Reckoning with Matter: Calculating Machines, Innovation, and Thinking about Thinking from Pascal to Babbage
336
Reckoning with Matter: Calculating Machines, Innovation, and Thinking about Thinking from Pascal to Babbage
336Hardcover
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Product Details
| ISBN-13: | 9780226411460 |
|---|---|
| Publisher: | University of Chicago Press |
| Publication date: | 11/29/2016 |
| Pages: | 336 |
| Product dimensions: | 6.30(w) x 9.00(h) x 1.10(d) |
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Reckoning with Matter
Calculating Machines, Innovation, and Thinking About Thinking from Pascal to Babbage
By Matthew L. Jones
The University of Chicago Press
Copyright © 2016 The University of ChicagoAll rights reserved.
ISBN: 978-0-226-41146-0
CHAPTER 1
Carrying Tens: Pascal, Morland, and the Challenge of Machine Calculation
In a letter of September 1646, Pierre Petit, engineer to the king, wrote a short history of techniques for facilitating arithmetical procedures. The most important development since logarithms was Blaise Pascal's arithmetical machine, a "piece invented truly with as much good fortune and speculation as its author has wit and knowledge" (see figure 1.1). Petit tempered his praise: "Since it comprises a number of wheels, springs and movement, and since it requires the head and hands of a good watchmaker to understand it and put it into practice, as well as the skill and knowledge of a good Arithmetician to be able to use it, I fear that its use will never become common." He accurately predicted that the machine would end up "in cabinets and great libraries," not in government bureaus and trading houses as Pascal had hoped. Contemporaries echoed Petit's concerns. One collector of gossip noted that only one artisan in Rouen could build the machine, and only with Pascal present. The projector and sometime fugitive Sir Balthasar Gerbier concluded his 1648 description of Pascal's machine by noting that "a man must first be exact jn Arithmeticke before he can make use of this Instrument, which cost 50 pistols." He deemed the machine "a Rare Invention farre saught, and deare baught: putt them jn the Storre house was the Prince of Orange wont to saye and lett us proceede on the ordinary readdy way."
In setting forth the impracticalities of Pascal's machine, Petit stressed its dependence on two forms of skill: that of the arithmetician and that of the watchmaker. The machine did not obviate the skills involved in doing arithmetic. Making something as complex as a calculating machine capable of performing addition and subtraction depended likewise on superior artisanal skills. The design of the machine was not sufficiently simple to allow ordinary artisans to produce it easily in a merely imitative, or a fairly machinelike, fashion — what David Pye calls the "craftsmanship of certainty." Its production, like its devising, required creativity and improvisation — the "craftsmanship of risk." The superior skills and creative problem solving necessary to build Pascal's machine meant that ordinary watchmakers or other artisans could not produce the machines in any standardized fashion. As a consequence, Pascal's machines were too dear for his envisioned markets of merchants, government tax officials, and architects.
Using the examples of the calculating machines of Blaise Pascal and Sir Samuel Morland from the seventeenth century, this chapter investigates the skills necessary to calculate and the skills necessary to design and build calculating machines. I intertwine a discussion of the major technical challenges involved in producing calculating machines with evidence about the nature of the contributions of the artisans involved in producing those machines. After analyzing Samuel Morland's detailed description of the work involved in producing his multiplying instrument, I look at Pascal's polemical portrayal of artisanal knowledge and skill. In Pascal's account, his mastery of arithmetic and of designing machines supplanted the need for such skills in users and the artisans producing the machines. Pascal and Morland treated the subject of the artisanal production of their machines very differently. In writing to patrons, Morland celebrated the world-class artisans who constructed his machines: he gave their names and detailed their labors. Pascal left his artisans nameless and depicted their labor as skillful but imitative. When advertising his machine, Morland directed prospective buyers to "Mr. Humphry Adamson" who was "the onely Workman" who could produce the machine "with that exactness that is absolutely necessary for such Operations." In contrast, Pascal advised "the curious" to visit Gilles Personne de Roberval, professor of mathematics at the Collège de France, at his lodgings. Morland brought together his buyers and his producers; Pascal insulated his buyers from his artisans.
The history of calculating machines reveals how often such tools have been mistakenly understood to be proxies, things capable of substituting for human beings; that history likewise shows how often genuine proxies, skilled artisans, have been mistakenly understood to be tools. By misattributing human activity, it is easy to disregard the skills necessary to use calculators and computers, just as it is easy to disregard the skills necessary to produce them. Such misattributions ease the dividing of intellectual from manual work and help justify the social hierarchies attendant upon that division.
The study of artisanal knowledge, tacit knowledge, and skill has been central to the history and philosophy of science and technology for many years. In this chapter and the next, I use the empirical case of early-modern calculating machines to clarify the distinct sorts of knowledge captured by those terms and to show the richness implicit in that array of meanings. The artisanal knowledge and skills involved in making calculating machines include the following:
1. Propositional knowledge, gained through long-term experience working with materials. Sometimes such knowledge is articulated, though rarely in the formal language of elite natural philosophers. Such knowledge need not be consciously cognized in linguistic terms at all. Examples might include properties like the ductility and malleability of different metals or the springiness of springs.
2. Discernment, or the acuity of senses in making judgments about perceptions, such as gauging the size of barrels or the quality of cheese or wine or metals.
3. Dexterity in doing work with hands, gained after long-term experience with materials, proceeding often without conscious mental reflection but with profound manual perspicacity.
4. Knowledge of the social world where other artisanal knowledge and skills can be found — essential knowledge in an age of deep imperfection of information.
In practice, the first three sorts of artisanal knowledge are often tightly bound together in the workshops of today as well as in the early-modern past. Dexterity in metalwork, for example, constantly involves using a powerful discernment about the qualities of various metals. Like many of their recent counterparts, numerous early-modern philosophers worked hard to deprecate the independent importance, if not existence, of artisanal knowledge.
Itemized Tasks
On the second of April 1669, the English inventor Samuel Morland wrote to Charles Stuart, Duke of Lennox, with a plea. Morland hoped soon to have "an Employm" of the "Instrument for Accompts & Numbers" he had loaned the duke. He asked the duke "either to let mee haue it again" or "to let mee have so much Money for it as will pay for ymaking of another." While we do not know whether the duke returned the calculating machine, a few years later Morland sent a similar machine, made in the same period, to a more important duke, Cosimo III of Florence (seefigure 1.2).
Morland's multiplication machine is a variation of Napier's bones given a circular form and a degree of automation. Like the bones, the instrument allows one to perform multiplication by reducing it to a series of additions of single-digit numbers. Skill in using Napier's bones to aid in multiplication was common among mathematical practitioners of Morland's time. Morland's machine automates this process.
The machine, shown in figure 1.3A, comprises a large number of disks engraved with numbers (S, T, V, W, X), posts to store and use the disks, a platform with a key (GH) to drive the internal mechanism, a pointer and a numbered line (EF), and a gate (AP) with viewing holes, shown open in figure 1.3A and closed in figures 1.3B–C. To use the machine to multiply, say, 1734 by 4, the user selects the disks for 1, 7, 3, and 4. Moving left to right, one places one disk on the first, one on the second, another on the third, and a last disk on the fourth pinion on the machine (labeled p, o, n, m). The gate is then closed; only the digits 1, 7, 3, and 4 are visible, as in figure 1.3B. The user then turns GH,moving the pointer along EF to whatever number he or she wishes to multiply by — in this case, 4 (see figure 1.3C). In the windows, a series of numbers are now visible: 42, then 81, then 21, then 6. The numbers in each window need to be added to produce the final result: 4 + 2 = 6, 8 + 1 = 9, 2 + 1 = 3, 6 = 6, so 1734 × 4 = 6936. Multiplying a number with more than a single digit, such as 44, requires the user to repeat the entire process and then add the two results obtained. To aid in this, Morland paired this multiplying machine with an adding machine to record the results.
Morland's asking price for the luxurious machine was a princely £67 7s. 6d.; in comparison, the sum total of yearly wages for all the Duke of Lennox's servants at his residences in London and Cobham came to £889. Lest the duke question this steep asking price, Morland included a breakdown of costs. This unusual document lists the stages and types of work involved in making the machine as well as the names of the three artisans involved. The cost breakdown Morland supplied to the Duke of Lennox reveals the variety of tasks and the materials involved in producing such a machine in a protoindustrial age.
In listing his expenses, Morland explained that he would not charge for the "great deal of trouble I shall have to follow & direct workmen." The duke was indeed getting a good deal. Morland hired the best artisans in England in their respective trades, among the best in all of Europe.
Morland's machine required a large number of disks; the exemplar in Florence has fifty-five silver disks and seventeen silvered brass disks (see figure 1.4). The cost breakdown details many of the stages required to convert silver into the numbered disks necessary for the machine. To create the general form of each disk, the first artisan, Blondeau, had to cut each disk out of metal, "planish" or flatten it, and then put a center in it. Among the finest makers of coins in early-modern Europe, using the most recent technical innovations, Pierre Blondeau had received the protection of Richelieu before being brought to Cromwell's Commonwealth in 1649 to help with the English coinage. An associate of Samuel Hartlib and his circle, he published a series of works defending the use of new mechanized methods for minting coins: "Monie coined with the hammer," he explained in 1653, "cannot bee made exactly round, nor equal in weight and bigness, and is often grossly marked." He probably flattened Morland's disks in a screw press, a mechanized technique that he had used to revolutionize coin making in Britain.
The second artisan, Sutton, next performed a large number of steps, at 3s. 6d. per plate: he had carefully to divide each disk into precise angles and then engrave the numbers at appropriate angles on each disk. The premier engraver of mathematical diagrams in England, Henry Sutton was a maker of especially fine metal and paper mathematical instruments. His death caused considerable concern among mathematicians, as there appeared to be no one else in England so skilled in the extremely precise engraving necessary for mathematical diagrams and instruments.
The third artisan, Fromantle, built the internal mechanism, a rack-and-pinion device where the key rotates the disks a precise number of degrees and moves the pointer to the appropriate number. The Dutchman John Fromantle came to England to make pendulum clocks after Christiaan Huygens's design. He and his family were famous for their fine clocks, which immediately became collectors' items. Morland hired Fromantle to manufacture other new inventions. He produced a "waywiser," or odometer, after Morland's design for the Duke of Lennox's carriage.
Each of Morland's artisans was a famous innovator in his craft; two of them were expatriates who had brought needed skills and innovations to England. They were not "simple" artisans capable only of reproducing extant works using repetitive techniques gained through habitual activity. The cost breakdown gives no sense of how fully Morland had specified his machine or what discretion he left to his innovative artisans to work out the details of their parts of the machine. In the chapters that follow, we will see the wide latitude early-modern inventors gave their artisans to fill out and often determine the technical details of their calculating machines. A clever inventor of all sorts of devices, Morland knew how to select artisans who would help bring his works to fruition. His numerous projects over the course of his life demonstrate that he understood the utility of coordinating the skills of others in order to refine and develop his designs. Morland recognized his limits and knew to ask for help (albeit sometimes too late). He was a savvy user of the expertise of others: he drew on the skills of the mathematician John Pell when he needed advanced mathematical help; he drew on the skills of the engine maker Isaac Thompson when he needed to turn his model of a steam engine into a workable product; late in life, he solicited the help of the future archbishop of Canterbury to vet his religious writing. He certainly took advantage of the skills of Blondeau, Sutton, and Fromantle in designing and implementing his multiplying machine. Morland's knowledge of the social world of skilled workmen made the materialization of his machine possible. Morland was, to be sure, the machine's inventor — the one who first envisioned it in general terms and brought together the knowledge needed to design and materialize it. All three of his skilled craftsman, however, shared in creating the device in an implemented form.
Automating Carry: From Morland to Pascal
Morland's multiplication machine was paired with a machine to aid in addition (see figure 1.5). The latter's lower asking price of twenty pounds reflects its relative simplicity; it is a pocket-sized device, of which several examples still exist. Unlike the more ambitious machines of Wilhelm Schickard, Pascal, and Leibniz, Morland's instrument cannot automatically perform carries. Leibniz remarked that Morland seemed "to have wanted to avoid" performing carries "in order to have nothing to do with teethed wheels," as he was "too skillful" to miss seeing how it could be done. Since machines like Morland's did not mechanically perform carries, Leibniz reckoned, they were little more than curiosities. Since Pascal's machines could not perform carries well, they too were amusements, not useful tools: "Addition and subtraction hardly become easier with such machines than they are with a pen: these Machines are more for curiosity than for real use. This does not prevent them from being charming." Making a machine capable of robustly performing carries was no small task. To see why, we need to analyze the steps involved in carrying in order to isolate the skilled human behaviors the machines were intended to facilitate or to replicate.
The competencies involved in doing arithmetic using arabic numerals remained rare in late seventeenth-century England, France, and Germany, if probably more widely distributed in Italy and the Netherlands. In his best-selling Mathematical Compendium, the noted pedagogue and engineer Sir Jonas Moore offered only a feeble explanation of addition and subtraction, before remarking, "If any Gentleman, especially Ladies, that desire to look into their disbursements, or layings out, and yet have not time to practice in numbers, they may from Mr. Humphrey Adamson ... , have those incomparable Instruments, that will shew them to play Addition and Subtraction in l. s. d. [pounds, shillings, and pence] and Whole Numbers, without Pen, Ink, or help of Memory; which were the invention of that worthy Person, and Ornament of his country, Sir Samuel Morland Baronet." Rather than explaining the basic rules and skills for arithmetic, Moore's mathematical compendium simply sent readers to purchase Morland's machines.
Morland's booklet of 1673 advertising his machines doubled as an arithmetical primer: "For the better understanding of the Arithemetical Instruments, I shall endeavor so to explain and demonstrate the reason of the Operations of Addition, Subtraction, Multiplication, Division, and Extraction of the Square, and Cube-Roots, as to render them plain and obvious to the meanest capacities." He worked from the assumption that his reader had no knowledge of either roman or arabic numbers. Having explained the numerals, he offered the following "Precept for ADDITION of Integers in Plain Numbers": "Having placed the Unites of the respective Progressions in Ranks and Files; then begin and add together the Unites of the right-hand-File, setting down the sum underneath, if it be under 10. but if it is just ten, set down 0. and carry 1. to the next place; and if above 10. set down the excess in the first place, for every 10. an Unite." In this rather unclear manner, Morland specified the general rules for carrying numbers in ordinary addition. If two digits add up to less than ten, write the sum in the first column; if they add up to ten, write zero in the first column and carry a one to the next digit; if they add to more than ten, write the amount greater than ten in the first column and carry a one to the next digit. Morland did not specify or illustrate how to keep track of numbers carried.
(Continues...)
Excerpted from Reckoning with Matter by Matthew L. Jones. Copyright © 2016 The University of Chicago. Excerpted by permission of The University of Chicago Press.
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