized, rather than independent agents with the capacity to think rationally and make valuable, original contributions.

Of course, this attitude was by no means universal. Samuel Morland’s relationship with the artisans he employed is indicative of the vastly different light in which he viewed them in. Morland directly names those he who worked with, outlining the work they did and praising them for their skill and ingenuity. It is unclear exactly how much of his model’s design was derived from his instruction, but there is potential for relatively wide latitude having been afforded to the artisans, given Morland’s willingness to draw on the expertise of others in many of his other projects (Jones, 20). It should not be ignored that the complexity of construction of Pascal’s vs Morland’s models varied significantly, which could perhaps partially justify the disparities between their perspectives on artisans, as it simply was more likely that one could misstep in reproducing Pascal’s machine. Regardless, Morland’s respect for artisans diversifies our understanding of their role in the production of complex models and the regard (or lack thereof) in which they were held.

Returning to Pascal’s understanding of the artisan, however, an interesting contrast can be observed. As the artisan was reduced to mere tool, for some, Pascal’s calculating model was elevated to the status of a rational agent (although Pascal himself did not take this perspective) (Jones, 42). In Reckoning with Matter, Jones refers to this as the misattribution of things as “proxies”, or “things capable of substituting for human beings” (Jones, 15). Considering artisans to be mere tools in production flattens their role to one stripped of any characteristics we attribute to humanity, such as creativity and innovation. (Although it is true that the introduction of Diderot’s Encyclopédie and the novel descriptive technologies it contained eventually made this picture of artisans possible, this did not occur until around one hundred years after Pascal’s invention of his computing model (Jones, 39)). Simultaneously, considering these early computation machines to be proxies overstates their ability and neglects the skill and mathematical knowledge required of their operator. This jumbling of proxyship provides an interesting look at the social construction and hierarchy of Pascal’s time, but also potentially generalizable insights into human interaction with novelty and tradition in regards to over/under attribution of value and agency.

Discovery

When using the abacus, I was confronted with the significance of “carrying the ones”. Keeping track of digits and place values was not a hugely easy task for me, and actually completing a calculation on the abacus caused me to appreciate the consequence of having the carrying of the ones integrated into a machine’s processes. This allowed me to better understand the weighting of a desire for simplicity with the desire for possessing a comprehensive calculator device, which Morland's and Pascal's models fulfilled very differently. This is a question which certainly extends to the modern day, as simplicity and functional capabilities must continually be weighed against each other in the development of all sorts of things.

[rshah1869]

The emergence of early calculating machines from Blaise Pascal to Gottfried Leibniz was driven by the need to address arithmetic problems, in fields such as commerce, science, and navigation. The fundamental challenge was not just computational efficiency but also the technical limitations of constructing reliable and scalable devices in a time where these tasks were undertaken by one man at a time. The transition from human to mechanical computation required overcoming significant obstacles, including mechanical precision, error correction, and the ability to perform complex operations beyond simple addition and subtraction.

Pascal’s Pascaline, despite being mechanically advanced, and solving many of the major issues of its time, was limited in its functionality and required frequent recalibration due to the imprecisions of 17th-century manufacturing techniques. These technical limitations illustrate the broader issue of designing novel devices in an era when the precision engineering required for automation was still in its infancy. The complexities of addition and subtraction, particularly with respect to “carrying” numbers, required increasingly complex mechanical solutions to achieve a higher level of accuracy and sophistication. Getting around the sufficient-force problem required Pascal to introduce a new kind of gear, the sautoir. Again, the keeping it digital problem required a level of self-correction by the calculator, once more a mechanical solution was employed. Physical intricacy as an input allowed for the intended output to be closer to an ideal. According to Matthew Jones, “Solving the sufficient-­force and keeping-­it-­digital problems with configurations of gears, springs, and weights was challenging conceptually and practically. These gears, springs, and weights had to be carefully specified and produced if the instrument was to perform according to the wishes of its inventors and the needs of its potential clients” (30).

Pascal’s polemical account of artisans, mathematicians, and philosophers in his letter to Chancellor Séguier illustrates the influence of a class of intellectuals on Pascal’s psyche. Pascal is hoping to break free from the critiques of the intellectuals of his time, those that might criticize him for practicality “continuing to perfect it still, I found reasons to change it…a difficulty in operating…a propensity for becoming too easily corrupted by weather or travel” (32). Beyond mechanical challenges, Pascal dealt with the social implications of his early computational machines. Later on, the advancement of calculation technology resulted in the de-skilling of human workers. Prior to these inventions, computation was an artisanal skill, requiring years of training and expertise. Yet, the increasing complexity of these machines resulted in what Jones calls, a “the movement toward a hylomorphic model of design and creation” (40).

Skilled human calculators, such as accountants and astronomers, held significant social and economic power. The introduction of machines threatened to displace certain manual computational roles while simultaneously creating demand for new skill sets, particularly in machine maintenance, programming, and numerical analysis. These Enlightenment Age social concerns sound very similar to contemporary fears about artificial intelligence and automation, where traditional expertise is both challenged and redefined by technological advancements.

Discovery
One intriguing discovery from this exploration is how the early history of computation was deeply intertwined with economic and imperial interests. The need for precise astronomical and nautical calculations, driven by European colonial expansion, underscores how technological advancements often serve strategic geopolitical purposes. This connection raises interesting parallels with modern computational advancements, such as AI and big data analytics, which are increasingly leveraged for surveillance, finance, and military applications. It suggests that the trajectory of computational development is rarely neutral; rather, it is shaped by the priorities and imperatives of its time, often reinforcing existing power structures while simultaneously creating new opportunities and disruptions.