Abstract
The comparison made by Ada Lovelace in 1843 between the Analytical Engine and the Jacquard loom is one of the well-known analogies between looms and computation machines. Given the fact that weaving – and textile production in general – is one of the oldest cultural techniques in human history, the question arises whether this was the first time that such a parallel was drawn. As this paper will show, centuries before Lovelace’s analogy, such a comparison was made by Gottfried Wilhelm Leibniz. During the 17th century, Leibniz compared his calculating machines with another textile machine, the stocking frame, a machine which mechanized knitting and which was invented in 1589. During the following centuries, this machine was considered as a technological wonder and as a creation of God, and, during the last decades of the 17th century, Leibniz emphasized the need to consider it and other textile machines mathematically. What, then, were the reasons for the parallel drawn between this machine and Leibniz’s automatic computation machines? And what were the consequences of this analogy concerning the artisanal knowledge embedded in manual textile practices?
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Notes
This claim (that such an invention was one of “a completely new type of machine”) is highly problematic from a historical point of view, and one may assume that Lee was inspired by or based the construction of this machine on some principles that already existed in other machines; however, a detailed history of the development of the stocking frame is beyond the scope of this paper.
“Ein Meisterstück der Erfindungskraft, und das künstlichste Werkzeug aller Handwerker und Künstler.”
As Birke Grießhammer notes, one had to constantly repair and oil the various parts of the stocking frame. Moreover, the physical conditions were far from optimal: When working, one needed good light and hence at night one used candlelight to use the stocking frame. Moreover, the stocking workers had to count the ‘rows’ (since the products produced had to be uniform in length), being a strenuous and at the same time monotonous activity. Treadling the machine, which needed to be done with a counterweight of about 10 kg, was exhausting. Moreover, the stocking workers suffered from various diseases: chronic chest pains were a consequence of the harsh and unhealthy working and living conditions; and the air in the workshops, contaminated by cotton dust, was particularly harmful, causing also and the chronic eye inflammation (Grießhammer, 1986, pp. 161–165).
Note however that the situation for the stocking frame was different: starting the last decade of the 17th century stocking frames were well present and used in Germany due to the arrival of Huguenot refugees, who brought with them those machines and were allowed to use them and sell their products.
“Schnur- und Mühl-Stühl auch im Römischen Reich teutscher Nation an sich selbst fast aller Orten / und in denen berühmtesten Handel-Städten allbereits vor geraumer Zeit […] gänzlich verbotten / und […] als ein hochschädliches Werck vielfältig abgeschafft / und ausgetrieben worden.” Also in Holland during several decades of the 17th century, the use or sale of Schnürmühlen was strictly forbidden due to the fear that this would lead to unemployment (Meyer, 1678 pp. 86–89, esp. p. 86). For an analysis of those ribbon looms, as well as of the stocking frame, see Reith (2000), who notes that these machines were often overestimated with respect to the technical aspects, especially in the secondary literature. Reith underlines (ibid., p. 41) that in view of the long development processes, the rejection of these innovations by craftsmen or guilds must take into account not only economic and cultural arguments but also technical arguments.
From now on, when referring to Leibniz’s edited works, I will use the letter ‘A’ followed by one Roman and one Arabic numeral (representing the series and volume number) to refer to the edition of Leibniz’s collected works published in the Akademie der Wissenschaften edition of Leibniz’s miscellaneous works (Leibniz, 1923).
The note is presented in (A VIII2, manuscript 11, pp. 126–132).
The title is written in the center of the right margin on the recto of the folio (A VIII2, p. 126).
(A VIII2, pp. 126–127): “Geometriae est explicare figuras quas natura et ars singulari quadam ratione producit: […] Geometria Sartorum. […] De artificio puerorum, quo fila digitis implicata educunt. […] De Textoria arte. De omnis generis telis. Velours etc. / De l’instrument des bas de soye.”
This note is hardly mentioned in the secondary literature on Leibniz. An exception is Carl Immanuel Gerhardt’s the introduction to: (Leibniz, 1849, pp. 8–9). Moreover, Giovanni Vacca (1872–1953), an Italian mathematician and historian of science, published in 1930 an article called “Della piegatura della carta applicate alla geometria” (“On Paper Folding Applied to Geometry”). The paper deals with the mathematics of folding, also containing a historical account of this domain. However, Sect. 7 of this article, titled “Desiderata di Leibniz” cites from Leibniz’ “Geometria Amoenior”, though without specifying that the citation came from this note (Vacca, 1930, p. 49). However, the citation is left without an explanation or reference, and it is not clear from where Vacca copied it. For an analysis of Vacca’s article, see (Friedman, 2018, pp. 319–323).
Here, it is interesting to note that Leibniz only referred to Descartes’ Les météores.
It is important to note that Leibniz already mentions briefly in 1673, in a letter to Christian Habbeus, that the artisans of Paris work with the stocking frame: “La Machine qvi fait en ouurier des bas et des ?toffes de soye, est icy en vogue” (A I1: 417). In this letter, Leibniz refers to numerous artisanal machines, instruments and practices, such as clock making, stone carving and crushing.
Dissertatio exoterica de usu geometriae, et statu praesenti, ac novissimis ejus incrementis, in: (A VII6, manuscript 491).
Leibniz’s wish to expand geometry beyond Cartesian limits is also evident in his 1675 note.
(A VII6, p. 484): “Quae saepe mihi cum Variorum Studiorum hominibus communicatio est, audire subinde fecit querelas de vanitate Geometriae, quibus illa frustra opponat demonstrationes suas, quando non de veritate sed usu quaeritur.”
See also Leibniz’s critique on Descartes’ conception of geometry, in: (A III1, p. 139): “Monsieur Descartes a travaillé après Viète, à reduire les questions de Geometrie, aux resolutions de Equations, dont le calcul est entièrement Arithmetique.”
(A VII6, p. 487): “Quemadmodum enim Oceanus idem est, qui prout varia litora alluit, nunc Atlanticus, nunc Aethiopicus, nunc Indicus appellatur; ita eadem sciendi ars omni argumento apta variorum theorematum velut sinus facit.”
Ibid.: “Unde sunt aliqui qui se Geometras esse ignorant ipsi, cum severe tamen et profunde in eo quod intelligent argumento ratiocinentur.”
(Ibid., p. 488): “Combinatoria ingenia plus habent felicitatis, minus laboris; simplicia sunt inventa eorum, et paucis verbis tota dicuntur; ut plerumque animadversione potius quam meditatione […].”
Ibid., pp. 488–489.
(Ibid., pp. 487–488): “Qui Geometrico sunt ingenio eorum inventa difficilia sunt, et profunda, et multa meditatione expressa. Qualia nec facile enuntiantur, nec statim a quovis auditore aut spectatore intelliguntur, unde Exemplum elegans habemus in Machina textrice, nunc passim frequentata, Scoti cuiusdam invento, quod novennio integro occupavit autorem suum, aut in Arithmetico instrumento, quod omnem animi laborem in rotas transfert.”
As we will see later, in another letter written by Leibniz several years after 1676, the same “weaving machine” ascribed to a “Scotsman” is referred to, this time noting explicitly that this machine produces stockings.
(A I11, p. 160): “[…] eine lebendige Rechenbank nenne, dieweil dadurch zu wege gebracht wird, dass alle Zahlen sich selbst rechnen, addieren, subtrahieren, multipliciren […].”
(A III2, p. 294): “II y a un autre curieux versé toute sa vie dans ce qui regarde les manufactures et le commerce, qui m’a écrit d’avoir trouvé et executé d’une façon si commode le mestier qui sert à faire les bas de soye.” As noted in: (ibid., footnote to line 17), the person to have really improved the stocking frame referred to is Johann Joachim Becher.
(A II2, part B, p. 147): “Cl. Siverus quem etiam a me salutari peto ni fallor aliquando et Textoriam Jungianam pertexendi spem fecerat, quod perutile foret, praesertim si vacaret illi theoriam cum praxis conferre, cuius rei multiplex Hamburgi materia est. Ea occasione possit adiici accurata description instrumenti aliquot abhinc annis in Scotia inventi, quo Tibialia fiunt.” Johann Vagetius (1638–1691) was a professor of logic and metaphysics in Hamburg, who, following the death of the former estate manager, Martin Fogel, was responsible for Joachim Jungius’s estate. Vagetius was also in charge of the second edition of Jungius’s Logica Hamburgensis.
The full title of the manuscript, probably given by Martin Fogel, is “Texturæ Contemplatio. Auct. Joach. Jung.” The manuscript is to be found in the Leibniz Library in Hannover (Gottfried Wilhelm Leibniz Bibliothek – Niedersächsische Landesbibliothek, Martin Fogel collection of Zettelkasten, folder: Ms XLII, 1923: delta 28; online at: http://digitale-sammlungen.gwlb.de/resolve?id=DE-611-HS-3665327). For an analysis of Jungius’s Texturæ Contemplatio see: Friedman (2022).
Leibniz expresses his wish again in September 1695 in a letter to Lorenz Hertel: “I wanted to remind you of what I said to you before about Mr. Cumberland [Heinrich Kummerfeld], Professor of Mathematics in Hamburg. Having joined practice to theory, and having the talents of the late Mr. Sivers, but more vigor to assert them; he would be the most suitable in the world for one of the most useful purposes, and from which he will return more honored, as he would be the first to work there as a mathematician. It deals with giving us mathematical descriptions and explanations of the mechanical arts: He could begin with the manufacture of fabrics and materials for all kinds of clothing, continuing what Messrs. Jungius and Sivers began with de arte Textoria, of whom he is the worthy successor; and without amusing, at the beginning [he should] examine things with all geometrical regularity, it would suffice that he begins by giving us definitions or constructions of all kinds of fabrics in order, marking their characteristic properties, both with regard to their manufacture and to their use […]. This would be more useful than one might think, even in physics, because the parts of plants and animals were made by nature, quodam genere texturae [as some kind of tissue, fabric].” (A I11, pp. 97–98) Here, it is clear that Sivers did not finish editing and revising Jungius’s notes on weaving. Leibniz hence offers this project to Heinrich Kummerfeld, who apparently also did not complete this task (or rejected it). Remarkable is Leibniz’s emphasis of the “geometrical regularity” of the fabrics, though it is not clear from the letter what is meant by this geometrical regularity, in particular because, in contrast to Leibniz’s 1676 manuscript Dissertatio exoterica de usu geometriae, no weaving machine is mentioned in this letter.
On Leibniz’s conception of “theory with practice,” see: (Poser, 2016, pp. 381–445).
(A IV3, part B, p. 491) “[…] il faut admettre l’introduction des instrumens, qui abregent le travail, et par le moyen des quels un seul homme peut faire autant que plusieurs.”
Ibid., p. 492.
(A IV4, p. 68): “Bishehr von Theoreticis so den grund zu aller praxi legen, nun komme auff practica Artium selbsten, und solche Erfindungen deren Nuzen alsbald erhellet. Habe demnach viel Neue erfindungen, so theils meine inventiones, theils von andern hehrkommen, aber noch wenigen bekand.”
Ibid.: “Man hat Leute an der Hand, die es in Machinis Textoriis weit gebracht, also daß die geblümte figurische bande und Zeuge mit unglaublichen Vortheil und geschwindigkeit zu verfertigen, und weilen dergleichen wenig in Teutschland sondern alles bey frembden gearbeitet wird […].” Leibniz refers later in this passage to bandmühlen.
(A I25, p. 190): “Und den anfang zu machen, so wolte man den H. Professor ersuchet haben, das so genante Mestier, Strumpfstricker instrument deutlich zubeschreiben und vorzustellen, daß man es sowohl perspectivisch im ganzen, als auch iedes theil absonderlich sehen und deren usum mit der ganzen invention aus der beschreibung und den figuren verstehen könne […].”
A similar claim is expressed in Nouveaux essais sur l’entendement humain (Leibniz, 1996, p. 360): “[…] geometers do not derive their proofs from diagrams, although the expository approach makes it seem so. The cogency of the demonstration is independent of the diagram, whose only role is to make it easier to understand what is meant and to fix one’s attention.”
Taking into account that the stocking workers had to count the ‘rows’ they were knitting with the stocking frame and constantly treadling the machine, one may wonder how this machine left any time for free reflection.
Although one can certainly claim that the Jacquard loom led to a marginalization of artisanal knowledge.
See: (A VI4, part B, p. 1226ff). These notes, which are a part of a larger set of notes called “Logica de notionibus: Jungianarum schedarum excerpta annotata,” contain references to numerous scholars, particularly to Joachim Jungius and his works, including Isagoge phytoscopica, Texturæ Contemplatio and Logica Hamburgensis.
(A VI4, part B, p. 1227): “Ob vicinitatem, implectere flechten texere; intricare verwirren, implicare bäugen, plica valte, fere implicare dicunt Latini pro implectere quia brachio et digitis plicamus, id est flectimus hoc est in angulum figuramus. Intricatio est quasi excessus implexionis, bendel machen ist ein weben, texere et plectere differunt quia texere fit compendio quodam, plectere ist wie 〈schnühr〉 machen und Knüppelen.”
(Ibid., pp. 1227–1228): “Nomina ambigua plerumque non tam inopia dictionum aut taedio onomathetisandi, sed quod censerent res aliquas falso notionem aliquam communem habere. […] Notionum confusio a sensus observatione imperfecta.”
One can claim, following Krämer (1992), that overcoming this sensuous incompleteness can be also achieved by introducing mathematical symbols and signs, being essential for creative thought (when the function of communication becomes secondary). Here it is important to stress that for Leibniz, signs and symbols are inscribed on surfaces (e.g. paper; see: ibid., pp. 226–227), hence also can be seen as a type of ‘manual work’ (of the mathematician or philosopher), but one which introduces distinct notions. Thus, these signs are not inner mental entities but are exterior and spatiotemporally situated. The exteriority of the cognitive use of such signs may be therefore seen as parallel to “carr[ying] over all the work of the mind” to an external medium, as noted by Leibniz concerning the arithmetical machine and the stocking frame. The exteriority of the signs enables not only to reduce “mnemonic errors […] when we replace images with formal notions [but also] […] when our reasoning is based on symbolic structures, [to] make new discoveries, which would be inaccessible to mental representations.” (Leduc, 2014, p. 56) Concerning Leibniz’s universal characteristic, Leduc also stresses that the “process by characters enables the mind […] conceiving of complex notions that would remain confused at the mental level”. Leduc highlights as well the metaphor of the ‘thread of thinking’ in Leibniz’s own thought on symbols: “By focusing on symbols, the method of the characteristic provides a thread of thinking, a filum cogitandi, which makes many definitions and demonstrations conceivable to the mind.” (Ibid., p. 67) I thank the anonymous referee who highlighted this aspect in Leibniz’s thought.
A similar statement appears when Leibniz discusses his vision for an encyclopedia which would encompass all rational knowledge in a set of notes from June 1679 titled “Consilium de encyclopaedia nova conscribenda methodo inventoria.” Leibniz notes that “this Encyclopedia should comprise all the sciences that are based on reason alone or on reason and experience […].” And presenting a list of these sciences, he notes “the eighth is Geometry, the science of place [situ] or figures […] This art includes also Tornatoria and Textoria, all of which insofar as they make abstraction of matter [omnes in quantum a materia abstrahuntur]” (A VI4, part B, p. 343, 346; translation from: Dascal et al., 2006, pp. 134, 137). How weaving or textiles practices, being obviously dependent on the senses, are to be “abstracted from matter” in order to be included within geometry is not explicated, however.
“Le métier à faire des bas est une des machines les plus compliquées & les plus conséquentes que nous ayons : on peut la regarder comme un seul & unique raisonnement, dont la fabrication de l’ouvrage est la conclusion […].”
“[…] presque dans l’état de perfection […] la machine fait presque tout d’elle-même […] d’atteindre dans la pratique à cette précision geométrique que la machine avoit dans l’esprit de son inventeur.”
Here, I follow: (Stalnaker, 2010, pp. 115–117).
“Les différences de l’ancien métier & du nouveau, sont très-légeres ; elles ajoûtent à la vérité quelque chose à la perfection du métier ; mais […] si ce métier devoit être exécuté par des êtres infaillibles dans leurs mesures, & mis en oeuvre par des êtres infaillibles dans leurs mouvemens, il auroit fallu le laisser tel qu’il étoit. On s’est seulement menagé par les changemens qu’on y a faits, la commodité de tâtonner, & d’atteindre dans la pratique à cette précision geométrique que la machine avoit dans l’esprit de son inventeur.”
“C’est une machine à réflexion, comme le métier à bas est une machine à ourdissage; c’est un être qui se plaît à méditer […].” ‘ourdissage’ is an operation which prepares the threads one next to each other.
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This research was supported by the Israeli Science Foundation (grant no. 461/21).
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Friedman, M. Leibniz and the Stocking Frame: Computation, Weaving and Knitting in the 17th Century. Minds & Machines 34 (Suppl 1), 11–28 (2024). https://doi.org/10.1007/s11023-023-09623-3
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DOI: https://doi.org/10.1007/s11023-023-09623-3